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Raman studies of low-dimensional conductors and superconductors Lin, Yuankun 2000

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R A M A N STUDIES OF LOW-DIMENSIONAL C O N D U C T O R S SUPERCONDUCTORS  By Yuankun L i n B. Sc. Nankai University, 1991 M . Sc. Nankai University, 1994  A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF D O C T O R OF P H I L O S O P H Y  in T H E F A C U L T Y OF G R A D U A T E STUDIES D E P A R T M E N T OF PHYSICS A N D A S T R O N O M Y  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A  June 2000 © Yuankun L i n , 2000  AND  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives.  It is understood that copying or publication of this thesis for  financial gain shall not be allowed without my written permission.  Department of Physics and Astronomy The University of British Columbia 6224 Agricultural Road Vancouver, B.C., Canada V 6 T 1Z1  Date:  Abstract Using a Fourier Raman spectrometer equipped with an infrared laser, together with cryogenics, three types of materials have been investigated as a function of temperature in this thesis. The first is the investigation of organic materials including K > ( B E D T - T T F ) C u ( N C S ) 2  2  (T =10.4 K ) , K - ( B E D T - T T F ) C u ( N ( C N ) ) B r (T =11.6 K ) , a - ( B E D T - T T F ) I (T =8 K ) c  2  and / 3 - ( B E D T - T T F ) A u I 2  2  2  c  t  2  3  c  (T =5 K ) which become superconductors at low temperature. c  The second is the study of the first organic conductor T T F - T C N Q which behaves in exactly the opposite way by becoming an insulator at low temperature. The third is the study of the strontium-doped lanthanum copper oxide superconductors with higher transition temperature. For B E D T - T T F based organic superconductors, the electron-phonon coupling is very strong. The frequencies and intensities of three strongest features ( v (A ), vg ( A ) and 3  g  9  ^60 (B3 ) modes) in the Raman spectra have been analyzed as a function of temperature. 9  The frequencies of some modes are observed to soften in the temperature range where antiferromagnetic spin fluctuations have been observed, providing evidence of interactions between the phonons and the magnetism. The VQ (B ) mode is observed to be very unusual in 0  3fl  many ways, such as having an inverse isotope frequency shift. Below T , this mode exhibits c  an increase of 2.2 c m ^ m «;-(BEDT-TTF) Cu(N(CN) )Br (T =11.6 K ) and a decrease of 1.7 2  2  c  c m i n a i - ( B E D T - T T F ) l 3 (T =8 K ) . This is the highest frequency phonon in any material _ 1  2  c  to be affected by superconductivity. For T T F - T C N Q , many new lines are observed at temperatures below 150 K as the fluctuating charge-density-wave occurs. The intensity of these lines increases with decreasing temperature.  These new lines are assigned according to the deuterium-isotope frequency  shifts. In the fluctuating charge-density-wave phase the Frohlich electron-phonon interaction is the probable cause of the appearance of Raman-forbidden scattering originating from the infrared-active-only modes. The strong out-of-plane vibrational Raman modes correspond  ii  to the large out-of-plane distortion of the T C N Q molecule, which is in agreement with the x-ray results. For lanthanum copper oxide materials, firstly we observe seven Raman-forbidden longitudinal optical phonons, which appear to be activated by the Frohlich mechanism, in the single-phonon Raman scattering of La Cu04. Good agreement is obtained between the peak 2  frequencies and those of the longitudinal optical modes measured by infrared reflectivity and inelastic neutron scattering. Secondly, strong magnetic Raman scattering is observed in one crystal of Lai. Sr .iCuO4, which has a suppressed T of 12 K , due to an ordered spin phase 9  0  c  below 40 K . A weak second peak indicates the possible existence of phase separation in the sample. In agreement with neutron scattering results, the Raman intensity of the intense peak increases with decreasing temperature below 40 K . The line shape and the temperature dependence of the magnetic scattering intensity are totally different from those observed in the parent compound La Cu04. The temperature dependences of the peak frequency and 2  damping, however, are similar to those of other two-dimensional antiferromagnets. The line shape is fitted within the traditional Loudon-Fleury Raman theory of two-magnon scattering. The resulting super-exchange constant is found to be 1519 K , in accordance with EPR-measurements on the same compound.  iii  Table of Contents  Abstract  ii  List of Figures  vii  List of Tables  xix  Acknowledgements  xxi  1 Introduction  1  1.1  History and Development of Superconductors  1.2  General Properties of the B E D T - T T F Based Organic Superconductors  ...  5  1.2.1  Crystal Structure  5  1.2.2  Electrical Properties  9  1.2.3  Intramolecular (Internal) Vibrational Modes  14  1.2.4  Infrared Conductivity  19  1.2.5  Raman Scattering  21  1.2.6  Energy gap  23  1.2.7  Isotope Effect  25  1.2.8  Electronic Band Structure and Fermi Surface  27  1.2.9  Thermoelectric Power  30  1.2.10 Superconducting Penetration Depth and Magnetic Properties  1.3  1  . . . .  33  1.2.11 Mechanism of Superconductivity  35  Similarity Between Organic and Cuprate Superconductors  40  iv  2 The Raman Effect  44  2.1  Introduction  44  2.2  Classical and Quantum Raman Theory  46  2.3  Selection Rules  48  2.4  Raman scattering efficiency  50  2.5  Advantages of Fourier Transform Raman Spectroscopy  51  3 Experimental Details  54  3.1  Bruker R F S 100 Spectrometer  54  3.2  Heli-Tran Refrigerator  57  3.3  Janis Dewar  60  3.4  Pumping Station  64  3.5  Sample Preparation  64  4 Raman Results for B E D T - T T F Based Materials  68  4.1  Low-temperature Softening of Raman Modes in Neutral B E D T - T T F  4.2  Electron-phonon Coupling  4.3  Temperature-dependence of v (A ) Mode  4.4  Phonon Softening Observed from i/ (A ) and ^ o (B3 ) Modes  85  4.4.1  Phonon Softening Observed in *>(ET) Cu(NCS)  85  4.4.2  Phonon Softening Observed in «>(BEDT-TTF) Cu(N(CN) )Br . . . .  4.5  . . . .  68 77  3  82  9  9  g  6  fl  2  2  2  Frequency Shifts Observed Below T  2  93 96  c  4.5.1  Frequency Shifts Observed Below T in «;-(BEDT-TTF) Cu(N(CN) )Br 98  4.5.2  Frequency Shifts Observed Below T in a ( B E D T - T T F ) I  c  c  2  r  2  2  3  101  4.6  Unusual Properties of z^ ( B ) Mode  106  4.7  Summary  108  60  39  5 Introduction and Results for T T F - T C N Q  v  110  5.1  Charge Density Wave (CDW)  110  5.2  T T F - T C N Q Structure and the C D W  113  5.3  Intramolecular Vibrations of T T F - T C N Q  118  5.4  Raman Scattering from T T F - T C N Q  119  5.4.1  Room-temperature Results  124  5.4.2  Low-temperature Results  124  5.4.3  Assignments  127  5.4.4  Discussion  129  5.4.5  TSeF-TCNQ  136  5.5  Summary  139  6 Introduction and Results for L a C u 0 and Lai.9Sr .iCuO 2  6.1  4  0  4  140  General Structure and Vibrational Mode Analysis of the Perovskite-like Superconductors  140  6.2  Raman Scattering-Previous Results  143  6.3  Raman Scattering-Present Results  149  6.3.1  Room Temperature Data Using an Infrared Laser: One-phonon Scattering  6.3.2  6.3.3 6.4  153  Temperature Dependent Data Using an Infrared Laser: Two-magnon Scattering  160  Theoretical Fits to Two-magnon Scattering  168  Summary  174  7 Overall Summary  176  Bibliography  178  List of Publications  191  vi  List of Figures  1.1  (a) Carbon chain molecule with alternating single and double bonds, and (b) polypropylene as an example of a molecular side group R incorporated in molecule (a)  1.2  2  (Left), the geometry of a neutral B E D T - T T F molecule; (Right), three different packing patterns of B E D T - T T F in the crystals, which are denoted by a, (3, and K. The rectangle represents the positions of the B E D T - T T F molecules as viewed along the long axis Z of the molecule  1.3  6  (Top), crystal structure of K - ( B E D T - T T F ) C U ( N C S ) ; (Middle), an arrange2  2  ment of C u ( N C S ) ; (Bottom), an arrangement of C u ( N ( C N ) ) X , where X 2  2  denotes Br or CI 1.4  8  Temperature dependence of the resistance along the 6-axis for K - ( E T ) C U ( N C S ) 2  at several pressure[16]  2  10  1.5  Pressure dependence of T s for ( E T ) X salts[24]. X represents a counter anion.  1.6  (Left), an overlay of resistivity as a function of temperature for K - ( E T ) C u ( N ( C N ) ) B r  c  2  2  cooled at different rates. The inset is a semilog plot of p versus T  2  12 2  at low  temperatures. (Right), resistivity as a function of temperature near the superconducting transition for the sample at different cooling rates[26]. The curves from N o . l to No.5 shift upward in the sequence of increasing cooling rate at 0.4 K / m i n , 1 K / m i n , 5 K / m i n , 20 K / m i n and 60 K / m i n , respectively.  vn  13  1.7  (Top) A sketch of the B E D - T T F molecule. (Below) Wavenumbers observed at room temperature and atomic displacement vectors for the 12 totally symmetric ( A ) normal modes of vibration, (assuming D s  2 / t  symmetry), of neutral  B E D T - T T F . The displacement vectors are in the molecular plane, except the out-of-plane C - H bends in z/ and v , which are indicated. The vectors were 4  5  calculated by Eldridge et al. [30], and are not to scale 1.8  15  Examples of normal modes belonging to the eight vibrational symmetry species of the B E D T - T T F molecule. The arrows indicate the direction of the atomic displacement, + indicates a displacement out of the page and — a displacement into the page  1.9  17  Temperature dependent optical conductivity a (to) of /c-(ET) Cu[N(CN) ]Br[36]. 2  2  20 1.10 The room-temperature Raman spectra of K - ( E T ) C u ( N ( C N ) ) B r taken with 2  2  a visible laser (solid line) and an infrared laser (dashed line), up to 1600 c m " [39]  22  1  1.11 Normalized absorption A(5.3 K)/A(10.5 K ) of K - ( E T ) C U ( N C S ) 2  2  as a func-  tion of frequency. The open circles represent the absorption of a typical B C S superconductor with T =10.4 K[34, 35]. The closed squares show the same bec  havior but with an enhanced residual absorption as determined by microwave measurements  24  1.12 Deuterium substituted E T molecule  27  1.13 The calculated band structure and Fermi surface of K - ( E T ) C U ( N C S ) 2  2  based  on the tight-binding method[60, 61]  28  1.14 The typical two-dimensional Fermi surfaces reconstructed from the original round surfaces[62]  29  1.15 The thermoelectric power measured for K - ( E T ) C U ( N C S ) 2  axes in the highly conducting plane[70]  viii  2  along the b and c 32  1.16 AA||(T)=A||(T)-A||(0) data for two samples of K - ( E T ) C u N ( C N ) B r (a, b) 2  and two samples of K - ( E T ) C U ( N C S ) 2  2  2  (C, d) plotted versus [ T / T ] i . c  The  data have been offset for clarity. The inset shows the data for samples a and d on a log scale[72]  34  1.17 The calculated nuclear spin-lattice relaxation rate 1/Ti (logarithmic plots). The dashed line indicates a T  3  behavior[95]. Insert shows 1 / T i T (normal  plots)  39  1.18 Schematic phase diagram of the K > ( B E D T - T T F ) X family of organic materi2  als.  Superconducting (SC), antiferromagnetic insulating (AFI), and param-  agnetic insulating phase (PI) are shown. The arrows denote the location of materials with anions X at ambient pressure. As the pressure decreases, the properties of the metallic phase deviate from those of a conventional metal. This phase diagram is qualitatively similar to that of the cuprate superconductors, with doping playing the role of pressure  41  1.19 spin fluctuation induced soft mode  42  2.1  Schematic spectrum of scattered light  45  2.2  Energy level diagram describing Rayleigh scattering, Raman Stokes scattering and Raman anti-Stokes scattering.  The dashed line represents the virtual  energy level. If the virtual energy level-c is close to the excited energy level-d, a resonant Raman scattering will be observed  48  3.1  The optical layout of the R F S 100 FT-Raman spectrometer  55  3.2  A back-scattering configuration used for all measurements  56  3.3  The platform used to support the Heli - tran refrigerator  58  3.4  A typical flow diagram of LT-3-110 Heli-tran system  59  3.5  A typical structure of the Janis SuperVaritemp Dewar  61  ix  3.6  (Left), a design of the room-temperature vacuum jacket.  (Right), a stand  supporting the Janis dewar for use with Raman R F S 100 spectrometer.  . .  3.7  The heating effect observed in an organic superconductor  3.8  The optical conductivity observed in«-(BEDT-TTF) Cu(NCS) [110]. The fre2  63 65  2  quencies of several visible laser lines and an infrared laser line are indicated in the figure 4.1  67  The Raman spectra of neutral B E D T - T T F at room temperature, 100 and 10 K, taken with an infrared laser of wavelength 1064 nm. The twelve totallysymmetric (A ) modes, (assuming D h symmetry), are labeled, along with g  2  one B?,g mode, u - The insert shows v\(A ) e2  4.2  69  g  The ratio of the wavenumber shift to the room-temperature value, as a function of temperature, for seven totally-symmetric ( A ) modes, which harden g  to some extent at lower temperatures, as is normally observed 4.3  70  The ratio of the wavenumber shift to the room-temperature value, as a function of temperature, for five totally-symmetric ( A ) and one non-totally sym9  metric (B ) modes, which unexpectedly soften at lower temperatures. 3g  The  wavenumber of the most intense component of a multiplet is plotted 4.4  71  Wavenumbers observed at room temperature and atomic displacement vectors for for seven totally-symmetric ( A ) modes, which harden to some extent at 9  lower temperatures The vectors were calculated in [30], and are not to scale. 4.5  72  Wavenumbers observed at room temperature and atomic displacement vectors for for five totally-symmetric (A ) and non-totally symmetric ( B ) modes, 9  3s  which unexpectedly soften at lower temperatures. The displacement vectors are in the molecular plane, except the out-of-plane C - H bends in v<± and 1/5,  4.6  which are indicated. The vectors were calculated in [30], and are not to scale.  73  B E D T - T T F structure: (a), top view; (b), side view; (c), dimer  75  x  4.7  The room temperature Raman spectra of K > ( B E D T - T T F ) C U ( N C S ) , where 2  2  B E D T - T T F is abbreviated as E T in the figure, taken with a visible lasr (solid line) by use of a Raman microscope spectrometer at Argonne and an infrared laser (dotted line). Eleven of the twelve totally-symmetric A (B ) 3G  4.8  G  modes and VQ  0  mode are labeled. The asterisk * indicates an atmospheric line  78  The room temperature Raman spectra of K > ( B E D T - T T F ) C u ( N ( C N ) ) B r taken 2  2  with a visible laser (solid line) and with an infrared laser (dotted line), from 100 to 1600 c m . Ten of the twelve assigned totally-symmetric A intramolec- 1  9  ular modes of the B E D T - T T F molecule have been labeled in the visible-laser spectrum, as well as ^ i ( A ) in the IR-laser spectrum 2  4.9  79  9  A comparison between the infrared-laser Raman spectrum and the infrared conductivity of A t - ( B E D T - T T F ) C u ( N C S ) , showing the electron-phonon fre2  2  quency shifts listed in Table 4.2  80  4.10 A comparison of the infrared conductivity of K - ( B E D T - T T F ) C u ( N ( C N ) ) B r 2  2  at 10 K with the Raman spectrum at 2 K , taken with an infrared laser, of the same material. The three prominent features in each spectrum are due to ^  ( A ) , v> (A ) and u  3  9  9  g  ( B ) and these has been labeled. The prime in the  60  3s  infrared label indicates that the feature has been shifted down in frequency due to the electron-phonon interaction. extends from 1200 to 1350 c m  - 1  In the infrared spectrum v'  3  (A ) g  and the fine structure is due to antiresonant  interference with u (A ) that is a quadruplet at the same frequency 5  81  g  4.11 The Raman frequency as a function of temperature of the feature due to u  3  (A ) in / c - ( B E D T - T T F ) C u ( N ( C N ) ) B r measured with an infrared laser in a g  2  2  Fourier-transform spectrometer. Independent measurements, taken in Janis Dewar at 2 and 15 K , above and below T at 11.6 K , are included. No increases c  below T is observed  84  c  xi  4.12 The temperature dependent Raman spectra of K-(BEDT-TTF) Cu(NCS) 2  be-  2  tween 400 and 600 c m . The intensity of vg (A ) Raman mode, a main feature - 1  g  of the spectra, has a strong variation with temperature  86  4.13 The Raman spectra of vg (A ) mode of K - ( B E D T - T T F ) C u ( N C S ) at 90 and g  2  2  10 K (dots) and the best-fitted results (solid lines) with five Lorentzians. Three of five Lorentzians are shown (dashed lines). The Lorentzian at 484 cm  - 1  is an unassigned Raman line clearly observed in the spectrum with the  visible laser in Fig. 4.7  87  4.14 The temperature dependence of the integrated intensities of vg (A ) doublet: g  upper component (solid line) and lower component (dotted line). The lines are guides for the eye  88  4.15 Raman frequencies of the lower component of vg (A ) doublet as a function g  of temperature  89  4.16 Raman frequencies of the v  m  ( B ) mode as a function of temperature.  4.17 Temperature dependence of a phonon frequency in Y B a C u 2  (open circles) and 5% A u doped Y B a C u 0 . 2  together with the  6 3  . . .  3s  3  6  8 4  3  0 .57 6  90  (T =60 K) c  (T =91 K ) (solid circles),  C u nuclear-relaxation rate ( T i T )  c  - 1  (triangles)[119].  . .  92  4.18 The temperature dependence of the Raman frequencies of the vg (A ) mode g  in natural and deuterated K - ( B E D T - T T F ) C u ( N ( C N ) ) B r 2  94  2  4.19 The temperature dependence of the integrated intensities of the vg (A ) doug  blet in protonated (natural) and deuterated / c - ( B E D T - T T F ) C u ( N ( C N ) ) B r . 2  2  The intensities of lower component were scaled down by half. The lines are guides for the eye  95  4.20 The atomic displacement vectors for the v  60  assuming D /i point-group symmetry 2  xii  ( B ) normal mode of vibration, 33  97  4.21 The Raman frequency as a function of temperature of the feature due to i/  (B ) in K - ( B E D T - T T F ) C u ( N ( C N ) ) B r measured with an infrared laser  6 0  3g  2  2  in a Fourier-transform spectrometer.  Independent measurements, taken in  Janis Dewar at 2 and 15 K , above and below T at 11.6 K , are included. c  The frequency increases below T were obtained when the samples were slow c  cooled. The results of rapid cooling are also shown  99  4.22 Temperature dependence of the relative frequency shifts, 5u)/u>o, of the bands 27.4, 69.3, 104.2 and 133.5 cm-Hn K - ( E T ) C u ( N ( C N ) ) B r . 2  2  Triangles and  circles represent data from different samples[45, 50] 4.23 A peak splitting for u  m  100  (B ) mode observed in a - ( B E D T - T T F ) I at 10 K . 3g  t  2  3  4.24 Temperature dependence of the z^ (B ) mode in a - ( B E D T - T T F ) I . 60  3fl  t  2  3  . . .  102 104  4.25 The Raman frequency as a function of temperature of the feature due to U^Q (B ) 3g  in a - ( B E D T - T T F ) I t  2  3  measured with an infrared laser in a Fourier-  transform spectrometer. Independent measurements, taken in Janis Dewar at 2 and 14 K , above and below T at 8 K , are included  105  c  4.26 Raman spectra of natural and deuterated «>(BEDT-TTF) Cu(N(CN) )Br. 2  5.1  2  . 107  The single particle band, electron density, and lattice distortion in the metallic state above TCDW and in the charge density wave state at T=0. The figure is appropriate for a half-filled band[140]  Ill  5.2  The T T F and T C N Q molecules  113  5.3  (Left), T T F - T C N Q crystal structure; and (Right), Stacking arrangement in TTF-TCNQ  5.4  114  Intensities of the diffuse x-ray scattering measured in a single crystal of T T F TCNQ[147]  116  xiii  5.5  (Left), the Kohn anomaly observed by inelastic neutron scattering in T T F T C N Q ; and (Right), dispersion relation of the longitudinal acoustic phonon measured by inelastic neutron scattering along the one-dimensional b-axis of TTF-TCNQ[148]  5.6  117  Examples of the normal modes belonging to each of the eight symmetry species A , Bi , B , B , A , Bin, B g  g  2g  3g  u  and B . The top two panels show in-plane vi-  2u  3u  brational modes; The bottom two panels show out-of-plane vibrational modes. The gerade modes are Raman active and shown in the left panel. The ungerade modes (except for the A mode, which is Raman- and infrared-inactive) u  are infrared active and shown in the right panel 5.7  120  Raman spectra of T T F ( h ) - T C N Q ( h ) , T T F ( d ) - T C N Q ( h ) , T T F ( h ) - T C N Q ( d ) a n d 4  4  4  4  4  4  TTF(d )-TCNQ(d )between 100 and 1700 c m " at 293 K . Seven of the ten 1  4  4  totally-symmetric ( A ) modes of T C N Q , which are the room temperature s  Raman features, have been labeled (i/ — i/g)  123  3  5.8  Raman spectra of T T F - T C N Q between 50 and 1650 c m  - 1  at temperatures 10,  60, 130 and 293 K . Seven of the ten totally-symmetric ( A ) modes of T C N Q , s  which are the room temperature Raman features, have been labeled (i> — u ). 125 3  5.9  9  Raman spectra of T T F ( h ) - T C N Q ( h ) a n d TTF(h )-TCNQ(d )between 50 4  4  4  4  and 1650 c m " at 10 K . The Raman lines of T T F ( h ) - T C N Q ( h ) have been 1  4  4  assigned and labeled by comparison with the data from Ref.[163, 166, 167] The Raman lines, which have a large deuterium-isotope frequency shift, have also been labeled in the spectrum of T T F ( h ) - T C N Q ( d ) . The line at 86 c m " 4  right below u (B ) 5i  3u  1  4  is an atmospheric line  126  5.10 The integrated intensity of the Raman lines assigned to v ±(Bz ) b  u  and v^(B ) iu  modes as a function of temperature. The lines are guides for the eye  130  5.11 Raman frequency of v (A ) and V4(A ) modes as a function of tempera3  g  g  ture.The lines are guides for the eye  xiv  131  5.12 Temperature dependence of the Raman scattering from T T F - T C N Q at 63 cm"  135  1  5.13 The TSeF molecules  136  5.14 The resonant Raman spectrum from a powdered sample of T S e F - T C N Q in K B r , at 10 K . Eight of the ten totally-symmetric A modes have been labeled g  (i>2 — fg). T W O new lines have been assigned to B  3u  6.1  modes (v  53  and u ). 5i  . . 137  The structure of tetragonal La Cu04. At the structural transition to the 2  orthorhombic phase the copper-oxygen octahedra undergo a tilt as indicated by the arrows. Also shown is the centered character of the crystallographic unit cell (dashed arrow) 6.2  142  Normal modes of La CuC>4 (assuming D 2  ih  symmetry) and their calculated  frequencies[181] 6.3  144  The temperature dependence of (c,c) spectra in La Cu04. Above 510 K the 2  crystal has tetragonal symmetry[199] 6.4  145  (Top), two-magnon Raman spectra of La Cu04 observed at room temperature 2  for the (x, x) configuration with excitation photon energies between 1.96 and 2.54 ev; the insert shows the optical conductivity spectrum for polarization along the x direction. (Below), two-magnon Raman spectra of YBa Cu3C>6 2  observed at room temperature with excitation photon energies at 1.96, 2.41 and 2.54 ev; the insert shows the optical conductivity spectrum for polarization along the x direction[204] 6.5  147  Theoretical fitting (a quantum Monte Carlo method) of the experimental spectrum (bold curve) of La CuC»4[216]. The almost indistinguishable solid and 2  dashed curves are for a 10x10 and a 16x16 lattice, respectively  xv  148  6.6  The strength of the two-magnon and the higher frequency two-phonon scattering as a function of incoming photon energy for Y B a C u 3 0 . Also shown 2  6  is the imaginary part of dielectric function e . The two-phonon scattering is 2  very strong when the incoming photon is close to the charge-transfer gap 2A, while the two-magnon scattering vanishes there and instead has a maximum when the photon has an energy equal to 2A+3J [219]. The same phenomena have also been observed in La CuO [203] 2  6.7  150  4  Two-phonon scatering as a function of incoming photon energy for L a C u 0 2  4  and YBa Cu O [204] 2  6.8  3  151  6  Raman spectra of L a C u 0 2  4  for two polarizations, E / / a b (upper trace) and  E / / c (lower trace) of the infrared laser light, with A=1064 nm, at room temperature. The laser power is 100 m W 6.9  154  Phonon dispersion curves of L a C u 0 measured by inelastic neutron scatter2  4  ing [222, 223, 224] in the room-temperature orthorhombic phase (left panel) and high-temperature tetragonal phase (middle and right panels). The A  9  modes are transverse optic (TO). The others are longitudinal optic (LO), except for the low L A modes. Our peak-frequency data are indicated by crosses. The zone origin data correspond to the A modes observed in the (cc) specs  trum of Fig. 6.8. The remainder are from the E / / ab spectrum of Fig. 6.8. The positions of two lower energy A  2 u  modes in the right panel are arbitrary. 156  6.10 Raman spectra of L a C u 0 , L a i . S r . i C u O , and L a C u O . 0 4 , at room tem2  4  9  0  4  2  4  0  perature and with the laser polarization E / / ab. The laser power is 100 mW. The vertical lines are guides to the eye  159  6.11 Raman spectra of L a i . S r . i C u O at 2 K and L a C u 0 9  0  4  2  and 4000 c m . The laser power is 6 m W - 1  xvi  4  at 8 K between 100 160  6.12 Low temperature Raman spectra from magnetic excitations in La .gSr .iCuO4 1  0  (T = 12 K ) . The polarization is e;||rr (x is an arbitrary direction). The c  laser power is 6 mW. The insert shows an enlarged view of the weak peak around 2770 c m . The spectra vary strongly with temperature and are much - 1  narrower than the two-magnon scattering around 3200 c m  - 1  in the parent  compound La CuO4[206]  162  2  6.13 Sr doping dependence of superconducting transition temperature, T , in  La2- Sr CuO\.  c  x  x  Closed triangle for x=0.115 shows the disappearance of the bulk SC down to the lowest temperature[231]  164  6.14 (Left), Model for the stripe order of holes and spins within a CuC»2 plane at n = l / 8 . Only the C u sites are presented. A n arrow indicates the presence of ft  a magnetic moment; shading of arrowheads distinguishes antiphase domains. A filled circle denotes the presence of one dopant-induced hole centered on a Cu site (hole weight is actually on oxygen neighbors). A uniform hole density along the stripes is assumed. (Right), Sketch showing relative orientation of stripe patterns in neighboring planes of the tetragonal phase[238]  166  6.15 The temperature dependence of the integrated Raman intensity of the peak at 3419 c m  - 1  of Lai.gSr .iCuO4 (T =12 K ) is compared with the temperature 0  c  dependence of the intensity of the elastic incommensurate magnetic peak of L a . S r o . i 2 C u 0 obtained from neutron scattering[235]. The solid line guides 1  88  4  the eyes  167  6.16 (a) Normalized peak frequency  UJ/LOQ  and (b) normalized line width  r / r  0  as a  function of normalized temperature. The results of our sample of Lai.gSr 1CUO4 0  (T =12 K , T = 4 0 K) are compared with the results of three antiferromagc  ord  nets, the three-dimensional system K N i F dimensional systems K N i F 2  4  3  (T =246 K ) [245] and the twoord  (T =97 K ) [245] and L a N i O . 2 (T =185 K) ord  2  [242]. The lines are guides for the eye  xvii  4  0  ord  169  6.17 The real-space picture of the two-magnon scattering. Dashed lines denote photons, and wavy lines denote spin waves. This picture is valid away from resonance[214] 6.18 The Raman spectrum and its theoretical fittings. The solid curve is the experimental data at 8 K . The long-dashed curve is a fitting from the formula given by Chubukov and Frenkel in Ref. [214]. The dotted line is a fitting which includes quantum fluctuations in the ground state (Canali and Girvin's work[212]). The short-dashed line is an exact spin-wave result give by Sandvik et al. [216]. The long-short dashed curve is a Gaussian fitting which provided the values for u and Y in Fig.6.16  xviii  List of Tables  1.1  Chronology of synthetic organic conductors and superconductors  3  1.2  Summary of room temperature crystallographic data for 5 B E D T - T T F (ET) based organic superconductors  7  1.3  The character table of D h  16  1.4  Correlation table for K > ( B E D T - T T F ) C u ( N C S ) . (R=Raman active; IR=infrared  2  2  2  active) 1.5  18  Summary of superconducting isotope effects ( A T ) for /c-(ET) Cu(NCS) crysC  2  2  tals for four different isotopic substitute in the B E D T - T T F molecule [58]. . . 1.6  The critical temperatures ( T (K)) of five B E D T - T T F based materials and c  their deuterated compounds (p.5 of Ref. [24] and Table 4 of Ref. [59]). 1.7  . . .  26  A comparison of Fermiological properties ( oscillation frequency, effective mass m and Dingle temperature T c  1.8  26  ) for several E T based materials  D  A list of the critical fields H i and H c  c 2  31  , the coherence length £ within the  highly conducting plane || and out-of-plane JL, evaluated at T=0 K for several organic superconductors (Ref. [72, 68, 73, 74, 75], p.176, 186 of [24] and p.145, 156 of [76]). (k=10 )  35  3  2.1  Allowed Raman modes and their Raman tensors for point groups D  4.1  The ratio (5u/vi) of the 10 K wavenumber shifts to the room-temperature  2h  and D±h-  49  wavenumber values, for twelve totally-symmetric (A ) and and one v^B-sg) g  modes of / i - B E D T - T T F and d - B E D T - T T F . Also listed are the observed and 8  8  calculated[30] deuterium shifts (Ai/j)  xix  76  4.2  Comparison of the experimental and calculated frequency shifts (in c m ) of - 1  the totally-symmetric A modes in K-(ET) [Cu(NCS) ] due to the electrons  2  2  phonon interaction 4.3  83  Lists of the temperatures of the various anomalies observed i n K - ( E T ) C u ( N C S ) . 2  2  91 4.4  Lists of the temperatures of the various anomalies observed in K - ( E T ) C u ( N ( C N ) ) B r . 2  2  97 4.5  Lists of the temperatures of the various anomalies observed in o;-(ET) l3 and 2  /MET) I 2  4.6  103  3  Inverse isotope shift of the Raman frequency of the ^  6 0  ( B ) mode in K35  (BEDT-TTF) Cu(NCS) ,«;-(BEDT-TTF) Cu[N(CN) ]Br, /?-(BEDT-TTF) AuI 2  2  and / ? - ( B E D T - T T F ) I 2  5.1  2  2  2  2  108  3  Phase diagram and 2k fluctuation regime of T T F - T C N Q and TSeF-TCNQ[142]. F  Upon lowering the temperature below Tin, first one-dimensional fluctuations start to occur; below T D these change over to two- and three-dimensional 2  fluctuations.  TD  is the actual temperature of the Peierls transition, where  3  three-dimensional ordering starts 5.2  122  Frequencies ( c m ) and assignments of the out-of-plane vibrational modes -1  of the T C N Q molecule in T T F - T C N Q at 10 K , by comparison with the room temperature data from Ref. [166] 5.3  127  Frequencies ( c m ) and assignments of the in-plane vibrational modes of -1  the T C N Q molecule in T T F - T C N Q at 10 K , by comparison with the room temperature data from Ref. [163] 6.1  Frequencies in c m  - 1  128  of the observed Raman peaks in La CuC>4 at room tem2  perature for E / / a b , compared with the calculated transverse and longitudinal optic (TO and L O respectively) modes from infrared (IR) measurements.  xx  . 157  Acknowledgements  I would like to thank deeply my supervisor Dr. J. E . Eldridge for his many good suggestions, knowledgeable supervision, helps, encouragement thoughout my studies. I wish to thank my wife, Hui, for her emotional support and encouragement, and my baby Ivy for bringing me the joy of life. I would like to thank all the scientists around the world who have supplied me the crystals, including Joerg Sichelschmidt, a former postdoctoral fellow in my lab. Finally I would like to thank all the technicians in the main departmental machine shop, the student machine shop, the electronics shop, the student technical service and the computer lab for their technical support.  