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Nuclear orientation studies of spin-lattice relaxation and hyperfine fields in ferromagnetic dilute alloys Kieser, Robert 1975

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i -NUCLEAR ORIENTATION STUDIES OF SPIN-LATTICE RELAXATION AND HYPERFINE FIELDS IN FERROMAGNETIC DILUTE ALLOYS by ROBERT KIESER M.Sc. University of New Brunswick, 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Physics We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA March, 1975 . In presenting this thesis in partial fill fi lment'of the requirements for an advanced degree at the University of Brit ish 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 representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of Brit ish Columbia Vancouver 8, Canada Date ^ 7 ^ - A ^ 7 ^ ABSTRACT Nuclear magnetic resonance experiments on impurity atoms i n a ferromagnetic host have shown that the measured s p i n - l a t t i c e relaxation time of those nuclei located i n domains i s strongly dependent on the degree of magnetic saturation of the host material (1, 2, 3). The re-laxation time increases as the applied magnetic f i e l d i s increased and reaches a constant value for a magnetically saturated specimen. Wall nuclei show a much shorter relaxation time than those i n the bulk. This fa c t , together with the increased number of walls present i n a magneti-c a l l y non-saturated specimen could explain the observed field-dependent decrease of the relaxation time i f an increasing f r a c t i o n of wall nuclei i s observed. Nuclei located i n walls experience a much larger enhance-ment than those i n domains. Therefore special techniques have to be applied to exclusively observe nuclei located i n the bulk (1, 4). For t h i s reason some uncertainty exists i n the interpretation of the nuclear magnetic resonance measurements. The theory of the s p i n - l a t t i c e relaxa-t i o n i n ferromagnetic metals (5) gives an estimate for the relaxation rate observed i n magnetically saturated specimens. No f i e l d dependence the relaxation time i s predicted. Pa r t l y due to the uncertainty i n the NMR r e s u l t s , t h i s theoretical problem has received l i t t l e attention so far. We therefore have employed low temperature nuclear orientation which predominantly measures bulk nuclei to investigate t h i s problem. In most of these experiments the combined technique of nuclear orienta-i i i t i o n and nuclear magnetic resonance (NMR/ON) (6) has been applied td pre-pare the i n i t i a l state from which the relaxation takes place. Some ex-periments have also been performed by an en t i r e l y non-resonant technique ( 7 ) . Our experimental results on 6^Co-Fe, 5tfMn-Fe and 5ttMn-Ni c l e a r l y confirm the f i e l d dependence of the relaxation time observed i n nuclear magnetic resonance experiments ( 8 ) . Thus the need for a detailed theoretical study i s evident. Performing an NMR/ON experiment the resonance i s detected by a change i n the observed y-ray i n t e n s i t y . Resonance lines f o r 6^Co-Fe, 5tfMn-Fe and 5t*Mn-Ni have been recorded. We have fo r the f i r s t time obser-ved that t h e i r f u l l widths at h a l f maximum show a strong f i e l d dependence. An explanation i n terms of a loc a l d i s t r i b u t i o n i n the demagnetizing f i e l d i s offered. We have also measured the in t e n s i t y of the resonance l i n e as a function of the applied f i e l d . An estimate shows that t h i s i s inadequate-ly explained i n terms of the expected f i e l d dependence of the enhancement factor. The d i s t r i b u t i o n of hyperfine f i e l d s has never before been studied by NMR/ON. We have employed t h i s technique successfully to investigate an alloy of one atomic percent 59Co-Fe_ which has been doped with a small amount of 6 0Co. A strong, well resolved s a t e l l i t e l i n e of the impurity nuclei i s observed. These data are interpreted i n terms of the effect of near neighbor impurity nuclei on the hyperfine f i e l d (9, 10). We have computed a theoretical curve based on parameters given i n the l i t e r a t u r e (10). This provides a moderately good f i t for most portions of our spectra. This p i l o t study demonstrates that NMR/ON i s indeed a valuable tool f o r the investigation of hyperfine f i e l d d i s t r i b u t i o n s . The advantages over nuclear magnetic resonance studies are that e s s e n t i a l l y only bulk as com-pared to wall nuclei are studied and that the s e n s i t i v i t y i s independent of the all o y concentration. Based p a r t i a l l y on our own data we present a short discussion of the question whether a spin temperature i s maintained by the impurity nuclei during relaxation. F i n a l l y we of f e r a comparison between relaxation data measured by NMR/ON and other nuclear orientation techniques (11) . For 6 0Co-Fe the relaxation times measured by NMR/ON are found to be almost 50% longer than those measured by techniques i n which the i n i t i a l condition i s known. This discrepancy i s generally attributed to the incomplete knowledge of the i n i t i a l conditions when the NMR/ON technique i s employed. We have computed the o r e t i c a l relaxation curves for a number of i n i t i a l conditions and find that the re s u l t i n g spread i n relaxation time for those curves that allow a good f i t to the measured curve i s larger than the difference obtained from the experiments. Thus our model indeed could explain the observed discrepancy. V REFERENCES V. Jaccarino, N. Kaplan, R.E. Walstedt, J.H. Wernick, Phys. Let. 2J5, 514, ( 1 9 6 6 ) , M.B. Salomon, J. Phys. Soc. Japan, 2 1 , 2746, ( 1 9 6 6 ) . M. Kontani, T. H i o k i , Y. Masuda, J . Phys. Soc. Japan, 32_, 416, ( 1 9 7 2 ) . N. Kaplan, V. Jaccarino, R.T. Lewis, J. Appl. Phys. 39, 500, ( 1 9 6 8 ) . T. Moriya, J . Phys. Soc. Japan, 19_, 6 8 1 , ( 1 9 6 4 ) . J.E.. Templeton, D.A. Shirley, Phys. Rev. Let. 1_8, 240, ( 1 9 6 7 ) . J.A., Barclay, D.H. Chaplin, C.G. Don, G.V.H. Wilson, Phys. Rev. B6, 2565, ( 1 9 7 2 ) . R. Kieser, N. Kaplan, B.G. T u r r e l l , Phys. Rev. B9_, 2165, ( 1 9 7 4 ) . M. Rubinstein, Phys. Rev. 172, 277, ( 1 9 6 8 ) . G.H\ Stauss, Phys. Rev. B4, 3106, ( 1 9 7 1 ) . R. Kieser, B.G. T u r r e l l , P.W. Martin, International Conference on Hyperfine Interactions Studied i n Nuclear Reaction and Decay, (K. 1 Kaflss'om,? R. Wappling, editors, Uppsala, Sweden, 1 9 7 4 ) , p. :2:4.8. v i TABLE OF CONTENTS ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENTS CHAPTER I NUCLEAR ORIENTATION THEORY Nuclear Orientation Theory Conditions for the Observation of Nuclear Orientation Hyperfine Fields on Impurity Nuclei i n a Ferro-magnetic Host Nuclear Magnetic Resonance on Oriented Nuclei NMR i n Ferromagnetic Metals CHAPTER II RELAXATION Spin-Spin Interaction Spin-Lattice Interaction Relaxation Theory for NMR/ON CHAPTER I I I EXPERIMENTAL APPARATUS AND PROCEDURE Cryostat Salt P i l l Assembly Superconducting Magnets Carbon Resistor Thermometry Transmission Line into the Cryostat. v i i Operating Modes and Electronics 56 Data Analysis 59 Magnetic Saturation of Specimen 63 CHAPTER IV FIELD DEPENDENT RELAXATION Relaxation time of 6 0Cp-Fe, 54Mri-Fe__and 5 4Mn-Ni 68 Specimen Preparation 70 Relaxation Results 73 Discussion of Results 83 CHAPTER V DEPENDENCE OF LINE WIDTH, RESONANCE FREQUENCY AND SIGNAL ON THE DEGREE OF MAGNETIC SATURATION OF.THE SPECIMEN 86 Dependence of Line Width on the Applied F i e l d 86 Resonance Frequency as a Function of the Applied 96 F i e l d Dependence of Signal on the Applied Magnetic F i e l d 100 CHAPTER VI OBSERVATION OF SATELLITE LINES BY NMR/ON 110 Specimen Preparation 112 Observation of S a t e l l i t e Lines 118 Data Analysis 123 Discussion 125 Relaxation measurements on the Alloy Specimen 132 CHAPTER VII SOME COMMENTS ON THE SPIN TEMPERATURE QUESTION AND THE DIFFERENT METHODS OF MEASURING THE RELAXA-TION TIME BY NUCLEAR ORIENTATION 135 CONCLUSION 152 REFERENCES 153 APPENDICES 162 v i i i LIST OF TABLES Table I I / l Estimates f o r the s p i n - l a t t i c e r e laxation of 31 5 5Mn-Fe and 6 0Co-Fe_ Table IV/1 Results from relaxation measurements on 6 0Co-Fe, 75 5I+Mn-Fe_ ,and 5l+Mn-Ni_ Table IV/2 Summary o f high and low f i e l d r e l axation times 81 Table V / l Zero f i e l d resonance frequency and slope of the 99 frequency versus applied f i e l d graphs ' Table V/2 Estimated radio frequency f i e l d to produce con- 104 siderable destruction of the anisotropy Table V/3 Measured and predicted values f o r signal observed 108 by NMR/ON at various applied f i e l d s Table VI/1 Center frequencies and signals observed on the 6 0{?o , „-Fe specimen 113 Table VI/2 Analysis of the s a t e l l i t e spectra 127 Table VI/3 Comparison of s a t e l l i t e spectra as measured 134 by NMR and NMR/ON Table VI/4 Summary.of s a t e l l i t e spectra measured by NMR/ON 132 Table VI/5 Korringa constants f o r the 1%, .1% and .02% . 134 Co-Fe specimens Table VII/1 Non-resonant re l a x a t i o n data measured i n low 143 and high applied f i e l d Table VII/2 Summary o f published r e l a x a t i o n data 145 Table VII/3 Dependence of the Korringa constant on the 150 i n i t i a l condition i x LIST OF FIGURES Figure 1/1 Anisotropy f o r various t r a n s i t i o n s ; 2 Figure 1/2 Typi c a l decay scheme 3 Figure 1/3 Magnetization vector i n the laboratory - and the r o t a t i n g frame 19 Figure I I / l Predicted r e l a x a t i o n of the anisotropy f o r 6 0Co-Fe 39 Figure I I I / l Cut-away, view of the cryostat 43 Figure III/2 Salt p i l l system 47 Figure III/3 Photographs o f the cryostat 49 Figure III/4 Superconducting magnet system 52 Figure 111/5 Block diagram of the pico-watt r e s i s t a n t bridge 54 Figure III/6 Block diagram of the el e c t r o n i c s 58 Figure III/7 T y p i c a l y-ray spectrum 61 Figure III/8 Typical a x i a l r e l a x a t i o n record 61 Figure III/9 Specimen magnetization versus applied f i e l d 65 Figure IV/1 T y p i c a l high and low f i e l d r e l a x a t i o n curves f o r 6 ° f n - - F P 74 Figure IV/2 Relaxation time versus applied f i e l d 78 Figure V / l 5 1 +Mn-Ni resonance l i n e s observed by NMR/ON i n the a x i a l and equatorial d i r e c t i o n 88 Figure V/2 " 6 0Co-Fe resonance l i n e s f o r various applied magnetic f i e l d s 91 Figure V/3 Line width versus applied f i e l d 93 Figure V/4 Model to i l l u s t r a t e the possible range of de-magnetizing factors near the specimen surface 95 X Figure V/5 Resonance frequency versus applied f i e l d 97 Figure V/6 Signal versus applied f i e l d 101 Figure V/7 Computed curve f o r the signal as a function of 103 the radio frequency f i e l d strength Figure V/8 Plot of measured and predicted signal as a 106 function of the radio frequency f i e l d strength Figure V I / l 6 0Co , 0-Fe spectrum showing s a t e l l i t e l ines 115 Figure VI/2 , 6 0Co l O-Fe spectra showing s a t e l l i t e lines 120 Figure VI/3 Predicted l i n e shape of s a t e l l i t e spectrum 128 Figure VII/1 Non-resonant relaxation measurement observed 142 by nuclear orientation Figure VII/2 Predicted relaxation curves for several i n i t i a l 148 conditions Figure VII/3 Dependence of the Korringa constant on the 156 i n i t i a l condition XI ACKNOWLEDGEMENTS The author wishes to express his sincere gratitude to The National Research Council of Canada for financial assistance in the form of an NRC Post-Graduate Scholarship. Dr. B.G. Turrell for his supervision and encouragement, Dr. P.W. Martin for his interest in this work, Dr. N. Kaplan for stimulating discussions which led us to the work represented in Chapter IV, " R.L.A. Gorling and P. Daly for their assistance during the f i r s t experiments; R.G. Butters, L. Redenback who were most helpful in the manu-facturing of the 1% Co-Fe alloy, J. Lees for manufacturing and servicing the glass, dewars, A. Fraser and the late R. Haines for making the services 'of the machine and student shop available, W. Dickson who assisted in the construction of the multi input multi scaling unit, and D. Kieser who added much to my l i f e and in many ways assisted to make this work possible. 1 CHAPTER I I NUCLEAR ORIENTATION THEORY Radiation emitted from a radioactive nucleus i s anisotropic. The d i r e c t i o n a l d i s t r i b u t i o n has a x i a l symmetry with respect to the nuclear magnetic moment y. The i n t e n s i t y , or p r o b a b i l i t y d i s t r i b u t i o n , W, i s a function of the polar angle 6. Figure 1/1 i l l u s t r a t e s W(8) f o r e l e c t r i c or magnetic radiation. Pure dipole and quadrupole cases are shown and denoted by the subscripts 1 and 2 respectively. The superscript gives the difference, 1^ - 1-^ , between the spin of the f i n a l and the i n i t i a l states. The arrow indicates the r e l a t i v e magnitude and d i r e c t i o n of W(9). Anisotropic radiation from an ensemble can be observed i f the nuclei are oriented, that i s i f the nuclear magnetic moments are predominantly p a r a l l e l to some externally defined axis. Nuclear Orientation Theory: The theory of nuclear orientation has been reviewed by various authors ( 1 , 2, 3, 4, 5 ) . Here we use the formulation given by Blin-Stoyle and Grace ( 1 ) ; i t i s also used by de'Groot, Tolhoek and Huiskamp ( 5 ) . A t y p i c a l decay scheme i s shown i n Figure 1/2. The parent state IQ with substates m^  i s oriented. An unobserved t r a n s i t i o n i n which an-gular momentum, LQ, i s radiated away populates the intermediate state 1^. The decay from 1^ to yields the observed y-radiation of angular momen-tum L., . , Its intensity i n a d i r e c t i o n 0 to the quantization axis i s given by: 2 Figure 1/1 The anisotropy i s i l l u s t r a t e d by the vector (,W(6). The axis of r o t a t i o n a l symmetry i s given by the nuclear mag-n e t i c moment y. The subscripts 1 and 2 r e f e r to dipole and quadrupole r a d i a t i o n r e s p e c t i v e l y while the super-s c r i p t s gg the difference between the f i n a l and the i n i t i a l spin. 3 Figure 1/2 A t y p i c a l decay scheme. IQ, 1^ and describe the parent, intermediate and f i n a l state respectively. The unobserved t r a n s i t i o n carries away angular momentum while the observed t r a n s i t i o n carries away angular mom-entum L., . 4 v max WO) = I B v uv F V P v (cos e) CD v=0 The summation i s from v=0 to v=v v with v = min ( 2 I n , 21 , 2L.) max U l l In a l l cases to be discussed only y- radiation i s observed; therefore the summation i s over even v only, since p a r i t y i s conserved i n electromagnetic interactions. Equation (1) i s an expression f o r the i n t e n s i t y only and gives no information concerning the polarization of the radiation. The orientation parameters describe the orientation of the parent state of spin IQ and are given by: B v = /2^T I £ ( I 0 , v, I Q ; mQ, 0) p^Q C2) m0=-I0 0 where C(I-., v, I_; m~, 0) are the Clebsch-Gordan coef f i c i e n t s and p U (J (J "'Q specifies the level population. The term 'orientation 1 i s used here as a generic expression f o r both 'alignment' and 'polarization^. Note that the Clebsch-Gordan co-e f f i c i e n t s are symmetric with respect to m^ : i . e . C ( I 0 , v, I Q ; mQ, 0) = ( - l ) v C ( I 0 , v, IQ; -mQ, 0) r p Thus i f 'ip/n^ = ,i+-Pm^, a l l B with v = odd w i l l vanish. This i s called align-m0 0' v ' ment. Polarization on the other hand i s described by even and odd orien-t a t i o n parameters. 5 I f the nuclear spin system i s at a temperature T g which can be either the l a t t i c e temperature or a spin temperature, different from the l a t t i c e temperature, then the populations w i l l be given by the Boltzmann d i s t r i b u t i o n : E m 0 exp - K.T' t - T e X P ~ V ^ o [' E -» mo (3) where E^ are the energy eigenvalues of the I-Q^ state. I f the unobserved t r a n s i t i o n from IQ to 1^ i s fast compared with the nuclear precession frequency, which i s of the order of 10 8 to 10~ 9 s e c , then the orientation of the intermediate state of spin 1^ i s described by'B^U^ with the 'reorientation parameters' given by: I +1 -L +v U v = C-l) U / ( 2 I 0 + 1 ) ( 2 I 1 + 1 ) W ( I 0 , I 1 , I 0 , I 1 ; L 0 , v ) (4) Here W(IQ)I1,IQ,1^ ;L Q,v) are the Racah c o e f f i c i e n t s . I f a sequence of unobserved transitions occurs from IQ to I'J,?to I ^ a .... then the reorientation parameters are given' by the product: (U U U , U ) v v va vb vn I f two radiations L Q and L Q ' populate the 1^ l e v e l then the mixing i s given by: 6 U v(L 0) + 6 2 Uv (L0») 1 + 6 2 We note that the crossterm vanishes and the mixing r a t i o i s given by: _ amplitude of the L ^ ' mode amplitude of the LQ mode TheE - coefficients relate to the observed t r a n s i t i o n and are given by: W 1 , F = (-1) 1 ^ T ~ r T C2L 1+l).C(L 1,L 1,y;.l,-l)«WC.