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Pulsed nuclear magnetic resonance in iron. Koster, Evert 1968

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PULSED NUCLEAR MAGNETIC RESONANCE IN IRON  by  EVERT KOSTER B . S c . , The U n i v e r s i t y of B r i t i s h Columbia,. 1966  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  i n the Department of Physics  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April,  1968  In  presenting  advanced  Library  agree  degree  shall  that  purposes  this  at  the  make  may  be  It  financial  gain  Department  University  for  granted  shall  by  not  be  of  British  f u l f i l m e n t of  British  available  the  that  Head  allowed  Columbia  for  of  my  the  of  this  Department  or  without  requirements  Columbia,  reference  copying  copying  of  Canada  of  extensive  is understood  University  V a n c o u v e r 8,  in p a r t i a l  i t freely  permission  tatives.  The  thesis  and  study.  thesis  or  publication  my  I agree  written  by  of  for  that  I  the  further  for  scholarly  his  represen-  this  thesis  permission.  an  for  ii  ABSTRACT  A pulsed N.M.R. spectrometer capable of operating over the frequency range 40 Mhz. to 100 Mhz. has been constructed.  It was used  to observe the nuclear resonance of F e ^ i n unenriched iron powder at 4.2°K. and 77°K..  Some preliminary experiments were performed and the  r e s u l t s of these experiments are in good agreement with other reported results.  This i n d i c a t e s that the spectrometer i s s u i t a b l e f o r use in future  experiments.  iii  TABLE OF CONTENTS  Page No. Abstract  i i  L i s t of I l l u s t r a t i o n s  iv  Acknowledgements  v  Chapter  -  I  Introduction  II  • -  N.M.R. in Ferromagnetic Materials  III  1 7  (i)  Hyperfine f i e l d s in Ferromagnets  7  (ii)  R.F. Enhancement in Ferromagnets  11  Experimental Procedure and Apparatus  15  Apparatus (i) (ii) (iii) (iv) (v) (vi) (vii) IV  The Pulsed O s c i l l a t o r  16  The Receiver  18  Sample C o i l  23'  Boxcar Integrator  26  Timing Apparatus  26  Samples  28  Dewar System  29  (a) Experimental Results  30  (b) Discussion of Results  35  (i) (ii) •Bibliography  Relaxation in Domain Walls  35  Relaxation in Domains  36 38  iv  LIST OF ILLUSTRATIONS  Figure  Page Ho.  1  B l o c k Diagram o f P u l s e d S p e c t r o m e t e r  17  2  Pulsed O s c i l i a t o r  19a  3  Narrowband P r e a m p l i f i e r  19b  4  Cascode I n p u t s t a g e and f i r s t Gain C o n t r o l l e d stage  21  5  Second Gain C o n t r o l l e d , O u t p u t , and D e t e c t o r  22  stages 6  Sample C o i l C i r c u i t  25  7  Boxcar I n t e g r a t o r  27  8  Longitudinal  Relaxation  of F e  Fe Powder a t  57 in Unenriched  31  in Unenriched  32  4.2°K. 57  9  10  Longitudinal  R e l a x a t i o n o f Fe  Fe Powder a t  77°K.  FID A m p l i t u d e  versus Frequency a t 77°K.  34  V  ACKNOWLEDGEMENTS  I wish for suggesting  to express my s i n c e r e g r a t i t u d e to Dr. B . G .  the w o r k , and f o r h i s  I-would l i k e  Turrell  guidance t h r o u g h o u t the work.  to thank D r . John Noble f o r  the h e l p f u l  discussions  on the equipment used i n t h i s work. I would.like.to  thank Mr. J . L e e s , g l a s s b l o w e r , f o r  making  the h e l i u m dev/ar used i n t h i s w o r k , and f o r making and s e a l i n g the g l a s s sample h o l d e r s . F i n a n c i a l a s s i s t a n c e p r o v i d e d by a Cominco S c h o l a r s h i p and a National  Research C o u n c i l S t u d e n t s h i p  gratefully  ackncv/ledged.  over the past two-years  is  also  1  CHAPTER I  INTRODUCTION  The Nuclear Magnetic Resonance (N.M.R.) technique has been established as a powerful tool f o r studying hyperfine i n t e r a c t i o n s i n a wide v a r i e t y of m a t e r i a l s .  Since the magnetic moments are of a r e l a t i v e l y  s m a l l magnitude the usefulness of the N.M.R. technique i s u s u a l l y l i m i t e d to those materials where there i s a r e l a t i v e l y high abundance of a c t i v e nuclei.  The technique i s e s p e c i a l l y u s e f u l f o r the study of hyperfine  interactions in s o l i d s .  The N.M.R. experiment y i e l d s important information  about the e l e c t r o n i c properties of s o l i d s and provides a r e a d i l y a c c e s s i b l e measurements of the properties of the hyperfine  interaction.  The experimental methods used in N.M.R. work may be divided into steady-state and pulse techniques.  The use of the steady-state technique  i s l i m i t e d p r i m a r i l y to narrow-1ine resonances and linewidth s t u d i e s .  An  advantage of the pulse technique i s that i t enables d i r e c t observation of the nuclear r e l a x a t i o n .  It i s e s p e c i a l l y useful f o r observation of broad-  l i n e resonances which are often d i f f i c u l t to observe using the steady-state technique. The aim of the work described in t h i s thesis was to construct a pulsed N.M.R. spectrometer with broadband c a p a b i l i t i e s to f a c i l i t a t e working over the range 40 Mhz. to 100 Mhz..  The spectrometer was tested by obser-  ving the nuclear resonance of F e ^ i n unenriched iron powder, and making some preliminary measurements.  2  A brief discussion of the principles of nuclear magnetism is now given. (For a complete discussion see Abragam^.) A nucleus with total angular momentum J/h, has associated with it a magnetic dipole moment /±,= tU\ where V* is the gyromagnetic ratio. t  The Zeeman interaction of the magnetic dipole moment  with  a magnetic field H_, is given by The energy eigenvalues £ corresponding to the eigenstates |m) of this m  Hami Tton'ian are aiven by where m denotes the eigenvalue of I , and z is the direction of the applied z  magnetic field H_.  ;  In thermal equilibrium the nuclear spin system can be described by the population densities of the energy levels E^, given by the Boltzman distribution function - ~/kT E  P  = —  (3)  where T denotes the lattice temperature, the lattice being the environment in which the nuclear spins are located. The net magnetization of a bulk sample containing N spins is then given by i i  M  3kT  ^  «  (4)  3  The behaviour of the magnetization M_ in the presence of a rotating r.f. field perpindicular to a static field H,is now discussed. If the interaction of the spins with their surroundings is neglected the equation of motion for M is which upon applying, the commutation relationships for the components of angular momentum becomes. Jf,(M"«.  (6)  This corresponds to the classical equation of motion of a magnetic moment _M in an applied field H_. The motion corresponds to an undamped precession of the magnetization M_ about the direction of the applied magnetic field with an angular velocity  M . If the applied field consists only of  a static field H_in the z direction then it is evident that M is time z  0  independent while the components M and My vary sinusoidally with time x  with a frequency  <^ -K H,. 0  H  is known as the Larmor frequency.  In order to solve (6) it is convenient to transform to a frame of reference rotating with angular velocity  with respect to the labora-  tory frame. In this rotating frame the equation of motion for M_ becomes , £ t " ett  using (6) this becomes  ~  M>frV f ]  (7)  If H_ is just the static field H_ along the z direction, then if we choose co = - )N H„ k  , where _k is a unit vector along the z direction, the mag-  netization is stationary in the rotating frame. In the laboratory frame it precesses about the field Hp at the Larmor frequency.  4  Suppose new.that the. total field H_ is the sun of a constant field Ho. and a field H_-j perpendicular to H_ and rotating about it with an angu0  lar velocity u>.  can be written ill l(j.cosu't + jsinwt )  (8)  =H  where-i_ and - j_ denote the unit vectors along the x and y axis respectively, of the laboratory frame. Taking Hj to lie along the unit vector J_' in the rotating frame, theequation of motion for M, in the rotating frame, becomes dt (9)  where  In the rotating frame , therefore, the magnetization precesses about an effective field  H_ ff G  When ly rfJ^>> M  with an angular velocity the effect of the r.f. field is negligible. The  N  effect of the r.f. field becomes appreciable when CJ^-^NK.. When <o--yH, N  M precesses about the direction j_ in the rotating frame with an angular velocity <^>, -  H, . This is the phenomenon of Nuclear Magnetic Resonance.  If the field H_-| is applied for a time r , then the magnetization would precess through an angle & - < ^ , r pulse, when o  = 7 r  ,  , when  =  the pulse is called a  , the pulse is called a 9 0 °  1 8 0 ° pulse.  In practice the sample is placed inside a coil which is part of an L-C circuit tuned to the resonance frequency. An r.f. voltage is applied to the coil producing a linearly polarized sinusoidal magnetic field inside the coil perpendicular to the static field kH . This oscil0  lating field can be decomposed into two counter-rotating components, one  5  with frequency  and the other with frequency-u. When the resonance  condition is satisfied for one component the other is 2^off resonance and its effect can be neglected. tion into the x,y plane.  The resonant component turns magnetiza-  Following the pulse the components of the magnet-  ization in the x,y plane precess about H_, with a frequency ^. and induce a voltage in the pick-up coil which is detected by the receiver. The preceeding.discussion has neglected relaxation effects. In any real system there are interactions capable of transferring energy from the excited spin system to the lattice, which allow the spin system to re-establish thermal equilibrium with the lattice.  The rate at-which  the spin system re-establishes equilibrium with the lattice is characterized by e spin-lattice relaxation time T-j. This 'longitudinal' spin-lattice relaxation time is determined essentially by the transverse components of the local fluctuating fields at the Larmor frequency .  Also present are inter-  actions among the spins themselves which tend to maintain thermal equilibrium within the spin system.  The rate at which these spin-spin interactions esta-  blish equilibrium within the spin system is characterized by a spin-spin relaxation.time T£. In many cases the approach to equilibrium can be described by 3  the phenomenological equations proposed by Dloch . JL tl  dt•  ,  , ,  " ~  '  - / MvH  —  M * i + M,i  —-  T  2  +  M -M. ,  ~A _l£ T;  The second and third terms represent relaxation effects.  (10)  In the abscence  of the r . f . field the solutions of this equation in the rotating reference frame may be written  t  M (ft = M > ) e ^ (11)  6  T-j and T  of  M  x  can.be determined experimentally  2  , M  y  , and M . z  by observing the time dependence  7  CHAPTER II  N.M.R.  IN.FERROMAGNETIC MATERIALS  (i) Hyperfine fields in Ferromagnets It has been found that in many magnetic materials there is, in the absence of an.applied magnetic field, a very large effective hyperfine field at the nucleus. The origins of these fields in ferromagnetic metals v/as first discussed by Marshall^. The most authoritative discussion of the subject is by Watson and Freeman '. Portis and Lindquist^ also discuss N.M.R. and hyperfine fields in ferromagnets. Atomic hyperfine fields arise from the interaction of the magnetic moment of the nucleus withthe electronic spin and orbital moments. Following Fermi^ and Fermi and Segre^, the Hamiltonian describing this interaction may be written  y Here  c  -  1  -  w  [  f  j  w  s  -  i  (  i  2  )  and J_ represent respectively, electron orbital, electron spin,  and nuclear spin angular momentum operators. y^y"* ?