xxi  Chapter 1 Introduction  1.1 History and Development of Superconductors In 1911, Kamerlingh Onnes[l] discovered the phenomenon of superconductivity in mercury. This phenomenon has been actively studied up to the present and is one of the major branches of condensed matter physics. There are two fundamental characteristics of superconductors: (1) the absence of any measurable resistance below a certain temperature which is named the critical transition temperature (T ) of a superconductor; (2) the Meissner effect-not only c  a magnetic field is excluded from entering a superconductor but also a field in an originally normal sample is expelled as it is cooled through T if the magnetic field is not too strong. c  Since the discovery of the superconductivity in mercury, scientists have been searching for superconductors with higher critical temperatures. Until the 1960's, twenty six metallic elements and thousands of alloys and compounds had been found to be superconductors with the highest T =9.26 K in Nb among the elements and the highest T =18.05 K in Nb Sn c  c  3  among the intermetallic alloys (Later it was discovered that a compressed sulphur shows superconductivity at 10-17 K and Nb Ge becomes superconducting at T =22.3 K , which are 3  c  the highest up to now among the elements and the intermetallic alloys, respectively). The BCS (Bardeen, Cooper and Schrieffer) theory[2] is very successful in explaining conventional superconductivity.  But the critical temperature given by the B C S theories in the weak  coupling or strong coupling approximation is limited - McMillam limit (30~40 K)[3]. To raise the critical temperature, a model of a superconducting organic polymer was proposed by Little[4] in 1964, which initiated a search for organic superconductors.  1  Chapter 1.  Introduction  2  a) hypothetical superconducting chain molecule  R  H  R  R  H  H  R  R  H  R i s a very polarizable side group b) polypropylene  R denotes C H J  Figure 1.1: (a) Carbon chain molecule with alternating single and double bonds, and (b) polypropylene as an example of a molecular side group R incorporated in molecule (a). Little[4] carried out calculations with chain molecules having alternating single and double bonds, called polyconjugate molecules, containing molecular groups attached to certain carbons along the chain, as shown in Fig. 1.1. He used highly polarizable side groups, which means that the electronic charge distribution of the groups can easily be effected by the presence of an electric field or a nearby charged particle. When an electron passes by a side group, its electric field shifts the charge distribution of the side group so that it is positive near the moving electron and negative away from that electron. This causes electrons on the side group to be pushed away from the chain. The electron moves much faster than the charge can be redistributed, so the onset of polarization lags behind the moving electron. The enhanced positive charge near the chain can attract another electron, which then follows the first electron, in effect forming a Cooper pair. When Little carried out detailed B C S theory calculations on this hypothetical molecule, he obtained the incredible value of 2,000 K as the transition temperature. Of course it is highly unlikely that the  Chapter 1.  Introduction  Table 1.1: Chronology of synthetic organic conductors and superconductors. 1962 Synthesis of T C N Q 1970 Synthesis of T T F 1973 T T F - T C N Q synthesized: first organic metal 1976 T M T S F synthesized 1978 B E D T - T T F synthesized 1981 (TMTSF) C104=first organic superconductor at ambient pressure at 1.4 K 1983 ( B E D T - T T F ) R e 0 = f i r s t S-based organic superconductor 1984-86 0- ( B E D T - T T F ) X , where X = l j , IBr , A u l j where T =1.4, 2.8 and 5.0 K , respectivly 1987 K - ( B E D T - T T F ) C u ( N C S ) , T =10.4 K 1990 K - ( B E D T - T T F ) C u ( N ( C N ) ) B r , T =11.6 K 1990 « - ( B E D T - T T F ) C u ( N ( C N ) ) C l , T =12.8 K under 0.3 kbar 2  2  4  2  2  c  2  2  c  2  2  c  2  2  c  hypothetical molecule exists at this temperature, but the possibility of room temperature superconductivity is certainly predicted in this article. Little's suggestion prompted a great deal of research into synthenic organic conductors (synmetal). A n important step in this direction occured in 1962, when Melby[5] synthesized the electron acceptor T C N Q (7,7,8,8-tetracyano-p-quinodimethane) and in 1970 T T F (tetrahiafulvalene)[6] was synthesized and became an important electron-donor molecule for use in preparing charge-transfer conductors. Then Ferraris et al. [7] reacted T T F and T C N Q and obtained a charge-transfer salt, T T F - T C N Q , which has become known as the first true organic metal because it was metallic down to 54 K . The results were significant because it was realized that charge-transfer salts formed by reacting an electron donor and an acceptor molecule could form metallic materials with resulting high electrical conductivities. These findings increased the interest in research directed toward the search for new electrondonor/acceptor molecules. In 1981, ( T M T S F ) C 1 0 2  4  (TMTSF=tetramethyl tetraselenaful-  valene) was found to be the first ambient pressure organic superconductor with a T =1.4 c  K . At present a great number of organic superconductors are based on B E D T - T T F (bis  Chapter 1.  Introduction  4  (ethylenedithio) tetrathiafulvalene) as the electron-donor molecule. A t least 20 superconductors of B E D T - T T F salts have now been synthesized, with K - ( B E D T - T T F ) C u ( N C S ) [ 8 ] pos2  2  sessing the third highest superconducting T of 10.4 K , K-(BEDT-TTF) Cu(N(CN) )Br[9] c  2  2  having the second highest T of 11.6 K , and K-(BEDT-TTF) Cu(N(CN) )Cl[10] having the c  2  2  highest T of 12.8 K at 0.3 kbar. Table 1.1 provides a chronology of synthetic organic conc  ductors and superconductors. In 1991, a new class of molecule-based superconductors was opened up by the discovery of superconductivity in alkali-metal-doped fullerenes such as K C o with a T of 18 K [ l l ] . The type of molecular structure of the fullerence molecules 3  6  c  belongs to a category different from those of T M T S F and B E D T - T T F , and the dimensionality of the crystal is three, in contrast to one and two for ( T M T S F ) X and (BEDT2  T T F ) X , respectively. However the superconducting alkali metal fullerides are similar to 2  conventional organic superconductors to the extent that they are charge-transfer salts and are molecular-based synthetic metals in which the conduction band is derived from the CQO electron-acceptor molecule. Much of the motivation for these increased activities in organic superconductors has also been based on the potential technological applications that may eventually be realized. In this regard, the organic materials are especially light-weight (density~ 1.5-2.0 g/cm ) com3  pared to both copper metal (density^ 9 g/cm ) and the ceramic superconductors (density^ 3  7 g/cm , discovered in 1986). Interestingly, copper has a high ambient temperature electri3  cal conductivity (~ 10 Q~ cm~ ) but it never becomes superconducting even at the lowest 6  1  1  temperature (milli-Kelvin) yet achieved.  For the organic superconductors, it is possible  that their low density may be useful in electronic applications in space vehicles, for example, where weight is often kept a minimum. They have also been proposed as components for compact high-efficiency electrical motors, and in computers where their very low-heat generation could allow construction of high-density circuits. In 1986, a breakthrough occured with the discovery of a new class of materials which displayed higher-temperature superconductivity when Alex Miiller and Georg Bednorz[12]  Chapter 1.  Introduction  5  discovered T of 30 K in the La-Ba-Cu-0 system. The supercondcuting phase was found to c  crystallize in the K N i F structure, which is a layered perovskite with a strongly anisotropic 2  4  crystal structure. The superconductor had the composition L a _ B a C u 0 4 ( a 2-1-4 com2  x  I  pound), with the superconducting properties strongly dependent on x. Later the barium was substituted by strontium (Sr) and calcium (Ca), and the transition temperature was raised to nearly 40 K . The record T was held by the material Lai.gsSro.isCuC^. In January 1987 c  T  c  beyond 90 K , which is above the boiling point of nitrogen (77 K ) , was recorded in the  USA, Japan and China, independently, in the material YBa Cu307_a;. At present, there are 2  several groups of superconductors with T higher than 100 K : Bi-Sr-Ca-Cu-0 compounds, c  Tl-Ba-Ca-Cu-0 compounds and Hg-Ba-Ca-Cu-0 compounds. In this thesis, three types of the above-mentioned materials, namely T T F - T C N Q (the first organic conductor), B E D T - T T F based organic superconductors and L a _ S r C u 0 4 (high T 2  I  a;  c  cuprate superconductors), have been studied with Raman spectroscopy. Some of my work included in this thesis has been published elsewhere (see List of Publications on page 191).  1.2  General Properties of the B E D T - T T F Based Organic Superconductors  Organic superconductors (or conductors) based on the B E D T - T T F [bis-(ethylenedithiatetrathiafulvalene)] molecule have been widely studied because, prior to the discovery of fullerene superconductors, they had the highest transition temperature (T R3 12 K) of an C  organic superconductor. This section gives a brief review of these organic materials focussing on the properties of the metallic, insulating and superconducting phases.  1.2.1  Crystal Structure  The structure of B E D T - T T F (further abbreviated to ET) is shown in Fig. 1.2. The neutral B E D T - T T F is nonplanar, twisted at the central double C = C bond and rings come out of the plane. When it forms a charge-transfer complex, the molecule is fairly planar and untwisted,  Chapter 1.  Introduction  6  a- type  (3-type  K-type  Figure 1.2: (Left), the geometry of a neutral B E D T - T T F molecule; (Right), three different packing patterns of B E D T - T T F in the crystals, which are denoted by a, (3, and n. The rectangle represents the positions of the B E D T - T T F molecules as viewed along the long axis Z of the molecule.  Chapter 1.  Introduction  7  Table 1.2: Summary of room temperature crystallographic data for 5 B E D T - T T F ( E T ) based organic superconductors. Materials T Structure q(A) 6(A) c(A) Vol.* (A ) Z Ref. 3  c  /?-(ET) AuI 2  a (/? )-(ET) I I  I ?  Triclinic 7-8 Triclinic 10.4 Monocline 11.6 Orthorhombic 12.8 Orthorhombic  5  2  2  3  K-(ET) CU(NCS) 2  2  «>(ET) Cu(N(CN) )Br /t-(ET) Cu(N(CN) )Cl • - U n i t Cell Volume. 2  2  2  2  6T60  9M  6.61  9.09  15.29  855.9  1  [14]  16.24  8.44  13.12  1688.0  2  [15]  1 2 . 9 4 3 0 . 0 1 8.53  3317  4  [9]  12.97  3299  4  [10]  15.40  29.97  845.2  8.48  1  and the packing density is increased. The central fragment of two C and four S atoms flattens to a plane but the outer rings remain slightly nonplanar. The end - ( C H ) - groups can take 2  2  on one of two degenerate out-of-plane conformations. Organic molecular crystals with the formula ( B E D T - T T F ) X consist of conducting layers 2  of B E D T - T T F molecules sandwiched between insulating layers of anions X . The layered structure leads to highly anisotropic electronic properties. The different possible packing patterns of B E D T - T T F in the crystals are denoted by different Greek letters a, /3, 8, K et al. as shown in Fig. 1.2. The basic unit of the packing pattern in the K phase is a "dimer" consisting of two B E D T - T T F molecules stacked on top of one another. Each dimer has one electron less than a full electronic shell because of the charge transfer to the anions. Fig. 1.3 shows the crystal structure of K - ( B E D T - T T F ) C u ( N C S ) along with the arrangements of anions C u ( N C S ) 2  2  2  and C u ( N ( C N ) ) X (X=Br, CI). Two B E D T - T T F molecules are paired with their central 2  tetrathioethylene planes almost parallel, and adjacent pairs are almost perpendicular to one another.  Without the anion, the B E D T - T T F donor layer is essentially centrosymmetric.  Infinite-chain polymeric anions (Cu(NCS) , C u ( N ( C N ) ) B r and C u ( N ( C N ) ) C l ) form insu2  lating layers. In Table  2  2  1.2 we summarize room temperature crystallographic data for 5  crystals we have investigated in this thesis.  Chapter 1. Introduction  8  Figure 1.3: (Top), crystal structure of K>(BEDT-TTF) Cu(NCS) ; (Middle), an arrangement of Cu(NCS) ; (Bottom), an arrangement of Cu(N(CN) )X, where X denotes Br or C l . 2  2  2  2  Chapter 1.  1.2.2  Introduction  9  Electrical Properties  The E T salts have a wide variety of electrical properties ranging from insulating to superconducting. In addition, the dimensionality changes from one to two, depending on the relative strength of the face-to-face and side-by-side interactions between adjacent E T molecules. Most of the 2:1 E T cation radical salts with linear or polymeric anions, such as triiodide and Cu(NCS)2, are of a two-dimensional structure, where a conducting layer formed by stacked E T molecules is alternately separated by an insulating layer of anions. The conductivity is consistent with the quasi-two-dimensional nature, with the intralayer (in plane) conductivity being larger that the interlayer (out-of-plane) conductivity. The 2:1 E T salts produce various kinds of metals and ambient-pressure superconductors, but they include semiconducting and magnetically ordered phases as well. Fig. 1.4 shows the temperature dependence of the resistivity along the 6-axis in K(ET) Cu(NCS)2[16]. At ambient pressure the resistivity reveals a pronounced maximum 2  around 90 K . After passing through the peak, the resistivity decreases rapidly and shows a sharp resistance drop at the onset of superconductivity (11.2 K ) . The transition temperature determined from the midpoint of the resistivity drop is 10.4 K . W i t h increasing pressure, the resistivity peak is suppressed, and T is reduced. At 3 kbar the high-temperature peak c  disappears while the residual resistance decreases at low temperatures. When the pressure reaches 6 kbar, the superconductivity disappears, indicating the overall pressure dependence is as high as dT /dP=-1.3 K/kbar. In the poorly conducting direction, perpendicular to c  the planes, the conductivity is lower by a factor of « 600. In order to clarify the origin of the resistance maximum, intensive investigations have been carried out. Measurements of the lattice parameters[17] have revealed an anomaly near 100 K , indicating a conformational change in the ordering of the terminal ethylene, - C 2 H 4 - , of the E T molecule. A structural anomaly has also been detected by extended X-ray absorption fine structure (EXAFS)[18], which reflects the local structure around the Cu atom. Taking into account the interlayer  Chapter 1.  Introduction  10  Temperature (K) Figure 1.4: Temperature dependence of the resistance along the 6-axis for K > ( E T ) C U ( N C S ) at several pressure[16]. 2  2  Chapter 1.  Introduction  11  spacing observed in the X-ray study, not only a conformational change but also an emergence of a valence mixed state of C u  1 +  and C u  2 +  in the polymer have been postulated in  the high-temperature phase[19]. The family of K - ( E T ) C U ( N ( C N ) ) X ( X : Br, CI) is isostructural. The K - ( E T ) C u ( N ( C N ) ) B r 2  2  salt has the in-plane conductivity « 48 (ftem)  2  -1  2  and is an ambient-pressure superconductor  with T =11.2 K[9]. Its resistivity exhibits a temperature dependence similar to that of Kc  ( E T ) C u ( N C S ) ; it also possesses a maximum around 90 K , which tends to disappear under 2  2  pressure. The spin susceptibility obtained from E S R experiments is almost constant between 300 and 50 K but shows a drop below 50K, indicating a strong decrease in the density of states at the Fermi level. This suggests the formation of a narrow gap or pseudo-gap[20]. A large enhancement of the relaxation rate and a drop of the Knight shift, which are ascribed to antiferromagnetic fluctuations[21], are also observed near 50 K, but they tend to disappear under pressure. A similar behavior has also been observed in «:-(ET) Cu(NCS) . 2  2  /c-(ET) Cu(N(CN) )Cl, with a room-temperature conductivity of « 2 ( Q c m ) , shows a -1  2  2  semiconductor-like temperature dependence at ambient pressure, but exhibits a metallic one under pressure[22]. It becomes superconducting with T =12.8 K under an applied pressure c  of 0.3 kbar[10]. Through the observation of the proton nuclear spin-lattice relaxation, a transition to an antiferromagnetic ordered state has been observed in the 26-27 K range at ambient pressure[23]. Application of pressure has a strong effect on T for these compounds, as shown in Fig. c  1.5[24]. The superconducting transition temperatures drop rapidly with applied pressure, which is correlated with the rapid decrease in the effective mass[25]. Very recently Su and Zuo et al. [26, 27, 28] have investigated the cooling rate effect on the resistivity and superconducting transition temperature in K - ( E T ) C u ( N ( C N ) ) B r as shown 2  2  in Fig. 1.6. The different cooling rate through 80 K has a dramatic effect: the rapidly cooled sample has a much larger resistivity and a lower transition temperature, which decreases linearly with increasing resistivity near the transition temperature. The fast cooling through  Chapter 1.  Introduction  12  i  ;  r  Pressure (GPa) Figure 1.5: Pressure dependence of T s for ( E T ) X salts[24]. X represents a counter anion. c  2  Chapter 1.  Introduction  13  80  T (K)  T (K)  Figure 1.6: (Left), an overlay of resistivity as a function of temperature for K - ( E T ) C u ( N ( C N ) ) B r cooled at different rates. The inset is a semilog plot of p versus T at low temperatures. (Right), resistivity as a function of temperature near the superconducting transition for the sample at different cooling rates[26]. The curves from N o . l to No.5 shift upward in the sequence of increasing cooling rate at 0.4 K / m i n , 1 K / m i n , 5 K / m i n , 20 K / m i n and 60 K / m i n , respectively. 2  2  2  Chapter 1.  Introduction  14  80 K will bring disorder into the sample and affect the superconducting volume fraction and the transition temperature. It has been reported[29] that the deuterated compound is in the critical region between the superconducting phase and the antiferromagnetic phase, with the crystals if they are slowly cooled containing both phases, but if they are rapidly cooled containing only the magnetic phase. 1.2.3  Intramolecular (Internal) Vibrational Modes  The B E D T - T T F molecule has symmetry belonging to the point group D h which contains 2  the elements (E, I, C$, C | , C f , o ,  <r , o ).  xy  yz  The characters of the group D  xz  in the Cartesian representation of the B E D T - T T F  2h  molecule can be calculated by multiplying the number of unshifted atoms in each symmetry operation by the appropriate contribution ( ± 1 +  2 C O S # R ) (OR  is the rotation angle. + for  proper rotation and - for improper rotation), which are 3, 1, -3 and -1 for the identity E, reflection a, inversion I and rotation C , respectively. The numbers UR of atoms which 2  remain unshifted under operation R are £ / ( £ ) = 26  U(C )  U(I) = 0  U(a y) = 0  Z  2  = 2  [/(Cf) = 0  U(C%) = 0  = 2  U(a )  x  xz  U(a ) yz  = 18  The characters x(R) in the Cartesian representation can then be calculated by: (R) = U (±l  X  .  which gives:  x(£)=78  x(/) = 0  R  ( C | ) = -2  x(C|) = 0  x(v )  X(<J ) = 2  x  xy  =0  (1.1)  + 2cosO )  R  XZ  The characters of the various classes of D  2h  x(Cf) = 0  x ( ^ ) = 18 2  in each irreducible representation  , are  listed in Table 1.3. The multiplicity of an irreducible representative ( the number of the times it appears in the reducible representation T) is given by the formula: n^  = -j:x (R)x(R) il)  9  R  (1-2)  Chapter 1.  Introduction  15  S  S"  BEDT-TTF  V!=2921 c m "  v =920 c m "  v =1552 c m "  1  1  2  1  7  V ! o=442 cm"  1  v =162 c m "  v = 3 1 1 cm"  1  12  n  Figure 1.7: (Top) A sketch of the B E D - T T F molecule. (Below) Wavenumbers observed at room temperature and atomic displacement vectors for the 12 totally symmetric (A ) normal modes of vibration, (assuming D h symmetry), of neutral B E D T - T T F . The displacement vectors are in the molecular plane, except the out-of-plane C - H bends in r/ and v , which are indicated. The vectors were calculated by Eldridge et al. [30], and are not to scale. 9  2  4  5  Chapter  1.  16  Introduction  Big Bg Bg A Bin B 2  3  u  2u  B  3u  E 1 1 1 1 1 1 1 1  Ta ble 1.3: Tiel character table of I o Cf c i Cf 1 1 1 1 1 1 1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 -1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 -1 -1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 -1  D  2h  yz  x ,y  ,z xy xz yz d  R Ry z  Rx T  z  T  x  where g is the order of the point group and is 8 for D h group. Hence the number of normal 2  modes of the B E D T - T T F molecule and their associated symmetry species are given by r = 12 A  + 7 Big + 8B  g  2g  + 12B  + 7A + 1 2 B  3g  where there are 3 translational modes B  Xu  U  +B  + 12B  lu  2u  + 8B  3u  + B , 3 rotational modes Bi + B + B .  2u  3u  g  2g  3g  Removing the normal modes due to translation and rotation gives the number of vibrational modes: ^vibrational  = YlAg + 6Bi + 7B g  where the A , Bi , B g  g  2g  and B  3g  2g  + UB  3g  + 7A + 1 1 B U  are Raman-active, Bi , B u  1U  + llB  and B  2u  3u  2 u  + 7B  3u  infrared-active, A  u  Raman and infrared silent. The twelve totally symmetric A modes of the B E D T - T T F molecule are shown in Fig. 1.7 9  while examples of the normal modes of the B E D T - T T F molecule belonging to each of the eight symmetry species are shown in Fig. 1.8. When the B E D T - T T F molecule is incorporated into the solid, there will be crystal fields which alter the characteristics of Raman and Infrared activity, but have only a small effect on the vibrational frequencies. The external forces on the molecule due to the crystal field are accounted for using group theory. For K > ( B E D T - T T F ) C U ( N C S ) , the B E D T - T T F molecules 2  2  Chapter 1.  Introduction  17  Figure 1.8: Examples of normal modes belonging to the eight vibrational symmetry species of the B E D T - T T F molecule. The arrows indicate the direction of the atomic displacement, + indicates a displacement out of the page and — a displacement into the page.  Chapter 1. Introduction  18  Table 1.4: Correlation table for « - ( B E D T - T T F ) C u ( N C S ) . (R=Raman active; IR=infrared active). 2  Molecular point group D fc 12 A, 6B 7B 11 B 2  Site group (no symmetry)  2  Unit cell group (Factor Group) P2 (Cf)[24, 76] X  72 A (R, IR) 72 A (R,IR) • 72 B (R, IR) 7 A„ (Inactive) 11 Bi„ (IR) 11 B (IR) 7 B (IR) 2 u  3u  occupy sites in the lattice about which there are no allowed symmetry operations. This lack of site symmetry removes all the molecular symmetry, with the result that all 72 vibrational modes derived assuming D h symmmetry become both Raman and infrared-active. 2  The effects of the site symmetry and the unit cell symmetry on the Raman and infraredactivity of the vibrational modes are demonstrated in the correlation table (see Table 1.4). The first column lists the 72 vibrational modes for the isolated B E D T - T T F molecule, assuming D h symmmetry. Distortion due to the lack of site symmetry is considered in the 2  second column, where all 72 modes become both infrared and Raman active. In the third column, the effect of the arrangement of two B E D T - T T F molecules in the unit-cell with P 2 i (Cf) symmetry[24, 76] is considered. For each vibrational mode for the isolated B E D T T T F molecule, there are 2 new modes depending on whether the vibrations of the different molecules are in phase or out of phase. A l l of these new modes are both infrared and Raman active. Using the infrared and Raman spectra of neutral B E D T - T T F and several isotope analogs,  Chapter 1.  Introduction  19  an assignment of the normal modes of the B E D T - T T F molecule has been performed by Eldridge et al. [30]. The frequencies and frequency shifts of the Raman features and the infrared powder absorption features were measured. These shifts were compared with those calculated using a realistic valence force model. The force constants produced excellent overall agreement between the measured and calculated frequencies and isotope shifts. Over half of the features have been re-assigned differently from those give by Kozlov et al. [31].  1.2.4  Infrared Conductivity  Infrared reflectance or conductivity spectra provide important information on band parameters for metals, such as the effective mass, the bandwidth, the collision time of carriers, and so on. By using polarized light one can also elucidate anisotropic features with respect to the orientation of the crystals. In fact, the reflectance spectra show a distinct difference depending on whether the polarization is parallel or perpendicular to the conducting direction. The reflectance spectra of the B E D T - T T F salts have been analyzed in terms of a Drude model which assumes that the plasma frequency u and the relaxation rate r are anisotropic. p  In our lab, Eldridge et al. [32, 33, 34, 35, 36, 37, 38] have conducted extensive measurements of the polarized reflectivity of K > ( E T ) C U ( N C S ) , « ; - ( E T ) C u N ( C N ) B r and 2  2  2  2  K - ( E T ) C u N ( C N ) C l from 50 to 5500 c m a t temperatures between 10 and 295 K . Fig 1.9 _1  2  2  shows the optical conductivity o{u) of K-(ET) Cu[N(CN) ]Br at 10 and 300 K[36]. The 2  2  optical conductivities, obtained through a Kramers-Knonig analysis, are very similar for Cu(NCS) and C u N ( C N ) B r salts, as expected on the basis of similar crystal structures and 2  2  temperature dependences of the d.c. conductivity[15]. The far-infrared conductivity rises dramatically at temperatures below 100 K , in agreement with the temperature dependence of the d.c. conductivity[15]. The far-infrared peak ( less than 1000 cm" ) is due to intra1  band transitions of free carrriers, while the mid-infrared peak (1000-4000 c m ) is due to - 1  the interband transitions, superimposed on the free carrier tail. Fig. 1.9 also shows some strong vibrational features from the totally-symmetric A modes. 9  Chapter 1.  Introduction  20  1000  1000  2000  3000  4000  Wave Numbers (cm ) _1  Figure 1.9: Temperature dependent optical conductivity o(uS) of/c-(ET) Cu[N(CN) ]Br[36]. 2  2  Chapter 1.  Introduction  21  The appearance of these A modes in the infrared spectrum is due to the electron-phonon s  coupling since these modes in the isolated molecule are not infrared-active.  1.2.5  Raman Scattering  In our lab, Raman scattering is performed with a Fourier-transform Raman spectometer, which uses a N d : Y A G diode-pumped infrared laser. This infrared laser eliminates the problems of fluorescence and photodegradation so often encountered with the usual argon-ion lasers, which operate in the visible region. Since the organic superconductors are always black in appearance, these problems were always very severe, but with the new infraredlaser Raman machine we are able to use Raman spectroscopy where it was not possible before. Fig. 1.10 shows the room-temperature Raman spectrum of K>(ET) Cu(N(CN) )Br 2  2  taken with the infrared laser[39]. Also shown in Fig. 1.10 is the spectrum taken with a Raman microscope spectrometer (Renishaw Ltd.) equipped with a He:Ne (A=632.8 nm) laser and a charge-coupled device detector. W i t h the infrared laser, we obtained a resonant Raman spectrum and the electronic transition responsible for the resonant scattering must be strongly coupled to the two modes around 500 c m a n d 1470 c m , as seen in Fig. 1.10. -1  - 1  The totally symmetric A modes (which are labeled) are seen in Fig. 1.10, along with other 9  non-totally symmetric modes, mainly B . 3g  To my knowledge, several resonance Raman studies have been performed on a and (3 phase organic materials in the low energy range (below 800 c m ) . Raman scattering from - 1  a and /3-(ET) I has been reported, by Ludwig and co-workers[40], Pokhodnia et al. [41], 2  3  Swietlik and co-workers[42], and Sugai and Saito[43], and also on /?-(ET) IAuI, by Swietlik 2  et al. [42], and Ludwig and co-workers[40], and one on a and /3-(ET) IBr [43]. In a - ( E T ) I 2  2  2  3  (Refs. [40] and [41]) and /3-(ET) IAuI (Ref. [40]) it was found that two low-energy phonon 2  bands near 30 c m , assigned to librational modes of the E T molecule, vanished below T . - 1  c  This behaviour agreed with a theoretical model of Behera and Ghosh[44], but was not seen in «-(ET) Cu(N(CN) )Br[45]. 2  2  Chapter 1.  Introduction  22  800  K-(ET) Cu(N(CN) )Br 2  2  700 t/3  visible laser IR laser  £ 600  295K  £500 • f 400 <L>  G 300  v12  | 200 cd  !|v,  v ii; \ 10  A  "v \ v 9  8  \  IK  100 0 100  400  700  1/ v. v  1000  1300  1600  Wave Numbers (cm - ) 1  Figure 1.10: The room-temperature Raman spectra of K>(ET) Cu(N(CN) )Br taken with a visible laser (solid line) and an infrared laser (dashed line), up to 1600 c m [39]. 2  2  - 1  Chapter 1. Introduction  23  Few Raman studies of K-type organic superconductors have been reported because the Raman scattering is very weak and long data collection times are required. This is due partly to the fact that the samples are black and tend to overheat. Thus low laser powers must be used. The only study of which we are aware which covers the entire phonon frequency range and was performed as a function of temperature is the one by Sugai et al. [46] in 1993 on «>(ET) Cu(NCS) . They reported no frequency changes at 4 K , which is below the 2  2  transition temperature T of 10.4 K . A variable-temperature Raman study of u (A ) at 1473 c  3  g  c m i n K - ( E T ) C u ( N ( C N ) ) B r was reported by Truong et al. [47] and they reported large _ 1  2  2  frequency shifts around 180 K . However, our Raman results disagree with this result. Both Zamboni and co-workers[48] and Garrigou-Lagrange et al. [49] have also looked at selected regions of the Raman spectrum of K - ( E T ) C U ( N C S ) 2  2  at low temperatures.  Pedron et al. [45, 50] have recently reported a study of the Raman spectroscopy of some low frequency phonons in K - ( E T ) C u ( N ( C N ) ) B r . They observed an increase in frequency 2  2  of up to 3.2% for all of the phonons studied when the samples were cooled to 1.8 K . These phonons had frequencies ranging from 27 to 133 c m , and the shifts were larger for the - 1  lower frequency modes. In Ref. [50] they compared their results to a strong electron-phonon coupling model and showed that they are more consistent with an s-wave than with a d-wave gap function, and that the upper limit on the B C S energy gap would be 28 c m ' . 1  The following sections are less concerned with the contents of this thesis but are included for completeness. 1.2.6  Energy gap  Kornelsen and Eldridge et al. [34, 35] have measured the far-infrared absorption covering the frequency range from 10 to 40 cm for /t-(ET) Cu(NCS) . The ratio of the absorption _1  2  2  at temperatures below T ( T=5.3 K ) and above T ( T=10.5 K ) is plotted in Fig 1.11 as a c  c  function of frequency in order to detect the opening of an energy gap. In order to improve the sensitivity, the absorption was detected by a bolometric technique. Within the experimental  24  Chapter 1. Introduction  30 (BEDT-TTF) Cu(NCS) 2  E  b  2  Absorption Ratio T = 5.3 K T = 10,5 K  20  ^ 10  2A = 25 cm - l Expected (BEDT-TTF) Cu(NCS) 2  2  p Scaled Al ,d T =10.4K C  0  ^  10  Cr ---oo-—  20  Frequency  30  40  (cm  A  )  Figure 1.11: Normalized absorption A(5.3 K)/A(10.5 K ) of /c-(ET) Cu(NCS) as a function of frequency. The open circles represent the absorption of a typical B C S superconductor with T =10.4 K[34, 35]. The closed squares show the same behavior but with an enhanced residual absorption as determined by microwave measurements. 2  c  2  Chapter 1. Introduction  25  error, there is no change in the frequency dependence of the normalized absorption between 10 and 40 c m a s the temperature is lowered. Thus no indiction of a superconducting _1  energy gap was observed by this optical method.  The reasons why a gap might not be  observed have been thought to be that K - ( E T ) C u ( N C S ) is in the clean limit, or that the 2  2  gap is an anisotropic function with nodes. For a clean limit superconductor, the conduction electrons in the normal state are scattered only occasionally, making the low-frequency Drude conductivity peak much narrower than 2A[51]. The best evidence for K - ( E T ) C U ( N C S ) 2 2  being in the clean limit comes from measurements of the Shubnikov-de Haas effect[52]. This technique provides a fairly direct measurement of the conduction-electron scattering time and gives a result of r = ( 3 ± l ) x 10~  12  s. So the scattering rate l / r = l l c m i s much less than the _1  energy gap 2 A = 2 5 cm calculated from B C S theory. However tunneling spectroscopy and _1  ultrasonic measurements have observed the value of 2 A / k a T to be up to 4.5[53, 54]. For c  a ( E T ) I , /3-(ET) AuI and K - ( E T ) C U ( N C S ) r  2  3  2  2  2  2  resonant Raman spectra did not show an  opening of the superconducting gap[40, 41, 48]. However a superconducting energy gap for /3-(ET) AuI has been observed by the tunneling method, giving 2A/kjgT fti4[55]. 