^ I f multipole mixing of radiation specified by and L ^ ' occurs, we have: F 1 + A 2 A represents the mixing r a t i o and the crossterm F v(L^,L^') i s : F v(L 1,L 1') = C-l) v ^ I ^ X C ^ ,L 1' , v ; 1, -1) F i n a l l y the Legendre polynomials P^(cos 9) determine the angular dependence of the radiation pattern. For the present work the above coefficients were computed i n each case from f i r s t p r i n c i p l e s . Instead of using the Clebsch-Gordon and 7 Racah coefficients the more elegant 3 j - and 6j - symbols we're employed. The computed orientation parameters have been 'spot-checked' against tab-ulated values. In fact the F-coefficients and the crossterms for 1^12 are given by Ferentz and Roaenzweig (6). Yamazaki (7) gives the U- and the F- c o e f f i c i e n t s , Vwhiil-e, Frauenfelder and Steffen (8), f o r example, give the Legendre polynomials as well as the F-coefficients f o r I^<4. A tabulation of decay schemes i s given for example by Lederer et a l . (9). Conditions for the Observation of Nuclear Orientation: The presentation of the nuclear orientation theory,in the pre-vious section gives l i t t l e insight into the physical requirements f o r nuclear orientation. In order to observe orientation of a system of nucle i by s t a t i c methods, the thermal random motion of the nuclear spinssis reduced by lowering the temperature and an orienting interaction i s applied. This may be the interaction with an external laboratory f i e l d or an inte r n a l hyperfine interaction. In terms of the orientation parameters this implies that at least some of the parameters are different from t h e i r high temperature values: B0 = 1 B = 0 v3 = 1, 2, 3, . The closed forms for Bi , B? and B^ are given by: / = 3 L ; I q »I - mo \ I [3mQ2 -1(1*1)] P , B 2 = . -a [ i 1(1+1)'(2.1+1) (21 + 3) ] h B4 = V \ - 5 ( 6 l 2 + 6 I - 5 ) ^ V V mft 0 mn 0 + 31(I 2-l)(1+2)]•[I(I 2-l)(1+2)(21+3)(21+5)(21-1)(21-3)] -h From these expressions i t can be seen d i r e c t l y that B^, B2, w i l l be zero i f a l l are equal or generally B^ = 0 for v = 1, 2, 3, .... There-fore f o r the system to be oriented, the substates m^  have to be unequally populated. In other words the expectation values of at least some of the moments of m^  have to be non-zero. In the case of a pure magnetic interaction between the nuclear magnetic moment y and a magnetic f i e l d H the Boltzmann exponent has the form 4 E kT s I kT s kT s H = 0 H>0 From equation (3) i t i s clear that s i g n i f i c a n t l y different l e v e l popula-tions w i l l result i f : mQ u H > 1 . I k T s 9 r For a nucleus with y = 1.0 nuclear magneton, I = 1, at a temperature Tg = .01 K, t h i s requires H > 300 kG. These conditions are quite stringent, but laboratory•fields i n excess of 100 kG are, i n fa c t , tech-n i c a l l y possible and can be produced by either conventional or super-conducting solenoids. This approach to nuclear orientation i s cal l e d appropriately the 'brute-force' method. Fortunately, i n some c r y s t a l s , u n f i l l e d electron shells pro-duce larger magnetic f i e l d s or e l e c t r i c f i e l d gradients at the nucleus. In the case of a paramagnetic c r y s t a l the Hamiltpnian describing the possible interactions between the c r y s t a l l i n e f i e l d s , the electron shells and the nucleus has been given by Abragam and Pryce (10): « - e B [ g | i ; H z S z + g l ( H X S x + H y S y « + D^U. l 6 ( S + l ) ] + t A S z I z + B ( S x I x + S y I y ) ] + Q[I z 2 - I l ( I + l ) ] - Y" H • I (6) Here Bg i s the Bohr •.magneton, g and g^ are the i o n i c g-factors p a r a l l e l and perpendicular to the z-axis. H (H^, H , Hz) i s the external f i e l d , S i s the effective electron spin and I i s the nuclear spin. The strength of the different contributions to the interaction H i s determined by the constants A, B,, D and Q. The f i r s t and the second terms give the s p l i t t i n g of the elec-tronic . levels by the external magnetic f i e l d and by the c r y s t a l l i n e e l e c t r i c f i e l d gradients 'respectively^.th^eh^Mrde-Mimsie^ribes - the- mag-net i c hyperfine s p l i t t i n g due to the interaction between the nuclear magnetic moments and the u n f i l l e d electron s h e l l s . The Q-term gives the 10 e l e c t r i c quadrupole s p l i t t i n g of the nuclear levels. F i n a l l y the l a s t term represents the direct interaction between the nuclear magnetic moment and the external magnetic f i e l d . ; Equation (6) points out the different ways available f o r s t a t i c nuclear orientation (11). To distinguish the different p o s s i b i l i t i e s only the major contributions w i l l be considered i n each case. As has been pointed put orientation can be obtained by the direct interaction between the nuclear magnetic moment and an external magnetic f i e l d as given by the term j- H • I . Alter n a t i v e l y the hyperfine interaction may be employed; t h i s i s the case i n a l l other methods. The quadrupole interaction i s given by the Q-term; very large e l e c t r i c f i e l d gradients with a common macroscopic symmetry axis are ' required. The A and B terms can be employed to produce nuclear orienta-t i o n . ' In t h i s case i t i s necessary that the electronic spins are oriented. This can be achieved either by a quadrupole interaction with the electronic spins given by the D-term or as indicated by the gg-term, an external magnetic f i e l d can be applied. As B g > u > complete orienta-t i o n of the electron spins w i l l set i n at comparatively high temperatures and a f i e l d of only a few thousand gauss. In a l l but the f i r s t method, the choice of the c r y s t a l i s very important., In our experiments we have employed ferromagnetic specimens. In these, microscopically the electronic spins-are polarized by the ex-change interaction. However, macroscopically an external magnetic f i e l d i s s t i l l required to magnetize the specimens and define a common quan-t i z a t i o n axis. Nuclear orientation i s achieved v i a the A term. The hyperfine f i e l d i n such a system w i l l be discussed i n the following section. 11 Hyperfine Fields on Impurity Nuclei i n a Ferromagnetic Host: The hyperfine interaction i s the interaction between the electrons and the nuclear magnetic dipole moment and higher moments. Its measurement can be useful i n studying nuclear properties (e.g. the nuclear magnetic moment). Alternately, as i n our experiments, the nucleus can be used as a probe to investigate the c r y s t a l l i n e environ-ment . Nuclear orientation i s only one of many techniques that can be used to study the hyperfine interaction. Other methods include o p t i c a l spectroscopy, nuclear s p e c i f i c heat measurements, Mo'ssbauer e f f e c t , angular correlation, interactions of polarized neutrons with polarized n u c l e i , NMR and EPR. The study of hyperfine interactions has co n t r i -buted greatly to the understanding of the magnetic properties of matter. The large hyperfine f i e l d found at many impurity nuclei i n a ferromagnetic host was f i r s t observed by Samoilov (12, 13). In the present experiments t h i s f i e l d , H , not only makes the orientation of nuclei of magnetic and 'non-magnetic' elements possible without a huge external magnetic f i e l d , but also provides the coupling that allows the nuclei to relax to 'their equilibrium.state and i s thus fundamental to the relaxation studies to be described. In the present section, however, only the s t a t i c part of th i s interaction w i l l be discussed. As indicated by the spin-Hamiltonian given i n equation (6) two types of interactions with the nuclear magnetic moment, \i, are important: the f i r s t i s l i n e a r i n the nuclear spin I and represents the magnetic dipole interaction with the hyperfine f i e l d , H^; the second i s quadratic i n I and gives the e l e c t r o s t a t i c interaction of the nuclear quadrupole moment with the e l e c t r i c f i e l d gradients. Higher order terms are small and 12 w i l l be neglected. An approximation to the hyperfine interaction i s given by Fermi (14). The Hamiltonian i s based on a one electron, free-atom theory that employs Dirac's r e l a t i v i s t i c description for the electron and i s given by: u r 8*" xr i c T * (L-S) -I ^ 3(S-r)(J-r), (7) Here gg, g j , yg, y^ are the electronic and nuclear spectroscopic s p l i t -t i n g factors and the Bohr and nuclear magneton respectively. The elec-tron o r b i t a l , electron spin and nuclear spin angular momentum operators are L, S and I. The f i r s t term represents the Fermi contact interaction. I t i s non-zero only when the coordinates of the nucleus and the electrons coincide. • This i s only possible for S-electrons. In t h i s case the re-maining terms are zero. As indicated by the 1/r 3 dependence, the second and t h i r d term describe the dipole interactions. Quadrupole effects are not inett-.u'd'e'din the above expression since a point nucleus i s assumed. These effects can be neglected i n the present experiments. This i n t e r -action can be quite large i n non-cubic materials (e.g. hexagonal cobalt). In fact even i n cubic materials quadrupole effects can be observed as has been' shown by the work of the Oxford group (16, 17, 18). Equation (7) can be written as: u T r . c E^S°r)3(S>r)r,, r 3 r° H = -y-H . 13 The interaction i s now represented by a magnetic f i e l d H which i s given by the expression i n the curly brackets and depends on the 'effective t o t a l electron angular momentum' S'. With the assumption that the diagonal elements of H are proportional to S' we have (15): H = A I S ' where A = — : i s the hyperfine constant for dipole interaction. S • S' For an unpaired s-electron the l a s t two terms i n equation (7) are zero and H becomes: H - - § I P j I.{g sy s §L k g (0)| 2 | } The 6-function has been replaced by the electron density at the nucleus t |4)g(0)|2 where ^g(r) i s the one electron wave function. The hyperfine f i e l d i s therefore: Generally we are concerned with multi-electron atoms. In t h i s • case the contributions to the hyperfine f i e l d can be written as a sum-mation over terms as given i n equation (7). However, the multi-electron wave functions are more successfully expressed by the Hartree-Fock for-malism (19) or the configurational interaction theory f i r s t employed by Fermi and Segr£ (20) and more recently for example by Abragam et a l . (21). Detailed studies show that only the unpaired s-electrons, 14 but also the closed s..-shells, do contribute s i g n i f i c a n t l y to the hyper-fi n e f i e l d (22), In 3dr-transition metals an unpaired s-electron den-s i t y may arise from (15, 23): a) polarized conduction electrons b) mixing of s^character into the d-electrons by the ex-change interaction c) core p o l a r i z a t i o n : i . e . p o l a r i z a t i o n of the inner s-electrons by the conduction o.ax-3d-ferromagnetic electrons, r e s u l t i n g i n a r e l a t i v e s h i f t i n the spin up and spin down density at the nucleus. Of these core p o l a r i z a t i o n provides the dominant contribution. Mar-s h a l l (15), Watson and Freemann (24) and Anderson and Clogston (25) for example discuss additional contributions. These, however, are small for 3 d -transition metals. Here we are interested i n the hyperfine f i e l d on impurity nuclei i n a ferromagnetic host. The mechanisms discussed above s t i l l apply, but the p a r t i c u l a r electronic environment of the impurity has to be considered. This si t u a t i o n i s described quite well by the l o c a l potential model of Daniel and Friedel (2,6:). Campbell (2<7j) applies t h i s model successfully to explain the hyperfine f i e l d f o r a variety of im-purity-host systems. In th i s model the d-moment, y^, of the host metal i s assumed to act as an effective f i e l d on a free-electron-like con-duction tban'd,, resulting i n a uniform conduction electron p o l a r i z a t i o n which i s proportional to y^ except at the impurity s i t e . There lo c a l square well potentials V+ and V+ act on the spin + and spin i con-duction electrons respectively. Thus an electronic p o l a r i z a t i o n i s produced at the impurity atom which i n turn generates the hyperfine f i e l d . 15 In addition to theoretical calculations i t i s helpful to look at the trends of the hyperfine f i e l d . For impurities i n a ferromagnetic host these are for example considered by Shirley (3, 28, 29) and Camp-b e l l (27). In an experimental s i t u a t i o n the loc a l magnetic f i e l d which arises from the bulk properties of the magnetic material, has to be also considered. Its contributions are the external f i e l d , the de-magnetizing f i e l d and the Lprentz f i e l d . Nuclear Magnetic Resonance on Oriented Nuclei: . Most of our measurements combine the nuclear magnetic re-sonance (NMR) technique with nuclear orientation; i . e . NMR i s performed on oriented nuclei (X'NMRyiONj)... A discussion of the nuclear orientation theory has been given i n the previous section. Here those concepts of NMR important to our experiments w i l l be presented i n order to permit a more comprehensive discussion of iN'MR/ONM „ Reference i s made to the excellent texts on NMR by S l i c h t e r (30) and Abragam ( 3 1 ) . A nucleus with magnetic moment, y, and spin,I, that i s located i n a magnetic f i e l d HQ can be described by the Hamiltonian: H = -y •• H 0 (8) The eigenvalues of th i s equation are given by the energies: E m -y m HQ ; m = - I , -1+1, +1 16 The difference between each p a i r of the (21 + 1) levels i s : AE = |E.., - E,| = 0 J i + 1 i 1 I This can be expressed i n terms of the resonance frequency 0 AE_ . ^ 0 h ni where "n i s Planck^s constant. . A nuclear spin i s excited from a lower to the next higher energy l e v e l by absorbing a quantum TIO)Q from the radio frequency f i e l d . This i s referred to as an upward t r a n s i t i o n . Alternately the de-excitation of a nucleus i s referred to as a down-ward t r a n s i t i o n . In this case energy noig w i l l be absorbed by a neigh-boring nucleus or dissipated into some reservoir, i . e . the l a t t i c e . A c l a s s i c a l picture of NMR can be obtained by considering the bulk magnetization M « y. In many situations 'the motion of t h i s vector i s described by the phenomenological Bloch equations: M _ _ . o t M x = - i f + " C M X H P x M _ . o T M y = " i f + ^ 0 P X X H H l y y o t M z " • ^ + V ° « x i V z (9) 1 TKee e.g.uaT^ itb/ri'.um magnetization i s : M Q = X Q H 0 and the gyromagnetic r a t i o Y i s given by: w 0 = Y HQ. The above equations show that when no 17 radio frequency f i e l d i s applied any non^equilibrium component of the magnetization w i l l relax exponentially to the respective equilibrium values: M ., M •> 0 x y M -»• Mn z 0 The 'longitudinal relaxation time',. T^, characterizes the relaxation of and describes a transfer of energy from t h e nuclei to the l a t t i c e . The 'transverse relaxation time', 1^, characterizes interactions which destroy the coherence of the precessing transverse magnetization, i . e . ; and M . These interactions conserve energy i n the s t a t i c f i e l d H^. An example of such a mechanism i n a s o l i d i s the dipolar coupling be-tween the nu c l e i . The l i n e a r l y polarized radio frequency f i e l d i s represented i n terms of two counter-rotating vectors to f a c i l i t a t e the solution. HjCt). =• H^exp (itOjt) + exp (-iu^t)] In a frame rotating with frequency u , about the z-axis and with i t s axis x along that component of H1 which rotates i n the same direc-K I t i o n as the n u c l e i , we have for the steady state solution of equation (9) ("VV YH 2 T2* M.. . = X H x R, [ 1 + OQ-V 2 T 2 2 + y 2 H l 2 T1 T2 18 t R 1 + CoiQ-^j)2 T 2 2 + Y 2H 1 2T 1T 2 J 1 + ( u ^ ) 2 T/ -R <• 1 + (COQ-CO^ 2 T 2 2 + Y 2H 1 2T 1T 2 J (10) Exactly at resonance, a). = c u n , these equations take the simple form: The transverse component i s 90° out of phase with respect to the radio frequency f i e l d , i n d i c a t i n g power absorption from t h i s f i e l d . The situ a t i o n i s i l l u s t r a t e d i n Figure 1/3. In conventional NMR the radio frequency f i e l d i s often applied by a small transmitter c o i l per-pendicular to the s t a t i c magnetic f i e l d H^. Resonance can be detected for example by monitoring the voltage which i s induced into a small re-ceiver c o i l by the precessing magnetization. nuclear orientation. The following geometrical interpretation (32) gives a greatly oversimplified picture. As before, the anisotropy i s 0 The sit u a t i o n i s more complicated when NMR i s detected by 19 Figure 1/3 The laboratory frame x,- y/,-,,zf and the rotating frame x^ y^, z^ _ are i l l u s t r a t e d . At resonance; to^  = WQ, the Block equations give the steady state magnetization M as a constant vector i n the y^z^ plane. On the other hand c l a s s i c a l spin dynamics of the magnetization pre-dicts that at resonance M. processes about H i n the y Dz D- plane with frequency yH-,'. 20 given by the expression u r = . J B U F P (0) (11) W(0) L v v v vK J v 1 v v For a certain equilibrium anisotropy the nuclear moments have a non-random d i s t r i b u t i o n about the z-axis. C l a s s i c a l spin dynamics of the magnetization predicts that, at resonance, t h i s d i s t r i b u t i o n w i l l pre-cess i n the y Dz plane of the rotating frame about the radio frequency f i e l d (See Figure 1/3). As the z-axis of the laboratory and the rotating frame coincide, the re s u l t i n g anisotropy i n th i s d i r e c t i o n i s given by: W(0=O) = T B U F P v F P (eD) d e n where p = 0 j v R B_ B [ p ] 2 This can be expressed i n terms of the attenuation c o e f f i c i e n t G^ , with this we have for the anisotropy Wt((0=O) : W(0=O) = T B U F G P (0=0) As GvPP(9=0) = 1, 0, 1/4, 0, 9/64, for v = 0, 1, 2, 3, 4,.., we see that at resonance the even order contributions to the anisotropy W(0) w i l l be non-zero. An incomplete destruction of the anisotropy i s p r e d i c t e d i i f even orientation parameters are observed. Note that the above model assumes that the resonance has a natural l i n e width and 21 that T.,ton , T o 0) n and Tx u n approach i n f i n i t y . Here Tj denotes the h a l f l i f e of the radioactive nucleus. A general theory using these ideas has been developed by Matthias et a l . (33). Alternately the evolution of a density matrix can be described (32, 33, 34). A phenomenological discussion i s given by Wilson et a l . (35). A l l of these treatments ;are of limited value be-cause so f a r none of these theories have successfully described the density matrix of the ir r a d i a t e d nuclei i n an experimental s i t u a t i o n . In any relaxation study t h i s knowledge i s indispensable f o r an accurate d e f i n i t i o n of the i n i t i a l stateoof the nu c l e i . Possible exceptions are the discussion of single passage experiments by Barclay et a l . (36) and the Oxford group (17). Barclay et a l . describe experiments i n which 3 and Y radiations are observed ( i . e . B for v even and odd) and the i n i t i a l condition i s defined i n terms of an average angle 9 between the p o l a r i z i n g f i e l d HQ and the direction, of the quantization axis. The second reference gives a detailed theoretical discussion i n terms of quadrupole effects which completely explain the experimental r e s u l t s . NMR i n Ferromagnetic Metals: The low temperature nuclear orientation experiments by Kurti et a l . (37) suggested NMR-measurements as an alternative way of study-ing the hyperfine coupling i n ferromagnetic metals. The f i r s t re-sonance was observed i n a specimen of f i n e l y divided fee cobalt par-t i c l e s (38). As the cobalt nuclei f e e l a hyperfine f i e l d , H n, which also defines a l o c a l quantization axis, the resonance can be observed i n zero external f i e l d , and the resonance frequency i s given by: • 22 yH f" = hi The signal strength and l i n e width are found to depend strongly on the method of sample preparation. In well-annealed p o l y c r y s t a l l i n e iron a strong resonance l i n e of approximately 45 KHz width i s observed (39). A cold-rolled iron specimen, however, displays a very weak signal several hundred KHz wide (39). Another example i s given by the resonance ob-served on a n i c k e l specimen. The signal disappears completely after cold r o l l i n g (40). Any metal placed i n a radio frequency f i e l d w i l l tend to ex-clude t h i s f i e l d from i t s central region. Currents are induced by the radio frequency f i e l d and the e l e c t r i c and magnetic f i e l d vectors decrease exponentially into the bulk of the material. A skin depth <S can be defined at which the f i e l d amplitude i s reduced by a factor i / e . The skin depth i s given by (41, 42): (IT a f y y j 2 m Here a i s the conductivity of the metal, f i s the frequency of the ap-p l i e d radio frequency f i e l d , y i s the permeability of the material and ]SQ = 4TT • 10 7 ~~~~ i s the permeability of free space. A pure iron specimeniafttvery low temperatures might have a conductivity of a = 10 9 ^ j - . Near magnetic saturation and at the very high frequencies employed the permeability approaches unity. With these assumptions we f i n d that a frequency of 250 MHz corresponds to a skin depth & = lym. 23 The induced radio-frequency currents also produce eddy cur-rent heating. Usually t h i s heating does not cause problems i n con-ventional NMRi, but i t i s a l i m i t i n g factor i n NMR/ON. experiments, i n which operating temperatures are so low that heat transfer and heat capacities are r e l a t i v e l y small. For a plate of area, A, with the magnetic f i e l d , B, applied along the surface the eddy current heating, Q, i s given by (43): B . 