>ro the Bohr and Nuclear magnetons, and g and g are the electronic and nuclear spectroscopic splitx  ting factors. The delta function term is called the Fermi contact term and is non-zero only for those electrons which have a non-vanishing probability of being found at the nucleus, i.e. the s electrons. (12) may be written in the form X ->"«-iJ'« s  where  ( 1 3  )  is the nuclear magnetic moment, and Hgff is the total magnetic  field at the nucleus arisinc from the rest of the atom. The contribution  8  to lieff arising through the Fertr.i contact term may be written where  = 1^)1  is the electron density at the nucleus.  The hyperfir.e field may be written as HeU  > . where  =  tfs  + &  * ^  + H  u o c  is the field due to the s-electrons, H_ is-the field due to the u  orbital angular momentum of the 3-d electrons, H_ is the dipolar field, D  and  H_LOC  is the local field at the nucleus. The l-s,2-s,3-s, and 4-s electrons interact with the nucleus  through the Fermi contact term. It is convenient to consider separately (i.) the core s electrons and (ii) the 4-s electrons. (i) The core s electrons' wavefunction are distorted by the exchange potential associated with.their interaction with the up-spin 3-d electrons This interaction is spin dependent and tends to pull, out the up-spin electron wavefunctions. This leaves a net down-spin s electron density at the nucleus , i .e.  2-.  {\%(°)\-\X(o)\}±° This gives a negative contribution to the hyperfine field via the Fermi contact term. In iron this contribution has been estimated to be -300 to -500 Kilogauss^.  .  .  (ii) The exchange interaction of the 3-d electrons with the 4-s elec trons is similar to the core 3-d exchange interaction but in this case the up-spin wavefunctions are pulled in. There is then a net up-spin s electron density at the nucleus due to the 4-s electrons which gives a positive contribution. Any admixture of the d band electron wavefunctions and the 4-s band also gives a positive contribution* Anderson and Clogston^O, however, have suggested that any covalent mixing of the 4-s electrons into the unfilled down-spin 3-d band gives a positive contribution  9  which may possibly cancel the admixture contribution to the hyperfine field. The net conduction electron contribution is uncertain but is probably about +100 Kilogauss. The orbital contribution H_, arises from the residual orbital u  moments associated with the 3-d electrons. For most 3-d ferromagnetic metals the orbital momentum is almost completely quenched. However, some orbital angular momentum is unquenched by the spin-orbit interaction resulting in a positive contribution to the field at the nucleus given by  r  (15)  3  For iron <S> = 2.2, and 2-g = 0.1, and H is then ~3xl0 ' Kilogauss. /  r  L  In rare earth ferromagnets there is very little quenching of the orbital angular momentum and this contribution is dominant. The dipolar field H_ results from the dipolar interaction of the B  magnetic moments associated with the nucleus and the electrons. The Hamiltonian describing this interaction is  (16) Here JJ , and ji are the nuclear and electronic di pole moments respectively. H  e  Marshall^ has estimated the dipolar contribution in hexagonal cobalt to be ~+80 Kilogauss.  In body-centered cubic iron this contribution is,  of course, zero. The local magnetic field at the nucleus is given by 1  'LOC  o  3  10  w h e r e Hp i s  the  external  field,  -DM i s  ~r  the demagnetizing f i e l d ,  f••  3 the usual for  Lorentz f i e l d .  determining  by o b s e r v i n g  Although s m a l l ,  the s i g n of  the s h i f t  in  this  the hyperfine  contribution  field.  This  is  important  can be  determined  r e s o n a n c e f r e q u e n c y when an e x t e r n a l  field  is  applied. • 11 12 Using Mossbauer and N.M.R. t e c h n i q u e s the measured v a l u e 1 1  of  the  hyperfine In  the  field  in  iron  is  magnetic materials  H^ff  the  ~  -330 K i l o g a u s s .  strong  e l e c t r o n i c s p i n s , d e s c r i b e d by t h e  exchange i n t e r a c t i o n  between  Hamiltonian  K» = -.21-Tcj 5i-5-  .  tends  to  order  may r e s u l t  the s p i n s .  ing  is  favoured.  uniform total  ization 180°. the  With  a domain.  exist  the  effective  ordering  of  exchange i n t e g r a l  felt  positive gives  J .  ordering In  rise  the  the s p i n s  by a n u c l e u s i s permits  the e x t e r n a l l y  in  applied fields  magnet-  rotate  a ferromagnetic  perform  of  the  opposite  t h e same d i r e c t i o n  one t o  order-  t o domains  gradually  electronic spins in  ferro-  and a p a r a l l e l  Between domains of  i n which  magnetic ordering  the use of  is  the s p i n s  sample.  domain w a l l s of  or anti-parallel  a r r a n g e t h e m s e l v e s s o as t o m i n i m i z e  the b u l k  ordering  field  This  ment w i t h o u t tional  This  energy of  there  the  the.exchange integral  magnetization which  free  17  Either a parallel  d e p e n d i n g on t h e s i g n o f  magnetic materials  ( )..  J  through metal  throughout  the N.M.R.  necessary in  expericonven-  N.M.R. In  hyperfine a result  practice  f i e l d which of  this  there leads  is to  inhomogeneity  some i n h o m o g e n e i t y a scatter the  in  the  associated with  Larmor f r e q u e n c i e s .  nuclear resonance i s  i z e d b y an i n h o m o g e n i o u s l y b r o a d e n e d r e s o n a n c e l i n e .  