2  1.2.7  c  2  Isotope Effect  In the B C S theory the electrons interact by the exchange of phonons. The relevance of phonons can be tested by the isotope effect. B C S theory predicts that the critical temperature T varies with the square root of the atomic mass M . c  In order to test the B C S theory, the Argonne group carried out extensive measurements of the isotope effect. They reported that the  1 3  C substituted samples of K > ( E T ) C U ( N C S ) 2  2  and /€-(ET) Cu(N(CN) )Br did not give measurable shifts of T within an uncertainty of 2  2  c  ± 0 . 1 K [56]. They also replaced all the eight sulphur atoms, mostly S , of E T with S and 3 2  3 4  statistically found the decrease of T to be 0.08 K in K>(ET) Cu(N(CN) )Br, i.e., A T / T = c  2  2  C  C  0.7%[57]. Since the frequencies of the two A 9 modes associated with C-S stretching decrease  by 2.7% upon this substitution, they concluded that the C-S stretching modes of E T are  Chapter 1.  Introduction  26  Table 1.5: Summary of superconducting isotope effects ( A T ) for « - ( E T ) C u ( N C S ) crystals for four different isotopic substitute in the B E D T - T T F molecule[58]. C  Isotopic substitute  AT  C(4) 5(8) C(4) #(8) C(4) S(8) H(8)  -0.12±0.05 0.00±0.06 0.17±0.06 0.28±0.06  13  34  13  2  13  34  2  2  2  (K)  C  Table 1.6: The critical temperatures ( T (K)) of five B E D T - T T F based materials and their deuterated compounds (p.5 of Ref. [24] and Table 4 of Ref. [59]). P (kbar) T [24] A T [24] A T [59] A T [58] Materials c  c  c  8  2  8  8  K  2  2  2  2  8  2  2  2  8  2  8  2  2  2  8  2  8  2  2  8  8  2  2  2  2  2  2  10.4 11.2 11.2 12.3 12.8 13.1 5.0 6.0[59] 11.8 11.2  0 0 0 0 0.3 0.3 0 0 0 0  K>.(h -ET) Cu(NCS) . K-(d -ET) Cu(NCS) K-(h -ET) Cu(CN)(N(CN) ) -(d -ET) Cu(CN)(N(CN) ) K>(h -ET) Cu(N(CN) )Cl K-(d -ET) Cu(N(CN) )Cl Ac-(h -ET) Ag(CN) H 0 K-(d -ET) Ag(CN) H 0 K-(h -ET) Cu(N(CN) )Br «-(d -ET) Cu(N(CN) )Br 2  C  C  +0.8  +0.7  +1.1  + 1.1  +0.3  + 1.0  C  +0.28  +1.0 -0.6  -0.9  not a dominant mediator of interelectron attractions. Rather they argued that the decrease is consistant with a small B C S isotope shift due to the change of intermolecular modes through the entire mass of E T . They substituted all S by S and peripheral C by 3 4  1 3  C in K-  ( E T ) C u ( N C S ) and obtained AT =-0.12+0.05 K[58]. The superconducting isotope effects 2  (AT ) C  2  c  for K - ( E T ) C U ( N C S ) crystals for four different isotopic substitute in the B E D T - T T F 2  2  molecule are summarized in Table 1.2.7[58]. Surprisely the replacement of hydrogens on the peripheral part by deuteriums (all eight hydrogen atoms are replaced with deuterium atoms-see Fig 1.12) was found to increase T of c  K-(ET) CU(NCS) , K-(ET) CU(N(CN) )C1 2  2  2  2  )  K - ( E T ) C U ( C N ) ( N ( C N ) ) and K - ( E T ) A g ( C N ) H 0 2  2  2  2  2  Chapter 1.  Introduction  27  dg-BEDT-TTF  Figure 1.12: Deuterium substituted E T molecule. (see p.5 of Ref. [24] and Table 4 of Ref. [59]). Table 1.6 lists the T ' s of these materials comc  pared with their deuterated compounds. Up to now this inverse isotope effect is still an open question.  1.2.8  Electronic Band Structure and Fermi Surface  There is a direct relation between the band structure and the measured quantities such as electrical conductivity, the effective mass of charge carriers, themoelectric power, optical conductivity, magneto-resistance and the semiconducting energy gap. Thus knowledge of the correct band structure is at the heart of explaining the physical properties on a fundamental level. A general procedure used to obtain reliable band structures is to perform the best possible calculation and then check for agreement with experimental results based on the Shubnikov-de Haas technique. These measurements reveal only details of the Fermi surface, not the entire band structure, because they are only sensitive to the most energetic electrons at the top of the bands. However, these limited results are quite useful for confirmation of  Chapter 1.  Introduction  28  -7.5H  OJ  -B.OH  >• cn c tu  -B.H  -9.<H  j-  Y  M'  Z  r  ^v/  >^  x  '  x < r  Figure 1.13: The calculated band structure and Fermi surface of K - ( E T ) C U ( N C S ) on the tight-binding method[60, 61]. 2  2  based  the calculations because they give such a direct picture of the allowed momentum states at the Fermi surface. The calculated band structure and Fermi surface[60, 61] of K - ( E T ) C U ( N C S ) based on 2  2  the tight-binding method are shown in Fig. 1.13. Metallic properties result from the halffilling of the upper band due to the loss of 1/2 electron per E T molecule. A cross section of the Fermi surface in the repeated zone is shown in the right side of Fig. 1.13. The surface is a slightly distorted cylinder which bulges out over the Brillioun zone along the M-Z boundary. At the intersection along the M - Z boundary the bands interact and split, effectively separating a continuous one-dimentional piece and a small ellipse-like two-dimensional piece. The calculated area of the ellipse is 18% of the Brillioun zone. The typical two-dimensional Fermi-surfaces for E T molecules in a, f3 and K type materials are shown in Fig. 1.14[62]. Magneto-quantum oscillation measurements provide experimental information on the Fermi-surface. When a strong magnetic field is applied in the direction perpendicular to the conducting plane at low temperatures, the electron energies are quantized into Landau  Figure 1.14: The typical two-dimensional Fermi surfaces reconstructed from the original round surfaces[62].  Chapter 1.  Introduction  30  levels. The periodic oscillations in the magnetization (de Haas-van Alphen effect) and the magnetoresistance (Shubnikov-de Haas effect-SdH) arise from the periodic oscillation of the density of states at the Fermi level E  as a function of the inverse of the magnetic field, 1/H.  F  From the oscillation period A (1/H), the cross-section area of the Fermi surfaces is derived from S  f  =  hcMl/H)  (  L  3  )  where e is the electron charge and c the light velocity. A full three-dimensional picture of the Fermi-surface is obtained by varying the angle of the applied field. SdH or de Haas-van Alphen measurements are generally difficult because quantization is only observable when the mean free path of the electron is comparable to or longer than the size of the orbit. Usually this condition can only be met using a combination of the strongest available magnetic fields and sample temperature well below 1 K or with the sample under high pressure. SdH oscillations at ambient pressure have recently been observed in K-(ET) Cu[N(CN) ]Br[25, 63] 2  2  only by the implementation of pulsed high magnetic fields extending to 60 T. The detailed measurements[25] of the interlayer magnetotransport of K>(ET) Cu[N(CN) ]Br indicated 2  2  that the Fermi surface underwent substantial topological changes at a superstructural trasition below 200 K . From the temperature and the magnetic-field dependence of the oscillation amplitude, one can derive the cyclotron effective mass m and the Dingle temperature c  TD, which represents the degree of scattering by sample imperfections. The oscillation frequency, the effective mass m and the Dingle temperature T c  D  for several E T based materials  are listed in Table 1.7. In most cases the observed values agree fairly well with the calculations.  1.2.9  Thermoelectric Power  The band structure can also be examined by the measurement of themoelectric power. A simple estimate of the thermoelectric power based on the free-electron gas with a Fermi-Dirac  Chapter 1.  Introduction  31  Table 1.7: A comparison of Fermiological properties ( oscillation frequency, effective mass m and Dingle temperature TD ) for several E T based materials, compound m /m T (K) Frequency (T) Ref. and Year c  c  K-(ET) CU(NCS)  2  K>(ET) CU(NCS)  2  2  2  K-(ET) CU(NCS) /c-(ET) Cu(NCS) 2  2  2  2  K - ( E T ) C u ( N ( C N ) ) B r (9 kbar) 2  2  K-(ET) Cu(N(CN) )Br K-(ET) Cu(N(CN) )Br K-(ET) Cu(N(CN) )Br 2  2  2  2  2  2  /c-(ET) Cu(N(CN) )Br 2  /?-(ET) I 2  2  3  distribution gives:  e  3.5 7.0 ((3) 3.2 (a) 3.5 (a) 6.5 ((3) 6.4 2.7 5.4 6.7 3.5 4.7  D  1 0.25 0.5 3.5 2.4 3.4 2.4 0.24 0.53  3900 ((3) 600 (a) 600 (a) 3900 ((3) 3799 (p) 3798 ((3) 3900 (13) 597 (a) 3730  [60] [64] [65] [66]  (1988) (1996) (1995) (1994)  [67] [63] [63] [25] [68] [69]  (1995) (1997) (1997) (1999) (1998) (1989)  =^k  S  (L4)  where KB is Boltzmann's constant, e the electronic charge, and Ep the Fermi energy. The most important information that can be obtained from thermoelectric power measuremnets is that S will be negative for electron-like charge carriers and positive for hole-like charge carriers. As shown in Fig. 1.15, the thermoelectric power of K>(ET) CU(NCS) [70] has the 2  2  unusual properties of being negative along the b direction and positive along the c direction. Considering the net charge of + | per E T molecule, a hole-like positive thermoelectric power would be expected. A n explanation for the unusual direction dependence can be found in the details of the calculated band structure. Electron-like thermoelectric power along the b axis is due to the one-dimensional part of the band, while the hole-like thermoelectric power along the c axis comes from the ellipse-like portion. It is known that when a band is almost filled, as it is for these closed ellipse portion, the electron transport will have hole-like properties.  Chapter 1.  Introduction  32  Chapter 1.  1.2.10  Introduction  33  Superconducting Penetration Depth and Magnetic Properties  Magnetic field expulsion from the interior of a superconductor is one of the fundamental characteristics of the superconducting state. The only allowed internal field is one which decreases exponentially with the distance from the sample surface. The length scale associated with this exponential decrease is called the penetration depth,A. In the B C S theory, the approach of A to a costant value at low temperature is a characteristic expected for all conventional superconductors with isotropic gag functions. Empirically, the temperature dependence of A is found to be approximately described by: A(T)«A(0)(1-(T/T ) )4  1 / 2  C  Very recently, a high precision measurement of the penetration depth of single crystals of K - ( E T ) C u N ( C N ) B r and K - ( E T ) C U ( N C S ) 2  2  2  2  was reported by Carrington et al. [72], at  temperatures down to 0.4 K as shown in Fig. 1.16. They found that, at low temperatures, the in-plane penetration depth (A||) varies as a fractional power law, Ay ~ T § . While this may be taken as evidence for novel pair excitation processes, they showed that the data are also consistent with a quasi-linear variation of the superfiuid density, as is expected for a d — wave superconductor with impurities or a small residual gap. The critical field is another fundamental property of a superconductor. The organic supercondcutors are type II superconductors with anisotropic critical fields. H  c l  , the lower  critical field within the highly conducting plane H ( | | ) and along the poor conducting dicl  rection H ( ± ) , and H , the upper critical field within the highly conducting plance H (||) c l  c 2  and along the poor conducting direction  c2  H (J_), c 2  are listed in Table  1.8  for several organic  superconductors, together with the coherence length £, within the conducting plane || and out-of-plane _L.  Figure 1.16: AA||(T)=A||(T)-A||(0) data for two samples of A c - ( E T ) C u N ( C N ) B r (a, b) and two samples of K > ( E T ) C U ( N C S ) ( C , d) plotted versus [ T / T ] i . The data have been offset for clarity. The inset shows the data for samples a and d on a log scale[72]. 2  2  2  c  2  Chapter 1.  Introduction  35  Table 1.8: A list of the critical fields H i and H , the coherence length £ within the highly conducting plane || and out-of-plane _L, evaluated at T=0 K for several organic superconc  Materials 2  3  2  2  2  1.2.11  H (Oe)  E UkOe)  0.36 20.5 30.0  17.8 61.5 190 68  cl  /MET) I /?-(ET) AuI «>(ET) Cu(NCS) K-(ET) Cu(N(CN) )Br 2  2  2  0.094.0 8.0 1.5xl0  c 2  3  l  H&kOe) 0.8 10.5 10  £" (A)  e (A)  626 254 182 23  28 20 9.6 5.8  x  Mechanism of Superconductivity  A n understanding of the mechanism of superconductivity will clarify how the magnitude of T can reach, for example, 11 K for K— ( E T ) C u N ( C N ) B r , and how it may be pushed c  2  2  higher, as well as why its pressure dependence is so large. B C S theory. I begin with a brief description of the B C S theory. The B C S theory assumes an attractive interaction between the electrons. This interaction is the exchange of phonons. Phonons "bind" two electrons together to form Cooper pairs. But Cooper pairs are quite unusual particles: they do not stick together like two protons forming a hydrogen molecule but are paired in a more general way, they are correlated. This means that their spins and momenta are coupled so that the electrons belonging to one pair move in opposite directions, thus pairing momentum p with momentum -p. The pair correlation is effective over a characteristic length, called the coherence length £. Usually £ is between 100 Aand 1 u,m. Consequently, the Cooper pairs interpenetrate largely, and it is perhaps not too difficult to understand that an ensemble of interpenetrating Cooper pairs behaves very differently from a gas of non-interacting electrons. The importance of electron-phonon coupling is reflected in the B C S expression for the critical temperature:  where LU is the Debye frequency (a characteristic phonon frequency), N(Ep) the electronic D  Chapter 1.  Introduction  36  density of states at the Fermi energy, and V* a constant characterizing the electron-phonon interaction and screened Coulomb repulsion. In the BCS theory the electrons interact by the exchange of phonons. The role of phonons can be tested by the isotope effect. In Equation 1.5 the critical temperature T is proportional c  to the Debye frequency u> - This frequency should vary with the square root of the atomic D  mass M . Consequently we expect T oc M- '  (1.6)  1 2  c  The effect of superconductivity on phonon frequencies is in general a very small one. In a microscopic picture, superconductivity changes only the electric states very close to the Fermi-surface. It has been proven difficult to observe these shifts experimentally in conventional superconductors.  Using inelastic neutron scattering a decrease of about 0.5  cm due to superconductivity has been observed in Nb[77] for a transverse acoustic phonon _1  along the [001] direction with frequency 30 c m . However, in YBa2Cu3C>7, a B i phonon - 1  5  around 330 c m  - 1  shows a softening due to superconductivity, from Raman and Infrared  measurements[78, 79, 80, 81, 82]. Ref. [81], for instance, finds a softening by 9 cm between _1  T and T / 2 in single crystals. It has been shown, for the Raman phonon at 330 c m , that - 1  c  c  the phonon softening in the superconducting state vanishes if superconductivity is destroyed by a magnetic field just below T keeping the temperature constant[83]. c  Furthermore, it  seems very unlikely that the above phonon softenings are caused by small anomalies observed in the lattice constants around T [84]: These anomalies near T c  c  are at least ten times  smaller than typical temperature variations in these parameters between 100 K and 200 K . The associated change in phonon frequencies would be at least one order of magnitude smaller those observed below T . So the phonon softenings below T are not associated with c  c  structural changes around T but reflect directly the coupling between these phonons and c  the electronic states which take part in the formation of the Cooper pairs. Theoretical attempts to explain the phonon softening below T have been made on d-wave c  Chapter 1.  Introduction  37  materials by Nicole et al. [85] and within the Eliashberg theory by Zeyher and Zwicknagl[86]. The derivations[86, 87] are based on an evaluation of the change of the complex electronphonon self-energy of a phonon when materials become superconducting: the real part of the self-energy corresponds to the frequency softening and the imaginary part to the broadening. In order to explain consistently the high transition temperatures for YBa2Cu3C>7 on the basis of the electron-phonon interaction Zeyher and Zwicknagl[86] assumed a total coupling constant X =2.9, tot  i.e. an average of 0.08 per each of the optical modes.  Superconductivity driven by electron-molecular-vibration coupling. There are two types of electron-phonon interactions in molecular crystals.  One interaction is in-  tramolecular in which the molecular distortions due to phonons shift the molecular orbital level up and down, working like perturbations of the potential energy. This type of interaction has been known as the Electron-Molecular-Vibration  ( E M V ) coupling.  The  other is intermolecular coupling in which the phonons modulate the interrelation between two neighboring molecules and so change the transfer energy between them.  It drives a  Peierls transition in T C N Q salts. Usually only acoustic phonons are considered to contribute to the superconductivity mechanism in the ordinary superconductors, but Yamaji[88] suggested that all of the totallysymmetric molecular-vibration modes cooperate with the acoustic modes to raise T . Comc  mon existence of strong interactions between the highest-occupied molecular orbital (HOMO) and totally-symmetric intramolecular vibration modes in the TTF-analog molecules was pointed out to lead to important attractive interactions between current carriers in the organic metals composed of these molecules. A model taking account of these interactions and of the Coulomb interaction was solved to give the superconducting transition temperature T . Yamaji[88] and Tanaka et al. [89] have used this model to calculate transition temperc  atures for B E D T - T T F materials. With reasonable values for other parameters, they found that the temperatures of the order of 10 K were attainable. Superconductivity due to spin fluctuation. Some research groups have asserted that  Chapter 1.  Introduction  38  since the superconducting and spin-density-wave (SDW) phases are neighboring in the phase diagram , the superconductivity can be mediated by spin fluctuations[90, 91]. Schmalian[93] has shown that short-ranged antiferromagnetic spin fluctuations are a promising candidate for the pairing interaction of the superconducting state of K-type ( B E D T - T T F ) X crystals. 2  Using a two-band description for the orbitals on a B E D T - T T F dimer and an intermediate local Coulomb repulsion between two holes on one dimer, the magnetic interaction and the superconducting gap function were determined self consistently within the fluctuationexchange approximation.  He found a transition at 13 K to a superconducting state, in  which the calculated occurence of nodes on the Fermi-surface is in agreement with various experimental observations. Furthermore, within the spin-fluctuation model, a close similarity of the origin of this pairing symmetry to the one in cuprate superconductors was demonstrated. Kondo et al. [94, 95] have investigated spin fluctuation-induced superconductivity in «:-BEDT-TTF salts (quasi two-dimensional organic compounds), within a fluctuation exchange approximation using a half-filled Hubbard model with a right-angled isosceles triangular lattice. A n energy gap of  (d 2_ 2)-type X  Y  was shown to develop with decreasing temperature below T more rapidly c  than in the B C S model. The calculated nuclear spin-lattice relaxation rate 1 / T i shows a T  3  behavior below T in accordance with experiments for K > ( E T ) C U ( N ( C N ) ) X ( X = B r and c  2  2  Cl)[96, 97, 98]. Estimated values of 1/Ti are roughly consistent with experimental results. Fig. 1.17 shows the calculated nuclear spin-lattice relaxation rate 1 / T i . Experimentally, the 1 3  C N M R relaxation 1/T in «-(ET) Cu(N(CN) Br[96, 97, 98]has shown an absence of the X  2  2  coherence peak below T , which is the case for B C S s-pairing state, and a rapid decrease c  of 1/Ti proportional to T well below T . In K - ( E T ) C U ( N C S ) the proton relaxation rate 3  c  1/Ti  2  2  was reported to exhibit a smooth temperature dependence from the high-temperature  side of T to the low-temperature side[99]; incidentally, it increased with further decreasing c  temperatures; this produced a giant peak around 4 K . Up to now the application of this mechanism to the organic superconductors has not yet been established conclusively.  Chapter 1. Introduction  10  P-  39  r  T  [ ^ 0.06 r .  1  "i—i—i—rq •..  7c/2 \r  £ 0.03 |-  0.00 0  1  20  40  0.1  f  J  T7T=0.8  o.oi tJ  I  10  L  I  15  I  I  I  20  T[K] Figure 1.17: The calculated nuclear spin-lattice relaxation rate 1/Ti (logarithmic plots). The dashed line indicates a T behavior[95]. Insert shows 1 / T i T (normal plots). 3  Chapter 1.  1.3  Introduction  40  Similarity Between Organic and Cuprate Superconductors  When superconductivity was discovered in organic solids based on the B E D T - T T F molecule, it was not clear if these peculiar materials were at all related to the equally unusual cuprates. However, recent work has shown that the organics exhibit the same interesting physics as the cuprates, including unconventional metallic properties. As described in Section 1.2, the family ( B E D T - T T F ) X consists of conducting layers of 2  B E D T - T T F molecules sandwiched between insulating layers of anions. The basic unit of the packing pattern in the K phase is a "dimer" consisting of two B E D T - T T F molecules stacked on top of one another. The hole ( missing electron ) can hop from dimer to dimer within a layer much easier than it can between layers. Consequently, as in the cuprates, the layered structure leads to highly anisotropic electronic properties.  For example, the conductivity  parallel to the layers is two to five orders of magnitude larger than that perpendicular to the layers. The family K- ( B E D T - T T F ) X has a particularly rich phase diagram as a function of 2  pressure, temperature, and anion (see Figure 1.18). Note that (i) antiferromagnetic and superconducting phases occur next to one another, (ii) recent experiments show that the metallic phase has properties that are quiet distinct from conventional metals, and (iii) the diagram is quite similar to that of the cuprate if pressure is replaced with doping. Many of the properties of the metallic phase have a temperature dependence that is quite distinct from that of conventional metals.  As have been described in Section 1.2,  those properties with unusual temperature-dependence include optical conductivity, electric resistance, thermoelectric power and magneto-oscillations. Yet at low temperatures (less than about 30 K ) some properties are similar to those of a conventional metal, but with a Fermi energy of the order of 100 K . This is almost an order of magnitude smaller than predicted by band structure calculations. Application of pressures of the order of 10 kbar restores conventional metallic properties over the full temperature range.  Chapter 1. Introduction  Cu [ N(CN) ] Cl 2  t  1  41  Cu [ N(CN) ] Br 2  -  1  Cu (NCS)  2  1  / / /  Pressure Figure 1.18: Schematic phase diagram of the K > ( B E D T - T T F ) X family of organic materials. Superconducting (SC), antiferromagnetic insulating (AFI), and paramagnetic insulating phase ( P I ) are shown. The arrows denote the location of materials with anions X at ambient pressure. As the pressure decreases, the properties of the metallic phase deviate from those of a conventional metal. This phase diagram is qualitatively similar to that of the cuprate superconductors, with doping playing the role of pressure. 2  Chapter 1.  Introduction  42  0.2  i i i i i rr i i  i i  i-i i i i r r  • ^2u  CM  O  0.0 IPOOOOW  <5-—0.2 3  B, 9 poooooooo  £-0.2 W -0.15J T - 0.069 J" 0  3-0.41  R V B  —Q.6 • » I 0 0.02 11  1  11  •  1  I»'  11  1  • • • • I  • n •  0.04 0.06 0.08 0.1 7/J  * I• • • 0.12  Figure 1.19: spin fluctuation induced soft mode. It is interesting to mention Fukuyama's work[100] on the unconventional metallic states of cuprate superconductors. The transport and magnetic properties show various anomalies in the underdoped region (the conducting state was then called anomalous metallic state). Those features were theoretically analyzed based on the mean-field approximation to the t-J model (where t is the nearest-neighbour transfer energy and J is the antiferromagnetic superexchange constant) and then the effects of spin-fluctuation around the mean-field solutions were discussed. His theory has predicted a Raman frequency shift well above T due c  to spin-gap effect (see Fig. 1.19) if the experiment is carried out in samples belonging to the underdoped region. Experimentally the softening has been observed for a B man scattering in YBCO(248)[101] and for a B  2u  lff  mode in Ra-  mode in neutron scattering in YBCO(123)  with T =60 K[102]. Similar phenomenon has been observed in some B E D T - T T F materials. c  The theory is helpful to understand the Raman results in this thesis. Experience with the cuprates suggests that the key physics involved in the above behavior is the layered structure and strong interactions between the electrons. The importance of the latter is supported by the large antiferromagnetic moment observed in the insulating phase.  Chapter 1.  Introduction  43  There is also increasing evidence that, like in the cuprates[103], the pairing of electrons in the superconducting state involves a different symmetry state than in conventional metals. A t low temperatures, the N M R relaxation rate 1/Ti ~ T , instead of the exponentially activated 3  behavior found in conventional superconductors[97]. This power law behavior suggests there are nodes in the gap. At low temperatures the electronic specific heat of X=Cu[N(CN) ]Br 2  also has a power law dependence on temperature, in contrast to the exponentially activated dependence of conventional superconductors.  Chapter 2 The Raman Effect  2.1  Introduction  In 1923 Smekal studied the scattering of light by a system with two quantized energy levels and predicted the existence of side-bands in the scattered spectrum[104]. This effect was subsequently observed by C. V . Raman in 1928 in the systematic study of the light scattered by liquids such as benzene[105]. At much the same time, Landsberg and Mandelstam[106] in Russia discovered a similar phenomenon in quartz. This inelastic scattering of light by molecular and crystal vibrations is now known as the Raman effect. It is caused by modulation of the susceptibility (or , equivalently, polarization) of the medium by the excitations including lattice vibrations, electronic transitions, plasmons, magnons. In this thesis the principal excitations studied will be lattice vibrations i n the form of optical phonons and magnetic excitations in the form of magnons. Fig.2.1 shows the scattered intensity distributed across a range of frequencies. The peak in the center of the spectrum is the contribution of the incident photons that have been elastically scattered with no change in frequency. The Brillouin component, resulting from scattering by sound waves, occurs close to the frequency of the incident light with typical shifts of 1 c m than 10 c m  - 1  - 1  or smaller. The Raman component lies at higher shifts, normally larger  and often of order of 100-3000 c m . Those scattered frequencies smaller than - 1  the incident frequency (uj) are known as the Stokes component (in which case a phonon is created), while the scattered frequencies larger than LOJ are called the anti-Stokes component (in which case a phonon is destroyed). From the Raman spectrum, the three most important  44  Chapter 2. The Raman Effect  45  1_L  J  + elastic I BriUouin  Stokes Raman  1 1 1 antiStokes  to.  Figure 2.1: Schematic spectrum of scattered light. parameters (peak intensity, frequency shift and line width) can be determined. The measurement of the peak intensity from the Stokes and anti-Stokes (IAS  a n  d Is, respectively)  components can help determine the temperature in the sample, if the temperature is high enough, by the following formula I AS  Is where coi,co  R  ,OJI  +  LOi -  UJ:  -) exp(-huj /kT)  RS  (2.1)  4  R  U  R  are the frequencies of incident laser and Raman scattering, respectively.  In a single Raman scattering process the energy and momentum are conserved. This thesis will concern itself primarily with first order processes in which a single excitation is created or destroyed so that the energy and momentum conservations are: UJS —  —  UJ  r  (Stokes) or  U>AS —  ks = ki — q (Stokes) or k^s where uj(kj),us(ks)  =  +  (o,nti — Stokes)  ki + Q (o,nti — Stokes)  (2-2) (2.3)  and LUAs(kAs) are the frequencies (wavevectors) inside the scattering  medium of an incident photon, Stokes scattered photon and anti-Stokes scattered photon, respectively, and q is the phonon wavevector.  Chapter 2. The Raman Effect  46  It should be mentioned that the momentum-conservation conditions are strictly valid only in transparent samples which possess translational symmetry (e.g. sufficiently large scattering sample with the absence of any significant absorption). The influence of mometum conservation is especially important in the scattering of light by those excitations in crystals whose excitation frequency co depends markedly on the excitation wavevector q, for example polaritons, single-particle excitations in an electron plasma, and Frohlich interaction induced scattering which will be intensively discussed in this thesis. On the other hand, the effect of momentum conservation can normally be neglected in the scattering by liquids and gases. Nevertheless, in the scattering of light by an extended medium of interacting atoms or molecules, the excitation involved is always strictly a travelling wave whose wavevector conserves momentum in accordance with the relation 2.3. Unlike infrared absorption, the energy of the incident photon is usually significantly greater than the energies of the excitations and does not correspond to the energies of any direct transitions, i.e., u  R  <C U>J,UJS,^AS-  The N d : Y A G infrared laser has a wavelength of  1.064 pm. So the incident light has a wavenumber of 9394 c m . By comparison, phonon - 1  energies are no greater than 3000 c m . On the other hand, phonon wavevectors at the - 1  edge of the first Brillouin zone have the magnitudes of the order of 10 c m . Compared 8  - 1  to the phonon wavevector, the incident and scattered photon wavevectors of 6000 to 9000 cm are therefore nearly zero implying that the phonons that can participate in the first _1  Raman scattering processes described by Equations 2.2 and 2.3 must come from near the Brillouin zone center T, so that q?»0. The resulting spectra will therefore consist of discrete lines at the q~0 optical phonon frequencies.  