2 ( " ) : 2dl « y y Q Assuming a skin depth <5 = lum and a = 10 9, u = 1 as above, we estimate: .32 . i o * B 2 2ES. sec.G Since a heat leak of 1 ^ r^- i s a s i g n i f i c a n t heat input i n our cryostat, the radio frequency l e v e l has to be kept below ^ 0.01 gauss for oper-ating frequencies of the order of 200 MHz. For M^ JMR/lONj experiments t h i s i s not as serious as i t may appear. The radio frequency f i e l d experienced by the nuclei i n a ferro-magnetic specimen i s many times larger than the externally applied f i e l d . Assuming that the electron spins and the nuclear spins are decoupled, i t can be shown that, i n a single domain with the external radio frequency f i e l d applied perpendicular to the applied d.c. f i e l d , H , the radio frequency f i e l d f e l t by the nuclei i s enhanced by a factor (1- + n) . n i s a function of the angle between the applied f i e l d H and the anisotropy f i e l d , H , and varxessfrom ^ — + ^ , when o a 24 H I IH , to ~ , when H A » H , For i r o n , H ^ 300 G so that for n M a H n ? 0 a ' a 0 H n, H-. > 1 kG, r\ — < 300. In the non-saturated regime the t r a n s i t i o n 0 ~ H Q ~ probiabicl-it.yi,2:and^.therefore..the....absorption rate also, w i l l be enhanced byc-ia. fa.cifcpr (1+n) 2. In multidomain p a r t i c l e s a different enhancement factor i s experienced by nuclei located i n walls and domains (44). When an ex-ternal f i e l d i s applied, the walls w i l l s h i f t u n t i l a demagnetizing f i e l d i s established which i s equal and opposite to the applied f i e l d . The magnetization vector varies i n direction through TT from one side of a domain wall to the other so that the nuclei experience a.large changing f i e l d as the wall moves. On the other hand, enhancement ex-perienced by the domain nuclei i s primarily due to the rotation of the domain magnetization. The wall motion serves to shi e l d the domain nuclei from the applied f i e l d so that the wall enhancement i s larger than the domain enhancement by a factor of -y, where d i s the domain size and 6 the wall thickness, t y p i c a l l y y'^ 10-100. In z e r o - f i e l d NMR only the wall resonance i s observed i n multidomain specimens under ordinary conditions. 25 CHAPTER II RELAXATION The two relaxation processes which are important i n th i s study have been introduced i n the Blbch equations as T^  and T^- Here we use T^ to characterize the spin-spin interaction. I t i s a coupling between the nuclear spins themselves, allowing energy exchange within the spin system. In an NMR experiment t h i s interaction destroys the coherence of the transverse precessing component of the magnetization. The spin-l a t t i c e interaction provides a mechanism f o r energy exchange between the nuclear spin system and the l a t t i c e , t h i s process being character-ized by a time T^ . Spin-Spin Interaction: Suhl (45) and Nakamura (46) have independently proposed a coupling mechanism f o r the spin-spin interaction which i s s p e c i f i c to magnetic materials. Two nuclear spins 1^ and I_. interact through the mutual emission and reabsorption of v i r t u a l spin waves v i a the trans-verse component of the hyperfine interaction. With the l a t t e r written as = SI'S the effective nuclear spin-spin coupling i n a cubic. cry s t a l i s (45) : 26 where r.. i s the distance between the site s i arid j , a i s the l a t t i c e i i • • spacing, A i s the hyperfine coupling constant, S i s the electronic spin, H i s an effective exchange f i e l d and H. . i s the effec t i v e d.c. f i e l d , ex 6 mt IT define the r a i s i n g and lowering operators (I^±il , where 1 ^ and th I ^ are the nuclear spin components of the i nucleus i n a plane nor-mal to the quantization direction defined by . In the long wave-length l i m i t the energy of a spin wave quantum of wave number k i s ~ defined by: H = * V H i n t + Hex a 2 k ^ . C 2 ) In equation (1). the expression i n curly, brackets i s the range function of the interaction. We f i n d that the interaction decreases as (1/r) for short distances and exponentially f o r large distances. I f we as-sume H ^ 10 6 G and H. . ^  10 3 G, i . e . values appropriate f o r cobalt, ex mt ' t h i s l i n e a r dependence on ( l / r ) i s dominant up to a distance of approxi-mately 30 l a t t i c e spacings making the Suhl-Nakamura interaction effec-t i v e over a f a i r l y long range. I t should also be noted that the i n t e r -action i s temperature independent at low temperatures (T<1K). A use-f u l discussion of the interaction has been given by Narath (51). The interaction given i n equation (1) leads to a nearly gaussian l i n e p r o f i l e with the rms width given by: i n t 6 KB ex 27 This yields an estimate of the spinr-spin relaxation time: T 2 . = (<Af>)^ For cubic cobalt T^  has been estimated (48) as: = 7.1 usee/and com-pares quite well with the measured zero f i e l d spin-spiri relaxation time (49, 50): ^ 2 5 usee. Weger et a l . (50) found experimentally that i t i s inversely proportional td the concentration of the active isotope. 'The relaxation observed i n these experiments has a pure ex-ponential decay which i s i n contrast to the predictions from the theory. A l o c a l s t a t i c inhomogeneity of 100 Gauss would account f o r t h i s dis-crepancy with the theory and also explains the observed l i n e width (37, 48). Equation (1) shows that the Suhl-Nakamura interaction decreases as an external f i e l d i s applied. This effect i s observed f o r cobalt i n low (52) and high (49) f i e l d s . tThus the Suhl-Nakamura interaction does indeed give the major contribution to the relaxation i n t h i s metal. On the other hand, studies (53, 54) of ,the effect of micro-scopic inhomogeneities on the spin-spin interaction show that these may decouple the nuclei i f the interaction energy i s not at least equal to the energy s h i f t caused by the inhomogeneity. Thus the Suhl-Nakamura interaction i s reduced and i n many cases i t i s found that the dipolar contribution i s dominant (54). With regard to our experiments i t i s clear that ^are^has to be taken i n interpreting the results i n terms of the Suhl-Nakamura theory. Although T 2 i n cobalt has been explained by t h i s i n t e r a c t i o n , no such study has been performed f o r iron or, i n p a r t i c u l a r , f o r a d i l u t e Co-Fe all o y . Moreover, as explained above, the interaction does have an 2 8 exponential ' c u t - o f f beyond a certain number of l a t t i c e spacings and for cobalt this i s approximately 30. Thus a d i l u t i o n of the active nucleus to more than (-|Q-) 3 ^ 4.10 5 should reduce the Suhl-Nakamura i n t e r -action d r a s t i c a l l y . Although we do not have a cobalt specimen we note that the concentration of our specimens i s i n the range 10 3 to 10 4 so that we might s t i l l expect a r e l a t i v e l y strong interaction between the nu c l e i . Spin-Lattice Interaction:• In the previous chapter we have discussed the time-averaged part of the hyperfine f i e l d <H >. Here, however, i t i s the time-dependent contribution 6h*n(t) that i s of interest where: H = <H > + <5H (t) . n n n The general expression f o r the s p i n - l a t t i c e relaxation of the nuclei due to magnetic interactions with the electrons has been derived by Moriya (55) and i s given by j + CO Y~=^n2 f dt exp (-iu)0t><|6H~(t).SH*(0)|> . (4). 1 ' h -oo Here <|xl> means the s t a t i s t i c a l average of X and co 0 •= Y [<H > ,+ H v 1 1 1 6 0 n L n l o c J i s the nuclear precession frequency about the z-axis. The r a i s i n g and lowering f o r the fluctuating part of the hyperfine f i e l d are given by SH-•= SH ± i6H . Equation-(4) i s a Fourier transform and therefore n nx .ny n K s i g n i f i c a n t contributions to 1/Tn w i l l only be obtained i f the fluctua-29 tions of the s t a t i s t i c a l average <| 6H n(t) • 5^(0) | > have frequency com-ponents near WQ. Experimentally T^T i s observed to be constant and therefore the possible relaxation mechanisms almost cert a i n l y involve the s and d-band conduction electrons. ' In a t r a n s i t i o n metal the main co n t r i -butions are (56, 57): a) the Fermi contact interaction with the s-b.and electrons (58), b) the contact interaction due to core p o l a r i z a t i o n of the f i l l e d s-shells induced by the u n f i l l e d d-band electrons(59), c) the interaction with the o r b i t a l magnetic moment of the d-band electrons(60), d) the spin-dipolar interaction with the d-band electrons (60). '(This contribution i s comparatively small and w i l l not be discussed further )L., Mo>F.iiyja>. (56) has given the expressions of the operators 6H~ f o r each case. Using these operators the relaxation rates are (57): a) b) c) [ 1 ) = 2 h B y n 2 [Hn(S.) N S(E£)] 2  T 1 T S (5) ^ c p = 2 h 8 y n 2 [ H n ( d ) N a ? ( E | ) ] 2 - | [ l + | ( l - C ) 2 ] - F (6) ' t f V o r b = 2 h & f n [ H n ( 0 r b ) N d ( E ^ ) ] 2 . f [ l - ( l - C ) 2 ] - K (7) where 30 N d(E F) = % [ N d f CEF) + N d + ( E F ) ] N d ( E f ) 2 K - N d ^ E F ) 2 + " £ ^ Z H nCS), H n f d ) and H^Corb) are the contributions to the hyperfine f i e l d due to the s-band electrons, the core p o l a r i z a t i o n of the f i l l e d s-shells induced by the u n f i l l e d d-band electrons and the o r b i t a l magnetic moment respectively. NgfJEpO denotes the density of s-electrons at the Fermi-energy EP and Nd(EF,i) i s the average of the densities of the up and down d-electrons Nd*(E*p and Nd|(EpO< respectively. The d-band wave function at the Fermi surface of the impurity atom enters the expressions for 1 1 the relaxation rates (sr-sr) and (V-^-) , v i a the parameter C. It spe-1 ^ 1 cp 1 j l orb c i f i e s the t„ (r r)-character of this wave function. The t o t a l relaxation rate i s : 1, _ , 1 ( 1 v ( 1 . T,T " lT,TJS + lT.T Jep + f S f ^ o r b 1 1 1 11 i OID j. Having formulated the problem, one must estimate the parameters i n equation (5), (6) and (7). Kontani et a l . (57) have done th i s and give the values compiled i n Table I I / l f o r 5 5Mn and 5 9Co i n Fe. I t seems that the o r b i t a l contribution i s the dominant one as predicted by Moriya. As for non-magnetic metals (58) , the theory predicts that the relaxation 31 Korringa constant 3 d impurity i n Fe (sec K)" 1 5 5Mn 5 9Co .23 .34 .10 a 0 3 6.0 1.7 ^ t h e o r . 6.3 2.1 (T.T)" 1 . v 1 exp 9 ± 1 1.3±.l l TN l J e x p . 2 0 . 1 0 "8 3 . 2 - 1 0 " 8 Table I I / l Theoretical estimates f o r the different contributions to the s p i n - l a t t i c e relaxation of 55Mn-Fe and 59Co-Fe_ are given. The t o t a l theoretical and experimental relaxation rates are also given. The l a t t e r are measured by NMR on magnetically saturated specimens. 32 rate 1/T^ i s proportional to the absolute temperature. A comparison between the theory and the z e r o - f i e l d relaxation rates measured by NMR on domain nuclei of the ferromagnetic metals Fe, Co and Ni as well as on impurities i n a ferromagnetic metal host (50, 61, 62, 63) shows that the theory underestimates the relaxation rate by at least a factor of four. NMR studies of the dependence of the s p i n - l a t t i c e relaxation on the external magnetic f i e l d HQ show that the high f i e l d relaxation rates of 59Cd-Cd_, 6 1 N i - N i , 5 5Mn-Ni and 55Mn-Fe are i n quite good agree-ment with the theoretical predictions (64, 65). However, the observed relaxation rates were found to increase when the external magnetic f i e l d was reduced, t i n makingtthese measurements an eff o r t was made to observe domain nuclei exclusively. In an attempt to confirm t h i s result cobalt single domain p a r t i c l e s have been studied (66). However, the p o s s i b i l i t y of p a r t i c l e clustering, thereby producing a multi-domain aggregate, casts some doubt even on the result of this experiment. To date, the field-dependent relaxation rates i n V, Mn, Co, Cu, Nb, Mo, Ru, Rh, Pd i n Fe have been observed by NMRi (57, 67, 68). A l l these studies suggest that f o r domain nuclei a) The relaxation rate 1/T^ decreases monotonically as the p o l a r i z i n g f i e l d , HQ, increases up to a value of Hg>4ftM at which f i e l d no domain walls remain. Then 1/T^ i s constant for large f i e l d values. b) At a l l f i e l d s 1/T^ i s proportional to the temperature, suggesting a conduction electron mechanism. c) The high f i e l d relaxation rates i n a l l cases agree quite well with the theoretical predictions of Moriya. For these reasons the high f i e l d values are taken as the i n t r i n s i c ones. 33 One must emphasize again that there i s some doubt concerning the interpretation of the low f i e l d NMR results. Whereas a magnetically saturated^.specimen has no domain wal l s , walls do appear as the f i e l d i s reduced and i t i s not completely clear that the measured signal does originate from domain nuclei only. The domain wall nuclei are more readily observed by NMR than those i n the bulk material and have a com-paratively short relaxation time. Thus the f i e l d dependence of the measured relaxation time might result from domain wall effects. Relaxation Theory for NMR/ON: The relaxation of the impurity nuclei from an i n i t i a l state |a(t=0)> to a f i n a l state |a(t=°°)> can be observed by monitoring the anisotropy 21 W(9.,t) = • I B (t)U F P (9) (8) v=0 where + 1 B Ct) = I /2v+l C(I,v.,*qm,l0)p..(t) (9) For a system with equally spaced energy levels E M = m h f = m — j — '= mAE and T^ <<T^  the nuclei interact with one another to establish a Boltz- , mann d i s t r i b u t i o n 34 and the nuclear spin system i s at a temperature Tg (69, 70). : Relaxation of the spins from an i n i t i a l temperature Tg(t=0) to a f i n a l temperature Tg,(t=°°), which i s normally equal to the l a t t i c e temperature T^, can be determined by the time dependence of the spin temperature Tg(t). The derivation of the equation describing the re-laxation of the spin temperature i s s i m i l a r to the one given by S l i c h t e r (71). However, i n this case the high temperature l i m i t i s not taken. We s t a r t with the master equation (72): dp +1 =• I (P W -p W ) (11) L T- m m,n K n n,m ^ } dt mm=-Ii ' ' 1-T As we are interested i n the time-dependence of 3 Q = rrfr— . we f i n d : KiS + 1 dp n <j>dBs +1 +1 £ T T n d l T H I - = ^ T n £ T ( p w - p w ) , nn=-II S n=-I m=-I ^ m m,n H n n,m ' where the summation over n has been added to f a c i l i t a t e the solution, We then obtain d3 c In I (p W - p W ) S. L L m,n n n,m = n m ' ' I n dp I I ^ ' ( 1 2 ) where p m i s given by equation (10) . The up and down t r a n s i t i o n pro-b a b i l i t i e s are (73, 74) : 35 W , . = A E [1(1+1) - m(m+l)] 6 X P C- PL A E ) m,m+l — —-2kC 1 - exp (-3T AE) AE W . = — [1(1+1) - m(m+l)] m + 1 , m 2kC ' " " l - exp (-3L AE) (13) where C = T^T i s the high temperature "Korringa constant". From equation (12) we obtain (appendix I ) : d3 g = 1 . I(I+l)-<m2§-<m> m exp (-B AE) - exp(-3LAE) dt 2kC <m2> - <m>2 1 - exp (-3. AE) L (14) Equation (14) can be solved numerically and describes the relaxation of the 1 nuclear spin temperature T g given by the expression 3 g = . This i n s turn defines the orientation parameters B^(t) which then permit the c a l -culation of the anisotropy W(9,t) given i n equation (9) and (8) respec-t i v e l y . The same expression i s given by Bacon et a l . (73) and i s equivalent to an expression which has been derived by Fox (75). The high temperature 'Korringa constant', C = T^T, gives a mea-sure of the relaxation time that i s independent of the temperature and allows a ready comparison with NMR res u l t s . (In f a c t , we employ th i s term following common usage i n NMR/ON l i t e r a t u r e . However, the Korringa re- , la t i o n (58) was o r i g i n a l l y used to describe the interdependence of the re-AHQ laxation time and the Knightshift and i s given by T-T ( 7 5 — ) 2 .) In fact 1 0 a more appropriate 'Korringa constant' would be T^Ty^n^2.- This r e l a t i o n has been shown to be approximately constant f o r a variety of systems (76, 77).) 