usually  Friedel  the As  character-  and de R e n n e s ^  11  have discussed the contribution to the inhomogenecus broadening in multidomain conducting particles due to the demagnetizing fields near the surface of the sample. They concluded that in a material with a low anisotropy,energy, such as iron, the inhomogeneous broadening from this mechanism will be the order of the magnitude of the anisotropy field H_. In a  y  H  iron 2  *v 70 Khz., which is in reasonable accord with the observed •  Tf  width. Due to the scatter in Larmor frequencies contributions from nuclei in different parts of the sample will interfere destructively causing the precessing magnetization to decay a short time following a 90° pulse. As a result the voltage induced in the pick-up coil will also decay in a short time following the pulse. This decay is characterized by a relaxation time +i i i T , so that the effective transverse relaxation rate is ~r*'i^*\ • For a 2  Lorentzian line-shape this effective relaxation rate is directly proportional to the line width. For iron T is approximately 20 microseconds. 2  In the spin-echo experiment^, the 180° pulse applied at a time r  after the 90° pulse, turns the precessing nuclei through 180° about the  x axis of the rotating frame. At a further time 2'f , the nuclei rephase and a signal maximum results which is called a spin-echo. The widths of the free induction decay and the spin-echo (which is essentially two free induction decays put back-to-back) is governed by the effective transverse relaxation time T . 2  (ii) R.F. Enhancement in Ferromagnets In ferromagnetic M.M.R. the nuclear resonance is driven indirectly via the nuclear-electronic hyperfine coupling. This indirect coupling produces an enhanced r.f. field at the nuclear site. The enhancement  12  factor is directly proportional to the angle through which <S) is turned by the applied r . f . f i e l d .  Since the hyperfine field is directly propor-  tional to (£> , the enhancement is strongly influenced by the detailed properties of the exchange coupled electron spin system.  In a multido-  main particle there are two sources of enhancement, coherent domain rotation and domain wall movement. Consider first a single domain which has an electronic magnetization M, aligned along the anisotropy field H-,.  Application cf a weak  transverse field H_ , produces an angular displacement of the hyperfine x  field given by  f jli \ _  Q „  ^  The resulting transverse hyperfine field Mjff, and the total driving field  a  n  transverse  .are given by  .  d  .  .  .  H ; „ , H*A"0  H  He*  1 = £  Typically for a spherical sample of iron  1-30 To estimate the domain wall enhancement consider a spherical particle of diameter d, s p l i t by a single domain wall in which the magnetization turns through 180° in a distance S, as indicated in the following diagram.  13  When a magnetic field  is applied parallel to the domain wall  surface, the wall is displaced a distance x in the direction perpendicular to the wall surface.  The maximum displacement x™ is limited by the increase  in the demagnetization energy.  For a sphere of diameter d, one finds  where. M is the saturation magnetization and D the demagnetization factor. s  As a result of the displacement x^, each moment in the domain wall is rotated approximately through an angle 6> = ^ i ? for a 180° wall. S tude of the resulting transverse field at the nuclear site i s ,  The magni-  o  6~ 2 D M Thus the enhancement factor is  s  For iron this enhancement is about 1500, in reasonable accord with measured values.  The domain wall enhancement i s , in general, at least an order  of magnitude larger than the domain enhancement.  This enhancement of the  applied r . f . field allows the N.M.R. experiment to be performed with relatively low power levels. When performing experiments with multidomain samples i t is impossible, due to the different enhancement factors, to satisfy simultaneously the 90° and 180° conditions for both^the domain and domain wall nuclei when a pulse of r . f . is applied.  It is possible, ha/ever, to select the  nuclei for which these conditions are most nearly satisfied by varying the power level of the applied r . f . . It is expected that nuclei in the domain walls are observed when low r . f . levels are used, while at high  14  r . f . levels one observes the domain nuclei.  In general one expects to  observe a mixture of the two, the relative contribution to the nuclear signal depending on the power level of the applied pulses.  15  CHAPTER III  EXPERIMENTAL PROCEDURE AND APPARATUS  The details of pulsed N.M. R. can be found in Abragarr^ and will not be.discussed here.  Rather, an outline of the procedure used will be  given and the spectrometer described. Spin-lattice relaxation times in unenriched iron powder, in which the observable Fe^7 nuclei are 2% abundant, were determined by monitoring the recovery of the nuclear magnetization to its equilibrium value after disturbing the system with a saturating pulse which gives rise to some non-equilibrium magnetization M . 0  This was accomplished by monitoring  the amplitude of the echo following a two pulse sequence that was applied at time t after the i n i t i a l saturating pulse.  The components of the pre-  cessing magnetization in the x-y plane following the two pulse sequence induce a voltage in the pick-up coil which is proportional to the magnitude of the precessing magnetization in the x-y plane.  The amplitude of  the echo is therefore directly proportional to the value of M just before z  the two pulse sequence is applied.  