2.2  Classical and Quantum Raman Theory  The main feature of the first order Raman effect as described in the previous section can be understood classically using a simple one-dimensional model. If a is the polarizability of the  Chapter 2. The Raman Effect  47  scattering medium then the polarization induced by the incident electric field is given by P = aE  (2.4)  Excitation such as phonons can then give rise to Raman light scattering by modulating the polarizability a. For example, if a is expanded about an equilibrium value a in terms of 0  atomic displacements Uj—cosujjt then a fa a  0  + ct\Uj = a  0  + ati cosuijt  (2.5)  If the incident electric field is produced by a monochromatic light source such as a laser then E = E cos co t 0  L  (2.6)  which when combined with Equations2.5 and 2.6 gives P = a E cosoj t + ^-aiE {cos(uj 0  0  0  L  L  + ujj)t + c o s ^ - u>j)t}  (2.7)  At  Since the scattered light is proportional to P , the first term in Equation 2.7 corresponds to 2  the elastically scattered light unshifted in frequency (Rayleigh scattering) while the remaining term corresponds to the Stokes and anti-Stokes Raman scattered light. Note that as assumed in the above derivation, ct\ and the higher order terms in Equation 2.7 are usually small when compared to a implying that the Raman scattering effect is relatively weak 0  when compared to the Rayleigh scattering contribution. Although this simple argument contains many of the essential features of the Raman effect it does not yield an expression for the actual Raman cross section. The anti-Stokes component, for example, vanishes at low temperatures, a feature which is not predicted by the previous derivation. A more complete description requires a quantum mechanical derivation. Born and Huang[107] have introduced a concept of a virtual energy level to understand the Raman scattering, as shown in Fig. 2.2. Raman Stokes scattering consists of a transition  Chapter 2. The Raman Effect  48  Excited State-d  Virtual State - c  Vibrational Energy Level-b  Rayleigh  Raman Stokes  Ground State -a Raman anti-Stokes  Figure 2.2: Energy level diagram describing Rayleigh scattering, Raman Stokes scattering and Raman anti-Stokes scattering. The dashed line represents the virtual energy level. If the virtual energy level-c is close to the excited energy level-d, a resonant Raman scattering will be observed. from the ground state to a virtual level followed by a transition from the virtual level to the final vibrational energy level. Raman anti-Stokes scattering entails a transition from the vibrational energy level to the ground state with the virtual state serving as the intermediate level. The anti-Stokes lines are typically much weaker than the Stokes lines because, in thermal equilibrium, the population of level-b is smaller than the population in level-a by the Boltzmann factor exp(—ktu b/kT). Poulet and Mathieu have given the fullest account of a  quantum mechanics calculations[108]. These calculations are not repeated here. In the following section I will summarize some basic ideas of selection rules and symmetry properties of Raman susceptibility, and Raman scattering efficiency.  2.3  Selection Rules  Equations 2.2 and 2.3 have already established two selection rules for Raman scattering on the energy and momentum conservation, respectively. We shall show a third selection rule  Chapter 2. The Raman Effect  49  Table 2.1: Allowed Raman modes and their Raman tensors for point groups D^h and PAHfa  (  d d  D-2h  B 19  B2  B 19  B 29  9  B.39  ( a  A 19  D,Ah  E  n  E  n  which is determined by the symmetry of the crystal. Infrared - active transitions are transitions which cause a change in the electric dipole moment of the system while Raman - active transitions are those that cause a change in the polarizability a. If the irreducible representation of a vibration mode is contained in the representation based on the components of the polarizability tensor a, then the corresponding vibration mode (phonon) is active in Raman scattering. This is always the case for the totally symmetric vibration modes. Since the polarizability tensor a is a quadratic function of the Cartesian coordinates (such as x , xy or x — y ), if the representation of a vibrational mode is based on the quadratic 2  2  2  function of the Cartesian coordinate, then the mode is Raman active. A simple way is to check the last column of the character table of a point group, and see whether there is a quadratic function of the Cartesian coordinate. In the groups possessing a symmetry center, the modes active in Raman scattering are in-active in infrared absorption and vice versa. This is called the mutually exclusive (or mutual exclusion) rule. Thus only u (odd parity) modes can be infrared - active while only g (even parity) modes can be Raman-active.  Chapter 2. The Raman Effect  50  The crystal symmetry gives further restrictions on the components of the so-called second rank Raman tensor Rij (it is called second-order susceptibility in the literature[109]) for those excitation symmetries (vibration modes) that are allowed in light scattering. For each allowed excitation symmetry, some of the Cartesian components ij are required to vanish while others are required to have related values. Table 2.1 shows allowed Raman modes and their Raman tensors for point groups D h and  which are two symmetries we have  2  studied in this thesis. As can seen from the Table, the scattering geometry (eje ) should be s  (yz) or (zy) in order to get a spectrum for B  mode for crystals with D h symmetry since  3g  2  only the yz and zy components of the Raman tensor are not zero in the matrix. 2.4  Raman scattering efficiency  If we know the Raman tensors, next we can calculate the Raman scattering efficiency S. For non-polar vibrations (the vibrations of homopolar crystals and those vibrations of polar crystals that do not carry an electric-dipole moment), the efficiency is: S =  where R  ap  is the Raman tensor.  (2.8)  A(£eZR, eZ)  2  p  For polar modes (modes that carry an electric-dipole  moment), the efficiency is:  S = A(Y.e-KM  T  + Wys)  (2.9)  2  where A, a and (5 are constants, p, a and r (p, a and r could be one of the Cartesian coordinates x, y, x or their combinations) the polarization directions of electric field, e is T  the r component of a unit vector in the phonon polarizing direction, and q the r component T  of a unit vector of the phonon wavevector.  Chapter 2. The Raman Effect  2.5  51  Advantages of Fourier Transform Raman Spectroscopy  A Fourier Transform (FT) Raman spectrometer makes use of a near - infrared laser exciting source and the interferometric techniques of a FT-infrared spectrometer to measure the scattered Raman radiation. Fourier Transform (FT) Spectroscopy is an advanced form of spectroscopy which is based on an application of the interferometer, invented by M . Michelson in 1888, and the mathematical concept of a Fourier Transform. F T - spectrometers have several advantages over conventional grating spectrometers. The so-called Jacquinot or throughput advantage arises from the fact that a FT-spectrometer can have a large circular source at the input or entrance aperture of the instrument with no strong limitation on the resolution. It also can be operated with large solid angles at both the source and the detector. The resolution of a conventional grating spectrometer, on the other hand, depends linearly on the width of the input and output slits. Also, for high resolution, a grating spectrometer requires long focal length mirrors, and this condition in turn necessitates small solid angles. Thus, for the same resolution, a FT-spectrometer can collect much a larger signal than a conventional grating spectrometer. The Fellget or multiplex advantage arises from the fact that in a F T - spectrometer the entire frequency range is simultaneously observed whereas in a conventional grating spectrometer, only a narrow band of frequencies is observed at any one time. Thus assuming that the signal-to-noise ratio depends linearly on \/T, where T is the time taken to observe the entire frequency range one can see that for the same signal - to - noise ratio, it takes a shorter time to observe a given frequency range using a FT-spectrometer compared to a grating spectrometer. In fact, the time is reduced by a factor of \[M where M is the number of bands in the entire frequency range, that were individually observed using the grating spectrometer. The Connes advantage is a statement of the high wavenumber accuracy present in a F T spectrometer. This is a consequence of the high precision used in the tracking of the moving  Chapter 2. The Raman Effect  52  mirror and the determination of the sampling intervals, both of which are controlled by the interference pattern of the monochromatic light of a He-Ne laser. The sampling positions in the interferogram are determined by the adjacent zero crossings in this monochromatic interference pattern. Since the spectrum sample spacing Au is inversely proportional to the sampling interval A x , the error in Au is of the same order as in Arc and thus is of the order of 0.01 c m " . 1  Since 1986, Raman spectroscopy using near-infrared excitation has emerged in the Fourier domain, providing an exciting new pathway for materials characterization. A number of advantages over conventional Raman spectroscopy have come to light besides all of the advantages mentioned above for a F T spectrometer. One of the main advantages of F T  Raman spectrometer, is the large reduction of fluorescence presented in most samples. This is due to the fact that, in most samples, the photon energy from the nearinfrared laser is usually not sufficient to cause the transitions between electronic states, that give rise to fluorescence. A further advantage is the possibility of obtaining Raman spectra in the absence of resonance enhancement, which arises from electronic transitions. This can be useful as the band intensities of non - resonant Raman spectra are more representative of the chemical species present. Also with these low photon energies, the possibility of sample heating and any subsequent photochemical sample degradation is less likely. Among the disadvantages of using FT-Raman is the anticipated decrease in sensitivity of the Raman lines. This is due to the fact that the intensity of Raman lines are proportional to the fourth power of the exciting frequency. Thus comparing the N d : Y A G laser, which has an exciting frequency of 9394 c m , to a conventional Argon-ion laser operating at 20492 - 1  c m , one sees that there is an anticipated decrease in sensitivity, by at least a factor of - 1  22.6. Secondly the noise equivalent power of near-infrared detectors is usually several orders of magnitude higher than that of photomultiplier tubes commonly used in conventional spectroscopy. This is however, becoming less of a problem with the recent development of  Chapter 2. The Raman Effect  53  high sensitivity NIR detectors. Finally there is a "multiplex disadvantage" in using F T spectroscopy as noise present in the exciting radiation, that is scattered, is transformed into noise at all wavenumbers, in the transformed spectrum. However in most cases this problem can be largely eliminated by carefully filtering the Rayleigh line out of the scatterred radiation.  Chapter 3 Experimental Details  3.1  Bruker R F S 100 Spectrometer  A l l measurements were made using a Bruker R F S 100 Fourier Transform Raman Spectrometer. The optical layout of the R F S 100 spectrometer is shown in Figure 3.1. The sample compartment is equipped with all of the necessary optics for collecting radiation scattered at 90° and 180°. It extends to the front of the R F S 100 giving ready access to the sample stage. Preadjusted, interchangeable lenses and sample stages allow easy adoption to most spectroscopic problems. For low temperature measurements, we remove the sample stage, use a collection lens with a longer focal length of 50 mm (at room temperature, a collection lens with a focal length of 16 mm is used) and set up a dewar or refrigerator in front of the collection lens. In all measurements a 180° back-scattering geometry was used as shown in Fig. 3.2. The exciting source is an infrared diode - pumped N d : Y A G laser operating at a frequency of 9394 c m  - 1  (a wavelength of 1064 nm) with a power output of (0—200) mW. The laser beam  enters the sample compartment via one of a series of apertures (which permits the selection of 90° or 180° scattering geometries) located in the bottom of the sample compartment. The beam is then deflected horizontally by a small prism, contained in the objective lens assembly, towards the sample, which is located at the focus of the objective lens. The scattered Raman radiation from the sample is then collected by the objective lens and passes through the interferometric assembly. After exiting the interferometer the radiation passes through a filter module, which removes the unshifted Rayleigh line, and is finally focused  54  Chapter 3. Experimental Details  55  Nd: YAG Laser 1064 nm  Sample Compartment Figure 3.1: The optical layout of the RFS 100 FT-Raman spectrometer  Chapter 3. Experimental Details  Prism  56  Lens I  j FT-Raman Spectrometer i Analyzer  Half wave plate  Nd:YAG Laser 1064 nm Prism  Back-scattering Configuration Figure 3.2: A back-scattering configuration used for all measurements. on the detector. The high sensitivity Raman Ge detector (D 418-S) must be cooled down to liquid nitrogen temperature. In order to reduce effects of stray light, the window of the detector dewar only transmits radiation below 11,750 c m " . 1  The R F S 100 spectrometer contains an on-board aquisition processor (AQP) which is used to perform the data aquisition and Fast - Fourier Transformations as well as to control all motor - driven optical components in the spectrometer.  The A Q P is interfaced to a  P C - based computer system running OPUS spectroscopic software designed by the Bruker Company. This enables an operator to remotely control variable parameters such as the incident laser power, resolution, polarization etc. during measurements. The software also contains a variety of facilities for the display and manipulation of a measured spectrum.  Chapter 3. Experimental Details  3.2  57  Heli-Tran Refrigerator  Two refrigerators were used for the low temperature measurements. The measurements at temperatures between 8 and 300 K were taken with an Air Products A P D LT-3-110 Heli-tran refrigerator with a copper cold finger and a room-temperature polypropylene vacuum-shroud window. The temperature was controlled by a Model A P D - K cryogenic microprocessor with dual sensors. The Heli-tran refrigerator was mounted on a platform as shown in Figure 3.3, in front of the collection lens with the sample at the focus. The platform can be adjusted in three perpendicular directions and rotated about one vertical axis for sample alignment and signal optimization. This platform was designed by Dr. Eldridge. A typical LT-3-110 Heli-tran system is shown in Fig 3.4. Cooling was accomplished in the refrigerator by the continuous controlled transfer of liquid Helium through a high efficiency evacuated transfer line to a heat exchanger which served as the mount or "cold finger" for the sample holder. Heat leak to the cryogenic flow stream within the transfer line was minimized through the use of an internal suspension system and the interception of incoming heat by the shield flow circuit which surrounds the central flow. The transfer line bayonet tube was placed into a pressurized Helium dewar (?» 5 psi) while the other end of the bayonet tube was placed into the Heli-tran refrigerator. The liquid flow was regulated by a needle valve at the tip of the refrigerator cold end bayonet. This valve was engaged by an adjustment knob on the transfer line. A radiation shield surrounding the sample inside minimizes the radiant heat load on the cold stage. The optical port in the radiation shield was made as small as possible to avoid any excess heating from room-temperature radiation. Activated Cocoanut Charcoal was attached to the inside of the radiation shield. The radiation shield was cooled with helium exhausting gas from the cold finger. The shield and tip circuits were completely open during cooldown and 100% liquid flow to the tip was maintained through the cooling of the anxiliary shield. (Sometimes one has to change the flow rate in order to control the cooling rate of the sample.) When the system  Chapter 3.  Experimental  Details  58  valve adjustment knob interface  suppon  helium exhaust port  to temperature controller  vacuum shroud pump out port  horizontal adjustment micrometer.  Figure 3 . 3 : T h e platform used to support the H e l i - t r a n refrigerator.  Chapter 3. Experimental Details  Figure 3.4: A typical flow diagram of LT-3-110 Heli-tran system.  59  Chapter 3. Experimental Details  60  reached the cooldown temperature (8 K for He), we reduced the tip flow by increasing the adjustment nut engagement on the refrigerator until a system equilibrium between thermal loading and refrigeration capacity was achieved. Next, we reduced the shield flow at the flowmeter (has not been shown in Fig 3.4) until the temperature became unstable; then increased slightly until the temperature stabilized again. Usually the shield flow is constant for all temperatures.  The tip flow has been regulated at the flowmeter to achieve various  temperatures with minimum liquid consumption. Two silicon diodes (from Scientific Instruments Inc.) for temperature measurement and control were mounted with one located just below the cold finger and the other on the copper disk containing the sample, and immediately adjacent to the sample . The automatic stability of the controller is ±0.01K from 8 to 300 K . The temperature between 8 and 60 K was controlled by regulating the tip flow of the flowmeter. Above 60 K the temperature was varied by adding heat from a small resistive heater wrapped around the neck of the cold finger.  3.3  Janis Dewar  The measurements at 2 K were performed in a second refrigerator, a Janis superVaritemp dewar. Fig. 3.5 shows a.typical structure of the Janis SuperVaritemp dewar. The liquid helium flow is controlled by a helium needle valve, and then passes through a capillary tube to the helium vaporizer. The helium vapor cools down the sample, goes up and vents to the atmosphere helium recovery system or mechanical vacuum pump for reduced temperatures. The Janis dewar is mounted on a platform in front of the spectrometer collection lens, with the sample at the focus. The sample is excited by a laser through two quartz windows, one at room-temperature and one at liquid helium temperature.  Two diodes for temperature  measurement and control are mounted with one underneath the helium vaporizer and the other above the sample.  Chapter 3. Experimental Details  Electrical Access Safety Pressure Relief Helium Valve Operator,' Nitrogen Fill Port —  Sample Positioner Helium Gas Sample Tube Vent Port Helium Reservoir Vent Helium Fill Port  Evacuation r=f Valve l  Liquid Helium Reservoir Liquid Helium Valve  Diode  Sample Holder Thin Liquid Helium Tube  Liquid Nitrogen Reservoir  Sample Chamber Vacuum Jacket Radiation Shield Quartz Windows Vaporizer/Heat Exchanger with Thermometer and Heater  Figure 3.5: A typical structure of the Janis SuperVaritemp Dewar.  Chapter 3. Experimental  Details  62  One of the basic advantage of the "SuperVaritemp" is that the sample to be cooled is suspended in flowing helium vapor. Unlike the Heli-tran refrigerator where the sample is mounted in vacuum, there are no thermal interfaces between the sample and its holder, and no elaborate heat sinking of instrumentation leads is necessary. This means that the temperature indicated in the sample zone is the temperature of the sample as well as the mount and holder. Samples with poor thermal conductivities do not require special loaded greases or other sophisticated methods of attachment, since they are continuously "washed" with helium vapor at the desired temperature. The operation of the Janis dewar is more complicated than the Heli-tran refrigerator. The liquid helium reservoir is precooled with liquid nitrogen. Before the precooling, one pumps the sample chamber. Otherwise some ice might be formed in the inner quartz window. After 15 minutes, the liquid nitrogen is blown out completely using helium gas and the reservoir is back-filled with helium gas. Also one has to make sure that the helium control valve, the helium capillary and the vaporizer are clean and open. Then one fills the helium reservoir to the desired volume of liquid helium, while checking the helium control valve constantly for freezing. Once liquid helium collection has been accomplished, one pressurizes the liquid helium reservoir, opens the helium control valve and cools down the sample chamber. Once the required temperature is approached, one sets the parameters on the heat exchanger and temperature controller. To obtain the lowest temperature of 2 K with the sample in liquid helium, one has to pump the liquid helium to a superfluid state. The vaporizer heater should be turned off, the helium valve controller should be fully opened 6 turns and the sample tube flooded with liquid helium. The helium valve should then be closed and the liquid helium pumped to the lowest temperature of 2 K . The laser power must be kept below 30 mW in order to maintain the liquid helium in a superfluid state without bubbles. The temperature was measured by a P A R model 152 cryogenic temperature controller  Chapter 3. Experimental Details  63  ^suriple Positioner Aluminum Plate Stand  Vacuum Jacket -Top View  AL  Sample  Radiation Shield Cjuartz Window  Table  Spectrometer  Collection Lens  Room Temperature Vacuum Jacket  Vacuum Jacket-Front View Figure 3.6: (Left), a design of the room-temperature vacuum jacket. (Right), a stand supporting the Janis dewar for use with Raman R F S 100 spectrometer. (Princeton Applied Research). The helium level indicator was made by Lake Shore Cryotronics Inc. The Janis dewar has a capacity of 5 liter liquid helium and 4 liter liquid nitrogen. It takes 3 liters of liquid He to cool down the dewar to 10 K when the sample is slowly cooled (about 3 hours). I have spent a lot of time in modifying the room-temperature vacuum jacket and the liquid-nitrogen radiation shield for the Janis dewar, and in building a stand in order to fit the Janis dewar into the sample stage of the Raman spectrometer. As has been mentioned in section 3.1, the collection lens has a focal length of 50 mm. So we have a square space  Chapter 3. Experimental Details  64  of side 100 mm for the Janis dewar. The He-chamber is 2 inch in square. To clear the thin liquid-He tube (see Fig. 3.5), we need a nitrogen radiation shield at least 3.5 inch square. The quartz window has a thickness of 1 /8 inch. To save the space we glued the window with an epoxy. T h e depth of the sample stage is also limited. I had to carefully design the vacuum jacket and the radiation shield to fit the Janis dewar into the crowded space. Fig. 3.6 shows the design of the room-temperature vacuum jacket and how the Janis dewar is supported in the sample stage of the Raman spectrometer.  3.4  Pumping Station  The Heli-Tran refrigerator and the Janis dewar were evacuated by a mechanical vacuum pump (Welch Scientific Company) and a diffusion pump with a liquid - nitrogen cold trap (Varian Associate) to a pressure of below 10~ Torr, prior to cooling. To obtain a superfluid 4  liquid helium temperature, we used the mechanical vacuum pump (Welch Scientific Company) to pump the sample chamber of the Janis dewar. We began with slow pumping by opening the valve a small amount. We opened the valve a little more when the gurgle sound from the pump had disappeared. When the pressure went down to 10 mm Hg, the liquid helium was then in a superfluid state and was consumed slowly at a rate of 0.5 liter/hour. Since the Janis dewar has not been used for a long time and the vacuum jacket was newly built, we had a problem of leakage which caused ice formation around the optical window. A leak detector (MS-9AB) has been used several times and the leaks around the vacuum jacket and valves have been successfully found and fixed.  3.5  Sample Preparation  The temperature of a sample may increase when it absorbs incident radiation. This means that sample heating is an inherent problem of laser Raman spectroscopy. The temperature rise is dependent on both the sample and the experiments, being influenced by such quantities  Chapter 3. Experimental Details  65  50  | p-(BEDT-TTF) AuI , T =4.9 K 2  2  c  Single crystal, 12 mW — Powder mixed with KBr, 50 mW  40 3  Heating Effect s^30  500  1000  1500  2000  2500  3000  3500  Wave Numbers (cm ) _1  Figure 3.7: The heating effect observed in an organic superconductor.  4000  Chapter 3. Experimental Details  66  as the thermal conductivity and color (ability to absorb radiation) of the sample as well as the laser power, wavelength of radiation and exposure time. When a sample is heated, the total energy emitted increases with the fourth power of absolute temperature.  The peak  wavelength of this emission decreases linearly with temperature and reaches a point where it becomes observable as a rising background superimposed on the Raman spectrum. The background has a characteristic shape which rises from about 2000 c m t o the detector cut- 1  off. Fig.3.7 shows the heating effect observed in \3-(BEDT-TTF) AuI . 2  2  Overheating was  observed in the single crystals with laser power levels as low as 12 mW. For the organic conductors or superconductors, the laser heating is a common problem. It is sometimes difficult to obtain a good Raman spectrum in a reasonable time from single crystals when keeping the laser power at a low level. We found, however, that the heating problem is considerably reduced if the crystals are ground into a powder with K B r , and then pressed into a copper sample holder, which then enabled us to increase the laser power to 70 mW and thence the Raman signal. In this thesis, for organic materials, the Raman measurments were performed with samples squashed with K B r . The size of the powder sample is in the range of 1 yum-10 yum measured by the scanning electron microscoper (SEM). Fortunately there is also strong electronic absorption for B E D T - T T F based materials as shown in Fig. 3.8 for « - ( B E D T - T T F ) C u ( N C S ) , and we obtained resonant Raman scattering with 2  a good signal to noise ratio.  2  Chapter 3. Experimental  Details  67  5 10 20 Wave numbers *10 [ cm" ] 3  30  1  Figure 3.8: The optical conductivity observed in«-(BEDT-TTF) Cu(NCS) [110]. The frequencies of several visible laser lines and an infrared laser line are indicated in the figure. 2  2  Chapter 4 Raman Results for BEDT-TTF Based Materials  4.1  Low-temperature Softening of Raman Modes in Neutral BEDT-TTF  Fig. 4.1 shows the Raman spectra at room temperature, 100 and 10 K , of neutral E T (ET is an abbreviation of B E D T - T T F ) . The twelve totally symmetric (A ) modes are labeled g  in Fig. 4.1. In Figs. 4.2 and 4.3 are shown the measured percentage wavenumber shifts as a function of temperature for all of the A  g  modes and one B  3 9  mode. Fig. 4.2 has  those assigned features which demonstrate the usual property of increasing frequencies with decreasing temperature, while Fig. 4.3 shows those with the unusual behaviour of softening at low temperatures.  In Fig. 4.1 the intensities of some of the Raman lines are seen to  increase with decreasing temperature, and many features become multiplets due to the four E T molecules per unit cell. The frequencies of the strongest component of the multiplets are plotted in Figs. 4.2 and 4.3. A sketch of the atomic displacements is shown in Fig. 4.4 for these modes which demonstrate the usual property of increasing frequencies with decreasing temperature, along with the observed wavenumber at room temperature. (These wavenumbers are 1 or 2 c m  - 1  higher  than those in Ref. [30] due to a longer focal length spectrometer collection lens used for low temperature measurements.) Fig. 4.5 shows the sketch of the atomic displacements for these modes with the unusual behaviour of softening at low temperatures. The mode softening in Fig. 4.3 indicates a structural instability. No evidence of a structural change, however, may be found in Figs. 4.2 and 4.3, which is also confirmed  68  Chapter 4. Raman Results for BEDT-TTF  Based Materials  69  Figure 4.1: The Raman spectra of neutral B E D T - T T F at room temperature, 100 and 10 K, taken with an infrared laser of wavelength 1064 nm. The twelve totally-symmetric (A ) modes, (assuming D h symmetry), are labeled, along with one B mode, z^ . The insert shows Vx(Ag). g  2  3g  62  Chapter 4. Raman Results for BEDT-TTF  Based Materials  70  0.018 0.016 0.014 0.012  3 0.010 3 ° ° 0.008 0.006 0.004 0.002 0.000  0  90  120  150  180  210  Temperature (K)  240  270  300  Figure 4.2: The ratio of the wavenumber shift to the room-temperature value, as a function of temperature, for seven totally-symmetric ( A ) modes, which harden to some extent at lower temperatures, as is normally observed. 9  Chapter 4. Raman Results for BEDT-TTF  Based Materials  71  0.001  -0.006  90  120  150  180  210  Temperature (K)  240  270  300  Figure 4.3: The ratio of the wavenumber shift to the room-temperature value, as a function of temperature, for five totally-symmetric (A ) and one non-totally symmetric ( B ) modes, which unexpectedly soften at lower temperatures. The wavenumber of the most intense component of a multiplet is plotted. ff  3g  Chapter 4. Raman Results for BEDT-TTF  Based Materials  72  Figure 4.4: Wavenumbers observed at room temperature and atomic displacement vectors for for seven totally-symmetric (A ) modes, which harden to some extent at lower temperatures The vectors were calculated in [30], and are not to scale. 9  Chapter 4. Raman Results for BEDT-TTF  Based Materials  73  Figure 4.5: Wavenumbers observed at room temperature and atomic displacement vectors for for five totally-symmetric ( A ) and non-totally symmetric ( B ) modes, which unexpectedly soften at lower temperatures. The displacement vectors are in the molecular plane, except the out-of-plane C - H bends in i/ and v , which are indicated. The vectors were calculated in [30], and are not to scale. 9  3s  4  5  Chapter 4. Raman Results for BEDT-TTF  Based Materials  74  by the low-temperature x-ray d a t a [ l l l ] . The reason for the difference in the temperaturedependent behaviour of the neutral E T molecule and that of the E T cation in the conducting salts, in which there is no such corresponding softening , is because the T T F framework in the cation is planar, whereas in the neutral molecule it is definitely non-planar[lll, 112, 59]. The only x-ray structure analysis of the neutral E T molecule was performed by Kobayashi et al. [112] and they found that the molecule is composed of three planes of tetrathioethylene moieties. The dihedral angles between these planes are 165.3 and 167.7° at room temperature (see Fig. 4.6b). The shape of the molecule, however, changes considerably on cooling. Young et al. [Ill] performed a low-temperature structure analysis of the deuterated compound by neutron diffraction. They found that at 15 K the dihedral angles mentioned above had decreased to average values of 158.9 and 158.4°. Thus, a significant bending of the molecule occurs at low temperatures compared with that at room temperature. This presumably is the reason why ^{Ag) softens, since it involves the two double-bonded carbon atom pairs, whose relative positions change when the dihedral angles change. Of the other modes which soften in Fig. 4.3, four of the A  g  modes, v^v^v^ and i/ , 7  all involve vibrations of the hydrogen atoms in the terminal ethylene groups, as may be seen from Fig. 4.5. ^{B^g),  which displays the greatest percentage softening of all of  the modes (Fig. 4.3), also involves the ethylene groups, as shown in Fig. 4.5. The reason for the softening of these modes involving the hydrogen atoms in the ethylene groups is also presumably due to the molecular deformation. With a decrease in dihedral angle the ethylene groups in one molecule of an E T dimer pair move away from the ethylenes in the other molecule (see Fig. 4.6c). A n altered interaction with the neighbouring E T molecule may therefore explain the observed softening. It is of course also known that the ethylene groups are disordered at room temperature and will order as the temperature is lowered, but this occurs in the cation as well as the neutral molecule and does not affect the frequencies in the conducting compounds. Since the low-temperature structural study was performed on the deuterated compound, we repeated the room-temperature and 10 K Raman measurements on  er 4. Raman Results for BEDT-TTF  Based Materials  (b) Side View of BEDT-TTF  Figure 4.6: B E D T - T T F structure: (a), top view; (b), side view; (c), dimer.  Chapter 4. Raman Results for BEDT-TTF  Based Materials  76  Table 4.1: The ratio (8v/vi) of the 10 K wavenumber shifts to the room-temperature wavenumber values, for twelve totally-symmetric (A ) and and one ^(B^g) modes of / i - B E D T - T T F and o? -BEDT-TTF. Also listed are the observed and calculated[30] deuterium shifts (Ai/j). g  8  8  i  h  d*s  Vi(RT)  1 2 3 4 5 6 7 8 9 10 11 12  2921 1552 1495 1409 1285 991 920 655 490 442 311 162  -0.10 +0.18 -0.19 -0.34 -0.29 +0.14 -0.23 +0.37 +1.35 +0.43 +1.32 +1.86  Av observed 774 1 1 393 255 6 178 45 2 2 12 5  Au calculated [30] 788 0 0 363 146 6 188 30 0 0 2 3  {  Ui{RT)  %6v/Ui  2147 1551 1494 1016 1030 985 742 610 488 440 299 157  +0.05 +0.25 -0.15 -0.59 -0.34 +0.18 -0.18 +0.20 +1.43 +0.70 +1.61  t  a deuterated sample to check for the same behaviour. These data are contained in Table 4.1, and confirm the same low-temperature softening in ^3,^4, v$ and u , with percentage shifts of 7  the same relative sizes in both compounds. u\ displays a small positive shift in the deuterated compared with a small negative one in the protonated compound. It may be noted that the sign and magnitude of the temperature-dependent wavenumber shifts help in the assignments in the crowded deuterated spectrum, and the calculated and observed isotopic wavenumber shifts, Au, are also listed in Table 4.1 for comparison. The agreememt is very good. It may be noted that the three modes which harden the most in Fig. 4.2, u (A ), 9  g  V\\(A ) g  and V12(A ), are those which would be expected to do so, since they are molecular breathing g  modes, which push on the rest of the lattice and will be strongly affected by the thermal contraction.  