36 The exact relationship between T^  and T which must be used at low temperatures (kT<hf) , i s : T l = C Cf|) t a n h n ' -Cf T) , showing that, i n f a c t , T^ w i l l approach a constant value at sufficiently-low temperatures. The above expressions (13) f o r the t r a n s i t i o n p r o b a b i l i t i e s assume an interaction between the nuclei and the conduction electrons of the form H = A I*S, where S and I are the electron and nuclear spin operators res-pectively. The energy levels are equally spaced by AE and we take the state |lm = -I> to be lowest. The selection rule under these conditions i s Am = ±1. I t i s noted that the up and down t r a n s i t i o n p r o b a b i l i t i e s are not equal and that the downward t r a n s i t i o n p r o b a b i l i t y can be expressed by: AF W™ +i m = W ™ m + i + §Fr [ r C I + l ) - m(m+l)] m l,m m,m+l zkL As; TT approaches zero W .. goes to zero while W . assumes a constant L r r m,m+l & m+1,m value, i . e . a process analogous to spontaneous emission i s s t i l l present while absorption np longer takes place. Alternately, i f the spin-spin interaction i s weak compared to the s p i n - l a t t i c e i n t e r a c t i o n , each nuclear spin interacts e s s e n t i a l l y only with the l a t t i c e . In an equilibrium s i t u a t i o n , the nuclei s t i l l reach the l a t t i c e temperature T^ . However, during relaxation the system cannot be described by a spin temperature. Based on the master equation (71) and the t r a n s i t i o n p r o b a b i l i t i e s (73) the appropriate relaxation theory (73) 37 can be formulated (appendix I I ) . The master equation i s written i n matrix notation (matrices are denoted by a lower bar): d_ p:(t) = p?p:) (15) dt F i s a tridiagonal matrix with the elements given by combinations of W . and W . m,m+l m+l,m The solution of equation (15) i s f ( t ) = exp K-~ •  pj(t) = exp (-F«t) £(0) + const. Applying the unitary transformation matrices U, U 1 where the columns of U are given by the eigenvectors of F, we f i n d : pT(t) = U • exp(-K-t) • U"1 • P£(0) (16) K i s a diagonal matrix with the elements given by the eigenvalues of F. In practice the evaluation of equation (16) i s complicated by the problem of finding the eigenvalues and eigenvectors of F which i s of dimension (21+1) x (21+1). A standard computer program i s employed' to diagonalize F and solve equation (16). To check the r e s u l t , equation (15) i s solved numerically. Provided a s u f f i c i e n t l y small time i n -crement i s chosen, both methods of course produce the same re s u l t . P r a c t i c a l l y , however, the simple numerical method requires f a r less computer time than the analytic solution. Once the time-dependence of the density matrix elements i s known, the time dependent orientation parameters B^(t) and the aniso-38 tropy W(9,t) can be computed as outlined above. For °^Co-Fe_ the relaxation of the nuclei as predicted by the above ^theories, i s il.Ius'.ter.afce;diin Figure I I / l . The anisotropy i s given as a function of time. We use a value for the Korringa constant C = 2.5 sec- K andaa l a t t i c e temperature T^ = 10 mK. We choose to des-cribe the i n i t i a l state of the system by a temperature T g(t=0) and calculate the -relaxation f o r cases with T g(t=0) i s 20, 50,and 1000 mK. Relaxation as measured by the anisotropy of the y-radiation i s i l l u s t r a t e d for the case where a spin temperature does exist and where a spin temperature does not ex i s t . In the l a t t e r case the system passes through states that cannot be described by a Boltzmann d i s t r i b u -t i o n (7558,7f79)) although the i n i t i a l and f i n a l states are given by a temperature. Especially for those relaxations s t a r t i n g from a higher i n i t i a l temperature the two casesscan be distinguished quite c l e a r l y , primarily by t h e i r different apparent relaxation rates, but also by the shape of the relaxation curve i t s e l f . The curves i n Figure I I / l have been com-puted numerically. The usual time increment i s 2.5 sec. Figure I l / l a shows an example where a 1.25 sec increment has been used. E s s e n t i a l l y rfoa difference exists between the two curves (in Figure II/1'a the curve '0,1' denotes either case). The relaxation as observed by an equatorial counter (6=TT/2) i s also shown. Figure I l / l b shows a curve that i s com-puted assuming that the spin temperature relaxes exponentially (as i s the case i n the high temperature l i m i t ) . F i n a l l y , as i l l u s t r a t e d i n Figure I I / l c when a high i n i t i a l temperature i s chosen the relaxation i s characterized by an almost horizontal i n i t i a l slope. This r e f l e c t s 39 ANISOTROPY s e c FIGURE I / l a Figure I I / l a b c Computed relaxation curves for 6^Co-Fe. The three figures.show relaxa-tion from i n i t i a l spin temperatures of 20, 50 and 1000 mK respectively. The l a t t i c e temperature i s 10 mK. It corresponds to the equilibrium anisotropy W(0,°°). The Korringa constant i n a l l cases i s 2.5 sec K. The curves labelled 0, 1 and 3 are computed under the assumption that a spin temperature does ex i s t . For those labelled 2 i t has been assumed that an independent spin temperature does not exist during the relaxation, the time increment employed i n the numerical solutions i s 2.5 sec except for the curve labelled 0 i n Figure l a for which 1.25 sec has been chosen. Curve 3 i n Figure b shows the very different result obtained when the 'high temperature l i m i t ' i s employed. 41 the fact that the anisotropy W(6,t) for 60Co-Fe^ i s almost equal to unity for temperatures greater than ^  100 mK. When the experiment i s conducted by rapidly changing the tem-perature of the l a t t i c e at time t=0 from T L(t=0) to TL(t=°°), then the i n i t i a l and f i n a l conditions are defined by the respective temperatures. I f the i n i t i a l state i s prepared by resonating the nuclei, a spin tem-perature may not e x i s t , especially i f a strong radio frequency f i e l d i s employed pr i f the radio frequency l e v e l varies throughout the specimen due to the skin depth or l o c a l l y different enhancement factors.' I f T2<<T^ these problems are <al"i-ev-iiat'.e':di because a Boltzmann d i s t r i b u t i o n i s established quickly after the radio frequency f i e l d i s switched off. It should be noted that measuring the anisotropy i n several directions. should define, at least i n p r i n c i p l e , the density matrix p (t=0) more completely. The theories presented do not describe the intermediate cases, where the spin-spin and s p i n - l a t t i c e interaction are approximately equal. To discuss t h i s case a detailed knowledge of the spin-spin i n t e r -action would be required. To avoid this d i f f i c u l t y , the experiment should be designed to allow for the use of either theory. As 1^ i - s inversely proportional to the concentration, i n p r i n c i p l e a wide range of spin-spin relaxation times can be realized. However,, i n practice there may be d i f f i c u l t i e s i n the specimen preparation, and, moreover, there i s a lack of measured T 0 values.. 42 CHAPTER III EXPERIMENTAL APPARATUS AND PROCEDURE In t h i s chapter the cryostat as well as the peripheral equip-ment for the observation of y-xadiation and the generation of the radio frequency f i e l d w i l l be discussed. The cooling of the specimentis\sac:eomprMis'hed'dirinfour.i:di-stinct stages. The cryostateassembiiyyis precdoled by l i q u i d nitrogen and l i q u i d helium to 77K and 4K respectively. Thepparamagnetic s a l t p i l l assembly i s located i n the inner jacket of the cryostateand i s cooled to a tem-perature of approximately 1.2K by thermal contact with a small volume of helium under reduced pressure. At t h i s temperature a magnetic f i e l d of 40kG i s applied to the sa l t p i l l s reducing t h e i r entropy; The s a l t p i l l s are then thermally isolated from the 1.2K bath.and the f i e l d i s slowly removed. Consequently the temperature drops as the entropy re-mains approximately constant (80). In th i s way a f i n a l temperature of the order of 10 mK i s obtained. Cryostat: The apparatuses shown i n Figure 111 /1. It i s suspended from the top pl a t e , which also seals the inner or helium dewar, which hangs inside the nitrogen dewar. Just below the top plate i s the 'nitrogen pot*. It provides thermal anchoring for the pump lines and the e l e c t r i c a l leads. This i s desirable i n order to minimize the heat input by con-43 110.7 Top plate Pumping lines Nitrogen pot Radiation trap Indium sealed flange Outer-jacket Helium pot Indium sealed flange Inner-jacket 22 kG solenoid 40 kG solenoid Nylon spacer Polarizing solenoid Specimen Glass tip on outer-jacket Helium dewar Nitrogen dewar Figure I I I / l A cut-away view of the cryostat. A l l dimensions are i n centimeters. 44 auction into the l i q u i d helium. Three pumping lines lead through the top plate and nitrogen pot to the 'helium pot', the outer-jacket and the inner-jacket. In cross^section the pumping lines are arranged at the corners of an approximately equilateral triangle,, an arrangement which p;rpjV/iid'esmaximum r i g i d i t y . As the pumping speed (81) as well as the e l e c t r i c a l conductivity (82) increase with lower temperatures both the pumping lines and the e l e c t r i c a l leads are reduced i n diameter i n the lower temperature zones. To reduce radiiafri.ve/e heat transfer (83), which can become an important heat leak for those sections of the cryo-stat below 4K, a radiation trap i s placed i n each pumping l i n e between the nitrogen pot and the outer-jacket. A second radiation trap i s located i n the end of the pumping l i n e before i t enters the inner-jacket. In addition several disc-shaped baffles are soldered to the pumping l i n e s . These ensure that as much heat as possible i s absorbed from tfeevaporated helium gas, especially during the i n i t i a l phase of the helium transfer i n t o the cryostat. The outer-jacket, which i s immersed i n l i q u i d helium, encloses thehhelium pot and the inner-jacket, which, i n turn, contains the s a l t p i l l assembly. After-thermal equilibrium i s reached at 4.2K, the helium pot is f i l l e d with l i q u i d helium and thermally isolated from the outer- . jacket by evacuating the l a t t e r . Now the helium pot i s pumped to ap-proximately 1.2K. Helium exchange gas at a pressure of approximately 0005 t o r r (measured at the room temperature end of the pumping l i n e ) i n the inner-jacket allows the removal of the heat of magnetization gener-ated i n the p i l l s when the solenoid f i e l d i s slowly raised to 40kG. When the s a l t p i l l assembly reaches the temperature of the helium pot, 45 the inner-jacket i s evacuated, thus thermally i s o l a t i n g the s a l t p i l l s . Now the solenoids are slowly demagnetized. This w i l l cause the tempera-ture of the s a l t p i l l s to drop. The f i n a l temperature reached i n zero applied f i e l d depends on the paramagnetic s a l t used. Other factors are the i n i t i a l temperature and magnetic f i e l d and the heat input from eddy currents and gas adsorption during demagnetization. The assembly of the apparatus i s f a c i l i t a t e d by the indium O-ring flanges (84) employed on the outer^ and inner=jackets. This avoids tedious soldering of the jackets. The flanges are machined from brass, have f l a t faces and are equipped with an inner shoulder to ensure precise alignment and to allow easy i n s t a l l a t i o n of the indium wire. Pressure i s applied on each flange by s i x screws. Even though spring loading has not been employed the design has been very r e l i a b l e . To avoid an accidental heat leak by metal-to-metal contact between the outer- and the inner-jacket and between the inner-.jacket and the s a l t p i l l assembly, two sets of star-shaped nylon spacers are employed. These spacers ensure the proper alignment of the jackets and the p i l l assembly. The superconducting magnets are slipped over the outer-jacket and are suspended d i r e c t l y from the top plate v i a three th i n wall stainless steel tubes of 1/8" diameter. The cryostat assembly along with the helium and nitrogen dewars i s suspended from a wood frame that i s placed into a sand f i l l e d box. This i n turn stands on a soft 2" foam pad. These precautions together with the basement location of the laboratory ensure that vibrations fromeexternal sources are not transmitted to the apparatus. 46 Salt P i l l Assembly: The design of the s a l t p i l l assembly i s i l l u s t r a t e d i n Figure III/ 2 . CA".;chTome:!*p:o*as.s>iuimT%uiph:at.eijpTisLl?-jyA*el-ds:&3^&rjS^x$s as low as 10 mK when demagnetization takes place from 1.2 K and 35 kG. Tempera-tures below 12 mK are maintained for up to 50 hours and no noticable warming occurs on careful retransfer of l i q u i d helium into the cryostat. The s a l t p i l l assembly.has a heat shield that i s maintained at approximately 50 mK by a f e r r i c ammonium alum s a l t p i l l . It encloses the main p i l l and the heat l i n k almost e n t i r e l y , reducing greatly the heat leaks v i a radiation (83), conduction (85) and gas adsorption (86). The t o t a l heat leak into the main p i l l has been estimated as approximately .1 erg. s e c . - 1 The s a l t p i l l assembly i s attached with 3 screws to the helium pot. A thin tubular spacer, machined from nylon (87), provides s u f f i c i e n t r i g i d i t y and thermal insulation between the helium pot and the guard p i l l . This p i l l and the small a u x i l i a r y guard p i l l at the lower end of the heat shield were loaded with 110 gm of a mixture of powdered manganese ammonium sulphate, water and rotary pump o i l . The r e l a t i v e proportions were respectively 77%, 3% and 20% by weight and were determined empiri-c a l l y . The amount of water was s u f f i c i e n t just to moisten the powder. Enough o i l was then added.to make a thick paste. Short pieces of enamel-insulated, gauge 36 copper wire were embedded i n the mixture to aid thermal contact between the sa l t and the copper walls (88). A t i g h t , re-movable s l i p - j o i n t between the guard p i l l and the heat shield provides thermal contact and allows the separation of the two parts during assem-bly. The a u x i l i a r y guard p i l l s l i p s into the lower end. of the heat shield. 4 7 3 9 . 5 4 . 3 5 . 2 . 2 5 _ 1 16.5 ~ 7 .25^ 3 . 0 7 0 3.0 T =s;a= -142 -L27 -3.9 -.63 - .3 -3.6 -14 -.81 -4.2 - 6 8 H e l i u m pot N y l o n s u p p o r t G u a r d p i l l and h e a t s h i e l d N y l o n s u p p o r t f o r m a i n p i l l N y l o n s p a c e r p o i n t s M a i n p i l l and h e a t s h i e l d A u x i l l i a r y g u a r d p i l l N y l o n s p a c e r H e a t l i n k N y l o n t i p Figure I I I / 2 . T h e . p i l l system. A l l dimensions are i n centimeters, 48 Apiezon N grease was used on these j o i n t s to improve heat contact. To minimize eddy current heating (89) the heat shield has four long narrow slots running p a r a l l e l to i t s axis. With demagnetization rates not ex-ceeding 4 KG/min., no eddy current heating was apparent. The main p i l l i s suspended by a long threaded nylon rod from the top of the guard p i l l . In t h i s way the p i l l s ;can be spaced very closely while allowing the use of a r e l a t i v e l y long nylon support to minimize the heat input due to conduction. The main p i l l i s centered within the heat sh i e l d by two sets of nylon points. These are located near either end and were fashion-ed from short pieces of f i s h i n g l i n e which were 'screwed* into tapped holes i n the heat shield . The main p i l l was loaded with 220 gm of a slur r y prepared from powdered chrome potassium sulphate, water and rotary pump o i l (77%, 3%, 2iD'.% by weight). Thermal contact between the sa l t and the specimen i s established by the heat l i n k . I t was made from a copper rod of .81 cm diameter. 42 OFHC copper leaves of .001" thickness were hard-soldered into a s l o t i n i t s upper' end while the lower end was machined f l a t to receive the specimen. The p i l l was loaded by packing the s l u r r y between the copper leaves while they were drawn into the thin walled bakelite s h e l l that i s employed as a p i l l -former. The main p i l l and the heat lin k are surrounded by the heat jshiielldvwhlchi has a nylon extension i n order" to allow radio-frequency f i e l d s to be applied to the specimen. Two photographs of the s a l t p i l l assembly as well as one of the assembled inner cryostat are shown i n Figure I I I / 3 . iapr.'.'-' o.:c>-cting Magnets: Figure H I / 3 The three photographs show a) the salt p i l l assembly, b) the inner jacket, helium pot and O-ring flange of the outer-jacket and c) the magnet assembly which is mounted over the lower part of the outer-jacket. 50 Superconducting Magnets: The f i e l d required f o r the magnetic cooling of the s a l t p i l l s as well as the po l a r i z i n g f i e l d are generated by superconducting mag-nets. Two of the three units used were designed (90) and b u i l t (91) by us. A high magnetic f i e l d i s applied to the entire 'salt p i l l as-sembly by two solenoids. The mainppill i s located within a Magnion superconducting solenoid which produces a maximum f i e l d of 50 KG at 55A. This f i e l d i s extended to the upper guard p i l l by a second, smaller solenoid, which was wound from copper-stabilized, Nb-Ti wire (92). Care was taken to use a r i g i d former, to avoid sharp bends i n the wire, to pack the layers well and to insulate each layer completely with a thin layer of mylar. The outermost winding i s protected by a layer of t i g h t l y woven nylon cord. The persistent mode switch and the contacts (93) between the normal and the superconducting wires are described i n Appendix I I I . The complete unit was vacuum-impregnated (94) i n pa r a f f i n wax, allowing a very r e l i a b l e quench-free operation up to 40 A. I t i s necessary to repeat the potting procedure occasionally since the wax does become ' b r i t t l e ' on repeated thermal cycling. The p o l a r i z i n g solenoid which s l i p s over the narrow t i p of the outer-jacket was designed.to have an approximate Helmholtz config-uration i n order to provide a r e l a t i v e l y open passage for both the ax i a l and equatorial y-rays. The design was optimized with the aid of a computer program which calculated the s p a t i a l f i e l d d i s t r i b u t i o n as 51 a function of c o i l parameters. The f i e l d inhomogeneity i s less than 1% over a sphere of 1.5 cm. diameter. E s s e n t i a l l y the same construction pri n c i p l e s as described for the large solenoid were employed. As the contacts between the superconducting wires of the magnet windings arid the persistent switch have a f i n i t e resistance we expect that i n the persistent mode the magnet current w i l l slowly de-crease with a time constant T = Even for the r e l a t i v e l y small induc-tance of the p o l a r i z i n g solenoid the current, and thus the magnetic f i e l d , remained constant to within 1% over several hours. This was satisfactory for the experiments. The current leads from the cryostat top plate to the magnets . were chosen to minimize the joule and conduction heat input into the l i q u i d helium (95). Special attention has been paid to the leads that carry the rather large current to the solenoids. In contrast to pre-vious designs copper-stabilized, superconducting wire was used. The copper cross-section was chosen to be the same as f o r an 'optimum lead' (95). The Nb-Ti core adds a ne g l i g i b l e conduction heat leak. Yetthose sections immersed i n helium are superconducting and thus contribute no joule heating. Figure III/4 i l l u s t r a t e s the series connection of the solenoids. The current i s normally passed through the f i r s t and la s t lead only. Therefore, the two wires from the interconnecting points between the magnets and the top of the cryostat can be made of comparatively small diameter. By having the appropriate magnets e i t h e r . i n the normal or persistent mode, they can be charged or'discharged i n any combination. For f u l l protection of the magnets against a quench, reverse biased diodes are connected to the leads at the top of the cryostat. 