The amplitude of the echo was measured  as a function of t, using the pulse sequence shown below,  16  For an exponential relaxation the echo amplitude is proportional to  M '0t>= M - (M^o) - M ) e > T  2  0  e  Due to the inhomogeneity in the hyperfine fields and as a result the scatter in the Larmor frequencies the resonance condition cannot be satisfied for a l l nuclei. is independent of frequency.  This, however, does not effect T-j which  The only effect is" to limit the size of the  attainable signal.  APPARATUS The spectrometer was essentially a broadband unit capable of delivering the required r . f . pulses: over the frequency range 40 Mhz. to 100 Mhz.. A low noise figure and a fast recovery time for the receiving system was also required since the signals of interest are often weak and of short duration (10-20 microseconds).  A block diagram of the spectrometer is shown  in figure 1. (i)  The Pulsed Oscillator This oscillator had to meet the following requirements; a fast  rise and fall time for the pulses (less than 0.5 microseconds) so that relatively short pulses could be used, a long term frequency stability that is much better than the linewidth of the resonances to be observed (i.e.  a fre-  quency-stability of better than +_ 50 Khz.), and a level output over the frequency range 40 Mhz. to 100 Mhz.. These requirements are met by the Arenberg Pulsed Oscillator Model PG-650c with the extra fast rise and f a l l time modification.  It can deli-  ver 300 volts peak-to-peak into a 100 ohm load over the range 2 Mhz. to 130 Mhz.. It is externally gated, and has a long term frequency stability of better  R.F. Pulse Sample Coil  Gated Pcv/er Oscillator.  Assemhlv  Preamp.  Wide-band Amplifier  Tek. 163 Puis 3 Generators Boxcar  Tf  JY 2  TT  Integrator  ^sTopej  Timinq Unit  Start. Input  HewlettPackard  Stop , Input  Time Interval Unit  Digital Recorder  Boxcar Sample Trigger  Figure 1  Block Diagram of Pulsed Spectrometer  A'arian Chart Recorder  18  than +_ 5 Khz.. Another favourable feature of the oscillator is that it can easily be modified for greater power output or for use as a gated r.f. power amplifier should it be desirable to-convert to a phase-coherent detecting system. • The power oscillator (figure 2) consists of a 6907 tube which is cross-connected to form a push-pull Colpitts oscillator. Although the anode voltage is supplied continuously, the plate current is normally cutoff because the screen voltage is zero and the cathode has a small negative bias. In order to cause oscillations a large positive pulse (about *300 to 800 volts) is applied to the screen and grid-leak resistors. This pulse is supplied by a pulse amplification and shaping network that is driven by the external + 10 volt gate. A 6X4 tube, used as a damper diode, is connected across the tank circuit to shorten the fall time of the r.f. .pulse. The wide frequency range of the oscillator is obtained through the use of a set of interchangeable tuning coils. The r.f. output is taken from the secondary windings of these tuning coils, ( i i ) The Receiver The receiver consists of two amplifiers, a narrowband preamplier, and a wideband amplifier,. The overall gain of the receiver is 100 db.. The preamplifier serves to supply enough gain to overide the noise of the following wideband amplifier, and to narrow the bandwidth of the receiver, thus improving the attainable signal-to-noise ratio. It was designed to have a gain of 30 db. and low noise, fast recovery characteristics. The tubes used, type 7788 pentodes, are probably the best high gain ...low noise broadband amplifier tubes available. The circuit (figure 3) consists of two pentode connected 7788's used in a cascaded amplifier configuration. The final stage is tuned to the desired .'frequency and the first  | [ A A A V  r . f . output  («^52 pf  9-«  4-J tuning coi 1  4r 56K' 560K  to  S56K  560K  >200  47  S1.3K  30 K 22 [AAAA—Lvwwi  X  -» 0 to 2000VDC  "170033 mfd. -r-4 mfd.  mfd.  Hr  22K  .01 mfd.  10K  -90 -no V  J l  input Figure 2.  Pulsed oscillator  Figure 3  Narrowband Preamplifier  20  stage is used as a broadband stage which can, i f desired, be tuned to increase the bandwidth of the preamplifier.  The variable inductance in the  input circuit is used to improve the signal-to-noise ratio by matching the input to the equivalent noise resistance of the tube. The wideband amplifier (figures 4 and 5) is a low noise,  fast  recovery unit designed by S. Koskennon of Telesignal Electronics to our specifications.  It has a frequency response which is flat to within + 1.0  db. from 40 Mhz. to 100 Mhz., and a gain which is variable between 60 db. and 80 db..  The recovery time is defined as the time elapsed before the  amplifier noise is visible after the amplifier has been subjected to an overload.  With the amplifier in the r . f . output mode the observed reco-  very time from an 150 volt overload was less than 2 microseconds, while in the detected output mode i t was 4 microseconds.  This appeared to be  the optimum attainable with the detecting diodes used.  This recovery time  is tolerable since the free induction tail is about 20 microseconds long. In practice the influence of the recovery characteristics of the amplifier is minimized by observing the echo, which appears well after the receiver has recovered from the overload. In order to minimize the saturation recovery time a special effort was made to keep the interstage capacities low and supply line impecances small.  The bandwidth of the amplifier is obtained through the use  of broadband la// Q interstage bandpass f i l t e r s .  The input stage consists  of two type 7788 pentodes in triode connection used in a cascode circuit. This type of circuit has good noise and broadband characteristics.  