Chapter 4. Raman Results for BEDT-TTF  4.2  Based Materials  77  Electron-phonon Coupling  Whereas there is no agreement on the mechanism of organic superconductivity, some experimental evidence points to a direct or indirect role of electron-phonon coupling[58]. As has been mentioned in Section 1.2.11, usually only acoustic phonons are considered to contribute to the superconductivity mechanism in normal metals, but Yamaji[88] suggested that all the totally symmetric molecular-vibration modes cooperate with the acoustic modes to raise T . c  The B E D T - T T F compounds are known to have strong electron-phonon coupling, not necessarily to the lattice modes as in conventional B C S superconductors, but to the intramolecular modes of the molecule ("internal" modes). In particular some of the totally-symmetric ( A ) 9  modes couple very strongly. This is because when the two molecules in a dimer oscillate 180° out of phase in one of these modes, charge will oscillate between the two molecules due to the changing size of the molecules (one expanding while the other contracts).  The  12 A modes of the B E D T - T T F molecule are Raman active and most of them may be seen g  in Figure 4.7 and 4.8 for « - ( B E D T - T T F ) C u ( N C S ) and K - ( B E D T - T T F ) C u ( N ( C N ) ) B r , 2  2  2  2  respectively, along with other non-totally symmetric modes, mainly B 3 . One can see that 9  the resonant enhancement is quite different for the two lasers. The spectrum taken with the IR-laser contains far fewer features than the visible-laser spectrum and the electronic transition responsible for the resonant Raman scattering must be strongly coupled to the two modes u ( A ) and v (A ) at 1470 c m s  9  9  and 500 c m  - 1  g  - 1  respectively. As we can see  from the figures the IR-laser spectrum misses v ( A ) and several other unlabeled lines. The 8  9  strongest enhancement in the IR-laser spectrum is for v (A ) and v (A ) followed by v 3  (A ) and the sharp line from u g  9  9  9  2  (B ) at 890 c m (labeled in Fig. 4.7). - 1  60  3g  We now compare in Fig. 4.9 and 4.10 the polarized infrared conductivities of «;-(BEDTT T F ) C u ( N C S ) and K - ( B E D T - T T F ) C u ( N ( C N ) ) B r , respectively, at 10 K with the Raman 2  2  2  2  spectra at 2 K , taken with an infrared laser, of the same materials. A clear similarity of the two spectra is evident. The appearance of the A modes in the infrared spectrum is due 9  Chapter 4. Raman Results for BEDT-TTF  Based Materials  78  4000  0  200  400  600 800 1000 1200 1400 1600 Wave Numbers (cm ) 1  Figure 4.7: The room temperature Raman spectra of /«-(BEDT-TTF) Cu(NCS) , where B E D T - T T F is abbreviated as E T in the figure, taken with a visible lasr (solid line) by use of a Raman microscope spectrometer at Argonne and an infrared laser (dotted line). Eleven of the twelve totally-symmetric A modes and u ( B ) mode are labeled. The asterisk * indicates an atmospheric line. 2  g  60  3g  2  Chapter 4. Raman Results for BEDT-TTF  Based Materials  79  800  K-(ET) Cu(N(CN) )Br visible laser IR laser  G 600 2 M  •3 C  2  2  700  295K  500 400  CD  « 300  HH  a | 200 cd  Viofc' \  12  \  '4.  A l  J.  100 0 100  400  1000  700  1300  1600  Wave Numbers (cm ) _1  Figure 4.8: The room temperature Raman spectra of K - ( B E D T - T T F ) C u ( N ( C N ) ) B r taken with a visible laser (solid line) and with an infrared laser (dotted line), from 100 to 1600 c m . Ten of the twelve assigned totally-symmetric A intramolecular modes of the B E D T - T T F molecule have been labeled in the visible-laser spectrum, as well as ^i (^4 ) in the IR-laser spectrum.. 2  2  - 1  g  2  9  Chapter 4. Raman Results for BEDT-TTF  Based Materials  80  240 Raman (IR Laser, 10 K) Infrared Conductivity (12 K)  180  v.  v: frequency shifted by electron-phonon interaction  K-(ET)XU(NCS), 0 400  700  1000  1300  1600  Wave Numbers (cm ) _1  Figure 4.9: A comparison between the infrared-laser Raman spectrum and the infrared conductivity of K - ( B E D T - T T F ) 2 C u ( N C S ) , showing the electron-phonon frequency shifts listed in Table 4.2. 2  Chapter 4. Raman Results for BEDT-TTF  81  Based Materials  1200  K-(ET) Cu(N(CN) )Br 2  Raman (IR laser,2K)  1000  infrared conductivity (1 OK)  <Z2  v':Frequency shifted by electron-phonon interaction  g 800 3  o  400  2  600  800  1000  /  1200  1400  1600  Wave Numbers (cm ) _1  Figure 4.10: A comparison of the infrared conductivity of / t - ( B E D T - T T F ) C u ( N ( C N ) ) B r at 10 K with the Raman spectrum at 2 K , taken with an infrared laser, of the same material. The three prominent features in each spectrum are due to u (A ), u (A ) and i / ( B ) and these has been labeled. The prime in the infrared label indicates that the feature has been shifted down in frequency due to the electron-phonon interaction. In the infrared spectrum i>' (A ) extends from 1200 to 1350 c m and the fine structure is due to antiresonant interference with v (A ) that is a quadruplet at the same frequency. 2  5  g  g  g  2  6 0  3s  3  - 1  g  5  g  Chapter 4. Raman Results for BEDT-TTF  82  Based Materials  to the electron-phonon coupling since these modes in the isolated molecule are not infrared active. The electronic resonance that is enhancing the Raman scattering with the infrared laser appears to be the same electronic transition that produces the electron-phonon coupling responsible for the infrared activation of the gerade modes in the infrared spectra, since u  3  (A ), vg (Ag) and u g  60  (B ) are also the strongest features in the infrared spectra. The 3g  primes on the infrared features indicate that they have been shifted down in frequency due to the electron-phonon interaction. These shifts have recently been calculated by Shumway et al. [113] as a percentage of the unperturbed Raman frequency, and in Table 4.2 we compare our measured shifts with those calculated for the totally-symmetric A modes in 9  K - ( E T ) [ C U ( N C S ) ] . It may be seen from the Table 4.2 that the agreement is very good. The 2  2  i / (A ) mode has a calculated and measured 13.7 % shift while Ug (A ) has approximately the 3  9  g  same shift. The frequency shifts in these modes are very big compared with other modes. As we have mentioned early, these two modes also have strong Raman intensity. So the electron-phonon interaction is not only responsible for the resonant Raman scattering but also for the frequency shift. In the following sections, we focus on the three strongest Raman features i.e. (Ag) and u  m  (A ), vg g  (B ). Some anomalies will be shown, due to the superconductivity, magnetic 3ff  fluctuations or structural changes in the crystals.  4.3  Temperature-dependence of u (A ) Mode 3  g  The temperature dependence of the frequency of one of the stronger features in. our Raman spectra of K - ( B E D T - T T F ) C u ( N ( C N ) ) B r , that due to v (A ), is shown in Fig. 4.11. The 2  2  z  g  frequency increases almost linearly over the entire range with no obvious discontinuities, as the sample is cooled and the lattice contracts. The Heli-Tran data show a possible increase below T but the Janis data confirm that this is not the case. So nothing unusual is seen c  below T of 11.7 K . The data in Fig. 4.11 disagree with those presented in Ref. [47] where c  Chapter 4. Raman Results for BEDT-TTF  Based Materials  83  Table 4.2: Comparison of the experimental and calculated frequency shifts (in cm ) of the totally-symmetric A modes in K - ( E T ) [ C U ( N C S ) 2 ] due to the electron-phonon interaction. Raman Raman TotallyInfrared 8u/u 5u/u symmetric frequency frequency (exp.%) frequency (calc.% ) Ref. [113] A mode . (R.T.) (10K) (10K E / / c ) :  9  2  a  g  2930 1475 1276 1400 1280 977 920  V\  1491 1470  1493 1478  1283 981 921 645 500 449 311 161  1283 985 926  6  "5 "6 V  1  v% ^10 ^11 ^12  505 466 316 170  Values measured with the visible laser. of 4-fold multiplet. a  c  431 456 311  b  1.2 ± 0.1 13.7± 0.4 0.0± 0.1 0.8± 0.4 0.6 ± 0.2 14.7± 0.4 2.1 ± 1.0 1.6 ± 0.3.  0.0 0.5 13.8 0.0 0.0 0.0 0.0 0.1 12.5 0.7 1.1 9.4  Value measured with the infrared laser.  c  Average  Chapter 4. Raman Results for BEDT-TTF Based Materials  84  1475  K-(ET),Cu(N(CN),)Br  1474  v (A ) Raman mode  in  1473  3  g  1472  11  o 1471 CD  0^1470 CD  ^1469 cd  11468 -±— Heli-Tran refrigerator - J— Janis dewar  1467 1466  S  0  40  80  120 160 200 Temperature (K)  240  280  320  Figure 4.11: The Raman frequency as a function of temperature of the feature due to v ( A ) in K - ( B E D T - T T F ) C u ( N ( C N ) ) B r measured with an infrared laser in a Fourier-transform spectrometer. Independent measurements, taken in Janis Dewar at 2 and 15 K , above and below T at 11.6 K , are included. No increases below T is observed. 3  2  c  2  c  9  Chapter 4. Raman Results for BEDT-TTF  85  Based Materials  authors reported an unusual frequency jump around 150 K , but those authors were working with a single crystal, which displayed a close doublet, and this is difficult to work with unless the signal-to-noise ratio is very good. A similar phenomenum has been observed for the u (A ) mode in K - ( B E D T - T T F ) C U ( N C S ) 2 , 3  g  2  / 3 - ( B E D T - T T F ) A u I and a - ( B E D T - T T F ) I (i.e. nothing unusual was seen in the entire 2  2  t  2  3  temperature range, even below T ) . c  4.4  Phonon Softening Observed from u ( A ) and u 9  4.4.1  Phonon Softening Observed in  9  eo  (Bz ) Modes g  K-(ET) CU(NCS) 2  2  Fig. 4.12 shows the infrared laser Raman spectrum of « - ( E T ) C u ( N C S ) between 400 and 2  600 c m  - 1  as a function of temperature.  2  We can see that the intensity increases strongly  with decreasing temperature until 70 K , after which it drops until 55 K and then grows again below 55 K . The frequency of the maximum also shifts down below 70 K . This unusual temperature-dependent shift of phonon Raman intensity has not been previously reported by others. In order to properly analyze the feature, it was fitted at each temperature to three Lorentzians, by a nonlinear least-squared method, and these may be seen at 90 K and 10 K in Fig. 4.13. It is clear that u (A ) is at least a doublet, and this is due to the 9  g  two B E D T - T T F dimers in a unit cell. No assignment has yet been made of the third small resonance. The two components of this doublet behave differently as a function of temperature. Fig. 4.14 shows the integrated intensity of both components versus temperature. The upper component (lower trace) is seen to have a broad maximum around 80 K and a minimum near 50 K . Fig. 4.15 shows the frequency of the lower component of the v (A ) doublet, 9  g  which is seen to soften below 80 K . In Fig. 4.16 we plot the frequency of the sharp line at 890 c m  - 1  which is also resonant with the infrared laser, and which we have assigned to f  6 0  (B3 ) in the D /j symmetry scheme. A pronounced softening below 80 K is again observed 9  2  Chapter 4. Raman Results for BEDT-TTF  400  420  440  460  480  Based Materials  500  520  86  540  560  580  600  Wave Numbers (cm ) _1  Figure 4.12: The temperature dependent Raman spectra of K - ( B E D T - T T F ) C u ( N C S ) between 400 and 600 c m . The intensity of z/ (A ) Raman mode, a main feature of the spectra, has a strong variation with temperature. 2  - 1  9  g  2  Chapter 4. Raman Results for BEDT-TTF  Based Materials  87  160  90 K  v ( A ) doublet Q  9  •3  80  C  60  a  HH  a  g  cd  g  /  10 K  Experiment Fit  40  v  20 0 400  420  440  460  480  500  520  540  560  580  600  Wave Numbers (cm ) 4  Figure 4.13: The Raman spectra of v (A ) mode of K > ( B E D T - T T F ) C U ( N C S ) at 9 0 and 10 K (dots) and the best-fitted results (solid lines) with five Lorentzians. Three of five Lorentzians are shown (dashed lines). The Lorentzian at 484 c m is an unassigned Raman line clearly observed in the spectrum with the visible laser in Fig. 4.7. 9  g  2  - 1  2  Chapter 4. Raman Results for BEDT-TTF  Based Materials  88  14 12  V  10  K-(ET) Cu(NCS) 2  2  :  v (A ) doublet Q  lower component 8 -  -  ; upper component  4 0  0  50  100  150  200  •: 250  300  Temperature (K) Figure 4.14: The temperature dependence of the integrated intensities of v (A ) doublet: upper component (solid line) and lower component (dotted line). The lines are guides for the eye. 9  9  Chapter 4. Raman Results for BEDT-TTF Based Materials  89  506  505  504  -  o  C 503  K-(ET)XU(NCS),  £502  e ed  S501 cd  v (A ) (lower component)  500  499  Empty symbol: 2K data from Janis dewar 0  100  50  150  200  250  Temperature (K)  300  Figure 4.15: Raman frequencies of the lower component of vg (A ) doublet as a function of temperature. g  for this feature. In order to understand these Raman anomalies, let's first check the anomalies observed by other methods. Recently, C - N M R , magnetic susceptibility and Hall effect measurements of 1 3  ft-(BEDT-TTF)Cu(NCS)  2  revealed the enhancement of antiferromagnetic spin fluctuations  in the temperature range of 50-60 K[21, 114]. Many other anomalies around 50 or 100 K have been reported, including resistivity[114, 115, 116], thermopower[114, 115], E S R spin susceptibility[117], and lattice expansion[18]. Table 4.3 lists the temperatures of the various  Chapter 4. Raman Results for BEDT-TTF  Based Materials  891 \0 890  ( 3g) B  I  o  c  I  CD  gn889 CD  fc  a  K-(ET)XU(NCS),  I 888  Empty symbol: 2K data from Janis dewar 887  0  50  100  150  200  Temperature (K) Figure 4.16: Raman frequencies of the i/  60  250  { 300  ( B ) mode as a function of temperature. 39  Chapter 4. Raman Results for BEDT-TTF  Based Materials  91  Table 4.3: Lists of the temperatures of the various anomalies observed in K - ( E T ) C U ( N C S ) 2 . Anomalies Temperature (K) References 50 K C NMR Phys. Rev. Lett.74, 3455 (1995)[21] Hall effect 60 K Solid State Commun. 76, 377 (1990)[114] Thermopower 50 K Solid State Commun. 65, 1531 (1988) [115] Resistivity, 45 K Sov. Phys. J E T P 68, 182 (1989)[116] 60 K XAFS* J. Phys. Soc. Jpn. 60, 1441 (1991)[18] 50 K Physica C 185-189, 2671 (1991)[18] Spin-susceptibility 50 K Solid State Commun. 67, 981 (1988) [117] Spin-susceptibility 100 K Solid State Commun. 67, 981 (1988)[117] XAFS* 100 K J. Phys. Soc. Jpn. 60, 1441 (1991)[18] Physica C 185-189, 2671 (1991)[18] Thermopower 100 K Solid State Commun. 65, 1531 (1988) [115] X-ray diffraction 100 K J. Phys. Soc. Jpn. 60, 2118 (1991)[17] * X A F S means X-ray absorption fine structure. 2  1 3  anomalies observed in K - ( E T ) C U ( N C S ) 2 2  A n electronic band calculation of K - ( B E D T - T T F ) C U ( N C S ) by Demiralp et al. [118] 2  found that the normal state of the system is a weakly antiferromagnetic conductor. As the temperature increases, the B E D T - T T F phonons couple tq the electrons strongly and promote transitions between the two bands. As we have mentioned in Section 1.18, the /c-type B E D T T T F based organic superconductors are similar to the high-T cuprate superconductors since c  both materials have a quasi-two-dimensional electronic structure and the interplay between magnetism and superconductivity. Several papers have reported on phonon anomalies associated with magnetic effects. Litvinchuk, Thomsen and Cardona[119] have showed a remarkable correlation between the temperature-dependent softening of the phonon frequencies and the magnetic susceptibility in the superconductors Y B a C u 0 8 and Y B a 2 C u 0 . 7 well above T where the 2  4  3  6  c  5  6 3  Cu  nuclear-relaxation rate shows an anomaly. For the case of Y B a 2 C u 0 . 5 7 , the results are 3  6  shown in Fig.4.17[119]. These softenings were explained as an effect of magnetic fluctuations  Chapter 4. Raman Results for BEDT-TTF  0  Based Materials  92  100 2 0 0  Figure 4.17: Temperature dependence of a phonon frequency in Y B a C u 0 . 5 7 (T =60 K) (open circles) and 5% A u doped Y B a C u 0 . 8 4 (T =91 K ) (solid circles), together with the C u nuclear-relaxation rate ( T x T ) (triangles)[119]. 2  2  6 3  - 1  3  6  c  3  6  c  Chapter 4. Raman Results for BEDT-TTF  Based Materials  93  above T on the phonon energy due to the opening of a spin pseudo-gap. For «>(BEDTc  T T F ) C u ( N C S ) 2 , the frequency softening appears similar to that reported by Litvinchuk, 2  Thomsen and Cardona[119] and is, therefore, probably due to the antiferromagnetic fluctuations. We note that this presents yet another similarity between the organic and high-T  c  superconductor. As we have mentioned in Section 1.18, Fukuyama's theory[100] has predicted a Raman frequency shift well above T due to a spin-gap effect (see Fig. 1.19 on page 42), for high-T c  c  materials in the underdoped region. Fukuyama's calculation shows a 2% frequency shift, while we observed 0.2 % frequency shift for u (A ) mode and 0.13% for u 9  g  (B ) mode in  e0  3g  «;-(BEDT-TTF) Cu(NCS) , compared with observed 1.2% softening for the phonon around 2  2  315 cm-Hn Y B a G u 0 .57 (see Fig.4.17). 2  4.4.2  3  6  Phonon Softening Observed in K > ( B E D T - T T F ) C u ( N ( C N ) ) B r 2  2  An unusual behavior has also been observed for the v mode in K - ( B E D T - T T F ) C u ( N ( C N ) ) B r 9  2  2  The VQ (A ) feature is also a doublet and Fig. 4.18 shows the temperature dependence of g  the Raman frequencies of the v (A ) mode (lower component) in natural and deuterated 9  g  K - ( B E D T - T T F ) C u ( N ( C N ) ) B r . For the protonated compound, no phonon softening is ob2  2  served. For the deuterated compound, a strong softening is seen below 130 K . Fig. 4.19 shows the temperature dependence of the integrated intensities of the v (A ) 9  doublet in protonated (natural) and deuterated K - ( B E D T - T T F ) C u ( N ( C N ) ) B r . 2  2  5  As has  been observed in K - ( B E D T - T T F ) C U ( N C S ) , the upper component of v (A ) doublet has 2  2  9  g  a strong temperature dependence. For the protonated compound, the intensity of the upper component of v (A ) increases dramatically when the temperature is below 60 K . For 9  g  the deuterated compound, the general increase with lowered temperature is seen for both components probably due to the changing electron resonance. There is a dip and a peak between 50 and 80 K for the lower component. The intensity of the upper component goes up quickly below 130 K .  Chapter 4. Raman Results for BEDT-TTF Based Materials  v (A ) (lower component)  s  1.005  9  1.004  S  w  g  i  i *'  * £l.003[  1  1  *  ¥ S 1.0021 1.001  94  f  • K-(h -ET) Cu(N(CN) )Br I • K-(d -ET) Cu(N(CN) )Br Empty symbols: data from Janis dewar g  2  2  8  2  2  1  1 .oooh 0  30  60  90  I  120 150 180 210 240 270 300 Temperature (K)  Figure 4.18: The temperature dependence of the Raman frequencies of the v (A ) mode in natural and deuterated K>(BEDT-TTF) Cu(N(CN) )Br. 9  2  2  g  Chapter 4. Raman Results for BEDT-TTF Based Materials  2000P  c =1 JD t-H C3  95  K-(h -ET) Cu(N(CN) )Br g  2  2  v ( A ) doublet Q  1600  9 v  „/  .§1200  • lower component • upper component •\*Empty symbols: data from Janis dewar  •  £ 1200  K-(d -ET) Cu(N(CN) )Br 8  1=1  •  »  2  v  9 (  A  2  g  )  d  o  u  b  l  e  t  xi 1000| >> 800|  • •  1 600|  lower component upper component  13  1 2 4001 +-> &  c  2001 01  Empty symbols: data from Janis dewar  0  50  100 150 200 Temperature (K)  250 300  Figure 4.19: The temperature dependence of the integrated intensities of the u (A ) doublet in protonated (natural) and deuterated K - ( B E D T - T T F ) C u ( N ( C N ) ) B r . . The intensities of lower component were scaled down by half. The lines are guides for the eye. 9  2  2  g  Chapter 4. Raman Results for BEDT-TTF Based Materials  96  Table 4.4 list the temperatures of the various anomalies observed in K - ( E T ) C u ( N ( C N ) ) B r . 2  2  We can see from the table that some possible interactions which may be responsible for the low-temperature softening could be magnetic fluctuations, conductivity maximum anomalies, structural anomalies, ethylene ordering[125], or the cooling effect[26, 27]. It has been reported recently[29] that the deuterated compound is in the critical region between the superconducting phase and the antiferromagnetic phase, with the crystals if they are slowly cooled containing both phases, but if they are rapidly cooled containing only the magnetic phase (we slowly cooled down the samples except those specially mentioned). It seems the deuterated compound is more magnetic than the protonated one. So we are inclined to attribute the softening to an interaction of the phonon with the fluctuating anti-ferromagnetism which is the same reason we gave for the softening in K > ( B E D T - T T F ) C U ( N C S ) . The soft2  2  ening is measured to be 0.2% (same magnitue for u (A ) in K - ( B E D T - T T F ) C U ( N C S ) ) , 9  g  2  2  compared with the Fukuyama's theoretical prediction of 2% [100] for Y B a C u 0 6 + - We 2  have not seen any softening in the u  60  (B )  3  X  mode in the / c - ( B E D T - T T F ) C u ( N ( C N ) ) B r  3g  2  2  compound (we will show the result later in Fig. 4.21 of Section 4.5.1), compared with the 0.13% softening in K - ( B E D T - T T F ) C U ( N C S ) (see Fig. 4.16 of Section 4.4.1). 2  4.5  2  Frequency Shifts Observed Below T  c  Finally we show in this section the most interesting results about the frequency shifts observed below T for the v c  m  assumption of planar D  2 / l  {B ) mode. Fig. 4.20 shows a sketch of u 3g  60  (B ) 3g  (with the  symmetry). As has been shown in Fig. 4.16, we have not ob-  served any strong softening or hardening of the ^  6 0  ( B ) mode below T 39  c  in K - ( B E D T -  T T F ) C u ( N C S ) (T =10.4 K ) compound. The same result applies to / 3 - ( B E D T - T T F ) A u I 2  2  c  2  2  (T =4.9 K ) . However we have observed a strong phonon frequency shift below T in Kc  c  ( B E D T - T T F ) C u ( N ( C N ) ) B r (T =11.6 K ) and c v ( B E D T - T T F ) I (T =8 K ) . 2  2  c  r  2  3  c  Chapter 4. Raman Results for BEDT-TTF  Based Materials  Table 4.4: Lists of the *>(ET) Cu(N(CN) )Br.  temperatures  Anomalies Thermal Expansion Magnetization Resistivity, Magnetization Resistivity dc/ac Susceptibility, H/ C NMR Resistivity, Thermopower Lattice parameter c Lattice parameter a C NMR Resistivity C NMR 1/TiT Hall effect C NMR l / ^ T  Temperature (K) 80 K 70-90 K 80 K 80 K 80 K 80 K 75 K , 95 K 80-90 K 150 K 150 K 140 K 50 K 55 K 50 K  2  X  of  the  97  various  anomalies  observed  in  2  1 3  1 3  1 3  1 3  References Physica B 191, 274 (1993) [120] Physica C 303, 185 (1998) [121] Phys. Rev. B 58, R2944 (1998) [27] Phys. Rev. B 57, R14056 (1998) [26] Phys. Rev. B 55, 14140 (1997) [29] Phys. Rev. B 55, 14140 (1997) [29] J. Phys. I (France) 2, 1257 (1992)[122] J. Phys. Soc. Jpn. 60, 3608 (1991)[123] J. Phys. Soc. Jpn. 60, 3608 (1991)[123] Phys. Rev. B54, 16101 (1996) [124] Solid State Commun. 107, 731 (1998)[125] Europhys. Lett. 28, 205 (1994)[126] Phys. Rev. B 55, 12529 (1997)[127] Phys. Rev. Lett.74, 3455 (1995)[21] Phys. Rev. B 52, 15522 (1995)[128]  Figure 4.20: The atomic displacement vectors for the z^ ( B ) normal mode of vibration, assuming D /j point-group symmetry. 60  2  3s  Chapter 4. Raman Results for BEDT-TTF Based Materials 4.5.1  98  Frequency Shifts Observed Below T in « - ( B E D T - T T F ) C u ( N ( C N ) ) B r c  2  2  The temperature dependence of the frequency of the feature due to z^o (B3 ) is shown in 9  Fig. 4.21. The measured frequencies above and below T , when the sample is slowly cooled c  (2.5 K/minute), are indicated for both refrigeration systems. The frequency increases are in very good agreement, being 2.2±0.7 c m c m " at 2 K ) and 2.2±0.4 c m 1  - 1  - 1  for the Janis (from 892.4±0.6 c m  - 1  to 894.6±0.3  for the Heli-Tran.(from 892.6±0.3 c m " to 894.8±0.3 era" at 1  1  7 K ) . The reason for the low value of the error (only 0.3 c m ) is because of the high intrinsic - 1  wave-number stability of the Fourier-transform machine, due to the laser interferogram. It should be noted that these two measurements were performed on crystals made in different batches. Upon rapid cooling (10 K/minute) we measured 892.9±0.3 c m " at 15 K and 893.0±0.3 1  cm  at 2 K , indicating no shift (see Fig. 4.21). For the deuterated compound we mea-  - 1  sured 901.9±0.2 c m  - 1  at 15 K and 902.8±0.2 c m  - 1  at 2 K , a superconductivity-induced  shift of 0.9±0.3, nearly one half of the shift seen in the natural compound. As we have mention early on page 96, Kawamoto et al. [29] have reported that the deuterated K > ( B E D T T T F ) C u ( N ( C N ) ) B r compound is in the critical region between the superconducting phase 2  2  and the antiferromagnetic phase, with the crystals if they are slowly cooled containing both phases, but if they are rapidly cooled containing only the magnetic phase. A l l of our results, together with the results of Kawamoto et al. [29], indicate that the frequency shifts observed above are due to the superconductivity transition. Pedron et al. [45, 50] have also reported a study of the Raman spectroscopy of some low frequency phonons in «>(ET) Cu(N(CN) )Br. They observed an increase in frequency 2  2  for all of the phonons studied when the samples were cooled to 1.8 K . These phonons had frequencies ranging from 27 to 133 c m , and the shifts were larger for the lower frequency - 1  modes. In Ref. [50] they compared their results to a strong electron-phonon coupling model and showed that they are more consistent with an s-wave than with a d-wave gap function,  Chapter 4. Raman Results for BEDT-TTF  Based Materials  99  896  K-(ET)Xu(N(CN)JBr v (B ) Raman mode  895  60  Heli-Tran refrigerator, slow cooling Janis dewar, slow cooling Janis dewar, rapid cooling  ^894 o (D =3  I  £893 PH G  cd c«892  891  3g  0  I  40  80  120  160  200  240  280  320  Temperature (K) Figure 4.21: The Raman frequency as a function of temperature of the feature due to u ( B ) in ft-(BEDT-TTF)2Cu(N(CN) )Br measured with an infrared laser in a Fourier-transform spectrometer. Independent measurements, taken in Janis Dewar at 2 and 15 K , above and below T at 11.6 K , are included. The frequency increases below T were obtained when the samples were slow cooled. The results of rapid cooling are also shown. G0  2  c  c  39  Chapter 4. Raman Results for BEDT-TTF  Based Materials  100  Figure 4.22: Temperature dependence of the relative frequency shifts, 5LU/U> , of the bands 27.4, 69.3, 104.2 and 133.5 c m ^ m «-(ET) Cu(N(CN) )Br. Triangles and circles represent data from different samples[45, 50]. 0  2  2  Chapter 4. Raman Results for BEDT-TTF  Based Materials  101  and that the upper limit on the B C S energy gap would be 28 c m . - 1  The average frequency increase is only 0.25% in our Raman results for K-(ET) Cu(N(CN) )Br, 2  2  compared with 3.2% measured by Pedron et al. [45, 50] for the lowest measured frequency mode at 27.4 c m , down to 0.6% for the highest frequency mode at 133.5 c m , but it is - 1  - 1  certainly statistically significant and unusual for such a high-frequency mode. This is the highest frequency phonon in any material to be affected by superconductivity. Superconductivity-induced changes in phonon frequencies are of course evidence for electron-phonon coupling. Such changes are also seen in the high-T superconductors. Thomc  sen et al. [87] and Friedl, Thomsen, and Cardona[129] used the temperature dependences of the frequencies and linewidths of some Raman-active phonons to obtain an estimate for the superconducting gap in several R B a C u 0 2  3  7  compounds, where R is a rare-earth element,  using the predictions of a strong-coupling model given by Zeyher and Zwicknagl[86]. A l tendorf et al. [80] looked at these changes as a function of oxygen concentration. In M 3 C 6 0 (T =19-29 K ) , on the other hand, Raman studies by Zhou et al. [130] and Brocard et al. c  [131] show weak or no temperature dependence of the high-frequency intramolecular modes through T . Zhou et al. [130] state that this is consistent with the fact that the frequencies c  of the modes are much greater than the energy of the superconducting gap. Since we also observed no temperature dependence of the frequencies of our high frequency A modes, z/ s  3  (A ) and u (A ), perhaps the normal electron-phonon coupling does not explain the increase g  9  g  in the frequency of UQ ( B ) . 0  3s  Frequency Shifts Observed Below T in a - ( B E D T - T T F ) I  4.5.2  c  t  2  3  The a ( B E D T - T T F ) I (T =8 K) is a thermally converted product of a - ( B E D T - T T F ) I . It r  2  3  c  2  3  is now known that a ( B E D T - T T F ) I is actually the high-T phase of/3-(BEDT-TTF) I [76] r  2  3  c  2  3  (T =1.4 K for low-T phase;T =8 K for high-T phase). We find a peak splitting for i/ o c  c  c  c  6  ( B ) mode in the a ( B E D T - T T F ) I compound at low temperature as shown in Fig. 4.23. 3s  r  2  3  We show in the same figure three other peaks, which are not split, for comparison. The  Chapter 4. Raman Results for BEDT-TTF  Based Materials  102  500  a -(BEDT-TTF) I , 10 K t  2  3  Peak Splitting  |>400  s5300  \ 0  200  ( 3g) B  c  ci  £ «3  IOO  o  400  500  600  700  800  900  Wave Numbers (cm )  1000  1100  -1  Figure 4.23: A peak splitting for v  m  (B ) mode observed in a ( B E D T - T T F ) I at 10 K . 3ff  r  2  3  Chapter 4. Raman Results for BEDT-TTF Based Materials  103  Table 4.5: Lists of the temperatures of the various anomalies observed in a - ( E T ) I and /?-(ET) I . 2  2  3  3  Anomalies ESR ESR Infrared Resistivity  Temperature (K) 135 K 140 K 135 K 135 K  a-(ET) I References Phys. Rev. B 32, 2819 (1985)[132] Phys. Rev. B 34, 117 (1986) [133] J. Physique 47, 137 (1986)[134] Mol. Cryst. L i q . Cryst. 119, 329 (1985) [135]  Anomalies Hall-effect Raman X-ray X-ray X-ray  Temperature (K) 40 K 125 K 125 K 175 K 180 K  /?-(ET) I References Phys. Rev. Phys. Rev. Phys. Rev. Phys. Rev. Phys. Rev.  2  2  3  3  B B B B B  41, 36, 37, 37, 30,  11646 (1990) [136] 6881 (1987)[42] 5113 (1988) [137] 5113 (1988)[137] 6780 (1984) [138]  peak splitting may be related to the superstructure formed in the sample since an incommensurate modulation was reported for / ? - ( B E D T - T T F ) I at low temperatures by X-ray 2  3  measurements[137, 138]. Fig. 4.24 shows the gradual splitting of the ^  6 0  ( B ) mode as the 3s  temperature is lowered from room temperature down to 10 K . At a temperature of 120 K , the splitting is clearly seen. The peak is fitted with two Lorentzians and we plot the frequencies of two components as a function of temperature in Fig. 4.25. The frequency of the lower component decreases gradually as the temperature is lowered. The upper component displays a dip between 140 and 190 K . Various anomalies have been found at these temperatures as listed in Table 4.5 for a - ( E T ) I and /?-(ET) I . The anoma2  3  2  3  lous behaviour around 150 K in Fig. 4.25 may be due to the phase transition from the metal to insulator[135]. When the temperature is lowered below T of 8 K , no frequency shift is observed for the c  lower component (see Fig. 4.25). However a definite frequency shift below T is observed in c  Chapter 4. Raman Results for BEDT-TTF  Based Materials  104  150  +->  •i-H  d  100 cd  10 K 60 K 120 K 160 K 190 K 293 K  a -(ET) I (T=8 K) t  2  V  60  3  ( 3g) B  m  °  d  e  C/3  a cd  50  cd  0 800  850  900 950 Raman Shift (cm ")  Figure 4.24: Temperature dependence of the u  m  1000  (B ) mode in a - ( B E D T - T T F ) l 3 . 3g  t  2  Chapter 4. Raman Results for BEDT-TTF  Based Materials  105  899 897  B 895 o o  a -(ET) I (T =8 K)  893  t  - a891  •  PH  2  v  (B ) (lower component) 3g  * 6o ^ 3g) ( P P component) Empty symbols: data from Janis Dewar  a  V  e 889 887 885  60  3  B  u  i  5 * 0  30  e r  60  90  120  150  I * 180  210  240  270  300  Temperature (K) Figure 4.25: The Raman frequency as a function of temperature of the feature due to u ( B ) in o ; t - ( B E D T - T T F ) 2 l 3 measured with an infrared laser in a Fourier-transform spectrometer. Independent measurements, taken in Janis Dewar at 2 and 14 K , above and below T at 8 K , are included. m  3p  c  Chapter 4. Raman Results for BEDT-TTF  Based Materials  106  the upper component. This time it is a decrease, not an increase as observed in K - ( B E D T T T F ) C u ( N ( C N ) ) B r , but is of a similar magnitude, 1 . 