52 QUENCH SENSE 100 A MAGNET SUPPLY HEATER CURRENT SUPPLY T 2$ PROTECTION DIODES 1 N 3260 i 1 4 K 22 kG SOLENOID 50 kG SOLENOID POLARIZING SOLENOID 1) 22kG solenoid i . d . = 4.9 cm,, I = 10.2 * 2.8 cm. Wire: Supercon type M T48B Nb-Ti, core = ,?254 mm 0, Cu mantel = .406 mm 0. 2) 40kG solenoid i . d . =5.1 cm., I = 17.8 + 3.8 cm,., B kG j = .794 ^ j - Ventron Magnion Inc., CF 40-200-45039. 3) Pol a r i z i n g solenoid i . d . = 3.4 cmv, t = 4.0 + .3 cm.,, B kG Y - .320 j-r inhonogeneity < 1% i n volume,of 1.5 cm. 0.-Wire as 22 kG solenoid. 4) • Ventron Magnion Inc. CFC-100. Figure III/4 The superconducting magnet system. The solenoids are suspended i n the helium dewar while .the protection diodes are mounted near the Cryostat's top plate. 53 Should a quench occur, these c l i p the large voltage and dissipate most of the energy, thereby avoiding excessive helium b o i l - o f f . Of course charging any of the magnets w i l l induce a small current into those that are already i n the persistent mode, and due attention was paid to this effect when operating the magnets. Carbon Resistor Thermometry: Carbon r e s i s t o r thermometry (96, 97) i s a very useful tool for monitoring the temperature at various c r i t i c a l points i n the cryo-stat . In order to make measurements down to temperatures of the order of 10 mK, a resistance bridge with ultra-low power dissipation i n the sensing carbon r e s i s t o r i s required. Such a bridge has been designed and b u i l t . Its block diagram i s shown i n Figure HI/5 while appendix IV presents a short discussion and the complete c i r c u i t diagram. With this instrument i t i s possible to monitor the temperature not only of the helium bath and the guard p i l l , but also of the main p i l l . Know-ledge of the temperature at these points ojptimiizes.hthexexperimen.tal pro-cedure and helps the diagnosis of experimental malfunctions. Transmission Line into the Cryostat: The radio frequency f i e l d required f o r NMR/ON experiments i s generated by two single wire loops wound i n a Helmholtz configuration. A small inductance was chosen to avoid self-resonance i n the c o i l . It was wound d i r e c t l y conto> the glass tip.which i s attached to the inner-jacket by a 1" diameter Kovar seal. G.E. 7031 varnish holds the two 54 33 Hz OSCILLATOR POWER LEVEL PHASE-SHIFTER .1-10 BRIDGE LOW NOISE PREAMPLIFIER GAIN=100 NARROW BAND AMPLIFIER 250 ADJUSTABLE GAIN AMP. .01-1000 MULTIPLIER METER AMPLIFIER 10 Figure III/5 Block diagram of the pico-watt resistance bridge. With a carbon r e s i s t o r sensing element temperatures as low as 10 mK were measured. 55 wire loops i n pos i t i o n . As a frequency band from 150 to 300 MHz was required, i t was not possible to tune the c o i l . Therefore a dras t i c mis-match existed between t h i s predominantly inductive load and the 50 fi transmission l i n e that connects the c o i l to the radio frequency gen-erator. A standard .50 fi coaxial cable was used between the radio f r e -quency generator and the top plate of the cryostat. From there a 50 coaxial cable of small diameter (approximately 1.8 mm diameter over a l l ) was taken to the multipin feedthrough (98) i n the flange of the outer jacket. This i n turn was soldered d i r e c t l y to a transmission l i n e transformer (99) which matches the 50 fi coaxial cabie to a p a r a l l e l transmission l i n e (100) of approximately 50 fi. The transformer which isolates input and output was wound onto a f e r r i t e ' t o r o i d ' ( i n n e r d i a -meter: .72 cm, outer diameter: 1.27 cm, height: .48 cm) which, f o r frequencies of above approximately 30 MHz, acts, merely as a support for the windings. Two pieces of #32 copper wire, insulated with enamel, were twisted together and "8 turns were placed on the t o r o i d as evenly as possible. A twisted p a i r of #38 enamel insulated copper wire was used for the p a r a l l e l transmission l i n e from the transformer to the 1 K bath and to the Helmholtz c o i l . • These wires were glued with G.E. 7031 varnish to the helium pot and to the inner jacket which were previously coated with a f i l m of the varnish. Measurements employing time-domain reflectrometry have indicated that t h i s arrangement has no major mismatches. The radio-frequency magnetic f i e l d i n the Helmholtz c o i l was measured at room temperature with a small single-turn test c o i l which i s connected d i r e c t l y to the probe of a radio frequency mV-meter. 56 A maximum f i e l d of approximately 10 mG i s obtained at the frequencies of i n t e r e s t . Operating Modes and Electronics: In our experiments three different modes of data acquisition were u t i l i z e d : pulse height analysis (PHA), the recording of resonance l i n e shapes, and relaxation measurements. In the PHA mode an axial or equatorial energy spectrum was accumulated i n the multichannel analyser. Simultaneously an estimate of the a x i a l and equatorial count rates was obtained from the single channel analyser (SCA) modules. These were displayed on scalers and gave an immediate indication of the state of the experiment. When studying the resonance l i n e shapes the analyser was set to the multiscaling mode and the counts from the a x i a l and equa-t o r i a l SCA's were accumulated for a )po?esett time i n t e r v a l (dwell-time). A record of counts versus frequency was stored i n the analyser memory. F i n a l l y , when a relaxation time was recorded the a x i a l and equatorial counts were also multi-scaled. A record of counts versus time was obtained.. The i n i t i a l state from which the nuclei relax to the l a t t i c e ' temperature, T^, was prepared by one of two methods. In the f i r s t method a modulated radio frequency f i e l d was applied during the f i r s t few channels, f o r example the f i r s t twenty. Alternately a small mag-neti c f i e l d was applied to the s a l t p i l l s thus warming the specimen to an i n i t i a l temperature.' When the multiscaling process reached a preset channel the specimen temperature was reduced by demagnetizing the s a l t 57 p i l l s . This technique w i l l be referred to as 'fast p a r t i a l demagneti-zation * . The experimental arrangement i s i l l u s t r a t e d i n Figure HI/6 which gives a block diagram of the electronics. There are three func-t i o n a l sections: the radio frequency equipment <3 detectors and associated electronics, and the multichannel analyser. A l i s t of the s p e c i f i c instruments used i s given i n appendix V. The Wavetek programmable radio frequency generator was modi-f i e d to produce an internal triangular (instead of sawtooth) frequency modulation of adjustable width and frequency. Inputs for externally blanking the radio frequency output and slowly s h i f t i n g the. centre f r e -quency have also been provided. This l a t t e r featu-recwasarequiijed- -when recording the count-rate as a function of frequency. The control voltage that slowly s h i f t s the center frequency was derived from the analyser's 'x-output'. v i a the 'frequency sweep interface*. In some experiments a radio frequency amplifier was required to boost the out-put from the radio frequency generator to approximately 1 V • Normally a 5" x 5" Nal detector and a Ge(Li) detector were used to count the y-Tadiat-ion along the a x i a l and equatorial directions respectively. For 6 0Co and 51fMn y-radiation the resolution of the Nal detector i s s u f f i c i e n t . The main disadvantage i s the strong dependence of the gain of i t s photo m u l t i p l i e r on the magnetic f i e l d . Nevertheless, a Nal. detector i s required to give the high count-rates needed especially i n the relaxation experiments. The t h i r d block i n Figure HI/6 contains the time base and control c i r c u i t as well as the multichannel analyser. In the PHA-mode -t I I r . f . AMPLIFIER r . f . GENERATOR FREQUENCY SWEEP INTERFACE EQUATORIAL Ge(Li) PRE-AMPLIFIER LINEAR-AMPLIFIER SCA SCALER AXIAL Nal PRE-AMPLIFIER LINEAR-AMPLIFIER SCA SCALER MULT I -INPUT MULTI-SCALING SCALER III on oo ANALYSER PAPER-TAPE PUNCH Figure H I / 6 Block diagram of the electronics.' The three major blocks contain ,the radio frequency".equipment, the y-ray detectors and counting equipment and the multi channel analyzer with i t s associate instruments. 59' only the multichannel analyser was used. Its input was connected to either the a x i a l or equatorial l i n e a r amplifier. Routing was not used since the count-rates i n the two channels were too high and too d i f f e r e n t . This would have resulted i n an interdependence of the recorded spectra. In order to record the counts from both the a x i a l and the equatorial SCA i n the multiscaling mode and to provide a time base (dwell-time) and the c r i t i c a l timing required i n the relaxation experi-ments a multi-input multiscaling interface (appendix VI) was designed and b u i l t i n t h i s laboratory. This allowed up to four inputs to be re-corded simultaneously with no dead-time. The counts were placed i n subsequent channels of the analyser which was set i n the multiscaling mode. For data storage the information accumulated i n the memory of the analyser was punched sontoi paper tape. At a l a t e r time these tapes were then converted into a disc f i l e on the IBM-computer: t h i s was the basis for a l l subsequent analyses. I f a more permanent storage of the information was required, magnetic tape was used. Data Analysis: The raw data were placed into-a disc f i l e either from the paper-punch tape v i a the routines *RDPTP and INTERP (10'1>) or from mag-net i c tape. Each 'spectrum' was stored as a sequence df 256 numbers corresponding to the 256 analyser channels used. At the beginning of each f i l e some space was reserved f o r i d e n t i f i c a t i o n and description. The analysis of an energy spectrum was accomplished by a computer program (102). F i r s t the spectra taken at 4 K (warm spectra) 60 were analysed. These yi e l d e d the normalization count (warm counts) and a reference centroid. A t y p i c a l s i t u a t i o n i s i l l u s t r a t e d i n Figure HI/7. Summation from ' s t a r t ' to 'stop' y i e l d e d the t o t a l count under the peak. The background count was obtained by f i t t i n g a s t r a i g h t l i n e between the two sections c a l l e d 'width'. The difference between the t o t a l and the background count i s the 1 corrected count'. The peak p o s i t i o n was checked and i f necessary corrected by comparing i t s centroid with the reference centroid. Values f o r the uncorrected and corrected anisotropy were obtained by normalizing the t o t a l and corrected counts r e s p e c t i v e l y with respect to the warm counts. lEjr/r.ojs estimate si based on the counting s t a t i s t i c s were calc u l a t e d . The l i n e shape data which represents a p l o t of count rate versus frequency i n an NMR/ON experiment were analysed by graphing the points. Usually to obtain b e t t e r s t a t i s t i c s and to reduce the number of points to be p l o t t e d , up to 10 successive data points were added. Information such as values f o r the resonance frequency, the l i n e width and the destruction o f the anisotropy were obtained d i r e c t l y from these p l o t s . The analysis o f the relaxation data was based on the theory discussed i n the previous chapter. The Fortran program FITT1 read the relevant nuclear and relaxation parameters as well as the information concerning the relaxation record from cards. The data p o i n t s , however,, were read d i r e c t l y - from a d i s c fiJTe?..- Figure HI/8 i l l u s t r a t e s a t y p i c a l r e l axation record as i t was observed from the a x i a l counts of a 6 0Co-Fe specimen. The radio frequency f i e l d was switched on f o r a period long enough to produce maximum destruction of the anisotropy over a s u f f i c i e n t 61 30000+ 2 0 0 0 0 -10000 0 COUNTS 0 O o o WIDTH G A P 0 " ° - o - ? . WIDTH >GAP START STOP -0-O-c 0 - O - r , . Y"°-0-0 o o o o o CHANNEL FIGURE TH / 7 ^he analysis of a t y p i c a l y-rsy energy spectrum i s i l l u s t r a t e d . 20000+ 18000 + COUNTS AXIAL 16000 0 NCH2 NCHI O o ° cf.on o o o o o o o NCH3 NCH4 100 200 300 400 sec FIGURE HI/ 8 A t y p i c a l a x i a l relaxation record i s shown. The i n i t i a l and the f i n a l anisotropy are obtained from the counts between NCHI - NCH2 and NCH3 - NCH4 res-pectively. The specimen was 60Co-Fe_ and the e q u i l i -brium l a t t i c e temperature was 12 mK. 62 number of channels between NCH1 and NCH2 y i e l d i n g a f a i r l y accurate count C0NT1. This represents the i n i t i a l condition. At the end of'NCH2 the radio frequency f i e l d was switched o f f allowing relaxation to occur. The relaxation was observed f o r a time long compared with the relaxation time T^. Thus the counts between NCH3 and NCH4, were taken when the impurity nuclei were at the equilibrium l a t t i c e temperature T . From Li these the average C0NT2 was obtained. The warm count was computed from C0NT2 and the anisotropy W(T ). The l a t t e r was obtained from a PHA measurement which was made after the relaxation record. The anisotropy W(e,t=0) was computed from the warm count and C0NT1. An i t e r a t i v e routine was employed to fi n d the i n i t i a l temperature corresponding to C0NT1. With the exception of the 'Korringa constant', for which an i n i t i a l estimate has to be given,, a l l the parameters required to spe-c i f y the relaxation were known and a theoretical relaxation curve f o r the anisotropy W(0,t) was computed under one of the following assumptions: 1) A spin temperature does exist (J2«T^) 2) A spin temperature does not exist 3) A purely exponential relaxation with time constant T^ i s assumed., The f i r s t two theories are exact, i . e . the high temperature approximation i s not made i n t h e i r derivation. The la s t assumption of course i s un-r e a l i s t i c . However, as computations are t r i v a l , i t provided a convenient check on the program. In addition, t h i s mode took.comparatively l i t t l e computer time and therefore was of some use for preliminary analysis and comparison. F i n a l l y a 2 and X 2 values were computed between the experi-mental and theoretical relaxation curves. Different weight could be 63 applied to up to ten sections of the relaxation record. In most cases only the f i r s t 90% of the decay curve was analysed with a l l channels weighted by unity. F i n a l l y an i t e r a t i v e process was employed that systematically found that 'Korringa constant'"for which the X 2 value was a minimum. Magnetic Saturation of Specimen: Many of our experiments were performed on samples which were not f u l l y magnetized. To analyse these data the following model was used. For a p o l y c r y s t a l l i n e ferromagnet^*cpartially magnetized i n an applied f i e l d , H Q , the normalized y-^ay intensity measured along the direction of the applied f i e l d , H ^ , i s given by wco)- = I f-. w(0.) (i) i where f i s the volume fr a c t i o n of domains for which the magnetic axis i s at an angle, 0^, to the direction given by fi^ (assuming uniform den-s i t y of active nuclei and complete alignment of the impurity atoms within each domain). Assuming a model where a f r a c t i o n , F, of the domains i s comr pl e t e l y aligned and the remaining ( 1 - F) domains have a random orien-t a t i o n , we can express the observed anisotropy W(0)' by W(0) ' = F • W(0) + (1 - F) • 1 t h u s F = 1 W(0) - 1 (2) 64 Here W(0) i s the anisotropy of the magnetically saturated specimen. In t h i s model the observed relaxation of the anisotropy i s attributed to those nuclei located i n the aligned domains. In our analysis of the relaxation data, this was realized by subtracting a f r a c t i o n , F, of the warm counts from the observed counts. Expressed i n terms of the observed bulk magnetization, M', th i s model of complete alignment and random orientation yields f o r the f r a c t i o n a l magnetic saturation M1 = FM or F .= ' §~ (3) Here M i s the saturation magnetization. Thus i n t h i s model the f r a c -t i o n of aligned domains can be estimated both from the observed aniso-tropy and the bulk magnetization measurement. We s h a l l c a l l the former measurement F^ and the l a t t e r F^. To obtain the magnetic saturation of the iron host at room temperature, a small c o i l was wound around the specimen. An a.c. wheatstone bridge was used to measure the inductance of the c o i l , while a d.c. magnetic f i e l d was applied p a r a l l e l to the specimen surface. F^ was computed from the observed values. The frac-t i o n a l saturation, F^, was also measured. Both curves are shown i n Figure HI/9. It i s apparent that the bulk magnetization reaches a constant value at a lower f i e l d than the anisotropy. This d i f f i c u l t y i n obtaining the f u l l y-rsy anisotropy has been noted f o r example by Cameron et al'. (106), Ben-Zui e t ' a l . (107) and Krane et a l . (108). The implications for precision nuclear orien-tation thermometry are discussed by Berglund ct a l . (1(5.0). 65 F 1.0 f . 8 e .6 + .4 1 .2 O- M M Wo)". x=COS 0 '0 LO 2.0 3.0 H 0 kG Figure HI/9 The f r a c t i o n a l magnetization, F, of the 6 0C0 ~ Fe specimen i s shown. The data points marked by a small c i r c l e were obtained by measuring the inductance of a c o i l that was wound over the speci-men, while the remaining points are derived from nuclear orienta-t i o n measurements. 