The  coupling between the tubes consists of a coupling coil that together with the tube capacities, forms a low-pass f i l t e r with a cut-off frequency at 105 Mhz.. The output of this cascode circuit is coupled to the next stage  100 ^VVVA  Figure 4  / +150V  Cascode Input stage and f i r s t Gain Controlled stage  Figure 5  Second gain Controlled, Output and Detector Stages  23  by  a network  Most of  the  The f i r s t ler  gain  to  t h a t used a t  provided  of  amplifier  than 0.1  amplifier  this  volts  (iii)  all to  nal-to-noise  it  is  circuit  noise  ratio  the  final  in  are  stage of  signal  taken w i t h  the  the  time.  tubes The  generator.  greater  doub-  amplifica-  all  recovery  output voltages  cascaded.-  a voltage  bias supply for  a V.H.F.  filter.  The  than 0.1  output voltage  lin-  volts. greater  detection,  circuit  is  usually  as p o s s i b l e , as w e l l to  the  the  the  100 ohm i n p u t  In  the  ideal  in  the  sample c o i l .  d e p e n d s on t h e  receiving  coil  designed to  as e f f i c i e n t  sample c o i l .  n e c e s s a r y t o match to  stages which  the b e s t s a t u r a t i o n  linear  a bandpass  Coil  pulsed o s c i l l a t o r  coil  mal  ratio  i.e.  Two d i o d e s  u s e d on the  measurements were  ensure  Sample  gain.  was c h e c k e d w i t h  A sample c o i l  ratio  is  three  following  was f o u n d t o be l i n e a r f o r  view of  the  detection  a low i m p e d a n c e f o r  the  input,  by t h e n e x t  Heavy z e n e r r e g u l a t i o n  earity  the  these have a v a r i a b l e  are used f o r  to maintain  In  is  two. o f  circuit  tion.  similar  high  impedance o f  If  this  parameters  in  all  is  case  a sig-  from  signal-to-noise  impedance c f  the  sample  preamplifier.  the n o i s e  the  the  the  as h i g h  power t r a n s f e r  F o r an optimum  relatively  circuit  obtain  originates  then  following  the  as  ther-  signal-to-noise  way  N  For f a s t is  the  filling  V is  the  volume o f  Q is  the  quality  recovery  n e c e s s a r y t h a t the  damped o u t q u i c k l y  where K i s  of  resulting  (i.e.  in  the  receiver  transient  in  a t i m e much l e s s  factor the  factor  following  coil of  the  the  r.f.  the sample c o i l than  the  tuned  circuit.  pulse  it  circuit  be  recovery  time  of  24  the  amplifiers  sample c o i l  in  circuit  been a p p l i e d . the  is  after  metal of  the  filling  factor  shown i n  the  diodes conduct h e a v i l y  The  tuned c i r c u i t  figure  is  then  and t h e  6.  low Q c i r c u i t When t h e  less  the  volts  gate behaves l i k e  circuit  whi.ch i s  This  circuit  and a l s o p r o v i d e s transient  diodes  the  following  a r e no l o n g e r i n  an o p e n c i r c u i t .  c o u l d be o b t a i n e d i n  It  was f o u n d  this  for  a given  ribbon  is  the Q i s  a  t o be  circuit  passively  are  switched  pulse is  applied  a short  circuit.  100 ohm r e s i s t o r .  the the  the  p u l s e has d e c a y e d conducting state a relatively  This  to  and  high Q  the  itself  c o n s i s t e d of  copper f o i l  inductance.  much l e s s  than  tuned c i r c u i t the  through  100 ohm i n p u t  that a satisfactory  a  impedance  signal-tc-noise  ratio  way.  The s a m p l e c o i l  the  the n u c l e a r s i g n a l .  used t o o b s e r v e the n u c l e a r s i g n a l .  preamplifier.  The use o f  of  proper matching to  This effects  of  It  and a h i g h  r.f.  s h u n t e d by t h e  c a p a c i t o r a n d no a t t e m p t made t o m a t c h t o  diameter.  during  is  When t h e  12 p f .  in  recovery  the sample c o i l  The n u c l e a r s i g n a l was t a p p e d f r o m  the  and f a s t  diode gate behaves l i k e  effectively  pulsed o s c i l l a t o r .  the  p u l s e has  s o t h a t a c o m p r o m i s e has  of  between a h i g h Q and low Q c o n f i g u r a t i o n .  than 0 . 5  the  two.  circuit  a very  of  the  p r e s e n t i n s i d e the sample c o i l  The low Q - h i g h Q r e q u i r e m e n t s  effects  ratios  optimum o b s e r v a t i o n  is  requires  and j u s t a f t e r  good s i g n a l - t o - n o i s e  pulse for  decreasing function  met by t h e  condition  n e c e s s a r y to have a low Q c i r c u i t  the  the  This  t o h a v e a low Q d u r i n g  When a f e r r o m a g n e t i c  made b e t w e e n  receiving circuit).  Thus f o r  receiver i t  Q circuit  the  was wound on a b a s e o f T e f l o n  4 turns  had the  Both  the  of 2 m i l . ,  advantage of self  an e q u i v a l e n t  3 mm. w i d e providing  and mutual length  of  copper  foil.  a maximum v o l u m e  inductance round  tubing 2.65  wire.  of  the  thin  cm.  1N3604 12  R.F. Input from (pPulsed O s c i 11a t o r  pf. -°  v  1N3604  7-50 100  Figure 6  .Sample Coil  Circuit  pf.  Output to Preamp.  26  The entire coil assembly was mounted inside a minibox for shielding, a hole being provided for the tip of the helium dewar to penetrate. The overall recovery time of the receiver was found to be 5 microseconds. (iv)  This was adequate for the experiments to be performed. Boxcar Integrator The boxcar integrator, a signal averaging device used to improve  signal-to-noise  ratios, was constructed after a design by Blume^ i t h  minor modifications.  w  The monitor output was modified to exhibit the posi-  tion of the sampling gate on the input waveform. the boxcar is given in figure 7.  A schematic diagram of  A thorough discussion of the boxcar has  been given by II.H. Hardy^. (v)  Timing Apparatus A suitable combination of Tektronix pulse and waveform generators  was used to supply the sequence of pulses used to gate the pulsed oscillator and the boxcar integrator. pulse sequence was used.  For most measurements a 180°-90 -180° o  This required a pulse to trigger the i n i t i a l  180° pulse and a sawtooth voltage to trigger the 90°-180° sequence.  