7 ± 0 . 4 c m (from 8 9 8 . 0 ± 0 . 2 c n r t o - 1  2  2  896.3±0.4  c m ) . Again this is a superconductivity-induced change in phonon frequency. - 1  However the normal electron-phonon coupling does not explain this decrease in the frequency of v  (B ) •  4.6  Unusual Properties of u  60  3ff  60  The properties of the u  (B )  eo  3g  (B ) 3g  Mode  mode are unusual for several reasons. First, it is strongly  activated in the infrared spectra of the conducting B E D T - T T F salts (along with other much weaker modes) whereas theory predicts activation of only the A modes. Second, 9  it is absent in the Raman spectrum of the neutral B E D T - T T F compound, but appears strongly in the spectra of the conducting salts. Third, it has the superconductivity-induced frequency changes observed in K - ( B E D T - T T F ) C u ( N ( C N ) ) B r and a - ( B E D T - T T F ) I de2  2  t  2  3  scribed above. This is the highest frequency phonon in any material to be affected by superconductivity. Fourth, it splits at low temperatures in a ( B E D T - T T F ) I while other modes r  2  3  show no splitting. This splitting, however, is not observed in K>(BEDT-TTF) Cu(NCS) , 2  2  K - ( B E D T - T T F ) C u [ N ( C N ) ] B r , or /3-(BEDT-TTF) A u I at temperature down to 2 K . 2  2  2  2  Finally, it has a positive isotopic frequency shift upon deuteration of the B E D T - T T F molecule. When the hydrogens are substituted by deuteriums in the B E D T - T T F molecule, we expect that the Raman frequency may be lowered due to the heavier mass if the hydrogens participate in the vibration. However we find that the frequency of u  (B )  eo  which does not involve the hydrogens, increases upon deuteration.  3g  mode,  Fig. 4 . 2 6 shows the  Raman spectra of v  (B )  at room temperature.  We also show in the same figure the feature of the v (A ) mode  m  3g  from natural and deuterated K - ( B E D T - T T F ) C u ( N ( C N ) ) B r 2  2  9  for comparison. As we can see from the figure the  (B ) 3g  g  mode has an inverse isotope  shift of 7.5 c m u p o n deuteration ( while the v (A ) mode has an almost zero shift upon _1  9  fl  Chapter 4. Raman Results for BEDT-TTF Based Materials  40  107  R o o m Temperature Natural K-(ET) Cu(N(CN) )Br Deuterated K-(ET) Cu(N(CN) )Br 2  CO  2  2  +-»  2  Inverse Isotope Shift  §30  \0  cd "S 20  (  B  3g)  CD  G ed  gio cd  0 400  500  600  700  800  900  1000  1100  W a v e Numbers (cm ") Figure 4.26: Raman spectra of natural and deuterated K - ( B E D T - T T F ) C u ( N ( C N ) ) B r . 2  2  Chapter 4. Raman Results for BEDT-TTF  Based Materials  108  Table 4.6: Inverse isotope shift of the Raman frequency of the u (B ) mode in «-(BEDT-TTF) Cu(NCS) , K - ( B E D T - T T F ) C u [ N ( C N ) ] B r , / 3 - ( B E D T - T T F ) A u I and /3-(BEDT-TTF) I . 60  2  2  2  2  Raman frequency from natural material ( c m ) 888.8 889.6 889.7 885.9 -1  «-(ET) Cu(NCS) K-(ET) Cu[N(CN) ]Br /3-(ET) AuI /?-(ET) I 2  2  2  2  2  2  2  3  Materials  2  3g  2  2  3  Raman frequency from deuterated material ( c m ) 896.7 897.1 900.4 895.4  isotope shift  -1  7.9 7.5 10.7 9.5  deuteration, in agreement with the theory calculation[30]). We have also investigated all available deuterated B E D T - T T F based materials and found that all of these materials show the positive isotopic frequency shift upon deuteration. Table 4.6 lists the observed isotope shift for the u  (B ) mode in « > ( B E D T - T T F ) C u ( N C S ) , « > ( B E D T - T T F ) C u [ N ( C N ) ] B r ,  60  3g  /3-(BEDT-TTF) AuI 2  2  2  and /3-(BEDT-TTF) I . 2  3  2  2  2  Isotope frequency increases over a range of  7.5-10.7 cm are observed upon deuteration. _1  As we have listed in Table 1.6 (see page 26), K - ( E T ) C U ( N C S ) 2  2  shows an inverse iso-  tope effect of T , while no frequency shift is observed below T for the v c  re-(ET) Cu(N(CN) )Br 2  2  c  (B )  60  3g  mode.  and a -(ET) I [139] show a normal isotope effect of T , while a fret  2  3  quency shift is observed below T for the v  c  c  m  ( B ) mode. Therefore the z/go {B ) mode may 3p  3g  play an important role in the B E D T - T T F based organic superconductors.  4.7  Summary  For neutral B E D T - T T F and d - B E D T - T T F , we report the temperature-dependent 8  frequen-  cies of the strong features in the Raman spectra. We note an unusual softening of the features due to the modes involving the C - H vibrations in the terminal ethylene groups, as well as one mode involving the central double-bonded carbon atoms. We relate these softening to the increased bending of the neutral molecule at low temperature. For B E D T - T T F based superconductors, firstly we compare the Raman spectra excited  Chapter 4. Raman Results for BEDT-TTF  Based Materials  109  by infrared laser with those excited by visible laser. Then we compare these Raman spectra with the infrared conductivity of the same material. The electronic transition responsible for the strong resonant Raman scattering is the same as that providing the infrared activity through electron-phonon coupling. The frequency shifts of the A modes, which appear in 9  the infrared conductivity, are compared with the calculated values and the agreement is very good. The frequencies of the u (A ) and u 9  g  G0  ( B ) modes in /t-(ET) Cu(NCS) and the fre39  2  2  quency of the UQ (A ) mode in /c-(ET) Cu(N(CN) )Br are observed to soften in the temperag  2  2  ture range where anti-ferromagnetic spin fluctuations have been observed, providing evidence of interactions between the phonons and the magnetism. The intensities of the VQ (A ) mode g  in these materials show effects of the magnetic fluctuations and the ethylene ordering. The u  eo  (B ) mode is unusual in many ways such as an inverse deuterium isotope fre-  quency shift.  3g  At temperatures below T , this mode exhibits an increase of 2.2 c m i n - 1  c  K - ( E T ) C u ( N ( C N ) ) B r (T =11.6 K ) and a decrease of 1.7 c m i n a - ( E T ) I (T =8 K ) . - 1  2  2  c  t  2  3  c  This is the highest frequency phonon in any material to be affected by superconductivity. This phonon has an energy (890 c m ) far greater than the superconducting gap (around 25 - 1  c m ) , so the current theory with the normal electron-phonon interaction can not explain - 1  the frequency change observed here. The resonance effect needs to be included, I thank, in any new theories trying to explain this frequency shift.  Chapter 5 Introduction and Results for T T F - T C N Q  5.1  Charge Density Wave ( C D W )  When metals are cooled, they often undergo a phase transition to a state exhibiting a new type of order.  Metals such as iron and nickel become ferromagnetic below certain  temperatures; electron spins order to produce a net magnetization in zero field. Other metals, such as lead and aluminum, become superconductors at cryogenic temperatures; electrons form Cooper pairs of opposite spin and momentum, leading to electrical conduction with zero resistance and to expulsion of magnetic fields. Since the mid-1970's, a wide range of quasi-one-dimensional materials have been discovered that undergo a different type of phase transition both above and below room temperature: they become charge-density-wave (CDW) conductors. These materials show strikingly nonlinear and anisotropic electrical properties, gigantic dielectric constants, unusual elastic properties and rich dynamical behavior. The C D W is a modulation of the conduction electron density in a material and an associated modulation of the lattice atom positions, as shown in figure 5.1. Although similar modulations are observed in many different types of solids, those that give rise to the unusual properties of quasi-one-dimensional materials have three special features: Like conventional superconductivity, they are caused by an instability of the metallic Fermi surface involving the electron-phonon interaction; they result in energy gaps at the Fermi surface; their wavelength A is n/kp, where kp is the Fermi wavevector. c  The mechanism by which CDW's might form was discussed by Rudolph Peierls in 1930[141].  110  Chapter 5. Introduction and Results for  TTF-TCNQ  111  Figure 5.1: The single particle band, electron density, and lattice distortion in the metallic state above TQDW and in the charge density wave state at T=0. The figure is appropriate for a half-filled band[140].  Chapter 5. Introduction and Results for  TTF-TCNQ  112  Consider a quasi-one-dimensional metal consisting of chains of equally spaced atoms. The allowed conduction electron states form a band, as shown in figure 5.1. States inside the Fermi surface, with energies less than Ep and wavevectors less than k , will be occupied, F  and states outside the Fermi surface will be empty. If an energy gap is opened at k — ±kp, then the energies of the occupied states just below Ep will be lowered, reducing the total electronic energy. Peierls pointed out that a modulation of the positions u  n  atoms of the form 5u  n  of the lattice  = Su cos [Qz + </>] with wavevector Q=2kp would produce gaps at  ±k . F  Many ideas of C D W ' s were developed in early attempts to explain superconductivity. In 1941, John Bardeen suggested that "in the superconducting state there is a small periodic distortion of the lattice" that produces energy gaps, and that these gaps would lead to enhanced diamagnetism[143].  Bardeen abandoned this idea when he realized the dif-  ficulty of obtaining an appropriate arrangement of gaps on the three-dimensional Fermi surfaces of common superconductors. In 1954, Herbert Frohlich described a detailed theory of "one-dimensional superconductivity" that predicted C D W formation and collective charge transport[144]. Frohlich's theory bears a striking formal similarity to the B C S theory that followed three years later. In 1973, Bardeen suggested that Frohlich's ideas might explain the unusual electrical properties of the quasi-one-dimensional organic conductor T T F - T C N Q (Tetrathiafuvalene Tetracyanoquinodimethane). The charge density wave ground state develops in low-dimensional metals as a consequence of electron-phonon interactions. The resulting ground state consists of a periodic charge density modulation accompanied by a periodic lattice distortion, both periods being determined by the Fermi wavevector kp, as shown in Fig 5.1. Consequently both the electron and phonon spectra are strongly modulated by the formation of the charge density wave.  Chapter 5. Introduction and Results for  5.2  TTF-TCNQ  113  T T F - T C N Q Structure and the C D W  T T F - T C N Q is a charge-transfer salt, which is the first synthetic organic metal. It consists of parallel segregated stacks of T T F + and T C N Q " molecules. (Both T T F and T C N Q are large planar molecules as shown in Fig. 5.2). As shown in Fig. 5.3 the T T F and T C N Q molecules are flat and stack one on top of another, but they are tilted in opposite directions in each stack. The axis along which the stacks are formed is traditionally labeled the b-axis of the crystal. The orbital overlap along the b-axis gives rise to a conduction band along this axis. There is very little overlap between adjacent stacks of the T T F and T C N Q molecules resulting in very little inter-stack interaction and hence in a very low conductivity along these axes, the a and c-axes of the crystal. Due to the large anisotropy in electrical conductivity ( the conductivity along the 6-axis being a factor of 500 or greater than that along the other axes), T T F - T C N Q is a quasi one-dimensional conductor. T T F - T C N Q crystallizes in the monoclinic system with unit cell constants a=12.298 A , 6=3.819 Aand c=18.468 A . Y  N  \  H  S ^ TTF  /  /  C  \  c=c  I  a  \ / C=C  \  ^c  •c-  N  C  x H  TT  TJ  / ^ H  C  / N  /  ,C=C  \  /  C=C  I T C N Q\  \ C  \ N  Figure 5.2: The T T F and T C N Q molecules As the temperature is lowered the conductivity of T T F - T C N Q increases in a metallic fashion until about 54 K where the crystal undergoes a Peierls distortion. Structural studies of T T F - T C N Q [145] indicate that there are 3 successive phase transitions: the C D W  Chapter 5. Introduction and Results for TTF-TCNQ  Figure 5.3: (Left), T T F - T C N Q crystal structure; and (Right), Stacking arrangement TTF-TCNQ.  Chapter 5. Introduction and Results for  TTF-TCNQ  115  transition occuring on the T C N Q stacks at 54K, the C D W transition on the T T F stacks at 49K and the establishment of three-dimensional order at 38K, due to the pinning of the oppositely charged CDW's on adjacent stacks by Coulomb attraction. The wavelength A of the C D W is incommensurate along the stacking direction, with A c  c  equal to 3.46 where 6 is the lattice period along the 6-axis. In terms of the reciprocal lattice vectors (a*=^-,b*= f-,c*= f), 2  2  the Q component of the modulation wavevector Q is equal a  to |a* at temperatures between 54 K and 49 K . Below 49 K it decreases approximately linearly with temperature, until 39 K , where it jumps and locks at the commensurate value of \a*. Q is equal to 0.2956* and Q is equal to zero. A second modulated structure having b  c  Qb=0.59b (the 4k/ modulation) has also being observed[146]. Fig. 5.4 shows the wave-vector dependence of the x-ray scattering intensity measured along the b*-axis[147]. Two anomalies are found in the intensity at Q = 0.2956* and 0.41b*. b  The value Q = 0.416* in the reduced zone scheme is equivalent to 0.596* = 6* — 0.416* b  in the extended zone scheme. These two anomalies are usually called the 2k/ and the 4k/ anomalies, respectively. The 2k/ anomaly is observed below about 150 K and grows with decreasing temperatures. The 4k/ anomaly on the other hand, is already present at room temperature. Fig. 5.5 shows the dispersion relation of phonons measured by inelastic neutron scattering[148]. At 2k/, a clear Kohn anomaly is observed in the transverse acoustic phonon with wave vector along the b-axis and the polarization parallel to the c-axis. Satellites in the inelastic x-ray diffuse scattering were used to show the C D W phase transitions in the low-temperature insulator phase and precursor lines in the high-temperature metallic phase showed the one-dimensional fluctuations with wavevector 2kp. However, detailed knowledge of the nature of the fluctuations above the metal-insulator transition temperature, T , or the lattice modulation causing the C D W below T are difficult to obtain c  c  from inelastic x-ray scattering from T T F - T C N Q using conventional x-ray sources since the scattering is so weak. This led to a work in 1987 by Coppens et al. [149] in which they used intense synchrotron radiation to study the modulated phase at 15K. They found the  Chapter 5. Introduction and Results for TTF-TCNQ  116  Figure 5.4: Intensities of the diffuse x-ray scattering measured in a single crystal of TTF-TCNQ[147].  Chapter 5. Introduction and Results for  TTF-TCNQ  117  Figure 5.5: (Left), the Kohn anomaly observed by inelastic neutron scattering in T T F - T C N Q ; and (Right), dispersion relation of the longitudinal acoustic phonon measured by inelastic neutron scattering along the one-dimensional b-axis of TTF-TCNQ[148].  Chapter 5. Introduction and Results for TTF-TCNQ  118  largest modulation to be a slip of the T T F molecules in the direction of the long molecular axis of the molecule. The T C N Q translations were similar but smaller. Both molecules showed rotations about the long molecular axis, which agreed with infrared measurements by Bates, Eldridge and Bryce[175]. Subsequently Bouveret and Megtert [150] in 1989 used a conventional rotating-anode x-ray source and many hours of data collection to improve the structural determination of the lowest-temperature phase by including the possibility of low-frequency intramolecular distortions. They found that the T T F molecules displayed no significant distortions and, in agreement with Coppens et al. [149], mainly slid upon their mean molecular plane. With T C N Q , however, they found, on the contrary, a large out-ofplane intramolecular distortion which involves a substantial displacement of the quinoid ring perpendicular to the mean molecular plane. 5.3  Intramolecular Vibrations of T T F - T C N Q  The T T F and T C N Q molecules both have symmetry belonging to the point group D h • 2  Hence the number of normal modes and their associated symmetry species are given by TTCNQ = lOA + AB g  T  TTF  + 6B  lg  = 7A + 3B g  + 10B  2g  + 4B  lg  + 4A + 10B  3g  2g  + 7B  U  + 3A + 7B  3g  + 10B  lu  U  2u  + 7B  lu  + 6B  3u  + 4B  2u  3u  Now T T F and T C N Q being non-collinear molecules have 3 translational degrees of freedom, 3 rotational degrees of freedom and 54 vibrational degrees of freedom. Thus removing the normal modes of vibration due to pure translation and rotation gives {VrcNQUb = lOA  g  (r TF)vib  =  T  where A , Bi , B , B g  mode.  g  2g  3g  7A  g  + 3B  lg  + 2B  lg  + 5B  2g  + 3B  2g  + 9B  3g  + 6B  3g  + 4.4 + 9B U  + 3A + 6B U  are Raman active, Bi , B , B u  2u  lu  3u  lu  + 9B  2u  + 6B  2u  + bB  3u  + 3B  3u  are infrared active, and A is a silent u  Chapter 5. Introduction and Results for  119  TTF-TCNQ  In this thesis only the vibrational modes from the T C N Q molecules are observed. Fig. 5.6 shows examples of the normal modes of the T C N Q molecule belonging to each of the eight symmetry species.  5.4  Raman Scattering from TTF-TCNQ  The Raman spectra of T T F - T C N Q crystals were first reported by Kuzmany et al. [151] in 1977. They measured the unpolarized 77 K spectra of several samples of T T F - T C N Q crystals using exciting laser wavelengths between 4545 and 6764 A. There was considerable scatter in the position of the main Raman lines among the various samples, and thus a representative distribution of these lines was obtained by averaging their frequencies and intensities over several samples. A n assignment of the observed frequencies in the Raman spectra of T T F T C N Q to the intramolecular modes of T T F and T C N Q was presented in a later paper by Kuzmany et al. [152]. They also reported that strong resonant scattering was obtained when changing the exciting frequency from blue to red. In the same year the polarized 300 K and 77 K Raman spectra of T T F - T C N Q were reported by Temkin et al. [153]. They reported difficulty in obtaining their Raman spectra due to the fragility of the small crystals and the weak scattering observed. However their results were in good agreement with those of Kuzmany et al. [152], with many of the observed frequencies lying between those of the neutral and completely charged T T F and T C N Q molecules, supporting the idea of an incomplete charge transfer occuring in T T F - T C N Q . Kuzmany et al. [151, 152, 154] have also reported the instability of the Raman spectrum of T T F - T C N Q upon prolonged irradiation, with the appearance of a set of new lines, which were either observed next to (within 10 c m  - 1  of) a  stable line, or which exhibited a doublet structure. They also observed this instability in the Raman spectrum of T T F [154] and thus they attributed this instability to a photochemical process taking place in some of the T T F molecules which probably caused the T T F molecule to break up at the center C = C bond. The room temperature spectra of T T F - T C N Q were  Chapter 5. Introduction and Results for  A g-modes  K  a  2 N/fi °  X  7  TCNQ  K J c=c H  H  ^-N \  N  H  v (A )  X  1 0  v (B )  g  2 6  u 42  '£ £  120  TTF-TCNQ  V - / ^  H  H  .  l u  ^ >  N  r  e S3  \  H v  0)  +N  \ X  49 ( 3 g )  X /  H  V  B  4 0  X  H  V  (B ) 2u  H  H  Vl4 (A ) u  3  v i(B )  v (B )  Raman active  Infrared active  3  O  2 g  5 4  3 u  Figure 5.6: Examples of the normal modes belonging to each of the eight symmetry species A , Bi , B , B , A , B\ , B' and B . The top two panels show in-plane vibrational modes; The bottom two panels show out-of-plane vibrational modes. The gerade modes are Raman active and shown in the left panel. The ungerade modes (except for the A mode, which is Raman- and infrared-inactive) are infrared active and shown in the right panel. g  g  2g  3g  u  u  2u  3u  u  Chapter 5. Introduction and Results for  121  TTF-TCNQ  also reported by Matsuzaki et al. [155] in 1980. They were able to obtain reproducible spectra only under weak laser-irradiation. They made an assignment of the observed Raman lines to the A fundamental modes of the T T F and T C N Q molecules. Later in 1985 Matsuzaki et g  al. [156] reported the low temperature (liquid nitrogen and helium temperatures) polarized spectra of powder samples of T T F - T C N Q . They observed an increase in the intensity of the (A )^3 G  mode of the T T F molecule with decreasing temperature. Apart from this, they failed  to notice any dependence of the spectra on temperature. Thus so far, only three Raman studies of T T F - T C N Q have been reported, all of which employed visible lasers. In all three cases difficulties with the measurements were reported, especially under prolonged laser irradiation, presumably due to the photo-dissociation of the T T F molecule under these conditions. In particular a detailed Raman study of T T F T C N Q at low temperatures is absent. Thus under these conditions it seems a temperaturedependent Raman study of T T F - T C N Q , it's partially and fully deuterated analogues, would be highly motivated. The use of the infrared laser in the present study has eliminated the problems of thermal dissociation and shows strong resonance Raman effects with the T C N Q molecule. Furthermore many quasi-one-dimensional materials show unusual phenomena resulting from the electron-phonon interaction. It is well-known that a Peierls phase transition or charge(spin)-density-wave (CDW &; SDW) instability will occur below the three-dimensional ordering transition,T , in these materials because of the 2k 3D  F  distortion[140]. Recently  studies [157, 158, 159, 160, 161] have shown the importance of fluctuation effects of the C D W between the temperatures T  3D  and T\  (T  D  one-dimensional fluctuations start to occur). Ti  XD  D  is the temperature below which first  can be estimated from the relation 2A =  2>.52h TiD, the well-known BCS relation between the zero temperature C D W gap A and the B  transition temperature. A can usually be found from infrared or tunneling measurements below the metal-insulator transition temperature T  3F)  (see Section 5.4.4). Fluctuations play  a very important role in the dynamic properties such as the increase in both the d.c. [157]  Chapter 5. Introduction and Results for  TTF-TCNQ  122  Table 5.1: Phase diagram and 2k fluctuation regime of T T F - T C N Q and TSeF-TCNQ[142]. Upon lowering the temperature below Tic, first one-dimensional fluctuations start to occur; below T these change over to two- and three-dimensional fluctuations. T is the actual temperature of the Peierls transition, where three-dimensional ordering starts. F  2D  3D  Salts TTF-TCNQ TSeF-TCNQ  TD  TD  54 K 29 K  60 K 40 K  3  2  regime of 2k fluctuations above T* One dimensional fluctuations until 150 K Quasi-one-dimensional fluctuations until 250 K F  and frequency-dependent conductivity[158, 159, 160, 161]. In this thesis we show that the fluctuations are also able to affect the observed resonant Raman scattering from a C D W system. Table 5.1[142] shows the phase diagram and the 2k  F  fluctuation regime of T T F -  T C N Q and T S e F - T C N Q , an analogue of T T F - T C N Q in which the four sulfur atoms in T T F have been replaced with the much heavier selenium atoms . In this thesis we report a resonant Raman scattering study on T T F - T C N Q from room temperature down to 10 K . We observe many forbidden Raman lines due to usually-infraredactive intramolecular phonon modes. These are probably becoming Raman active through the Frohlich interaction[162]. These new low-temperature lines'persist in the fluctuation regime above T £> up to Ti . 3  D  We have been able to observe almost all of the T C N Q in-  tramolecular modes of vibration, both the Raman active and the infrared active. (None of the T T F modes are seen since it is not resonant with the infrared laser.) By far the strongest features are due to the out-of-plane T C N Q B  3u  modes, with the most intense one of these  being the low-frequency out-of-plane distortion of the quinoid ring. As mentioned already, this has been shown in a previous x-ray study[150] to be a strong component of the C D W distortion.  Chapter 5. Introduction and Results for TTF-TCNQ  123  25  C/3  -4—>  TTF-TCNQ  300 K  20  =3  TTF(d )-TCNQ(d )  i-H  4  s5l5  C  cd  .A.  I  - A .  TTF(h )-TCNQ(d )  C/3 CD  4  10  V  .  X ^.  £  i  I  8  II  TTF(d,)-TCNQ(h )  £  cd  TTF(h )-TCNQ(h )  100  300  500  700  1100  900  1300  1500  1700  W a v e Numbers (cm ) 4  Figure 5.7: Raman spectra of TTF(h )-TCNQ(h ), TTF(d )-TCNQ(h ), T T F ( h ) - T C N Q ( d ) a n d TTF(d )-TCNQ(d )between 100 and 1700 c m " at 293 K . Seven of the ten totally-symmetric (A ) modes of T C N Q , which are the room temperature Raman features, have been labeled ( i / — 4  4  4  1  4  4  4  9  3  4  4  Chapter 5. Introduction and Results for  5.4.1  TTF-TCNQ  124  Room-temperature Results  The room  temperature Raman spectra of  TTF(h )-TCNQ(h ), 4  4  TTF(d )-TCNQ(h ), 4  4  T T F ( h ) - T C N Q ( d ) , and TTF(d )-TCNQ(d )between 100 and 1700 c m " are shown in 1  4  4  4  4  Fig.5.7. The room temperature Raman features are due to seven of the ten totally-symmetric A  g  modes[163, 164, 165] of the T C N Q molecule, with which the N d : Y A G 1064 nm Raman  laser frequency is resonant. No features due to the T T F molecule are observed. v (A ) and x  "io  g  were not observed, and u (A ) is outside the frequency range shown. As can seen 2  g  from Fig.5.7 3 modes (u , is and u ) are shifted upon deuteration. We did not observe the 3  5  7  VQ (A ) mode from the deuterated T C N Q molecule. g  5.4.2  Low-temperature Results  The temperature dependence of the Raman spectra of T T F - T C N Q between 50 and 1650 cm  - 1  is shown in Fig.5.8. As we can see from Fig.5.8 new Raman lines appear and become  stronger with decreasing temperature. As expected, the low-temperature spectra of T T F ( d ) - T C N Q ( h ) and T T F ( d ) - T C N Q ( d ) 4  4  4  4  are identical to those of T T F ( h ) - T C N Q ( h ) and T T F ( h ) - T C N Q ( d ) , respectively, since no 4  4  4  4  T T F features are present (the Raman spectra of T T F ( d ) - T C N Q ( h ) a n d T T F ( d ) - T C N Q ( d ) a t 4  4  4  4  low temperatures are not shown in the thesis). Fig.5.9 shows the Raman spectra of  TTF(/i )-TCNQ(/i ) 4  4  and TTF(ft )-TCNQ(c/ ) be4  4  tween 50 and 1650 c m " at 10 K . The Raman lines of T T F ( h ) - T C N Q ( h ) have been assigned 1  4  4  and labeled by comparison with the data from Refs.[163, 166, 167]. The Raman lines, which have large deuterium-isotope frequency shifts, have also been labeled in the lower spectrum of T T F ( / i ) - T C N Q ( d ) in Fig.5.9. 4  4  Chapter 5. Introduction and Results for  125  TTF-TCNQ  2000 I II 1  1800 :  Hi 600 \  )v  50  , , , i ,  250  r r - i • -,- ,-r-r—r, r ; ' i — — ,  450  650  850  , i , , , , i , , , ,  1050  1250  1450  i  1650  W a v e Numbers (cm ) _1  Figure 5.8: Raman spectra of T T F - T C N Q between 50 and 1650 c m at temperatures 10, 60, 130 and 293 K . Seven of the ten totally-symmetric (A ) modes of T C N Q , which are the room temperature Raman features, have been labeled (v — u ). - 1  fl  3  9  Chapter 5. Introduction and Results for  126  TTF-TCNQ  1200  TTF-TCNQ 1 0 K TTF (h )-TCNQ(h ) TTF(h )-TCNQ(d )  I fj\  I!  \\  \|  2 8  V,  V n  27'! V  0 50  250  450  650  4  4  4  4  h  37  850  1050  1250  1450  1650  Wave Numbers (cm ) 4  Figure 5.9: Raman spectra of T T F ( h ) - T C N Q ( h ) a n d TTF(h )-TCNQ(d )between 50 and 1650 c m " at 10 K . The Raman lines of T T F ( h ) - T C N Q ( h ) have been assigned and labeled by comparison with the data from Ref. [163, 166, 167] The Raman lines, which have a large deuterium-isotope frequency shift, have also been labeled in the spectrum of T T F ( h ) - T C N Q ( d ) . The line at 86 c m right below u (B ) is an atmospheric line. 4  4  4  4  1  4  4  - 1  4  4  5i  3u  Chapter 5. Introduction and Results for  127  TTF-TCNQ  Table 5.2: Frequencies (cm ) and assignments of the out-of-plane vibrational modes of the T C N Q molecule in T T F - T C N Q at 10 K , by comparison with the room temperature data from Ref. [166] :  Symmetry  Bi  9  1S  U  "l6 "l5  B  2g  "31 "30 "29 "28 "27  B 3 u  "54 "53 "52 "51 "50  5.4.3  TTF-h TCNQ-h 4  TTF-h TCNQ-d  expt.  TCNQ-h Ref. [166]  Ref. [166]  4  4  4  4  U  U  Au  V  Au  186 469 804 297 412 567 706 991 125 236 489 589 840  179 466 631 294  7  3 173 3  169 428 816 300  8 4 178 9  558 655 804 122 232 426 571 734  9 51 187 3 4 63 18 106  593 752 1002 103 225 483 585 836  11 58 173 2 5 60 20 104  Assignments  With the aid of the measured deuterium-isotope frequency shifts, we were able to assign all of our measured Raman features in Tables 5.2 and 5.3. Some Raman lines have one or more shoulders, which have been fitted with several Lorentzians, from which we have determined the resonant frequencies.  It is straightforward to assign eight of the ten in-plane totally-  symmetric A vibrational modes which are the only Raman features at room temperature. g  The 10 K spectra contain several strong lines at low frequency with the strongest at 125 c m , - 1  the next at 236 c m at 589 and 840 c m  - 1  - 1  and a third at 489 c m . These three, along with two other weaker lines - 1  have been assigned to the out-of-plane B  3u  intramolecular vibrational  modes of T C N Q by comparison with the data in Refs.[163, 166]. We note that these strong B  3u  modes are usually infrared-active-only. Three Raman active B  3g  modes have median  Chapter 5. Introduction and Results for TTF-TCNQ  128  Table 5.3: Frequencies (cm ) and assignments of the in-plane vibrational modes of the T C N Q molecule in T T F - T C N Q at 10 K, by comparison with the room temperature data from Ref. [163] x  Symmetry  "8  u  7  "6 "5 "4 "3 "2  "44 "43  Blu  "25 "24 "23 "22 "21 "20  "19  B  2 u  "39 "38 "37 "36 "35 "34  TTF-h TCNQ-h  TTF-h TCNQ-d  expt.  TCNQ-h Ref. [163]  Av  V  4  4  4  4  4  V  V  347 621 726 964 1204 1420 1608 2212 1180 1336 1395 550 607 1015 1070 1511 1548 1582 2185  347 620 702  0 1 24  875 1416 1574 2212 979 1318 1390 542 597 869 1043 1380 1507 1541 2185 308 515 847 1292 1334 1441 1461  329 4 34 0 201 18 5 8 10 146 27 131 41 41 0 0 2 270 34 30 14 21  308 517 1117 1226 1364 1455 1482  Ref. [163] Av  337 613 725 978 1196 1391 1615 2206 1183* 1326* 1398* 541 600 987 1008 1361 1504  0 1 24 8 325 2 34 0 227* 18* 7* 13 -2 161 34 139 43  2181 301 498 1125 1210 1358 1540  2 2 2 270 29 38 30  • Data measured at 77 K from Ref. [167]  Chapter 5. Introduction and Results for  129  TTF-TCNQ  intensity. They are assigned by comparison with the Raman spectra of R b T C N Q measured at 77 K[167]. The assignment of these three modes in this paper is different from theirs. The other smaller features at low frequencies in Fig.5.9 are assigned to out-of-plane vibrational modes of the T C N Q molecule, with B  and B  l p  2g  symmetry[166]. We assign the weaker  features mostly in the middle frequency range of Fig.5.9 to the usually infrared-active-only Biu and B  modes of the T C N Q molecule[163]. We are unsure of the assignments of the v  2u  ( B ) and f lu  20  34  ( B ) modes from the deuterium-isotope frequency shifts. The lowest Raman 2u  peak has a frequency of 63 c m , which is the same as that of the longitudinal acoustic - 1  phonon observed by neutron scattering[148]. 5.4.4  Discussion  We will now discuss the following issues raised by the results: (i) the fluctuation of the C D W at low temperatures, (ii) the appearance of the Raman scattering originating from the infrared-active-only modes, (iii) the out-of-plane distortion of the T C N Q molecule in the C D W phase, (iv) the condensation of the longitudinal acoustic phonon. Infrared measurements[168, 169, 170] have determined a low-temperature gap of approximately 290 c m , which starts to develop in the temperature range T D < T < T , as - 1  3  iD  a result of fluctuations, and leads to a strong reduction of the spectral intensity near the Fermi edge. From the relation 2A = 3.52k TiD, TID is calculated to be 120 K . Upon lowerB  ing the temperature below TID, one-dimensional fluctuations start to occur first, which then change over to two and three-dimensional fluctuations until T D, the actual temperature of 3  the Peierls transition. Fig. 5.10 shows the integrated intensities of the lines assigned to v  54  and u  53  (B ) modes, 3u  the two strongest Raman lines at 10 K , as a function of temperature. One can see that v is 53  still present at 130 K and v  54  at 170 K . The fluctuating C D W produces the lines as well as  the three-dimensionally ordered C D W . The temperature limit around 150 K would seem to correspond to the 2kp diffuse x-ray and neutron scattering, rather than the 4kp scattering,  Chapter 5. Introduction and Results for  35  TTF-TCNQ  i  |  i  i  i  i  |  i  i  i  i  |  i  i  i  i  |  i  i  i  i  |  i  i  i  i  30 C/3  TTF-TCNQ  G  * 25  cd  20  '  v  54  •  V  5 3  (B ) (B )  .  