66 We should note that an alternate model that i s perhaps less r e a l i s t i c has been used i n the l i t e r a t u r e (36, 106, 108). In this model i t i s assumed, that the d i s t r i b u t i o n of angles, 0^, can be replaced by an average angle, 0. Expressing the observed anisotropy by W(0)' we have: W(0)• = W(0) (4) Keeping only terms to second order, we f i n d : W ( 0 J ' - 1 , h 3Ccos*0 - 1) ' (5) W(0) - 1 The same model yields f o r the magnetization M' — = C O S 0 = FM (6) which i s the same result as given i n equation (3). Employing equation (5) we have computed cos0 from our nuclear orientation data. These values are also plotted i n Figure HI/9. This model, of course, should be appropriate only f o r small angles. Indeed good agreement with the values f o r F^ i s found i n this range, suggesting that the above model might be more appropriate than the one of complete alignment and random orientation of the domain magnetization. However, two independent explanations have been given that account for the di s -crepancies observed under the f i r s t model. Bozorth (103) explains the apparent d i f f i c u l t y of obtaining magnetic saturation by an increase i n the c r y s t a l l i n e anisotropy cons-tants for i r o n , cobalt and n i c k e l on cooling. (Unfortunately we have 67 no measurement of the magnetization at helium temperatures. Such mea-surements are given i n reference (106). These indicate that a compara-t i v e l y large magnetic f i e l d i s required to achieve saturation at low temperatures.) So f a r we have assumed that complete alignment of the impurity atoms within a domain occurs independently of the applied f i e l d . How-ever, as discussed by Aharoni (104) the impurity atoms may align along certain c r y s t a l l i n e axes because of magnetbstrictive effects and to a lesser extent magnetocrystalline and magnetostatic forces. That i s , a l o c a l magnetic hardness e x i s t s . Consequently the magnetization measure-ments and the nuclear orientation experiments would not measure the same property. We note that i t has been shown recently (105) that magnetostrictive effects are n e g l i g i b l e at least f o r Cd-Ni_, throwing some doubt on Aharoni's explanation. 68 CHAPTER IV FIELD DEPENDENT RELAXATION TIME OF 6 0C6-F_e, 54Mn-Fe_ AND 5t*Mn-Ni It has been pointed out i n Chapter I I I that the theory'of Moriya for nuclear s p i n - l a t t i c e relaxation of the bulk nuclei i n a ferromagnetic material i s found to be applicable only to magnetically saturated samples. A f i e l d dependence of t h i s relaxation time has been observed by NMR measurements. As the relaxation of the wall nuclei i s faster than that of domain nuclei this f i e l d dependence could be ex-plained i f an increasing number of wall nuclei i s observed as the ap-p l i e d f i e l d i s lowered. These nuclei are observed more' readily since the enhancement of the radio-frequency f i e l d f o r them i s much larger than for those i n the bulk. Although special methods e.g. pulsed NMR at high power levels or s h i f t i n g of the walls with a magnetic f i e l d pulse (57) have been applied there s t i l l exists an uncertainty i n the interpretation of the experimental r e s u l t s . Possibly because of these uncertainties l i t t l e interest had been shown i n explaining these phenomena t h e o r e t i c a l l y . I t was im-perative to demonstrate whether or not the observed effect was, i n f a c t , due to an unexplained, field-dependent relaxation process for the domain nu c l e i . Nuclear orientation would appear i d e a l l y suited f o r an inde-pendent investigation of the f i e l d dependence of the s p i n - l a t t i c e re-laxation because a l l impurity nuclei i n the specimen are observed with 69 equal p r o b a b i l i t y and most are i n the domains. Assuming a uniform d i s t r i b u t i o n of the impurity atoms, the fraction of wall nuclei that i s observed i s given by the 'wall volume' as compared to the domain volume. Assuming a wall thickness (61) of 10~ 6 cm. and a domain size of 10 - 1 + cm. we fi n d that only ^1% of the nuclei are i n walls at zero applied f i e l d . At applied f i e l d s greater than a few hundred gauss the domain size i s increased, and consequently the fr a c t i o n of wall nuclei i s reduced. When a resonant radio frequency f i e l d i s employed to pre-pare the i n i t i a l state from which relaxation w i l l take place the des-truction of the anisotropy w i l l be greater f o r those nuclei located i n the walls. I f , for example, a 1% abundance of wall nuclei with a 100% destruction of t h e i r anisotropy i s assumed and a signal s = .1 i s ob-served, then the wall nuclei w i l l contribute approximately 10% to the observed signal. Even with t h i s very pessimistic estimate f o r the NMR/ON method only a very small change i n the relaxation time could be explained. Alternately the fast p a r t i a l demagnetization method can be employed i n the nuclear orientation relaxation experiments. This w i l l completely eliminate the possible disadvantages of the NMR/ON method and provide a check on these measurements. Relaxation measurements ob-tained with t h i s rion-resonant technique and a discussion of these re-sults, i s given i n the last chapter. f§p'e:co)ments3.o:ff• 6 QC6-Fe, 54Mn-Fe_ and 5*Mn-Ni have been chosen for investigation. Both 5 9C6-Fe and 55Mn-Fe have been studied by con-ventional NMR and thus a comparison of the measurements can be made. 5t|Mn-Ni affords an opportunity to investigate the effect i n a different 70 host material. In addition both 6 0Co and 5ttMn have a conveniently long h a l f - l i f e and the decay schemes are Well known. Specimen Preparation: The host materials were cut from iron or n i c k e l sheets of .3 mm thickness and 99.99% purity (obtained from tU:6hnson>Mat;.they/ Ltd. (109)). The specimens were prepared by d i f f u s i n g the a c t i v i t y a short depth into the host material. The surface of a sheet of the host material was caref u l l y po-lished with emery cloth of progressively f i n e r grades and then with various polishing compounds f i n i s h i n g with jeweller's rouge. A piece measuring approximately 5 mm x 5 mm was cut from the sheet. A drop of the active solution was placed on the polished surface and evaporated to dryness. The carrier-free solutions of 6 0CoCl2 and ^ MnCl^ were ob-tained from New England Nuclear Corp. (110). Since cobalt i s more electronegative than i r o n , the cobalt atoms'plate the surface of the iron host spontaneously. Manganese does not plate spontaneously onto either iron or n i c k e l . However, i t was found that providing a c a r r i e r -free solution of the a c t i v i t y was used, approximately 50% diffused into the host material on annealing the specimen. As these specimens were to be used f o r NMR/ON experiments, i t was important that the radio-active atoms were located within the skin depth of the radio frequency f i e l d which i s approximately 1 ym. The di f f u s i o n of a material that i s evenly spread on one side of a plate can be adequately described by the one-dimensional d i f f u s i o n * 71 equation (111) : dc_ _ D d 2c, dt dx 2 Here the concentration of the material being diffused i s c m o \ e and & cm3 D i s the di f f u s i o n c o e f f i c i e n t . From this equation the mean d i f -sec fusion depth A i s found to be: A = /fPF Values f o r D are given i n the l i t e r a t u r e (112) i n terms of the norma-l i z e d d i f f u s i o n c o e f f i c i e n t Dn and the activation energy Q —^— : 0 b J mole D = D exp (-9<L •) RT with R = 1.987 C a l mole«K For the di f f u s i o n of the Co-atoms i n the iron host a di f f u s i o n time of 60 minutes at 850° C was estimated and used i n the specimen pre-paration. The various data found f o r the diff u s i o n of Mn i n Fe and Mn in.Ni were inconsistent. In practice, a d i f f u s i o n time of 30 minutes ' at temperatures of 900° C was found satisfactory. A di f f u s i o n depth of approximately 1 ym was obtained i n each case. This was estimated by chemically 'polishing' and weighing a test specimen into which a few yCi of a c t i v i t y had been diffused. From a plot of the a c t i v i t y remaining in the specimen.versus etching time the mean diff u s i o n depth was ob-tained. For the iron host a solution of n i t r i c acid: hydrofluoric acid: water i n the ratios 3:7:30 by volume (113) was used while a mixture of 7 2 n i t r i c acid: s u l f u r i c acid: orthophosphoric acid: g l a c i a l acetic acid i n ratios 3:1 : 1:5 by volume was employed for the chemical etch-ing of the n i c k e l . In a l l cases concentrated acids were used. The a c t i v i t y was diffused into the specimen by annealing i n a hydrogen atmosphere. The sample was placed i n a small ceramic boat which i n turn was put i n a long quartz tube. This tube was placed i n an oven such that the specimen i t s e l f would be outside the central hot area. A\ stow continuous stream of hydrogen was passed over the specimen and the oven was preheated to the required temperature. Then the quartz tube was shifted so that the specimen was located i n the center where i t warmed up quickly. This defined the s t a r t i n g time of the d i f f u s i o n process. After the appropriate time period had elapsed the quartz tube was pulled out of the oven far enough for the specimen to cool quickly. After cooling, the specimen was- etched to remove any undiffused surface activity.' For the iron host, a 10% solution of hydrochloric acid i n water was used while a 10% solution of the second p o l i s h i n g mixture described above was used on the n i c k e l specimens. No d i f f i c u l t y i s to be expected for the preparation of the 6 QC6-Fe specimens. However, iff i s reported that the preparation of specimens of 5tfMn i n Fe or Ni i s not so reliable.' Cameron et a l . (114) report that they encountered considerable d i f f i c u l t y especially with Mn-Fe. They observed evaporation of the manganese a c t i v i t y during annealing. < Also t h e i r experiments suggested that a considerable f r a c -t i o n of the manganese atoms were not located i n substitutional l a t t i c e s i t e s because after cooling, the change i n angular d i s t r i b u t i o n of the radiation was much smaller than expected. In fact no such d i f f i c u l t i e s 73 have been' experienced with bur specimens provided a carrier-free solu-t i o n of 51fMnCl2 was used. Perhaps the surface preparation of the specimens i s also ; an important factor. Relaxation Results: The relaxation times of 6 0Co-Fe, 5t*Mn-Fe and 5t*Mn-Ni were measured by nuclear orientation methods. Two specimens of 6 0Co-Fe have been investigated. Considering the amount of a c t i v i t y present, and the volume through which i t i s diffused, the concentration of radio-active nuclei i n the two 6 0Co-Fe .samples investigated was estimated as 0.02 and 0.1 aatat%% on average over the skin depth, while the con-centrations ,of the 5t*Mn-Fe and the 5ttMn-Ni specimens were .0012 and .0018 att,%,respectively?;y. Typical high and low f i e l d relaxation records are shown i n Figure IV/1. Note that a drast i c change i n the relaxation rate i s evident. Similar measurements were made on a l l our specimens and the results are shown i n Table IV/1 and Figure IV/2. The Korringa constant has been computed under the assumption that (I) a spin temperature does exist and (II) that a spin temperature does not e x i s t . The goodness of f i t between the theoretical curves and the experimental data i s expressed i n terms of a X 2-value. Assump-tion (I) provides a marginally better f i t than assumption ( I I ) . • There-fore we have plotted only the results computed under the assumption that a spin temperature e x i s t s . It i s found f o r a l l four specimens that the Korringa constants computed under assumption (II) are approxi-mately 15% larger than those computed under the spin temperature COUNTS 74 10000+ 9 0 0 0 + 8000+ ' 0 Ho=2.0 kG r?f. o n i — i 100 200 300 400 t sec 1000+ 10000+ 9 0 0 0 V COUNTS 0 H0=.94kG rrf.on 100 200 300 400 sec 02 Figure IV/1 Typical high and low f i e l d relaxation records obtained from the 6 0Co specimen. The l a t t i c e temperature was approximately 12 mK. The reso-nant radio frequency f i e l d was modulated to a width of 1 MHz at 100 Hz, Its strength was approximately .005 G while the channel dwell-time was 5 sec. Note, d r a s t i c a l l y different relaxation rates are apparent for the two po l a r i z i n g f i e l d s . 75 Relaxation data, 6 0Co 0 2%-*± > 1 8 > 2 e A p r i l , 7 May 1973 Concentration of the impurity nucleus : .02 at . % , a c t i v i t y : 16 yC : H 0 K G Magnetic C sec K X 2 C sec K ±5% Saturation SPIN-T1 :MP. NO SPIN-r rEMP. .40 .26 .7591.190 5.86 .8751.200 5.12 .54 .49 .522+.043 1.15 .5971.037 .572 .67 .63 .5031.073 4.71 .5751.083 4.41 .81 .80 .575+.092 7.82 .6531.082 4.82 .94 .87 .5981.052 2.30 .6861.033 .932 1.07 .92 .7531.056 2.21 .8751.078 2.77 1.21 .95 1.005±.036 .645 1.1621.058 1.14 1.34 .98 1.1361.038 .772 1.3001.069 1.77 2.01 1.00 1.9051.140 4.52 2.2751.210 8.07 2.68 1.00 2.2091.110 2.62 2.5501.220 8.72 2.68 1.00 2.1441.140 3.89 2.4811.210 8.14 2.68 1.00 2.1521.170 4.82 2.6021.310 7.87 6.70 1.00 2.2271.240 1.10 2.6411.200 1.68 6.70 1.00 2.5781.110 .850 3.0621.182 1.23 Relaxation data, 6 0CO i n 0-Fe , 15 Dec. 1973, 18 March 1974 Concentration of the impurity nucleus : .1 at . % , a c t i v i t y : 47 yCi f _____ ' ! L_ j -H 0kG3 Magnetic C sec'K X 2 C sec K X 2 15% Saturation SPIN-T EMP. NO SPIN-TEMP. .50 .286 .981.05 6.56 1.161.07 8.15 .75 .602 1.021.05 2.17 1.201.07 3.65 1.00 .719 1.231.05 1.67 1.451.07 2.78 3.00 .868 2.79 1.15 2.30 3.581.20 2.84 3.00 .868 3.05 1.15 1.96 3.731.20 2.38 6.00 1.000 2.741.15 1.02 3.361.20 1.73 6.00 1.000 2.72 1.15 1.22 3.301.20 1.58 Table IV/1 The Korringa constants C = T^T computed from our NMR/ON measurements on 6 QC0-Fe , 5ttMri-Fe and 5 t tMri-Ni are tabulated. 76 Relaxation data 5tfMn-Fe , 25 March 1974 Concentration of the impurity nucleus :.0012 at . % , a c t i v i t y : 13 yCi > HH KKG uO Magnetic C seccK X 2 C sec'K X 2 ±is% Saturation SPIN-T :MP. NO SPIN-T1 BMP . .50 .272 .1051.015 3.40 .1201.015 3.44 .50 .272 .1551.030 5.29 .1931.030 5.67 .7.75 .484 .195+.015 1.98' .2451.015 2.12 .75 .484 .1«50±.O15 2.39 .2321.015 2.64 .75 .484 .1651.015 2.73 .1901.015 2.73 1.00 .630 .2051.015 1.89 .2301.015 1.78 1.00 .630 .21O+.0<15 1.31 .2731.015 1.31 1.50 .702 .2001.015 1.74 .2631.015 1.87 1.50 .702 .2251.015 2 .96 .3001.015 3.07 • 2.00 .817 .3471.020 1.51 .4501.020 1.52 3.00 .858 .323±.020 1.75 .4101.020 1.77 3.00 .858 .3601.020 1.57 .4601.020 1.63 3.00 .858 .3951.020 1.40 .5201.020 1.43 3.00 .858 .3551.020 .788 .4301.020 , .715 6.00 1.0 77 Relaxation data 54Mn-Ni_ ., 1; A p r i l , 22 August 1974 Concentration of the impurity nucleus : .0018 at . % , a c t i v i t y : 24 l i H Q KG ± 5% Magnetic Saturation C sec"K' SPIN-T X 2 EMP. C sec' K NO SPIN-T X 2 EMP. .30 .392 .0637±.02£.' 4.29 .0731±.02 4:61 .50 .524 .129 ±002 1.96 .148 ±.02 1.97 .75 .630 .106 ±.02 1.64; .121 ±.02 1.80 1.00 .714 . .111 ±.02 1.19 .126 ±.02 1.16 2.00 .867 .0900±.02 1.32 .102 ±.02 1.42 3.00 .971 .104 ±.02 1.02 .119 ±.02 1.28 4.00 .987 .0981±.02 .7742 .111 ± .02 .817 6.00 1.000 .119 ±.02 1.43 .135 ±.02 1.62 8.00 .968 .135 ±.02 .393 .153 ±.02 .427 .20 .339 ..020.6+- .020 4.809 . ..0,231'! .020 4.605 .20 .339 .0550±.025 4.349 .0638±.025 4.359 .30 .444 .O881±.025 3.771 .10001.025 3.791 .30 .444 .05501.025 • 3.045 .0631±.025 3.080 .40 .510 .0706±.025 1.935 .0794±.025 . 1.971 .440 .510 .0600±.025 3.042 .0663±.025 3.019 1.00 .747 .12631.025 1.931 .13881.025 1.916 1.00 .747 -.1213+.025 . 1.437 .1356±.025 1.457 3.00 1.000 .11441.025 .890 .12631.025 .869 iTT sec-K T 8 T I ic o o 0 I 2 TrT sec-K T o 1 T o 8 _ 18 o 1 '0 T o i T o 1 <>0 C q M % - F e - 1 — % — i - H0 7 kG 5* Mn-Fe He 6 kG 0-IT sec-K T V F sec-K .12 .08| .044 0 o o o oo 0 T o 1 o o I X 40 Co.,%-Fe 4 5 _ ^ H 0 6 kG X Mn-Ni 6 8 kG Figure IV/2 Each of our four specimens shows a strong dependence of the Korringa Constant T^T on the magnetic •field HQ. The values obtained under the assumption of a spin temperature are plotted. 79 assumption. The i n i t i a l condition was computed fxom the anisotropy just before relaxation started. A spin temperature i s assumed to exist for the i n i t i a l state and consequently the density matrix and the orienta-tion parameters are defined. For those samples characterized by T « T ^ this assumption i s correct. In t h i s case, even though a spin temperature may not exist i n the presence of the radio frequency f i e l d , a temperature w i l l be established quickly after the f i e l d i s switched off. There i s some doubt that the assumption of an i n i t i a l temper-ature can be j u s t i f i e d f o r samples in which T^ i s not much less than T^. An ensemble of nuclei with equispaced energy levels and o r i g i n a l l y at a temperature T^ i s expected to maintain a Boltzmann d i s t r i b u t i o n i n the presence of a radio frequency f i e l d even i f the spin-spin interaction i s n e g l i g i b l e (69). This was expected to be the case f o r our samples. Recently, however, i t was shown (17) that at resonance quadrupole effects may render the assumption of equispaced energy levels i n v a l i d . Not withstanding t h i s objection, u n t i l the i n i t i a l state i s better speci-f i e d by measuring the anisotropy W(0,t=O) i n several directions, or u n t i l a detailed theory i s available, an i n i t i a l spin temperature would appear to be the best possible assumption. Fortunately we expect the spin temperature to be a reasonable approximation f o r at least the more concentrated 6 0Co-Fe specimen, thus providing a reference for the other samples. In addition we are only looking for changes that are large as compared to variations produced by assuming a variety of different i n i t i a l conditions. This point i s d i s -cussed i n the l a s t chapter. By keeping the radio frequency le v e l cons-tant, we have attempted to minimize such effects. 8 0 In the present experiments the measured equatorial counts were not used to check the i n i t i a l conditions as t h e i r s t a t i s t i c s were too poor to give additional information. We note that a high accuracy of axia l and equatorial counts i s required.before one can hope to deduce additional information about the density matrix defining the i n i t i a l state. The data from the a x i a l and the equatorial counters were re-corded simultaneously. These equatorial relaxation records with good s t a t i s t i c s f o r the 6 0Co-Fe specimen were analysed and are i n agreement with the a x i a l ones. The complete set of results i s tabulated i n Table IV/1. In addition to the magnetic f i e l d the Korringa constants and the X 2 values WfO") • are given forfealfchreir theory. ' The f r a c t i o n a l magnetic saturation F ^ = w ^ i s also tabulated. I t i s found that small uncertainties i n t h i s value for the magnetic saturations cause but a small error i n the computed Korringa constant. The high f i e l d and the low f i e l d Korringa constants'are sum-K marized i n Table IV / 2 . The normalized relaxation times Y 2 T - , T — : — T T > ' 1 sec Gz are given.., ailbwinigg an immediate comparison between the results from different isotopes. In addition to the present NMR/ON results and those derived from NMR measurements the t h e o r e t i c a l l y predicted high f i e l d values are also l i s t e d . For Co-Fejthe,Y2T^T values deduced from either NMR or the present NMR/ON measurements agree w e l l . The NMR results l i e between those we have obtained from the . 