The  repetion rate of the sequence was such that the spin system had time to re-establish equilibrium with the lattice between each sequence.  The  time between each i n i t i a l 180° and the 90°-180° combination was swept slowly from 0 seconds to several T-j's either electronically or manually depending on whether the data was being recorded with boxcar integrator and stripchart recorder, cr by oscilloscope photographs.  When the boxcar was used,  a sampling gate 4 microseconds wide was set to sample the central portion of the waveform of interest.  The time between the 180° pulse and the 9 0 ° -  180° pulse sequence was printed out by a Hewlett-Packard 5245-c electronic  9  + 150V  +225V*  o-j [ j — - y v h ^ ~ ^  to recorder o  •170V  Capacitors in pf. i f greater than 1 " " mfd. i f less than 1  monitor output  Figure 7  Boxcar Integrator  28  counter.  An event marker on the strip-chart recorder was activated  whenever the counter printed out.  In this way the signal amplitude and  the time interval could be correlated.  The overall repetition rate was  controlled by a free running Tektronix type 162 waveform generator.  This  generator supplied a sawtooth voltage which triggered two type 163 pulse generators.  One supplied the 180° pulse, and the other, a modified unit,  supplied a delayed pulse-which triggered a 162 waveform generator.  This  generator in turn triggered a pair of 163 pulse generators used to supply the pulses for the 90°-180° sequence.  It also triggered a modified 161  pulse generator which was used to gate the boxcar integrator.  In practice  the time between the f i r s t and second pulses was swept linearly with time and the time between the second and third kept fixed.  The amplitude of  the echo then represents the recovery of M . z  The Tektronix generators v/ere modified as follows: the resistors in the phantastron circuit of a Tektronix 162 waveform generator were increased to give a miximum rundown time ofllOO minutes; the output of a Tektronix 161 pulse generator was modified to give both the positive and negative pulses required to gate the boxcar; a Tektronix 163 pulse generator was modified to allow the triggering discriminationlevel to be set ^either internally or externally, (vi)  Samples The materials studied were sealed in pyrex glass sample holders  11 mm. in diameter, under 2 mm. of Helium pressure.  The samples were in  powder form and mixed with an equal amount of aluminum oxide powder which served as a spacer to facilitate r . f . penetration of the r . f . field throughout the sample.  29  (vii)  Dewar System. The cryostat consisted of an exposed tip helium dewar and a  suitable nitrogen dewar constructed by J . Lees, glassblower.  The tip of  the helium dewar was left unsilvered to allow penetration of the r . f . field. In practice the dewar tip was placed inside the sample coil and the sample placed inside the helium dewar.  Cooling of the exposed tip was accomplished  by allowing liquid nitrogen to drip over the exposed tip.  30  •  (a)  CHAPTER IV  EXPERIMENTAL RESULTS  The nuclear resonance of the Fe^- nuclei in unenriched iron powder was observed at liquid helium and nitrogen temperatures, and the spin-lattice or longitudinal relaxation time at various power levels determined as a function of time following the i n i t i a l saturating pulse.  This was done  by monitoring the amplitude of the echo as the magnetization relaxed to its equilibrium value.  Oscilloscope photographs were used to record the helium  temperature' data.  Due to poor signal-to-noise ratios the boxcar integrator  and strip-chart recorder were used to record the nitrogen temperature data. A signal-to-noise ratio of 15 to 1 was observed at helium temperature, in good agreement with the expected value. The frequency of the nuclear signal was determined by beating i t with a reference signal from a V.H.F. signal generator.  The accuracy of  this determination was limited by the finite width of the echo to +_ 20 Khz.. Within this accuracy the resonant frequency was determined to be 46.62 Mhz. at 4.2°K. , and 46.52 Mhz. at 77°K.. other reported values  These values are in good agreement with  17 18 ' .  Typical longitudinal relaxation curves are shown in figures 8 and 9 for various r . f . levels.  An r . f . level of 1 corresponds roughly to satu-  rating pulses of such length t that  & H , t « "/zooo .  Pulses 3 to 6 microseconds long were used for the 90°-180° pulse sequence. The relaxation is strongly power dependent and appears to be exponential at 77°K. , but non-exponential at 4.2°K..  One can define an instantaneous  31  10  20  30 40 50 60 70 80 90 100 t-rr.i H i seconds. Longitudinal Relaxation of F e in Unenriched Fe Powder at 4.2°K. s /  32  1.0  n  1  2  3  4  5  6  7  8  9  .10  t-milliseconds Figure 9  Longitudinal Relaxation of F e  5 7  in Unenriched Fe Powder at 77°K..  33  relaxation  rate  9M(t)  <  where M(t). i s  the  amplitude  The e x p e r i m e n t a l and p o w e r l e v e l , power  of  results  indicate  t.  t h a t T] value for  increases with large  times  time  and h i g h  levels. observed r e l a x a t i o n  1 to 6 m i l l i s e c o n d s , w h i l e  seconds.  These r e s u l t s  lation,  that for  the f r e e  metric  about  a frequency  induction the  4.2°K.  b a s i s of  they  decay (FID)  asymmetry..  other  r.f.  reported  milli9  2 0  v e c t o r model  . calcu-  amplitude  o f f r e q u e n c y w o u l d be s y m -  The e x p e r i m e n t a l  dependent enhancement f a c t o r .  