3u  3u  \  <u 15  \  §10  B «  •  •  5 0  )  0  20  .  40  .  .  .  (  .  60  .  .  i  80  i  100  • 120  140  160  ,  ,  • : , ,  180  Temperature (K) Figure 5.10: The integrated intensity of the Raman lines assigned to V^A(B modes as a function of temperature. The lines are guides for the eye.  )  3U  and ^53(-B  3  Chapter 5. Introduction and Results for  TTF-TCNQ  131  1416  ^1415 i  B  o o 1414 C  TTF-TCNQ  £ 1413 C cd cd  1411  v.4 ( Ag'J ^ v (A) D v  1412  •  0  50  3  100  150  >  200  250  300'  Temperature (K) Figure 5.11: Raman frequency o{y (A ) lines are guides for the eye. 3  g  and v^Ag) modes as a function of temperature.The  Chapter 5. Introduction and Results for  132  TTF-TCNQ  since Kagoshime£ al. [147] and Pouget et al.[146] found that the 4k  F  still clearly visible at room temperature whereas that due to the 2k  x-ray scattering was  scattering disappeared  F  around 150 K , as shown in Fig. 5.4. The new lines also cover the temperature range in which the dc conductivity is enhanced by the fluctuating C D W . [157] The T  ljD  inferred from  the infrared measurements is slightly lower than the value measured here and from the 2k  F  x-ray measurements. The temperature dependences of the frequencies of the two strongest totally-symmetric A  g  modes are shown in Fig. 5.11. Within the accuracy of the data there is no indication  from Fig. 5.10 and Fig. 5.11 of the phase transitions at 54, 49 or 38 K . In Figs. 5.8 and 5.9, we observe many new Raman lines from usually infrared-active-only modes, below T\£>. The Frohlich electron-phonon interaction below 7\r> induces the C D W fluctuation. It is natural to consider the Frohlich interaction to be the cause of the additional lines. Forbidden Raman scattering by infrared-active-only L O phonons has been observed for many materials[171, 172, 173]. This scattering does not follow the selection rules for zone-origin phonons. The scattering efficiency is modified due to electro-optic coupling: the LO-phonons are accompanied by a longitudinal field which modulates Raman susceptibility X through the first-order electro-optic effect. The longitudinal polarization can be written in terms of the normal coordinate £[162]: p=  ^  ^exp ^ l  R  ULOt)  +«f e x p - ' * - ^ ) l ( 9  o t )  (5.1)  where e is dielectric constant, V and \i are the volume and effect mass of the unit cell, c  respectively. This polarization produces a longitudinal field of magnitude which, in turn, produces a potential. This potential is actually the electron-phonon interaction Hamiltonian  H i - he e  P  The exponential factors in Equation 5.1 take care of momentum and energy conservation in the scattering process. The Hamiltonian H i ^ h e  e  P  can be written in second-quantied notation  Chapter 5. Introduction and Results for  TTF-TCNQ  133  by making the substitutions:  and introducing the electron creation and annihilation operators c and c: +  H ele  = ^ ( 6 + + b_ )ct_ c V- l  (5.2)  l 2  ph  q  q  k  where the Frohlich constant Cp is given by  The divergant nature of the Equation 5.2 is the source of the anomalies we want to discuss. The forbidden L O scattering may arise from the intra-band matrix elements of the Frohlich electron-phonon interaction if the dependence of these matrix elements on the phonon wavevector q is taken into account. The matrix elements[162] between the electronic states 1 and j such that kj = ki — q are: <n + l,j\H _ \n,l>=C [-^+ ele  ph  F  <J\j^\ > (! -^/)] l  where k, p are the photon wavevector and momentum, respectively. <  > $ji is the  nonvanishing term of the lowest order when there is a center of inversion and describes first-order intra-band scattering of L O phonons.  Because it is zero for q=0 this term is  often referred to as dipole "forbidden". Under a resonance condition, however, this term can become considerable even for the small q imparted to the phonon by the incident laser in a first-order process. A number of facts support the Frohlich model: (i) the strong electron-phonon interaction developed below Ti , (ii) the presence of a center of inversion in T T F - T C N Q (iii) the D  N d : Y A G laser is resonant with the T C N Q molecule, (iv) the resonance enhancement of the forbidden Raman lines makes them stronger than the allowed phonons, (v) the frequencies of three of the B  3 u  modes observed here are higher than the frequencies measured by Bozio and  Chapter 5. Introduction and Results for  134  TTF-TCNQ  Pecile[174] in powders of T T F - T C N Q at 23 K by infrared absorption. The latter of course are the transverse optic(TO) frequencies, which are necessarily lower than the longitudinal optic(LO) frequencies involved in the Frohlich mechanism. Bozio and Pecile report frequencies of 834, 575 and 477 c m 589, and 489 c m  - 1  - 1  for u , i / , and u 50  5 1  respectively, whereas we measure 840,  52  (see Table I), a good indication that they are L O modes. f , however, 53  is not as clear. We measure only 236 c m  - 1  here, whereas Bozio and Pecile report 237 c m  and an earlier infrared paper by Bates et al. reported 240 c m  - 1  for both polarizations[175].  (Furthermore the assignment was confirmed by the correct 4 c m fortunately in neither Ref. [174] or Ref. [175] was u  - 1  - 1  isotope shift[175]). Un-  observed, or any more ungerade T C N Q  5i  modes. From Fig. 5.9 and table 5.2, we can see that the low frequency out-of-plane vibrational modes are much stronger than other modes.  V5A(B ), 3U  which is the assignment of the most  intense line at 125 c m , is the out-of-plane bend of the quinoid ring and is the lowest - 1  frequency B  3U  mode. This is shown in Fig.5.6 on page 120. v (B ), 53  3U  the second strongest  line at 236 c m , is the out-of-plane bend-of the quinoid wing of the T C N Q molecule. Thus - 1  there is a large out-of-plane distortion of the T C N Q molecule in the C D W phase below TID, which is consistent with the x-ray result[150] (see page 118). As shown in Fig. 5.5, the Peierls distortion in T T F - T C N Q is accompanied by the condensation of a transverse acoustic (TA) phonon[148] which is not observed here since it has a frequency below 50 c m , which is in the range removed by our Raleigh line filter. The neu- 1  tron scattering study[148] revealed that the 2k p satellites arising from the condensation of the longitudinal part of the 2k anomaly correspond to the same modulation of the lattice as F  the 2kp satellites originating from the condensation of the 2kp transverse acoustic anomaly. The longitudinal acoustic (LA) phonon is observed to be at 63 c m  - 1  at temperatures between  60 and 150 K.[148] We also observe a Raman line at 63 c m . The temperature dependence - 1  of this line is shown in Fig. 5.12. We can see that the intensity goes down as the temperature goes up. The line disappears around 150 K . This temperature dependence of the intensity  Chapter 5. Introduction and Results for  TTF-TCNQ  135  140 ^120  TTF-TCNQ  CZ)  -(->  •rH  c 3  cd  - o . -  100 80  05  §  60  §  40  A  42K 60K 90K 11 OK 150K  cd 20  0 50  55  60  65  70  Wave Numbers (cm )  75  _1  Figure 5.12: Temperature dependence of the Raman scattering from T T F - T C N Q at 63 c m . - 1  Chapter 5. Introduction and Results for  136  TTF-TCNQ  H  H  ^Se  X  H  TSeF  Figure 5.13: The TSeF molecules enables us to consider this mode to be the L A phonon observed by neutron scattering. 5.4.5  TSeF-TCNQ  In this thesis, some work has also been done on a sample of TSeF-TCNQ, an analogue of T T F - T C N Q in which the four sulfur atoms in T T F have been replaced with the much heavier selenium atoms. Fig. 5.13 shows the structure of the TSeF molecule. The crystal structure of TSeF-TCNQ is essentially the same as that of T T F - T C N Q . A t low temperatures, TSeFT C N Q shows a phase transition at 29 K[176], which was assumed to be due to the C D W condensation on the TSeF stacks. The possibility of a much weaker C D W occuring on the T C N Q stacks exists but has not been confirmed yet. Far fewer experimental studies have been performed on T S e F - T C N Q than on T T F - T C N Q . In fact, to the best of the author's knowledge, no Raman studies of TSeF-TCNQ have been previously reported and the only noteworthy infrared study of TSeF-TCNQ is a far-infrared study by Bates, Eldridge and Bryce [175]. They used a bolometric technique to measure the polarized low-temperature  Chapter 5. Introduction and Results for  137  TTF-TCNQ  03 > •rH  G rO rH  CZ3  G G cd  a cd  0  250  500  750  1000  1250  1500  1750  2000  2250  W a v e Numbers (cm ) _1  Figure 5.14: The resonant Raman spectrum from a powdered sample of TSeF-TCNQ in K B r , at 10 K . Eight of the ten totally-symmetric A modes have been labeled (i/ — "9). Two new lines have been assigned to B modes (u and ^54). g  3u  53  2  Chapter 5. Introduction and Results for  TTF-TCNQ  138  infrared spectra of T S e F - T C N Q (as well as those of natural and partially and fully deuterated T T F - T C N Q ) . The intense features in the spectra of T S e F - T C N Q were very similar to those of T T F - T C N Q but considerably reduced in wavenumber. This should be expected for the vibrational mode as the molecular weight of TSeF (392g) is almost double that of T T F (204g). A n assignment of the observed spectral features was made, based on the predicted wavenumber shifts and the visual similarity of the T S e F - T C N Q and T T F - T C N Q spectra. Fig. 5.14 shows the Raman spectrum of T S e F - T C N Q at 10 K . The room-temperature spectrum is virtually identical to the room-temperature spectrum of T T F - T C N Q shown in Fig.  5.7. But on cooling to 10 K there is no comparably dramatic effect.  Nevertheless  the medium-strength feature at 133 c m a n d the weak feature at 237 c m c a n probably be _1  _1  assigned to u 4(B ) and ^ ( 5 ) , respectively. This means that in T S e F - T C N Q the C D W 5  3u  5 3  3 u  on the T C N Q chain is very small. (Alternatively it could mean that the C D W does not involve out-of-plane distortions.) A small contribution from the T C N Q chains to the C D W is in agreement with previous suggestions that in T S e F - T C N Q the C D W is mostly confined to the TSeF chain, leading to the one strong observed transition at 29 K [176]. (A recent measurement [177] of the specific heat of TSeF-TCNQ found another smaller anomaly at 33 K, which could be due to the T C N Q chains.) Diffuse x-ray scattering from TSeF-TCNQ measured by Yamaji et al. [178] have shown that the C D W involved a shift of the TSeF molecules in a direction nearly parallel to their mean molecular planes. The large scattering factor of the massive selenium atoms made it hard to observe any scattering contribution from the T C N Q molecules. A n infrared analysis of T S e F - T C N Q by Bates, Eldridge and Bryce [175] has also indicated that the predominant contribution to the C D W came from the TSeF molecules.  Chapter 5. Introduction and Results for  5.5  TTF-TCNQ  139  Summary  We have studied the Raman spectra of T T F - T C N Q at room temperature down to 10 K . The N d : Y A G laser is resonant with the T C N Q molecule. Many new lines appear at temperatures below Ti£>=150 K as the fluctuating C D W occurs. The intensity of these lines increases with decreasing temperature. We have assigned the new lines according to the deuterium-isotope frequency shifts. In the fluctuating C D W phase the Frohlich electron-phonon interaction is the probable cause of the appearance of Raman-forbidden scattering originating from the infrared-active-only modes. The strong out-of-plane vibrational Raman modes correspond to the large out-of-plane distortion of the T C N Q molecule, which is in agreement with the x-ray results. The above mentioned new lines are much weaker in T S e F - T C N Q . This may indicate that the C D W on the T C N Q chain is very small. Also the Raman spectroscopy is shown here to be a power tool to study a charge-density-wave system and the electron-phonon interaction if the laser is resonant with the material.  Chapter 6 Introduction and Results for L a C u 0 2  6.1  4  and L a i . g S r o . i C u C ^  General Structure and Vibrational Mode Analysis of the Perovskite-like Superconductors  From a structural point of view the various high-T superconductors are quite similar. They c  are either exactly tetragonal or slightly distorted into orthorhombic symmetry. For many purposes the structure of the superconductor can be treated in an approximately tetragonal symmetry. Then, a 45° rotation of the idealized tetragonal unit cell with respect to the crystallographic axes has to be taken into account in the diagonally-distorted structures. Structurally, the different high-T materials are closely related, which will, in turn, facilitate c  the normal-mode analysis. Several types of calculations have appeared to estimate theoretically the eigenfrequencies and eigenvectors. These calculations have been useful both to give insight into various structural aspects of these superconductors and to help assign modes of equal symmetry to particular atomic displacements. These calculations can be classified into three major types. Force-constant methods assume massless springs between the atoms and attempt to reproduce the observed spectra by adjusting spring constants for best agreement with experiment[179, 180, 181]. The trouble with this method is that a large number of parameters has to be adjusted, which requires a certain knowledge or assumptions about available experimental spectra. Furthermore, the same spring constants are usually not applicable to different crystal structures involving similar bonds, as in the cuprate superconductors. A significantly improved and generalized approach to the lattice dynamics of high-T  140  c  Chapter 6. Introduction and Results for La CuC>4 and Lai. Sro.iCu0 2  9  141  4  materials has been brought forward by shell-model calculations[182, 183, 184, 185]. The polarizability of electronic shells around the ions is taken into account in the calculation. Spring constants are replaced by so-called Born-Mayer potentials. The potential parameters, while still determined empirically, are taken from other well-understood substances. Thus this approach reduces the arbitrariness in the calculations considerably and has a certain amount of predictive power. Also, since knowledge about the entire BriUouin zone is contained in the calculations, they can be used to reproduce the phonon density-of-states as measured with neutron scattering[182, 186] and related thermodynamic properties such as the specific heat[187]. Furthermore, within one superconductor family the potentials can be set to be the same. Entirely without parameterization are ab initio total-energy calculations in the localdensity approximation[188]. Results reported for the phonon frequencies of La2Cu04[189] and YBa Cu3O [190, 191] agree well with experiment. 2  7  La2Cu04 is the substance which first led to a high-temperature superconductor[192]. Bednorz and Muller obtained a "possible" transition temperature, as determined by the onset of the drop-off in resistivity at 35 K , by doping La2Cu04 with Ba. For many experiments, is still used as the prototype of the high-T superconductor in spite of its now  La2CuO"4  c  relatively low T . c  It has a comparatively simple structure of single CuC>2 layers and only  seven atoms per formula unit. La CuO"4 becomes a superconductor by either replacing some 2  of the L a  3 +  ions with cations such as Sr and Ba, which have 2 valence, as in La2_3;Sr Cu04 +  x  and La2_ Ba Cu04, or by intercalating excess oxygen into interstitial sites to create holes 3;  :r  in the C u - 0 planes. The crystal structure of L a C u 0 4 is orthorhombic at room temperature 2  and tetragonal above about 515 K [193, 194]. The transition temperature depends on the oxygen deficiency. It also decreases with the increase of B a and Sr concentration x. At x=0.07 the transition temperature is about 300 K . The K N i F - l i k e structure of L a C u 0 is shown in the idealized tetragonal form in Fig.6.1. 2  4  2  4  The complete CuCVoctahedra are easily recognized. The body-centered character of the  Chapter 6. Introduction and Results for La CuC>4 and L a i . S r . i C u O 2  9  0  4  142  Figure 6.1: The structure of tetragonal L a C u 0 . A t the structural transition to the orthorhombic phase the copper-oxygen octahedra undergo a tilt as indicated by the arrows. Also shown is the centered character of the crystallographic unit cell (dashed arrow). 2  4  Chapter 6. Introduction and Results for L a C u 0 4 and Lai.9Sr .iCuO 2  0  143  4  crystallographic unit cell is indicated by the dashed arrow. The crystallographic space groups are IA/mmm  and Abma (D\l)  (DH)  for the tetragonal and the orthorhombic structure,  respectively. The group-theoretical analysis of the eigenmodes yields [195, 196, 197, 198] 2 A + 2 E Raman-active and 3 A + 4 E „ infrared-active modes and one B l p  5  2u  2 u  silent mode for  the tetragonal phase. The larger, orthorhombic phase has 5 A + 3 B i - t - 6 B + 4 B 9  active modes, 6 B i + 4 B + 7 B u  2 u  3 u  g  2s  Raman-  3s  infrared-active and 4 A silent modes. Fig. 6.2 shows the U  normal modes of La Cu04 (assuming D± symmetry) and their calculated frequencies[181]. 2  6.2  h  Raman Scattering-Previous Results  Several Raman scattering studies of L a C u 0 , L a _ S r C u 0 4 and L a C u 0 2  4  2  I  a;  2  4 + x  , using visible  exciting lasers, have been reported[195-204]. For non-superconducting L a C u 0 the general 2  4  findings are as follows. For the case when the incident laser electric field is polarized along the crystal c axis of La CuC>4 no unusual scattering is observed. Instead, at temperatures 2  below the tetragonal-orthorhombic phase transition, the scattering from the five A modes a  expected for the orthorhombic structure is observed. A t low temperatures these are at 126, 156, 229, 273, and 426 c m  - 1  [198]. In Fig.6.3 we show the Raman spectra of L a C u 0 2  4  as  reported recently by Udagawa et al. [199]. The polarizations of incident and scattered field in the figure are parallel to the z-direction. We want to point out the strong mode at 126 cm  - 1  (the lowest-energy mode) in the orthorhombic phase of La Cu04 is a soft mode, which 2  has disappeared in the tetragonal high-temperature phase. It is apparently one of the A  9  modes generated by the distortion. Weber et al. [196] have shown that this mode is the classical soft mode, whose frequency tends to zero at the phase transition temperature. We mention here the known assignments of the other modes of L a C u 0 for complete2  ness. The mode at 426 c m  - 1  4  in Fig.6.3 is due to A motion of the apical oxygens and is 9  present in both the orthorhombic and tetragonal structure. Characteristic for all high-T  c  superconductors is the strong Raman polarizability for vibrations involving displacements in  Chapter 6. Introduction and Results for La CuC>4 and  Lai, Sr ,iCuO  2  9  0  144  4  i  0  G-  O  CD  -  o  o  -O  e (b^g  431 cm  1  g  -l  246 cm  228 cm  1  79 cm  1  1 C)  O-  M> 2u 353 cm A  -l  469 cm  0, -  o  (J) 2u ^215 cm A  t  1  6  B  2u 284 cm-l  CD  0  -  0 u 662 cm E  1  a  o  -  o  0  355 cm  1  Figure 6.2: Normal modes of La2Cu04 (assuming frequencies[181].  220 cm  1  116 cm-l  symmetry) and their calculated  Chapter 6. Introduction and Results for La Cu04 a n d Lai.gSro.iCu0 2  T  0  La Cu0  i  200  2  1  4  4  145  r  400  600  ENERGY SHIFT(cm- ) 1  Figure 6.3: The temperature dependence of (c,c) spectra in L a C u 0 . Above 510 K the crystal has tetragonal symmetry[199]. 2  4  Chapter 6. Introduction and Results for La Cu04 and L a . S r o . i C u 0 2  1  the c-direction (see Fig. 6.1). The modes at 156 and 273 c m  - 1  9  4  146  occur only in the orthorhombic  system. These two Raman peaks become weaker and disappear when approaching the phase transition. They have A symmetry and should be two of the additional modes generated g  by the distortion. At 229 c m  - 1  in the spectrum of La Cu04 we find a second tetragonal 2  A mode. It is assigned to the L a z-vibration and is Raman active in both tetragonal and g  orthorhombic La CuC>4. 2  For the case when the electric field of the incident laser photon is polarized in the conducting ab plane of L a C u 0 2  4  crystal, a broad two-magnon peak[204, 205, 206, 207] is ob-  served centered around 3200 c m  - 1  as shown in Fig 6.4 (The same phenomenon has been  observed in YBa Cu3Oe[204, 208] as also shown in Fig. 6.4.) The peak is asymmetric with 2  a long tail at higher energies. Remarkably it has been demonstrated even for superconducting compositions that two-magnon Raman scattering exists, although with a reduced peak intensity[205, 209]. Many theories have been developed to explain the anomalous broad two-magnon Raman line shapes in the high-T cuprates. The standard Loudon-Fleury theory[210] within a spin c  wave formalism by Parkinson [211] was examined again by several groups[212, 213, 214, 215, 216]. These theories were successful in obtaining the superexchange constant J s=:1400 K , which is in good agreement with that obtained from neutron scattering measurements[217, 218]. However the total line shape given by the theories is still in rather poor agreement with the experimental line shape as seen from Fig. 6.5. Singh et al.[207] evaluated the first three frequency moments and cumulants of the line shape, which provided a quantitative, parameter-free check on the theoretical prediction for the effect of quantum fluctuations in the system, which are believed to give an important contribution to the linewidth[207]. The importance of resonance phenomena was emphasized in the triple resonance theory[213, 214, 215]. These theories have successfully explained the dependence of the two-magnon peak intensity on the incoming photon frequency, which was one of the key experimental puzzles as shown in Fig.6.6[203, 219]. Chubukov et al. [213, 214, 215] have demonstrated that a  Chapter 6. Introduction and Results for La Cu04 2  5  and  La\. Sr ,iCuOi 9  Q  147  Lo CuO^  id  2  Y(X.X)Y RT  3'6  0 1 7 3 PHOTOU ENEROY (»V>  2A1eV  196eV 200  1000 2000 RAMAN SHIFT  3000 (cm ')  4000  -  YBa Cu 0 2  3  6  Z(X,X)2  = 2.54eV x1/2 2.41 eV xl/2  i  i  i  i  i  i  ...  1.96eV  J 200  i  1000 2000 RAMAN SHIFT  4000  3000 (cm ) -1  Figure 6.4: (Top), two-magnon Raman spectra of L a C u 0 observed at room temperature for the (x,x) configuration with excitation photon energies between 1.96 and 2.54 ev; the insert shows the optical conductivity spectrum for polarization along the x direction. (Below), two-magnon Raman spectra of Y B a C u 0 observed at room temperature with excitation photon energies at 1.96, 2.41 and 2.54 ev; the insert shows the optical conductivity spectrum for polarization along the x direction[204]. 2  2  3  6  4  Figure 6.5: Theoretical fitting (a quantum Monte Carlo method) of the experimental spectrum (bold curve) of La Cu0 [216]. The almost indistinguishable solid and dashed curves are for a 10x10 and a 16x16 lattice, respectively. 2  4  Chapter 6. Introduction and Results for La^CuO^ and Lai.g&ro.iCuC^  149  maximum of two-magnon Raman scattering appears when the photon has an energy equal to 2A+3J, which is in agreement with the experimental results[203, 219] (see Fig.6.6). At lower energies is found a series of strong resonant two-phonon features as shown in Fig. 6.7. The dependence of the strength of two-phonon scattering on the incoming laser energy has already been shown in Fig. 6.6. As we can see that the intensity of the twophonon scattering is strongly dependent on the frequency of the incident laser photon, and is a maximum when this photon energy is close to the charge-transfer gap 2A (2.0 eV) [201, 204] (Same phenomena have also been observed in Y B a C u 0 ) . 2  3  6  At still lower energies are found broad single-phonon features, which have been identified as originating from Raman-forbidden (infrared-active) modes of vibration. These appear to be the longitudinal optic (LO) modes, rather than the transverse optic (TO) modes, and furthermore not to be restricted to the q=0 Brillouin zone origin, as is usual for momentumconserving one-phonon Raman scattering, but to come instead either from the zone boundary or across the entire Brillouin zone. The signal-to-noise ratio in some of these one-phonon Raman spectra has been poor. Various explanations have been forwarded to explain this one-phonon scattering. Concerning the anomalous one-phonon scattering for E parallel to the ab plane, Heyen, Kircher and Cardona [220] also observed similar features in the insulator Y B a C u 0 6 - They 2  3  assigned four of their forbidden peaks to L O phonons of E symmetry. The intensity of the u  features was strongly dependent on the frequency of the incident laser, with the strongest at the lowest frequency of 1.8 eV. They suggested that the mechanism is the Frohlich interaction [226] and presented a detailed discussion of the arguments supporting this suggestion.  6.3  Raman Scattering-Present Results  To our knowledge no Raman study of L a C u 0 has been performed using an infrared laser 2  4  with an energy far less than that of the usual visible lasers. It was of interest to observe  Chapter 6. Introduction and Results for La Cu04 and Lai. Sro.iCu0 2  9  150  4  2-magnon 2-phonon m  c 3 3  co  CC  1  1  Energy (eV) Figure 6.6: The strength of the two-magnon and the higher frequency two-phonon scattering as a function of incoming photon energy for Y B a C u 0 . Also shown is the imaginary part of dielectric function e . The two-phonon scattering is very strong when the incoming photon is close to the charge-transfer gap 2A, while the two-magnon scattering vanishes there and instead has a maximum when the photon has an energy equal to 2A+3J [219]. The same phenomena have also been observed in La CuO [203]. 2  2  2  4  3  6  Chapter 6. Introduction and Results for L a C u C > 4 and L a i . S r o . i C u 0 2  i  i  9  i  i  i  i  151  4  1 —  200 400 6 0 0 800 1000 1200 1400 R A M A N SHIFT ( c m " ' )  YBa Cu 0, 2  3  2(X,X)Z  i  200  i i i i_l £00 600 800 1000 1200 WOO RAMAN SHIFT (cm"') i  1  Figure 6.7: Two-phonon scatering as a function of incoming photon energy for La Cu04 and YBa Cu O [204]. 2  2  3  6  Chapter 6. Introduction and Results for La Cu04 and Lai.gSro.iCuC^  152  2  the resonance effects of this laser on the three separate regions of the E parallel to the ab plane spectra, and to use the high signal-to-noise ratio in the one-phonon region to compare with the phonon dispersion curves, measured by inelastic neutron scattering. The L a C u 0 4 2  crystal was prepared at Bell Laboratories. After annealing in A r gas, the crystal had a Neel temperature T^r = 315 K , close to the accepted value of T  N  = 320 K for the stoichiometric  compound. We also investigated samples of L a 2 _ S r C u 0 4 and L a C u 0 4 . The crystals x  x  2  +;r  of La _: Sr. Cu04 were prepared by spontaneous crystallization from a CuO flux at the 2  r  c  University of Osnabriick [221]. The L a C u 0 4 2  + x  crystal was prepared by heating the single  crystal of L a C u 0 4 under 20 bar of pure oxygen at 600 °C for 24 hours. The value of x is 2  about 0.004. We have performed Raman measurements at low temperatures on five L a 2 _ S r C u 0 4 x  x  crystals (x=0, 0.05, 0.075, 0.10, 0.16), with an infrared laser. In only one crystal, which had a nominal value of x = 0.1 and a suppressed T of 12 K , was there found a strong and c  narrow Raman peak at 3419 c m  - 1  below 40 K . The integrated Raman intensity of this narrow  peak increases with decreasing temperature and persists at 2 K . This result is interpreted in terms of two-magnon Raman scattering from a spin-ordered phase. For comparison we also investigated another crystal with x=0.1 but with a regular T = 27 K . This latter crystal c  was borrowed from Simon Fraser University (it was made in Japan). The Raman measurements were made on the interior surface of the crystals exposed by mechanical fracture and repeated on the polished surfaces of the crystals. A l l crystals are (001) platelets with z perpendicular to the C u - 0 planes. The crystals have a twinned structure and therefore it was not possible to perform exact polarization measurements in the ab plane. However we did measurements with scattered photons polarized either parallel (xx) or perpendicular (xy) to the incident photons for the crystal with a nominal value of x=0.1 (T = 12 K ) , where x and y denote two arbitrary but mutually perpendicular c  directions in the (001) plane. We also measured the spectrum with ei\\x (where x is an arbitrary direction) and unpolarized scattered light. The relation of the integrated Raman  Chapter 6. Introduction and Results for La CuC>4 and Lai.gSro.iCuC^  153  2  intensities of these three configurations is: / ;:7 :/ || =l:1.04:3.36. We learned from the xa  X2/  ei  x  above relation that the main symmetries of the strong and narrow peak around 3400 c m were Bi +B g  assuming  2g  small. The B  2g  crystal symmetry. The contribution of A\  g  - 1  symmetry is very  contribution is also expected to be small. Measurements with ej||c-axis could  not be performed as the crystal thickness in the c-direction was only 0.4 mm which was too small for proper beam focusing.  6.3.1  Room Temperature Data Using an Infrared Laser: One-phonon Scattering  Figure 6.8 shows the polarized room-temperature Raman spectra below 1600 c m  - 1  with  the incident laser either parallel or perpendicular to the ab ( C u 0 ) planes. For the (cc) 2  polarization (lower scan), the spectrum is identical to that seen in the visible-laser studies [198,  199, 200, 202], which have been shown in Fig.6.3, and shows 5 peaks at 105, 155,  227, 269 and 426 c m . The soft mode has decreased in frequency at 300K to 105 c m , - 1  from 126 c m  - 1  - 1  at 30 K [198]. These 5 peaks are due to the expected A modes in the D g  2h  orthorhombic structure. In the E / / ab polarization, first of all we report that the two-phonon scattering above 800 c m  - 1  is very weak in Fig. 6.8 (upper trace). This scattering is usually very strong in the  Raman spectra obtained with visible-laser excitation due to the electronic resonance. This is because the infrared laser frequency of 9394 c m cm  - 1  - 1  is below the charge-transfer gap of 16,100  ( 2.0 eV ) [204] and so the intensity of the two-phonon scattering will be very weak.  We observe instead for E / / ab very strong one-phonon scattering with broad peaks, as shown in the upper trace of Fig. 6.8, where they have been labeled. In Fig. 6.9 we have reproduced some phonon dispersion curves of La CuC>4 measured by inelastic neutron 2  scattering for different directions. The left (££0) figure shows the branches for the roomtemperature orthorhombic phase, measured by Pintschovius [222], while the middle figure shows the same (££0) branches for the high-temperature tetragonal phase, measured at 580  Chapter 6. Introduction and Results for La CuC>4 and Lai. Sr .iCuO4 2  9  154  0  Room Temperature  5 6 7  693  —La Cu0 E//ab plane -La CuQ (c,c) 2  4  2  4  1141  227  0  200  "•••v.