0 2 % and .1% 60Co-Fe_ specimens. The discrepency p a r t i c u l a r l y between the low f i e l d Korringa constants ob-Xm N M R NMR/0 \ T N K R / O N XMR/ON s 9Co, 1% f o i l 5 9Co, \% powder . 6 0Co, f o i l 6 0Co, . 0 2 4 f o i l "Co, 1'. f o i l P --once | 5 7 57 68 115 this work this work ' r f i e l d 1 . 1 1 S . 1 08 . 0 3 2 8 . 1 0 8 . 0 8 5 4 . 1 0 8 .0647 . ! 0 3 .129 . I 0 8 -. _ T hich .118 .10 3 .321 . 1 0 8 . 3 6 3 ,10 8 . 2 5 9 , 1 0 8 . 2 9 3 . 1 0 S . 3 7 5 . 1 0 A T i e 2.72 3 . 9 5 3.03 4.61 2 . 9 1 Mn-Fe: H?thod Theory N m NMR NMR/ON Specimen i [ i •"Mn, 1% powder 5 5 t o . — 5:*Mn, f o i l ^ , ! 57 S7 62, 64 th i s work• Y 2 T T j £ | . 0 2 2 8 . 1 0 S . 0 1 9 7 . 1 0 E . 0 2 9 2 . 1 0 8 , T T high Y 1 f i e l d . 0 6 9 2 . 1 0 3 . 0 4 8 2 . 1 0 8 . 0 3 9 4 . 1 0 8 . 1 0 3 . 1 0 S h h — 2 . 1 1 2 . 0 0 3 . 5 3 Mn-Nj_: Method NMR NMR/ON F.P.D. • NMR/ON NMR/ON Specimen . 1 - 2% powder 5 1 * H . i , f o i l 5,*Mn, f o i l 5 "*MJI f o i l 5"'Mn> f o i l 6 5 74 page 47 74 page 47 th i s work t h i s work • r T;T Hew .00513 .103 .0177 . 1 0 ° . 0 1 3 9 . 1 0S , T T high Y 1 f i e l d . 0 1 2 4 . 1 08 . 0 2 2 3 . 1 0 S .0184 .10° . 0 3 0 6 . 1 0 3 . 0 3 3 3 . 1 0 8 lis 2.3S — 1.73 2 . 4 0 Table IV/2: Experimental and theoretical high and low f i e l d relaxation times for Co-Fe, Mn-Fe and Mn-Ni are given. For Co-Fe an independent NMR/ON measurement i s reported by Kohzuki et a l . (115). The l a t t i c e temperature in the NMR experiments was 4.2 K while in the present NMR/ON measurements i t was approximately .012 K. 82 tained from these two specimens i s rather large. Magnetic hardness of the 6 0Co ^-Fe specimen could be responsible f o r the comparatively high values of the Korringa constants observed on this specimen. This explanation i s supported by the results reported i n the following sec-tions. (A r e l a t i v e l y large resonance l i n e width and a comparatively small signal were observed f o r the 6 0Co , 0-Fe specimen at low f i e l d s . In addition a plot of the center frequency versus the p o l a r i z i n g f i e l d shows a s h i f t between the measurements on either specimen.) The low f i e l d NMR values are actually taken i n zero f i e l d while those measured by NMR/ON are made i n a f i e l d small compared to the one required to magnetically saturate the specimen, but large, enough to produce s u f f i c i e n t y-ray anisotropy. As the dependence on the pol a r i z i n g f i e l d i s quite weak i n this region the NMR/ON measurements should approach the zero f i e l d value quite closely. An independent NMR/ON measurement to confirm the f i e l d de-pendence of the relaxation time i s reported by Kphzuki et a l . (115). Their data are sparse and less accurate than ours. Their low f i e l d value agrees with the NMR and our measurements, but t h e i r high f i e l d value appears too low. In ceon,triasit; to the present measurements, most of which are taken at l a t t i c e temperatures of approximately 12 MK, the measurements of Kohzuki et a l . were, made at 25 mK. In t h e i r short communication no details of data analysis are given.. We note that t h e i r r e l a t i v e l y short values f o r T^  would be explained i f an exponential f i t and/or the high temperature approximation had been used i n the data analysis.. Kontani et a l . (57) give the t h e o r e t i c a l l y computed relaxation time for Co-Fe. This value i s s l i g h t l y lower than any of the high f i e l d 83 measurements. Considering the complexity of the theory, the agreement has to be considered satisfactory. In the case of Mh-Fe- and Mn-Ni the values f o r the Korringa constant measured by NMR/ON are i n most cases s i g n i f i c a n t l y larger (by a factor of two) than those obtained by NMR. Care has been taken i n our. measurements to make the dwell-time of the multichannel analyser s u f f i c i e n t l y short i n order to obtain a reasonable number of data points along the relaxation curves. No difference was found on reducing the dwell-time from 1.0 sec. to .5 sec. A possible difference between NMR and NMR/ON results might be that i n the former experiments the relaxation of some wall nuclei i s observed i n addition to that of the domain n u c l e i . In spite of this difference we f i n d that the f i e l d dependence of i s confirmed by the "present NMR/ON re s u l t s . We f i n d a good agree^. ment for the ratios of i n high and low f i e l d as obtained by the d i f -ferent techniques. Discussion of Results: We note that the spin l a t t i c e relaxation receives no s i g n i f i -cant contribution from spin di f f u s i o n to the rapidly s&jbaxih&j spins i n the domain walls. Using a random-walk, spin-di'ffusion model (31) i t can be estimated that the spin l a t t i c e relaxation by th i s process i s several orders of magnitude slower than the observed rate. Several attempts have been made to develop a theory and ex-p l a i n the observed f i e l d dependence of the relaxation rate. Recently 84 M. Butler and Y. Yafet (116) have been looking f o r a mechanism that i s f i e l d dependent and allows the nuclei to relax v i a low energy spin waves into the conduction electron bath. Unfortunately none of the f i e l d dependent interactions that have been investigated have given s i g n i f i c a n t contributions to the relaxation. . IKbntarii et a l . (57) discuss the following processes that could lead to a f i e l d dependent relaxation. The f i r s t p o s s i b i l i t y i s a direct process i n which a nuclear spin f l i p s and a spin wave i s absorbed or emitted. Of course only spin waves with frequency equal to the nuclear, resonance frequency can take part and the frequency spectrum of the spin waves has no components at the r e l a t i v e l y low frequencies required. In fact low frequency components might be generated by a temperature independent damping process. However, no such process has been found for the 3-d metals. Alternately an indirect relaxation process from the nuclear spins to the conduction s-electrons v i a spin waves,(localized d-spins) can be considered. In this model the electronic excitations are des-cribed by spin waves and independent conduction electron excitations. Based on the s u s c e p t i b i l i t y formalism (117) an expression f o r the f i e l d dependent part of the relaxation rate i s derived: / 1U V Here A and B are constants independent of H Q . The term g— i s derived from the expression f o r the energy of the spin waves of momentum q. For an external f i e l d large compared to the anisotropy f i e l d and the demagnetizing f i e l d ^ i t i s given by: • E^ .^2ugHg .+ Dq 2. In 85 a high f i e l d the second term becomes negligible and E^ ^ i s propor-t i o n a l to H Q . • For an iron host material B i s estimated as approximately 20 KG. . Unfortunately this i s too large by at least a factor of ten to produce the sharp f i e l d dependence of the relaxation rate observed at about 1 KG. Lacking accurate theoretical values f o r the constants, one might attempt to compare the predicted and the measured curve shape for the f i e l d dependence of . However, neither the theories nor the measurements are accurate enough to make such a comparison meaningful. The need for an adequate theory i s evident. 86 CHAPTER V DEPENDENCE OF tl'NENW/IDTHfjRRESQNA^CELFREQWlNCM AND SIGNAL ON THE DEGREE OF MAGNETIC SATURATION OF THE SPECIMEN The measurements discussed i n th i s chapter have been obtained from l i n e shape records. Figure V / l i l l u s t r a t e s some t y p i c a l experi-mental data for 6 0Cd-Fe. The count rate was recorded as a function of frequency. The resonance l i n e was swept i n a time much greater than the relaxation time i n order to obtain an undistorted l i n e shape. Care was taken to keep the amplitude of the radio frequency f i e l d constant (a variation of about 10% i s estimated). Also i t had to be low enough to avoid radio frequency heating of the specimen. For analysis the data points were f i t t e d by hand drawn curves. Its maximum defines the cen-t e r frequency, f^. The l i n e width, Af^, was measured as the f u l l - w i d t h -at-half-maximum, while the s i g n a l , or f r a c t i o n a l destruction of the anisotropy, i s defined by W(H ) - W(H = 0) S = ± i 1 - W(H1 = 0) where W(H^ = 0) i s the equilibrium anisotropy at the l a t t i c e temperature T , while W(H ) i s the anisotropy measured from the peak of the resonance. J_j -L Dependence of Line Width on the Applied F i e l d A change i n the li n e width was observed as a function of the 87 to face page #88 Figure V / l An a x i a l and equatorial spectrum from the 5ttMn-Ni specimen. The resonance frequency f g , f u l l l i n e width as h a l f maximum Af^ and the anisotropy W(T ) and W(r.f.) measured with the radio frequency o f f and on respectively are shown. The experimental parameters are given below: f = 270 - 273 MHz V , V 4 V r . f . rms Av = .3 MHz v = 100 Hz T L =11.0 mK W(T ) =.535 S ax i a l = .084 Warm counts = ^ 52.50 .535 Experimental dwelltime = 10 sec. experimental 5 sequential experimental points are added for each point plotted. 88 295-EQUATORIAL i COUNTS *I00 290-285+ -J x * 480-AXIAL ^COUNTS x\00 470+ 4 6 0 + 450-+ 270 -X-J X X 1 A \ \ / Afo \ / / \ \ \ W(r.f) W(r.f.) : fo=2720 MHz - X - W( t o f 271 272 273 MHz Figure V/1 89 degree of magnetic saturation of the specimen. This i s i l l u s t r a t e d i n Figure V/2. It shows several l i n e shape records obtained from the 6 0C6 -Fe specimen. The radio frequency l e v e l was kept at approxi-mately 5 mG and the modulation-rate was 100 Hz. The modulation width was set to .2 MHz i n a l l but the record taken at H Q = .40 kG. In thi s case, a modulation width of .1 MHz was chosen. Similar changes i n the width of the resonance line have been observed for a l l our specimens. Plots of the l i n e width versus p o l a r i z i n g f i e l d are shown i n Figure V/3. The rather large l i n e width observed by NMR/ON has long been of concern. Single c r y s t a l specimen y i e l d smallefil'inelwiathshthan poly-c r y s t a l l i n e ones and the narrowest l i n e reported f o r a single c r y s t a l specimen of .60C6-Fe i s 130 KHz (32). Usually values from 0.6 to 1.2 MHz are measured for p o l y c r y s t a l l i n e specimen at or near magnetic satura-t i o n . In a l l our marginally diffused p o l y c r y s t a l l i n e specimens the lin e width i s found to decrease considerably when the p o l a r i z i n g f i e l d i s reduced. The h i g h - f i e l d l i n e width for our 6 0Co-Fe specimen's i s approximately 700 KHz, but reduces to nearly 200 KHz i n low f i e l d . This field-dependent l i n e width observed i n our NMR/ON mea-surements i s explained i n terms of non-uniform demagnetizing f i e l d s . Assuming, for the moment that the specimen i s of e l l i p s o i d a l shape then the f i e l d inside the specimen i s given by: H' = H - DM Here H i s the internal f i e l d , including the applied f i e l d and the Lorentz f i e l d and D i s the shape-dependent demagnetization factor, which f o r a 4TT sphere i s — . For a very long, thin prolate e l l i p s o i d i t i s zero, 90 to face page #91 Figure V/2. The signal S measured by NMR/ON on the 6 0C0 Q2°i~^e specimen i s plotted against frequency f for a number of diffe^entopoTarizingifie'lds HQ. It i s evident that for small p o l a r i z i n g f i e l d s the li n e width i s much smaller than for large f i e l d s . The radio frequency f i e l d was modu-lated to a width of .2 MHz at a rate of 100 Hz. The resonance l i n e taken at H^ = .40 kG i s an exception, i n t h i s case the modulation width was .1 MHz. 91 .34-0. -<?-161 0 Hc=6.7 kG ° f MHz .24-162 .14-o o 163 K,=2.67 kG 0. S o o f M H z 0 f o + - ^ - f 164 .14-0 | 9 P -165 166 .24-Ho=2.0l kG H r+ 164 H 1-165 f MHz - 6 0. 166 H 0 =.67 kG o _ o f M H z 165 —I 166 167 o 1 H „ = . 5 4 kG o o o o f M H z 4 H h — - + 165 166 167 .24-0 . o o o 0 S o I H0=.94 kG .34-' .24-H g , L_ 165 166 o f MHz . O H L_ 0 . 1 H , . 4 0 kG 167 -4 • + f MHz -o U 165 166 167 Figure V/2 92 to face page #93 Figure V/3 The dependence of the NMR/ON lin e width (F W H M) on the p o l a r i -zing f i e l d H Q i s shown. Three of our specimens have been measured, each one shows an increase of the l i n e width with increasing pol-a r i z i n g f i e l d . Typical error bars are shown. .6 Af MHz T o 1 60 Co.M %-Fe 0 Figure V/3 .7-.6-Af MHz T o i .5-60. H kG Af MHz - f - h He 2 3 4 5 6 kG .6+ .4-o o . 2 -T o 1 St Mn-Ni H f 0 2 3 4 5 6 kG 94 while for a long, wide oblate e l l i p s o i d of small height i t i s 4TT. In the present situation i n which a thin plate i s magnetized i n i t s plane we would expect D to be small. However,, the thickness of the active layer i s only 1 ym and even after polishing, surface i r r e g u l a r i t i e s may not be much smaller than this dimension. Figure V/4 i l l u s t r a t e s the si t u a t i o n . I f we take a surface with spherical i r r e g u l a r i t i e s , then the demagnetization factor at the 4 • peaks w i l l be approximately -gn while at the bottom of the active layer we expect D to be small. Thus a d i s t r i b u t i o n i n demagnetizing factors from D^ O. to 'v^ rr arises. An average demagnetizing f i e l d DM re s u l t s . This i s demonstrated i n the plots of the center frequencies versus magnetic f i e l d shown i n the next section (Figure V/5). For 6 0Cb ^0-¥e, for example, we fi n d DM ^ 800 G for HQ>2 kG. Assuming a magnetization 2 of 800 G and a spread AD = -^ rr we fi n d : Af = |ir .160 * 1.0 MHz This i s quite close to the observed high f i e l d l i n e width. On lowering the p o l a r i z i n g f i e l d , H^, the bulk magnetization i s reduced by the formation of domains. Consequently t h i s contribution to the li n e width i s reduced as observed.. The NMR, z e r o - f i e l d , l i n e width observed on 59Co-Fe_ speci-mens (119) with a cobalt concentration between 4 and 10% i s Af = .2501 50 KHz. For 6 0Co th i s gives Af = 144130 KHz.which i s i n good agreement Af = 250 ^ Khz. with our value of Af = 200150 KHz. The l i n e width i s strongly influenced by specimen preparation 95 Figure V/4 A simple model of spherical surface i r r e g u l a r i t i e s i s used to i l l u s t r a t e the possible range of the demagnetizing factor. 96 and i n p a r t i c u l a r by c r y s t a l l i n e imperfections and magnetic hardness. This i s observed i n NMR experiments (37). Our two 6°Co-Fe_ specimens show that specimen preparation has a larger influence on the l i n e width at small f i e l d s than at high f i e l d s . The minimum l i n e width observed on these specimens i s .2 and .43 MHz; the l i n e width f o r the saturated specimens i s .7 MHz i n both cases. A broadening of the zero f i e l d resonance l i n e width when an external magnetic f i e l d i s applied has also been observed i n NMR experiments on powder specimens (57). A s i m i l a r explanation i n terms of a d i s t r i b u t i o n i n the demagnetizing f i e l d can be given i n t h i s case also. NMR/ON measurements on t h i n f o i l specimens (approximately 1 ym thick) do not show a reduction i n the resonance line width when the p o l a r i z i n g f i e l d i s reduced (148). As w i l l be seen i n the following section these specimens also show a l i n e a r dependence of the centre frequency on the applied f i e l d , indicating that no demagnetizing effects are present. This behaviour i s surprising and may well be linked to t h e i r f i e l d independent l i n e width. Resonance Frequency as a Function of the Applied F i e l d The center frequency has been observed as a function of the p o l a r i z i n g f i e l d . The results f o r the 6 0Co-Fe. v 54Mn-Fe and 5tfMn-Ni specimens are given i n Figure V/5. I f the hyperfine f i e l d i s notsaffected by the applied f i e l d , then the resonance frequency i s given by: Figure V/5 Center frequency versus polarizing f i e l d . Typical error bars are given. DM denotes the average demagnetizing f i e l d . 98 f0 = h <Hn + V thus and d£ v IIP- = _ dHg 2TT7I ^ 0 2± = i dH Q Y The center frequency and the"slope can be taken from Figure V/5 and are df'^O^ given together with the value ^ j ^ - - ^~ i n Table V / l . We f i n d no devia-t i o n from unity within our error l i m i t s . That this may not always be the case has been reported by Hagn and Eska (118). They have measured the f i e l d dependence of the resonance frequency f o r a large number of d f Q specimens and f i n d that the expression -TH— — y i e l d s values between f dH Q Y .74 ± .11 for 1 8 1Re-Fe and 1.248 ± .031 for 1 9 2Tr-Fe where the value for 60Co-Fe_ has been taken as unity for c a l i b r a t i o n purposes. The deviation from unity indicates that the hyperfine f i e l d , H^, i s not independent of the p o l a r i z i n g f i e l d , H^ .• It i s interesting to compare the present frequency versus f i e l d curves as shown i n Figure V/5 with those given by Stone (121) for a p o l y c r y s t a l l i n e f o i l 1 liiri thick and a single c r y s t a l specimen of 6 0Co-Fe. A li n e a r dependence of the resonance frequency on the po l a r i z i n g f i e l d i s shown for the p o l y c r y s t a l l i n e f o i l specimen, while a single c r y s t a l sample shows a d i s t i n c t non-linearity f o r small p o l a r i z i n g f i e l d s . The l a t t e r specimen was of approximately e l l i p s o i d a l shape with dimensions of the order of several millimeters. Our experi-99 Specimen f MHz 8 H0=0 df MHz dH 0 KG df 2TT dH Q y Reference 6 0 f n -Fe 165.8±.l -.572±.02 . 1.00±.03 thi s work 7 May 73 6 0Co .--Fe .i.'o 165.8±.1 -.572±.02 1.00±.03 this work 18 March 74 51+Mn-Fe 190.2±.l -.863±.05 1.03±.05 \ t h i s work 25 May 74 5ItMn-Ni 273.4±.l -.794±.04 j'.952±.05 I t h i s work . 1 A p r i l 74'. 5 9 f n -FP L 0 1 to 4% — 289.2(165.8) 119, 120 52Mn-Fe 88.7(190.8) -.369(-.794) , .952(.952) 118 Table V/1: The zero f i e l d resonance frequency and the slope of the frequency versus p o l a r i z i n g f i e l d graphs (Figure V/2) are given. The expression i s expected to be approxi-mately equal to one. The values i n brackets are computed from the data given i n the table and refer to 6 0Co and 5I+Mn respectively-. 