ranged  values"' '  enhancement, the  as a f u n c t i o n  This e f f e c t  d e p e n d e n t e n h a n c e m e n t has n o t y e t  at 77°K.  r a n g e d f r o m 9 t o 60  result  shewn i n  has a l s o b e e n r e p o r t e d  t h a t a good a g r e e m e n t w i t h e x p e r i m e n t  a frequency  times  a straightforward  independent  resonant frequency.  10 shows a d e f i n i t e She f o u n d  at  are c o n s i s t e n t with  One e x p e c t s , on t h e  of  time  a p p r o a c h i n g some l i m i t i n g  E x p e r i m e n t a l l y , the from  the echo a t  figure  by S t e a r n s  c o u l d be o b t a i n e d by  using  The s o u r c e o f s u c h a f r e q u e n c y  been e x p l a i n e d .  34  45  46  47  Frequency-" Ihz. Figure 10  FID Amplitude versus Frequency at 77°K..  35  (b)  DISCUSSION OF RESULTS  It has been noted (chapter I I , i i ) that the domain and domain wall nuclei are characterized by different r . f . enhancement factors, the domain wall enhancement being much larger than the domain enhancement. It is then expected that the short relaxation time observed at low r . f . levels is characteristic.of the domain wall nuclei, while the limiting value for long times and high r . f . levels is characteristic of the domain nuclei. (i)  Domain wall and domain relaxation mechanisms w i l l now be discussed, Relaxation in Domain Walls It has been suggested by Weger^O, that the dominant relaxation  mechanism in the domain walls is due to the thermal fluctuations of the domain walls. To estimate the order of magnitude of this relaxation consider a small sphere of diameter d, consisting of two equal and opposite domains with a domain wall lying between them, and imagine the only low lying wall excitation is a uniform displacement. x, a net magnetization M ^ 3 M * / c L 5  magnetization. is  If the wall shifts by a distance  is created where M  s  is the saturation  The demagnetizing energy resulting from this magnetization ,3  where N is a demagnetizing factor of order tition theorem an average energy jkl  ^  .  Applying the equipar-  is ascribed for each degree of freedom,  so that (E) = i kT since here only one degree of freedom is considered. mean squared displacement is then given by  The  36  The component of the internal field perpendicular to the static field is  H-t-He^-p  , v/here  S  is the domain wall thickness.  Thus  Assuming a Lorentzian correlation spectrum  where X. is the correlation time, the relaxation rate caused by these fluctuations is given by^2 /tit  H \ i f r " ? )  For iron v/e may assume M ~ 11 ,000 Oe., s  5.0xl0~ .cm., and -'- 2^x45xl0 sec" . 6  1  6  Assuming a temperature independent correlation time of ~* 10"^ seconds, i t is found that T-| equals 10 milliseconds and .5 milliseconds at 4.2°K. and 77°K. respectively.  These values are in reasonable accord with the experi-  mental findings. (ii)  Relaxation in Domains The reported linear temperature dependence of the domain spin-  lattice relaxation rate  suggests a conduction electron mechanism  .  A general expression for the nuclear spin-lattice relaxation rate due to magnetic interaction with electrons is given by  where ^ is the nuclear gyromagnetic ratio, H> the resonant frequency, <$"H. N  the fluctuation of the internal magnetic field at the nucleus:  and  1  37  Moriya  has treated possible relaxation mechanisms in detail  and found that the dominant relaxation mechanism is supplied by the fluctuation in the orbital current of the d band electrons.  He found that for  the orbital contribution (T,TK)~'K'IO  6  =-3  which gives ~1 second for i y at 4.2°K. and 55 milliseconds for T-j at 77°K.. Moriya's estimates are based on a band model calculation in which the 3-d electrons are treated in a tight-binding approximation.  Due to the poor  knowledge of {y^) > and the density of states for the d electrons near the p  Fermi surface, the relaxation times are estimated within a factor of two. It is seen then that the experimental results are in reasonable accord with the range set by these theoretical estimates of the domain and domain wall relaxation times. The results of the experiments performed indicate that the spectrometer is suitable for use in future experiments.  These will include  studies of ferromagnetic alloys and possibly a more thorough study of the properties of the FID.  38  BIBLIOGRAPHY  1)  A. Abragam, Thz Vfu.ncu.plu  Uuc.lz.oji  Magnetism,  (Oxford University Press, London, 1961). 2)  T. Moriya,  3)  F. Bloch, Phij6.  4)  W. Marshall, Ptuj*. Rev., U 0 , 1280, (1958).  5)  R.E. Watson and A.J. Freeman, Phyi.  6)  R.E. Watson and A.J. Freeman, MagneXJAm Vol. 1 1 A , ( Acedemic Press, Nev/ York, 1965), Chapter 4. A.M. Portis and R.H. Lindouist, Magn&tl&m Vol. 1 1 A , ( Acedemic Press,  7)  J . Phtp.  1_9, 861 , (1964).  Soc. Japan,  Rev., 70, 460, (1946).  Rev., 123, 2027, (1961).  New York, 1965)', Chapter 6. • 8) 9)  E. Fermi, Z. PhyUk,  60, 320, (1930).  E. Fermi and E. Segre, Z. Phyi>lk,  82, 729, (1933).  10)  P.W. Anderson and A.M. Clogston, Bull.  Am. Phyn>. Soc, 2, 66, 124, (1961),  11)  S.S. Hanna et. a l . , Pky*.  -12) 13)  C. Robert and J . M . Winter, Compt. Rend., 250, 3831, (1960). J . Friedel and.P.G. de Gennes, Compt. Rend"., 251 , 1283, (1961).  14)  E . L . Hahn, Phys.  15)  R.G. Blume, Rev. Sci. Inst.,22,  16)  W.N. Hardy, Ph.D. Thesis,  17)  D.L. Cowan and L.W. Anderson, Phys.  18)  J . I . Budnick et. a l . , J . Appl.  19)  M. Weger, E . L . Hahn, and A.M. Portis, J . Appl.  20)  M. Weger, Phys.  21)  M.B. Stearns, J . Appl.  22)  J . Korringa, Physlca,  Rev. Lcttzn*,  £ , 177, (1960).  Rev;., 80, 580, (1950). 1016, (1961).  University of British Columbia, 1964. Rev., T35., A1046, (1964).  Phut,.,  32, 120S, (196.1).  Rev. 128, 4, 1505, (1962). Phys.,  38, 1141, (1967).  J6, 601, (1960).  Phys.,  32, 124S, (1961).  

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