~/:J-:'i:-\S  400  600  800  ,  •j--'*  A  1428  ,.y.....7-V-^^^  V  '-  V  ^-"'  1  1000 1200 1400 1600  Raman Shift (cm' ) 1  Figure 6.8: Raman spectra of L a C u 0 for two polarizations, E / / a b (upper trace) and E / / c (lower trace) of the infrared laser light, with A=1064 nm, at room temperature. The laser power is 100 mW. 2  4  Chapter 6. Introduction and Results for La Cu04 sjid Lai.gSro.iCuC^  155  2  K also by Pintschovius et al. [223]. The right figure shows the branches along (00£) also for the tetragonal phase, taken from Chaplot et al. [224]. We are not aware of the corresponding data for the orthorhombic phase. Our one-phonon peak frequencies have been added to Fig. 6.9 as crosses. Although we measured the room-temperature Raman spectrum, our data agree slightly better with the tetragonal curves than with the orthorhombic. Considering the middle (££0) figure, seven branches are presented. Two of these are transverse-optic (TO) A modes, and have been 9  so labeled. Our (c,c) data of 426 c m  - 1  and 227 c m  agree with these curves at the zone  - 1  origin, as expected for normal Raman scattering. (The 227 c m  - 1  data point does not sit  on a phonon curve in the orthorhombic case.) The remaining five branches are longitudinal and of  symmetry, with the lowest being longitudinal acoustic, L A , and the upper four  longitudinal optic, L O . (The transverse optic, T O , branches of the E„ modes may be found in Ref. [224].) Our one-phonon E / / ab broad-peak values of 169, 300, 487 and 693 c m "  1  are seen to lie on each of these E L O branches, as has been previously noted, but at points u  close to half-way across the Brillouin zone. Another observation is the indication from the right-hand column in Fig. 6.9 that there is also coupling to three of the A  2 u  L O branches in  the (00£) direction. This was not observed in Y B a C u 0 6 by Heyen et al. [220]. 2  3  Support for these assignments may be found from previous infrared measurements and analyses, as listed in Table 6.1. Our one-phonon E / / ab peak frequencies are listed, along with the L O and T O frequencies and symmetry of the fitted infrared spectral features from S. Koval et al. [185], F. Gervais et al. [225] and M . Mosteller et al. [184]. It may be seen that, apart from some ambiguity over the assignment of the 396 c m  - 1  feature, the overall  agreement is very good. (The atomic displacements in the normal modes of the tetragonal structure have been shown in Fig. 6.2.) For a non-resonant case, the Raman scattering is restricted to q=0 phonon for a perfect crysatl. For a resonant case, the q=0 restriction can be lifted. In Y B a C u 0 , Heyen et 2  3  6  al. [220] have also explained the forbidden one-phonon scattering in terms of the Frohlich  Chapter 6. Introduction and Results for L a C u 0 4 and Lai.gSro.iCuC^  156  2  5?o  go  ooc  Figure 6.9: Phonon dispersion curves of La Cu04 measured by inelastic neutron scattering [222, 2 2 3 , 224] in the room-temperature orthorhombic phase (left panel) and high-temperature tetragonal phase (middle and right panels). The A modes are transverse optic ( T O ) . The others are longitudinal optic ( L O ) , except for the low L A modes. Our peak-frequency data are indicated by crosses. The zone origin data correspond to the A modes observed in the (cc) spectrum of Fig. 6.8. The remainder are from the E / / ab spectrum of Fig. 6.8. The positions of two lower energy A modes in the right panel are arbitrary. 2  9  g  2 U  Chapter 6. Introduction and Results for La CuOi 2  and Lai.gSro.iCuC^  157  Table 6.1: Frequencies in c m of the observed Raman peaks in La2Cu04 at room temperature for E / / a b , compared with the calculated transverse and longitudinal optic (TO and L O respectively) modes from infrared (IR) measurements. - 1  Raman (this work) 169 300 396 461 487 567 693  IR (Ref.[185]) U>LO ^TO sym. 168 98 E 260 168 E„ u  229 330 480 673  460 461 566 692  A E A E„  2 u  IR (Ref.[225]) U>LO ^TO sym. 162 183 E« 250 220 E„ 390 363 E„ 463 320 A 2 u  IR (Ref.[184]) UJLO ^TO Y s  =  m  300 360 498  148 342 234  E„ A„ A  535 689  516 669  A  2  2 u  u  2 u  574 683  501 671  A  2 u  2 u  interaction by considering a contribution from a finite q (which is the same mechanism as used to explain the T T F - T C N Q results of Chapter 5) and given detailed and convincing arguments to support their interpretation. We wish to make just a few further observations. Hamilton[226] demonstrated in 1969 that forbidden L O scattering may arise from the intraband matrix elements of the Frohlich electron-phonon interaction if the dependence of these matrix elements on the phonon wave vector is considered. It was shown that the Raman efficiency is proportional to q (Eq.(4) in Ref. [220]), as well as several other factors, where q 2  is the phonon wave vector. This q dependence, along with the high density-of-states, would tend to push the peaks of the broad one-phonon features towards the zone-boundaries of the phonon branches. Our data, however, seem to lie approximately half-way across the zones rather than at the boundary (see Fig. 6.9). (The neutron data for the tetragonal structure was taken at 580 K , which would soften the phonons compared to room-temperature, but the orthorhombic data is at room-temperature). We suggest, therefore, that the data are kept closer to the zone origin because of the wavevector conservation, in which for backscattering geometry q~2nk^, where k  L  is the laser wavevector. k  L  for an infrared laser is of course  very small. The reason that we see any significant departure at all from the zone origin may  Chapter 6. Introduction and Results for La Cu04 and Lai.gSro.iCuC^  158  2  therefore be due to strongly scattering crystal imperfections, as argued by Heyen et al. [220] to explain the independence of their results on the direction of k^. Some explanation is also necessary for our observation of L O modes of A  symmetry, i.e.  2 u  with q parallel to the c axis of the crystal ( z direction ), since these were not observed in Y B a C u 0 6 by Heyen et al. [220], even with the laser wavevector in the z direction, which 2  3  should lead to the observation of such A  2 u  phonons. They attributed their zero intensity  to the vanishing zz component of the inverse mass tensor. In our data, on the other hand, the 567 c m  - 1  peak attributed to an A  2 u  phonon is the strongest feature in our spectrum.  Previous Raman studies of L a C u 0 4 with visible lasers [198, 200, 203, 204] have not seen 2  a feature at 567 c m . They have seen a weak feature ranging in energy from 505 c m - 1  - 1  up to 530 c m . Of interest are the data of Yoshida et al. [203, 204], which show a 505 - 1  cm  - 1  feature using a 1.96 eV laser, with the frequency increasing to 530 c m " using a 2.4 eV 1  laser. Clearly the intensity and frequency of these one-phonon features are very dependent on the particular electronic transition resonant with the laser, which affects the inverse mass tensors. It is also essential to note that there is strong coupling of the c-axis phonons to the a-b plane in high-Tc superconductors, as reported by Reedyk and Timusk[227]. Finally we should mention the remaining observations which support the Frohlich mechanism. Firstly there is no effect in the (cc) polarization, because of a lack of structure in the zz dielectric function [220]. Secondly, the resonance produces an intensity of the forbidden one-phonon peaks greater than that of the allowed A Raman peaks (for E / / a b ) . Thirdly, g  the one-phonon mechanism is clearly different from the two-phonon mechanism, as indicated by the clear cut-off between the top of the one-phonon spectrum near 700 c m  - 1  and the  beginning of the weak two-phonon scattering. This two-phonon scattering is very strong in visible-laser Raman spectra. Finally in metallic materials in which the E phonons are u  shielded and the charge-transfer resonance does not exist any more, the effect is no longer observed, or is much weaker. In Fig. 6.10 we show the room-temperature Raman spectra of Lai. Sr .iCuO4 and La Cu04.oo4, as an example of the weak or absent one-phonon scattering. 9  0  2  Chapter 6. Introduction and Results for La CuC>4 and L a i . S r . i C u O 2  °0  200  400  9  0  159  4  600 800 1000 1200 1400 1600 Raman Shift (cm ) 4  Figure 6.10: Raman spectra of L a C u 0 , Lai. Sr .iCuO4, and L a C u O . 0 4 , at room temperature and with the laser polarization E / / ab. The laser power is 100 mW. The vertical lines are guides to the eye. 2  4  9  0  2  4  0  Chapter 6. Introduction and Results for La CuC>4 and Lai.gSro.iCuC^  160  2  35  30  CO  E//ab plane  =*25 cd  '20  CO  §15  §10 cd  La Cu0 2  5  0  0  500  4  L  1000  1500  « I . 9  2000  S  t  O ,  C  u  ° 4 -  2500  3000  3500  4000  Raman Shift (cm ) 4  Figure 6.11: Raman spectra of La . Sr .iCuO4 at 2 K and L a C u 0 4 at 8 K between 100 and 4000 c m . The laser power is 6 mW. 1  9  0  2  - 1  These compounds have a (cc) spectrum (not shown), identical to that of the stoichiometric La Cu04 compound. 2  6.3.2  Temperature Dependent Data Using an Infrared Laser:  Two-magnon  Scattering Fig. 6.11 shows Raman spectra of Lai. Sr .iCuO4 at 2 K and L a C u 0 at 8 K between 100. 9  0  2  4  and 4000 c m . However, we did not observe any magnetic scattering around 3200 c m in - 1  - 1  Chapter 6. Introduction and Results for La Cu04 and Lai.gSro.iCuC^  161  2  L a C u 0 as observed by other groups[205, 206, 207]. This is due to our low laser frequency 2  4  of 9394 c m  - 1  (1.16 eV) which is far below the charge transfer gap of 2.0 eV[228]. There-  fore, as has been observed previously[204, 208, 219] (see Fig. 6.6) and explained by a triple resonance theory[213, 214] two-magnon Raman scattering from L a C u 0 4 will be very weak 2  when using our infrared laser. In Sr-doped L a C u 0 4 , on the other hand, one expects con2  siderable spectral weight of charge transfer excitations at the laser energy of 1.16 eV [228]. Therefore, if any magnetic order exists in Sr-doped L a C u 0 4 we would expect to observe 2  the magnetic Raman scattering in our experiment. temperature-dependent  Indeed we did observe very-strongly  Raman scattering around 3400 c m f o r the crystal with the nom_1  inal Sr-concentration of x=0.1 and a reduced T = 12 K . This is shown in Figs. 6.11 and c  6.1-2. The very strong and sharp peak centered at 3419 c m linewidth of 250 c m  - 1  in Fig.6.12 has a very narrow  - 1  (T =8 K , F W H M ) and is much more symmetric than the two-magnon  scattering from L a C u 0 4 , which has a broad Raman feature covering from 2000 c m 2  - 1  to over  7000 c m [206, 207]. The line in Fig. 6.12 has an energy too high to be phonon scattering. - 1  Luminescence as a possible origin of the peak can clearly be excluded. Luminescence has no such temperature dependence and infrared reflectivity measurements on the same crystal showed no absorption around 6000 cm"" which is the energy for the luminescence in question 1  (9394 c m  - 1  Raman excitation minus 3400 c m  - 1  Raman shift). Photoluminescence is also  very unlikely with our infrared laser. In order to understand the origin of the strong feature around 3400 c m , let's firstly - 1  examine the phase diagram of L a _ ( S r , B a ) C u 0 4 system, especially the interplay between 2  x  x  magnetism and superconductivity. The parent compound La CuC»4 of the high-temperature 2  superconductors L a _ B a C u C > 4 and L a _ S r C u C > 4 is an insulating 5 = 1/2 antiferromagnet 2  x  x  2  x  x  with the spins localized on Cu atoms within single C u 0 planes. Upon increasing the dopant 2  x above 0.06 the magnetic order disappears and these compounds become superconductors.  162  Chapter 6. Introduction and Results for La Cu04 and Lai.gSro.iCuC^ 2  2400  2800  3200  Raman  3600  4000  Shift (cm ) 4  Figure 6.12: Low temperature Raman spectra from magnetic excitations in Lai.gSro.iCuG^ (T — 12 K ) . The polarization is ei\\x (x is an arbitrary direction). The laser power is 6 mW. The insert shows an enlarged view of the weak peak around 2770 c m . The spectra vary strongly with temperature and are much narrower than the two-magnon scattering around 3200 c m in the parent compound La CuO4[206]. c  - 1  - 1  2  Chapter 6. Introduction and Results for La2CuC>4 and Lai. Sr .iCuO4 9  163  0  However, at x around 0.12 the superconductivity is suppressed and magnetic ordering reemerges[229, 230, 231]. Fig.6.13 shows the suppression of the superconductivity in a very narrow range near x=0.115 in La _ Sr Cu04[231]. Several methods have been applied to 2  study this phenomenon.  :r  x  Among these, N M R and N Q R measurements on the Sr-doped  compounds demonstrate magnetic order below 32 K for x = 0.115 with the Cu-spin moments being in the CuO"2 plane perpendicular to the c-axis[232, 233]. The internal magnetic field and the magnetic ordering temperature reach their maximum values at the Sr-concentration around which the superconducting transition temperature T is most suppressed. c  Most  recently, elastic neutron scattering has also established static long-range magnetic order in Lai. Sr .i2CuO4 isotropically in the CuC>2 plane[234, 235]. It seems that the appearance of 88  0  the strong feature around 3400 c m i s related to the magnetic ordering in the system. A _1  study of doping, T and temperature dependences of the strong peak might solve this puzzle. c  We have studied the Raman scattering from the crystals with the nominal Sr-concentration of x=0.05, 0.075 and 0.16 at low temperatures own to 8 K . But we did not observe any comparable peak at all. This might be due to the fact that the magnetic order reemerges only in a very narrow range of Sr-concentration as suggested by Fig. 6.13[231]. The other crystal with the same nominal Sr-concentration of x=0.1 but with a regular T of 27 K , by contrast, c  showed only a very broad and weak feature around 2000 c m  - 1  similar to that reported on  the same crystal by Naeini et al. [236]. Without further exact polarization measurements, the assignment of the strong and narrow peak to the two-magnon scattering cannot be supported by the polarization selection rules.  Our assumption of magnetic order is, however, strongly supported by several re-  ports on the temperature dependence of the magnetic order in L a _ S r C u 0 with x around 2  x  x  4  0.11[232, 233, 234, 235]. Most notably, according to neutron scattering and N M R / N Q R results [232, 233, 235], the strongly suppressed T = 12 K of the crystal with x?«0.1 indicates c  long range magnetic order.  Chapter 6. Introduction and Results for La Cu0 2  4  and L a i . g & o . i C u 0  164  4  Figure 6.13: Sr doping dependence of superconducting transition temperature, T , in La2-xSr Cu0 . Closed triangle for x=0.115 shows the disappearance of the bulk SC down to the lowest temperature[231]. c  x  4  Chapter 6. Introduction and Results for La Cu04 and Lai. Sr .iCuO4 2  9  165  0  Phase separation in striped phases has been proposed to explain the suppression of the superconductivity and the concomitant appearance of magnetic order[237] (A model for the stripe order of holes and spins is shown in Fig.6.14). This became obvious especially in superconducting Lai. Ndo.4Sr .i2Cu04 by neutron scattering and //SR experiments[238, 48  0  239]. In the stripe phase, the doped holes are concentrated in domain walls separating antiferromagnetic antiphase domains. It may be seen that in Fig.6.12 there is a very weak and broad feature centered at 2770 cm . - 1  The intensity of this feature has a similar temperature dependence to that of the  main peak. A similar double-peak structure has been found for the two-magnon excitations in the insulating compound Lai. 7Sr .33NiO4[240, 241]. In this compound it was possible 6  0  to investigate a spin/charge ordered "stripe" phase by magnetic Raman scattering, where the different peak energies have been assigned to magnetic bonds with a different number of magnetic nearest neighbours in the Ni04 plane. Stripe phases of separated charge and spin have also been observed by Raman scattering in the insulating nickelate homologue La2Ni04 j[242]. A spatial modulation of spin and charge density in the CU-O2 planes has +(  been suggested to be related to the mechanism of superconductivity in phase-separation models[243]. The best evidence for stripes in L a 2 _ S r C u 0 4 comes from neutron scattering x  x  measurement[235, 237]. Below 40 K , therefore, our sample may also be in a stripe phase. The peak intensity of the feature around 3400 c m is obtained by integrating the spectra - 1  and by averaging the results with and without the background. As shown in Fig.6.15 the intensity strongly decreases with increasing temperature up to 40 K where it merges into the background. This behavior is substantially different from that observed in La2Cu04 where no appreciable temperature variation of the magnetic scattering was observed for 0 < T < 300 K[206, 207]. Furthermore Fig.6.15 demonstrates a striking similarity of our data with the temperature dependence of the magnetic peak intensity of elastic incommensurate neutron scattering of Lai. 8Sro.i2Cu0 [235]. As was done for the neutron scattering results, we also 8  4  conclude for our sample an antiferromagnetic ordering temperature around T <2 = 40 K . or  Chapter 6. Introduction and Results for La Cu04 and La . Sr .iCuO4 2  1  9  166  0  Figure 6.14: (Left), Model for the stripe order of holes and spins within a C u 0 plane at n =l/8. Only the Cu sites are presented. A n arrow indicates the presence of a magnetic moment; shading of arrowheads distinguishes antiphase domains. A filled circle denotes the presence of one dopant-induced hole centered on a Cu site (hole weight is actually on oxygen neighbors). A uniform hole density along the stripes is assumed. (Right), Sketch showing relative orientation of stripe patterns in neighboring planes of the tetragonal phase[238]. 2  h  Chapter 6. Introduction and Results for L a C u 0 4 and Lai.gSro.iCuC^ 2  167  T ( K )  Figure 6.15: The temperature dependence of the integrated Raman intensity of the peak at 3419 c m of Lai. Sr .iCuO4 (T =12 K ) is compared with the temperature dependence of the intensity of the elastic incommensurate magnetic peak of Lai.ssSro.^CuO^ obtained from neutron scattering[235]. The solid line guides the eyes. - 1  9  0  c  Chapter 6. Introduction and Results for La Cu04 and Lai.gSr ,\Cu0 2  Additional evidence for this value of T  ord  0  168  4  comes from N M R where for x=0.11 and x=0.12  magnetic order has also been reported to establish below 45 K [232, 234]. The peak is still seen at T = 2 K , below T , suggesting a local coexistence of superconductivity and c  magnetism in the same sample volume as has been seen in Lai.4 Ndo.4Sro.i5Cu0 [238, 239] 5  4  and also in La _ Sr Cu04[244]. 2  x  x  Fig.6.16 provides further evidence of the magnetic origin of this peak. Figures6.16 (a) and 6.16 (b) demonstrate the similarity in temperature dependence of the frequency co and linewidth T with those of the two-magnon peak in other isostructural two-dimensional antiferromagnets K NiF [245] and La NiO . [242]. Unlike three-dimensional systems such as 2  4  2  4  02  KNiF3, for which data[245] are also shown for comparison in Fig.6.16, two dimensional systems have a small magnon energy renormalization with temperature. The linewidths are also clearly distinguishable. The magnon damping grows much more slowly in the 2-D system, than in the 3-D system.  6.3.3  Theoretical Fits to Two-magnon Scattering  In this section we will discuss how the spectra may be understood by the theories of twomagnon Raman scattering. The magnetic interactions in the C u 0 planes can be described 2  by a Heisenberg Hamiltonian of a two-dimensional square lattice (neglecting the weak interlayer coupling), H = J Z l < i j > S i • Sj, where Si is the spin-1/2 operator at site i and the summation is over nearest-neighbour Cu spins. Within this description of the C u 0  2  layers, the standard theory of Raman scattering is based on the Loudon-Fleury (LF) coupling between the light and the spin system[210]. The coupling is obtained in second order perturbation theory with virtual states containing one doubly occupied site, and is given by HlF  (Bin  =  • 0-ij)(E  out  • Gij)Sij  (6.1)  <i,j>  where E  in  and E  out  are the polarization vectors of the incoming and scattered light and  is  the unit vector connecting sites i and j . The scattering process involves a photon stimulated  1^1  c  0.0  0.2  0.4  0.6 T7T  0.8  1.0  1.2  ord  Figure 6.16: (a) Normalized peak frequency UJ/OJQ and (b) normalized line width r / r as a function of normalized temperature. The results of our sample of Lai.gSro.iCuO^ (T =12 K , T d—4Q K ) are compared with the results of three antiferromagnets, the three-dimensional system K N i F (T =246 K ) [245] and the two-dimensional systems K N i F (T =97 K ) [245] and La NiO .02 (T =185 K ) [242]. The lines are guides for the eye. 0  c  or  3  2  ord  4  2  ord  4  ord  Chapter 6. Introduction and Results for La Cu04 and Lai.gSro.iCuC^  170  2  '  CO 1  w w -q Figure 6.17: T h e real-space picture of the two-magnon scattering. Dashed lines denote photons, and wavy lines denote spin waves. T h i s picture is valid away from resonance[214]. v i r t u a l charge-transfer excitation that exchanges two spins[214], as illustrated in Fig.6.17. In terms of the eigenstates {|n)} of the Heisenberg model, the frequency dependence of the scattering intensity at inverse temperature /? is given by the Fermi golden rule: 7  M  = \ Eexp(-/3£ ) £  | < n\H \m  m  > \ 5(co - (E 2  LF  n  - E )) m  (6.2)  T h e R a m a n spectrum can be computed in the spin-wave approximation where the LoudonFleury operator is expressed as a quadratic form in terms of the spin-wave operators. In the B  g  geometry, the m a t r i x element is thus .  r \  j-,-  i•  < f\H \i  c  o  s  k — cos ky x  >=  LF  (6.3)  where jk is defined as 7fc = \  e  x  P  i  k  '8  5 as a sum over the Z nearest neighbors of the site at the origin. In the case of square lattice, z  7/c = (cos k + cos k )/2. x  y  Chapter 6. Introduction and Results for La2Cu0  and  4  Lai, Sr ,iCuO 9  0  171  4  The Raman intensity obtained from the Fermi's golden rule, Equation 6.2, then is: J  (  u  )  a  E  ( c o s ^ c ^ ^ _ 1  k  2  n  i  )  ]  (  6  4  )  7fc  where Cl = AJS^X — 7 | is the frequency of the magnon. This expression exhibits a dik  vergence at LO = 8JS since the density of states diverges at the boundary of the magnetic BriUouin zone. It is known that this result is strongly modified when one takes into account the magnonmagnon interactions in the final state. The final expression for the Raman intensity is given by  with 8JS R  {  U  )  =  1^^  ^  (cosA; - cos k )  2  x  y  .-2Q  f c  *  +  '  g  ( 6  -  6 )  In the thermodynamic limit, Eq.6.6 for S = l / 2 leads to a narrow two-magnori peak around w=2.78J. In the above calculation the magnon-magnon interactions have been included only in the final two-magnon states. The main effect of interactions in the ground state is to renormalize the spin-wave velocity: C —>• Z C, leading to a profile peaked at co = 2.78 • Z J[211, 212, C  p  C  214, 216]. We use an averaged value of 1.172 for Z from various calculations[212, 246, 247]. c  For T = 8 K we obtained a peak frequency of w =3419 c m . Thus we get J = 1056 c m - 1  - 1  p  (1519 K ) . This value is in very good agreement with the results of E P R measurements of the same crystal of Lai.9Sr .iCuO [248], in which a value J E P R = 1500 K was used to fit the 0  4  temperature dependence of the E P R (/-factor, which reflects the interaction of three-spin polarons with their surrounding Cu-spin system. The associated Raman spectrum has been first calculated by Parkinson[211]. For the traditional two-dimensional antiferromagnets like K N i F 2  4  Parkinson's theory turned out to  be very successful in reproducing the experimental Raman line shape[245]. However, this  Chapter 6. Introduction and Results for La2CuOi and Lai.gSro.iCuC^  172  theory cannot reproduce the very broad peak-linewidth and the high-energy tail of the spectra generally observed in high-T cuprates. For these cuprates several theoretical approaches c  took into account higher order magnon excitations and specific characteristics in S = 1/2 systems like quantum fluctuations[207, 212, 214]. Chubukov and Frenkel carried out a spinwave expansion of the profile around its peak position by keeping S large and evaluated the results at S — 1/2. They obtained the following formula for the Raman intensity of the B  l f f  mode[214] (From equation (A9) of Ref. [214]. A n error in the denominator of the formula is corrected.): gyi-CT ln(l2  B l 9  where  w  — u>/(8Z JS). c  a  2 C T  )  l n ( l - w ) + TT (1 - (S + 1)VT^^) 2  2  2  2  (  )  The long dashed line in Fig.6.18 (labeled "Chubukov, Frenkel")  shows the result of fitting our 8 K data, by a least-square method with the above formula and the parameters, J and S.  We found J = 1511 K and S = 0.500024 from the best  fit. Obviously the Chubukov-Frenkel formula successfully gives a suitable superexchange constant and value for 5, but the line shape is obviously too broad. Canali and Girvin considered quantum fluctuations in Parkinson's spin wave theory[211, 212], including also four-magnon excitations, and obtained a line shape (labeled "Canali, Girvin" in Fig.6.18), which still looks too wide for the observed data. Numerical calculations of the B  l 9  Raman spectrum of the two-dimensional Heisenberg model were carried out  by Sandvik et al. within the Loudon-Fleury theory in the spin wave formalism[216]. The corresponding exact spin wave results provided a comparatively good fitting for our experimental data (see Fig.6.18, labeled "Sandvik et al. "). Although theoretically not predicted, a Gaussian fit best describes the spectrum with the least deviation as shown in Fig.6.18. Based on these fits and the fact that we observe quite narrow spectra with no highenergy tail, we believe that the main features of the spectrum are due to the standard Loudon-Fleury mechanism. Quantum fluctuations are not dominating the spectra. This can be seen as follows. According to Singh et al. [207] a calculation of the frequency moment and  Chapter 6. Introduction and Results for La Cu04 and Lai.gSro.iCuC^ 2  173  Figure 6.18: The Raman spectrum and its theoretical fittings. The solid curve is the experimental data at 8 K . The long-dashed curve is a fitting from the formula given by Chubukov and Frenkel in Ref. [214]. The dotted line is a fitting which includes quantum fluctuations in the ground state (Canali and Girvin's work[212]). The short-dashed line is an exact spin-wave result give by Sandvik et al. [216]. The long-short dashed curve is a Gaussian fitting which provided the values for to and T in Fig.6.16.  Chapter 6. Introduction  and Results for La Cu0 2  aad Lai.gSro.iCu0  4  174  4  the cumulant of the spectrum gives information about the peak symmetry and a parameterfree check on the quantum fluctuation effect. The n  t h  moment of the spectrum is defined as  [207, 212, 216] (at T =0): p = j-J oo I(cu)dco, where I n  n  T  = J I(u)du. For n > 1 (6.8)  T  holds with p\ — Mi. The first cumulant, M i , gives the mean value of the Raman frequency, while the second and third cumulants M and M measure the width and the asymmetry of 2  3  the line shape. Using the Raman data at 8 K , we obtain Mi = 3411 ± 4 c m , M = 121 ± 3 - 1  2  cm  - 1  and M = 62 ± 5 c m , where the uncertainties reflect whether or not the background - 1  3  is taken into account for the calculations. The ratios M / M i = 0 . 0 3 5 , M / M i = 0 . 0 1 8 are far 2  3  away from the values ( M / M i = 0 . 2 3 , M / M i = 0 . 2 6 )[207, 212] which were obtained including 2  3  quantum fluctuation effects and are also three times smaller than Parkinson's results for S = 1/2 ( M / M i = 0 . 1 0 7 , M /Mi=0.056)[211]. The smaller M and M values tell us that 2  3  2  3  the line width is small, the line shape is almost symmetrical, and therefore quantum fluctuation effects are very weak in our Lai.gSro.iCuO^ crystal. In La Cu04 quantum fluctuations 2  have been demonstrated to be the dominating contribution to the large two-magnon Raman linewidth[207]. 6.4  Summary  Firstly, the single-phonon Raman scattering in L a C u 0 2  4  is strongly resonant with the in-  frared laser parallel to the ab plane. We observe seven Raman-forbidden L O phonons, which appear to be activated by the Frohlich mechanism which is the same mechanism as used to explain the T T F - T C N Q results of Chapter 5. Good agreement is obtained between our peak frequencies and those of the L O modes measured by infrared reflectivity and inelastic neutron scattering. Three of the phonons appear to have A  2u  observed in the case of Y B a C u 0 6 2  3  symmetry, which was not  Chapter 6. Introduction and Results for La Cu04 and Lai.gSro.iCuC^ 2  175  Secondly, we observe strong magnetic Raman scattering in one crystal of Lai.gSro.iCuC^, which has a suppressed T of 12 K , due to an ordered spin phase below 40 K . A weak c  second peak indicates the possible existence of a spin ordered phase as reported for Raman scattering in the nickelates[240, 241]. In agreement with neutron scattering results[235] the Raman intensity of the intense peak increases with decreasing temperature below 40 K . The line shape and the temperature dependence of the magnetic scattering intensity are totally different from those observed in the parent compound La Cu04. The temperature 2  dependences of the peak frequency and damping, however, are similar to those of other twodimensional antiferromagnets. The line shape is fitted within the traditional Loudon-Fleury Raman theory of two-magnon scattering. The resulting superexchange constant is 1519 K , in accordance with EPR-measurements on the same compound[248]. Quantum fluctuation effects appear to be small.  Chapter 7 Overall Summary  This thesis investigates the behaviour of electrons, phonons and magnons in the organic conductors, organic superconductors and the high-T copper-oxide superconductors. Interest c  in T T F - T C N Q is driven mainly by the electron-phonon interaction induced charge-densitywave state and its unusual nature of the collective quasiparticle interactions. B E D T - T T F molecule based compounds are interesting because the electron-acceptors of the compounds can be systematically modified and the compounds cover the metallic, insulating and superconducting states (it is very unusual for such non-metallic compounds to become superconductors). Spin-fluctuations, long-range antiferromagnetic ordering, and electron-phonon interactions influence the properties of these materials. Interest in L a 2 _ S r C u 0 4 is driven x  x  by the interplay of the magnetism and superconductivity, and the magnon-magnon interactions in the spin ordered phase. A spatial modulation of spin and charge density in the CU-O2 planes is suggested in Lai.gSr .iCuO4. 0  Raman measurements provide information on electron-photon, electron-phonon, electronmagnon, phonon-magnon, and magnon-magnon interactions in these materials. The laser source is playing a key role in the measurements. For B E D T - T T F molecule based materials, because the infrared laser is resonant with the B E D T - T T F molecule, the Raman features of v and u modes are greatly enhanced by the electron-transitions (electron-photon 3  9  and electron-phonon interactions). The same electron-phonon interactions activate these normally-inactive modes in the infrared spectrum, and cause large frequency reductions in the infrared spectrum for these two modes because of the charge transfer which occurs between two neighbouring molecules vibrating out-of-phase. The superconductivity-induced  176  Chapter 7. Overall Summary  177  phonon frequency changes in K - ( B E D T - T T F ) C u ( N ( C N ) ) B r (T =11.6 K ) and a - ( B E D T 2  2  c  t  T T F ) l 3 (T =8 K ) are a result of electron-phonon interactions. The current theories can 2  c  not explain this experimental result. I think the resonance effect needs to be included in the theory to account for this effect. Phonon softening is also observed at temperatures where the spin-fluctuations are observed. This phonon softening is caused by phonon-magnon interactions, possibly, in a way similar to the electron-phonon interaction which causes the phonon softening in the infrared spectrum. For the T T F - T C N Q molecule, also because the laser is resonant with the T C N Q molecule, the g = 0 restriction is lifted. The electron-phonon interaction including a contribution from a finite q (Frohlich mechanism) successfuly explains why the infrared-active-only modes are observed in the Raman spectrum, and why these modes are stronger than the Raman-allowed modes. The same electron-phonon interactions drive the material into the charge-densitywave state. For lanthanum copper oxide materials, impurities can contribute a finite q to the scattering process, unrelated to the change in q between the incident and the scattered photon. As happened in T T F - T C N Q , the same Frohlich mechanism explains the activation of the infrared-active-only modes in the Raman spectrum of La CuO"4. Strong two-magnon scatter2  ing is observed in Lai. Sr .iCuO4 providing information, such as the superexchange constant, 9  0  on the magnon-magnon interactions in the spin ordered phase. 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