100 merits were performed on 0.3 mm thick p o l y c r y s t a l i i n e specimens and show a frequency versus f i e l d behavior that i s very s i m i l a r to that observed from a single c r y s t a l . Thus whether the specimen i s p o l y c r y s t a l i i n e or a single c r y s t a l appears to be unimportant. In a l l cases the specimens are much longer than thick and the magnetic f i e l d was applied along the easy direction of magnetization. Therefore, we expect the demagnetization f i e l d s i n the bulk material to be small. In f a c t , for 'thick' p o l y c r y s t a l i i n e and single c r y s t a l samples the variation of frequency and l i n e width with f i e l d can be f u l l y explained by surface demagnetizing effects. I t would appear then that the behavior of very thi n f o i l s i s anomalous: no surface demag-netization effects are observed. Dependence of Signal on the Applied Magnetic F i e l d The dependence of the signal on the p o l a r i z i n g f i e l d , H ^ , i s shown i n Figure V/6. A decrease i n the observed signal with increasing H p o l a r i z i n g f i e l d i s expected as the enhancement n ^ r r — (we assume H _ >• H Q 0 H ) experienced by the applied radio frequency f i e l d , H , decreases as H Q increases. To obtain a theoretical estimate of the signal,'s depen-dence on the degree of magnetic saturation of the specimen, we use the steady state solution to the Bloch equation to express the dependence of the anisotropy on the resonant radio frequency f i e l d at the nucleus H l ' ' For our computation we assume the existence of a spin tempera-ture. Then the z component of the magnetization i s given' by: T o .8 -.64-T o 1 .354-60. Co.02./o-Fe .25 T o l o b i + 60 T o i T o 1 5* Mn-Ni o o 0 1 2 3 4 5 6 kG Figure.V/6 The signal S measured on the 60Co-Fe_, 5l+Mn-Fe_ and 51+Mn-Ni specimens against the p o l a r i z i n g f i e l d H^ . Typical error bars are.shown. 4 5 i s plotted 6 kG ^ T i 6 kG 102 W = M o I pm C V C 1 ) m From the solutions to the Bloch equations we have: M (H ') = M. Knowingg M (H^?) we therefore can fi n d the corresponding spin tempera-ture T g which i n turn w i l l y i e l d the anisotropy W(6,TS) = W(0,H1'). No analytic solution exists f o r T g. However, we note that a £ P m {" m Consequently we have i. e . B i ^ H i = V 0 ) ' where ,i|i2=CYH1')2 (3) A tabulation of T g and W(6,Tg) w i l l give us TgfH^) and WGe,^') for any H^( value. The predicted dependence of the anisotropy on the radio frequency f i e l d i s shown i n Figure V/7 for 6 0Co-Fe. The aniso-tropy i s plotted as a function of H> = V ( Y H ^ ' ) z T j T 2 . A l a t t i c e tem-perature of 10 mK was assumed. Because the sLgnaT observed i n NMR/ON experiments i s inhomogen-ieusl^sftroM , where X = i — i s the 1 • ~ 1 A 2 natural l i n e width (32). With the enhancement factor-n we have for the applied radio frequency f i e l d : H^ = H^1* • . By setting fp = 1 we can obtain a theoretical estimate of the radio frequency l e v e l that i s required to reduce the anisotropy to approx-imately 0.9. Table V/2 shows these values f o r 6 0Co-Fe ,and 5t*Mn-Fe as well as the parameters that have been assumed. 103 Co-Fe \ 1 1 1 1 1 1 1— (p°<H| 2.0 24 Figure V/7 The t h e o r e t i c a l l y predicted destruction of the anisotropy from a 6 0Co-Fe specimen i s shown as a function of i | j which i s proportional to H^. The theory i s based on the Bloch equations, The existence of a spin temperature has been assumed. 104 Y (G sec) 1 T sec T 2 sec HJ G H G 51+Mn-Fe .5270-10 1 + 20 2 .30-10 _ t + .11 60Co-Fe_ . s s g T ' i o 4 200 20 .44-10 _ t + .15 Table V/2, The theory developed i n the text indicates that an ap-preciable NMR/ON signal (S'v.S)) i s expected i f (H| Y ) 2 ' I T^2 = 1» where i s the radio frequency f i e l d effec-i t i v e at the nucleus. Estimates for = (y T-^Tp and the corresponding applied f i e l d =-^l_ • ^ , where 1 n x A = =— are given f o r 5t|Mn-Fe and 6 0Co-Fe. In addition 2 to the values shown i n the table we have assumed T = 10 mK, Af = .5 MHz and n =300 (we expect the l a t t e r two values for H n % 1 KG). 105 During the relaxation experiments, anisotropics of 5I*Mn-Fe were measured for different applied radio frequency voltages, , and i t i s int e r e s t -ing to see what values the above theory predicts. The result i s shown i n Figure V/8. As a l l other parameters are kept constant we have H^' <* V^. A computed curve based on equation (3) i s also shown. B^(0) was deter-mined from the anisotropy measured at V = H^ * = 0/ The best f i t between experimental points and the theoretical curve was obtained f o r a 'v* 0.08. As a i s given by A = * = Y H ^ / F ^ V V 1 1 we can obtain an estimate of a based on the values given i n Table V/2. H 1 H n • \ A - it m -17 l. 1 1 "n«. X- m 300 • .5 _ n r i-c Assuming H^ = .01 we have = ' ^ j r - = '.01 — ^ ^ = 3*10 0. With t h i s our predicted value for a i s : a = .527 • <Wk *• 3 • 10" 6 • /20^2 =0.1 Thus quite good agreement i s obtained between the experimental and the . predicted value f o r a. With the large uncertainties i n the estimated parameters the good agreement has to be considered somewhat fortuitous. However, the above comparison shows that the model i s at least a plau-s i b l e one. To interprete our measurements of the signal as a function of the p o l a r i z i n g f i e l d we used an over-simplified r e l a t i o n between the anisotropy and the radio frequency f i e l d suggested by Figure V/7 of the form: 106 lW( 0,H.) THEORY o MEASURED V 7 m s 4 M « H , Figure V/8 The points give the anisotropy that has been measured for a number of d i f f e r e n t radio frequency l e v e l s . The curve i s based on the theory described i n the text and represents the best f i t to the measured points. It i s given by WCOiV1)=-f(Bri(yu)) and B ^ V ^ = 1^(0)-[1 + ( a V ^ 2 ] " 1 , where B (0) = -1.1006 and a = .0787. The l a t t i c e tempera- . ture was 11.0 mK and the following parameters were used i n the measurement: H Q = 1 kG, v = 100 Hz, Av = 1 MHz. 107 where n = 2 for low levels of and n = 1 for intermediate levels, We also have n • X H ' = . H 1 1 Af 1 1 and with X = =r- , n s , H ss V. : T 2 H Q 1 1 tf(0,H ) s / V l /"__.'Y W C O J H J ' J a (V H Q . A f / T 2 y In our measurements was kept constant. Assuming = constant we can write f o r the predicted sig n a l : / F T For 6 0Co A o 0 - F e and for 51tMn-Ni we have compiled the measured signal S, line width Af and relaxation time i n Table V/3. Employing the signal measured at or near H Q =• 1 K G as a reference point, we have com-puted the si g n a l , S_ as predicted by the above theory. Comparing the predicted and the measured signal values we find that the linea r r e l a t i o n predicts the observed values better than the quadratic one. For intermediate signal levels t h i s i s to be ex-pected. We note that the predicted s i g n a l , S , for the largest pol-a r i z i n g f i e l d s i s considerably smaller than the measured one. This discrepancy i s larger than the uncertainty i n our values f o r the signal l e v e l s . 108 H Q kG S Af MHz T 1 ff. •T Sjfif 1 Af «H 0 ^2" \Af-H n/ .40 .53 .67 .94 2.0 2.7 6.7 .97 .38 .29 .21 .16 (.16) .17 .24 .28 .32 .38 .62 .66 .66 .5 .5 • .6 .7 1.9 2.1 2.3 .66 (2.1) .43 .32 .21 .10 ,'..0.73 . C031 .87 .50 ,21 .047 .025 .0045 CD e • H O CD OH tn <D\ I o\° CM O O H Q kg ,30 .50 .75 1.0 2.0 3.0 4.0 6.0 S Af MHz T, ff S^s_ i l AAfKHn - uO =2 y 3 .28 .26 .24 .19 .15 .12 .095 28 .40 .43 .45 .46 .47 .48 .49 04 .08 .10 .11 .11 .11 .11 .11 c CD P= ^Mn-Ni Specii 77 .46 .32 .24 .12 .076 .056 .037 ^Mn-Ni Specii • 5) .88 .42 .24 • .057 .024 .013 .0056 i n Table V/3 Averaged measured values for signal S, l i n e width Af and re-' laxation time T are given for the 6(^Co -...^ -Fe and the 5ttMn-Ni specimens. We have predicted the signal S S [ 1 \ where n \Af-II 0 / n = 1 or 2. We also have adjust S„ to S at H. =.94 and 1.0 J n 0 ' respectively. Especially for large p o l a r i z i n g f i e l d s , H^, Hg£ S and S n are d r a s t i c a l l y d i f f e r e n t . (Signal values l a r -ger than unity are not possible and therefore are put i n brackets.) 109 Two explanations are possible: either H^' does not decrease 1 as fast as i s predicted by the re l a t i o n H.* « — or we are not r e a l l y 0 looking at an intermediate signal l e v e l generated by a l l n u c l e i , but rather at a system where most nuclei are l i t t l e affected by the radio frequency f i e l d and some are almost t o t a l l y saturated, i . e . t h e i r anisotropy i s ^ T. In this l a t t e r case the signal would be much less dependent on the radio frequency l e v e l . , The p o s s i b i l i t y of par- , t i a l saturation of some nuclei i s discussed i n the last chapter. In concluding we note that the model used above to describe the saturation behaviour of the resonance line i s rather naive.' In the NMR/ON experiments the rather unusual si t u a t i o n i s met i n which the modulation rate i s faster than both the spin-spin and s p i n - l a t t i c e re-laxation rates. The l i n e broadening induced by the radio frequency f i e l d , yHj, i s much larger.than I/T2 yet much smaller than the inhomo-geneous l i n e width. I f 1/T2 were faster than the modulation rate the problem' could be solved by considering a succession of fast passages through the resonance l i n e . There i s obviously a need for both a more sophisticated theoretical model and more experimental data. 1 110 CHAPTER. VI OBSERVATION OF SATELLITE LINES BY NMR/ON The measurement of the d i s t r i b u t i o n of hyperfine f i e l d s i n a dil u t e ferromagnetic a l l o y can give useful information concerning the conduction electron polarization i n the system. These measurements are p a r t i c u l a r l y valuable when compared with determinations of the magnetic moment d i s t r i b u t i o n obtained from neutron scattering experiments. At very low concentrations of impurity atoms i n a host material p r a c t i c a l l y a l l the impurity atoms are surrounded by host atoms up. to a distance of many l a t t i c e spacings. A l l nuclei w i l l experience nearly the same hyperfine f i e l d and a singl e , inhomogeniously broadened re-sonance l i n e i s observed (assuming no quadrupole interactions). As the concentration i s increased, impurity atoms are more l i k e l y to be near neighbors.. Those impurity nuclei close to each other w i l l experience a different hyperfine f i e l d than i s found i n the very d i l u t e specimen . and t h e i r resonance frequency w i l l be shi f t e d . I f this s h i f t i s at least as large as the l i n e width and a s u f f i c i e n t number of impurity atoms experience the same s h i f t then a s a t e l l i t e l i n e w i l l be observed. NMR (122, 123, 124, 125, 126) and MSs:sb„auer (127, 128, 129) experiments have been performed f o r example on Co-Fe_ alloys i n the concentration range from approximately 1 to 10 atomic %. A small s h i f t and broadening of the main resonance l i n e as well as a s a t e l l i t e l i n e are usually ob-served. Both continuous wave and pulsed NMR (122, 123, 126) have been employed to study these effects. Usually some instrumental I l l broadening i s introduced and s e n s i t i v i t y becomes a problem for the more dil u t e alloys (<.5 atomic % impurity). Most of the spectra have been obtained i n zero f i e l d , and i t i s not clear whether nuclei i n the walls or i n the bulk or a mixture of both are observed (130). This d i f f i c u l t y does not occur i n MOssb.auer measurements. However, spectra taken by this technique show a large instrumental broadening; the s a t e l l i t e i s unresolved and much information i s l o s t . . Thus i t i s not surprising that the measurement (123) and interpretation of s a t e l l i t e spectra have been the subject of much argument i n the l i t e r a t u r e . NMR/ON measurements have not previously been employed to study s a t e l l i t e lines i n alloy samples. I t appears that these measure-ments could provide independent and r e l i a b l e information about the hyperfine f i e l d d i s t r i b u t i o n i n d i l u t e a l l o y systems such as Co-Fe. The advantages offered are four-fold: a) as discussed before the NMR/ON method observes predomin-antly nuclei i n the bulk; b) i t s s e n s i t i v i t y i s e s s e n t i a l l y indeperidentooftthes alloy concentration and very d i l u t e specimens can be studied; c) with some care (slow frequency sweep, narrow frequency modulation) the resonance observed by NMR/ON shows no instrumental broadening; d) the observed narrowing of the l i n e width on lowering the p o l a r i z i n g f i e l d could be used with advantages to separate the s a t e l l i t e lines more c l e a r l y . The samples used i n t y p i c a l NMR/ON experiments have a concen-t r a t i o n between 10 2 and 10 3 atomic % and s a t e l l i t - e l l i n e s i a r e not 112 expected. By increasing the amount of a c t i v i t y used and reducing the area over which i t i s spread before d i f f u s i o n , the concentration can be increased by a factor of ten oi- so. One of our 6 0Co-Fe specimen which has been employed i n the relaxation study, has a concentration of approximately 0.1 atomic %.' A spectrum of t h i s specimen was care f u l l y recorded and i t indicated the presence of a small s a t e l l i t e l i n e . The frequency and the signal o f the central resonance l i n e as well as the s a t e l l i t e l i n e are given i n Table VI/1. Figure VI/1 shows that the s a t e l l i t e l i n e at frequency f^, i s quite well resolved and there i s a suggestion of a l i n e at frequency, Z^- Encouraged by t h i s r e s u l t , we prepared a specimen with a higher impurity concentration. Of course, the best way to prepare such a sample i s to dope the radioactive im-purity into an al l o y containing the desired concentration of a stable isotope of that element. Specimen Preparation The specimen was prepared by d i f f u s i n g the 6 0Co a c t i v i t y into an alloy of 1 atomic percent of 59Co-Fe_. The all o y was made from metal powders of purity greater than 99.9%. One atomic percent of cobalt powder and 99 atomic percent of iron powder were mixed thoroughly and put i n a small aluminum oxide crucible. . This i n turn was supported with 'glass wool' i n the center of a quartz tube. The crucible was then placed i n the tank c o i l of an induction furnace and heated i n a hydrogen atmosphere to well above the melting point of either constituent. A pyrometer indicated a temperature i n excess of 1500 0 C. The all o y was kept at t h i s temperature f o r 5 minutes. Cooling to room temperature f. MHz 1 S. 1 165.66 ± .05 167.7 ± .1 169.3 ± .2 326 ± .005 ,020 ± .008 .008 ± .008 Table V I / l Center frequencies f.£ and signals observed on the 6 0Co 1 0-Fe specimen. 114 to face-page #115 Figure V l / l a The spectrum of the 6 0C6 ^-Fe specimen i s shown. The s a t e l l i t e l i n e at frequency•f^ i s quite d i s t i n c t . The parameters used are shown i n the pl o t . Two channels have been added, a t y p i c a l error bar i s shown. Counts in X X X X X X X X X X " 2 x X x x x Dwelltime = 100 sec Av ' = 0.3 MHz = 100 Hz v V H, 7,0.9 V-L rms = 20 mK = 1.0 kG x ? x x " xx xx x ..x*x x X X x . . X x x '* x ..x x x X X X XX 1 5 4 . 0 164.7 - 1 1 6 5 . 4 I 166.1 166. a -1 167.5 168.2 -1 1 6 8 . 3 ~1 1 6 9 . 6 -1 1 7 0 . 3 1 7 1 . 0 MHz Figure VI/la 116 to face page #117 Figure VI/lb The data given i n the f i r s t part of this figure are replotted. Five successive channels have been added. Counts o crj s- V a in L ^c"7 kG i n iCT! . "*0 1 6 4 . 0 ~\ 1 6 4 . 7 -I 1 6 5 . 4 - 1 — 1 6 6 . 1 6 6 . 8 " I — 1 E 7 . 1 E 8 . 2 I 1 6 8 . 9 — 1 1 6 9 . 6 I 1 7 0 . 3 171 . MHz Figure V I / l b 118 took less than 30 minutes. The resulting,slug was cleaned and homo-genized f o r 20 hours i n a hydrogen atmosphere at 900° C from which temperature i t was allowed to cool slowly. After cooling,, any oxide or other deposits were mechanically removed from the : surface. The slug was then cut with a piercing saw into discs of approximately 12 mm dia-meter by 2 mm thick. R o l l i n g to approximately 0.3 mm thickness was accomplished by twelve passes between the r o l l s of a large r o l l i n g m i l l . The specimen showed no cracking, but a pronounced longitudinal surface structure and considerable work hardening was noticed. After a further anneal f o r 12 hours at 800° C i n a hydrogen atmosphere, the thickness was reduced to .2 mm on a small hand r o l l i n g m i l l . The r e s u l t i n g a l l o y sheet was smooth and f l e x i b l e . The preparation of the radioactive sam-ples proceeded as described i n Chapter IV f o r the pure host metals. Two specimens were f i n a l l y obtained with an a c t i v i t y of 35 and 38 yCi respectively, both were used simultaneously in,the NMR/ON experiments. Observation of S a t e l l i t e Lines • The 6°Co1^-Fe_ specimen was cooled to approximately 12 mK and a p o l a r i z i n g f i e l d of 1.0 KG was applied. The modulated radio f r e -quency f i e l d was swept automatically from 160 to 170 MHz while counts were accumulated for fixed time i n t e r v a l s . .Threeiaxiaixspectra'-are shown i n Figure VI/2. The spectra show one well resolved s a t e l l i t e l i n e as well as additional unresolved contributions to the s i g n a l . The condi-tions under which these data were taken are given i n the figure. 119 to face page #120 Figure-VI/2 Three ax i a l spectra from the 6 0Co l O-Fe specimen are shown. The parameters used i n each measurement are shown i n each figure. Note: a i s the slope of the base l i n e that has been subtracted to correct for radio frequency heating. Counts x X* Spectrum #9 Dwelltime = 10 sec Av = 0.5 MHz v = 100 Hz x V = 0.7V rms TT = 12.5 mK x X W(TL>'&3 kG = 0.629 x Xx H0 = 1-° k G . * WCTL)@;H0 = 0.754 • ' V • An A counts = 4 0 . 4 ^ -x .x X x X X X X X X X x x x x x x * x Xx v x x X x # v * x x * x xx x*x H v t - Xy Xv X x X X ^ V * * " *x X > <x " V * A * xx " x l * " x * * * * x x x Xx x x X X • • I *1~ • i 1 1 1 1 •  1 1 : X v . 1 6 0 . 0 1 6 1 . 0 1 6 2 . 0 1 6 3 . 0 1 6 4 . 0 1 6 5 . 0 1 6 6 . 0 1 6 7 . 0 1 6 6 . 0 1 6 9 . 0 1 7 0 . 0 m z Figure VI/2a Counts x V x "xx X X X * yxx*>* x x** 'XX 160.0 -1 161.0 162.0 ~1 163.0 ~1 164.0 -1 165.0 X X Xx x xx xx Spectrum #12 Dwelltime ' = Av v = V •W(T )@-3 KG H, W(TL).@110 xx*< x x x x x ^ 166.0 ~1 167.0 168. D -I 169.0 " I 170.0 60 sec 0.5MHz 100 Hz-0.7 V rms 12.5 mK 0.629 1.0 0.754 160.5 counts MHz MHz Figure VI/2b Counts Spectrum #15 o in X Dwelltime = 60 sec Av = ' 0.3 Mhz , v = 100 Hz x X X * X V , = 0.7 V H< rms T L 12.5 mK WCTW)@;3)k6 k i 0.629 LJ 'Li -HQ = 1 . 0 W(TL)@,H0 = 0.754 ;X X X X x X X x X X X y X «!»<x..'.':. H x ^ r ' " x . x X XX X X _ V _< X X X y x * \ x , x y x V x x * x x Xx - x x x \ x x x x X x X X x x * *S< x< _ counts x • ' MHz x X* x X x x xx x x x x x x X v * Xx x x / ^ x V X Xxx x x x * X x v x rvil 1 1 r 1 1 1 1 1 1 ; 1 16D.0 161.0 162.0 163.0 164.0 165.0 166.0 167.0 16B.0 169.0 170.0 Figure VI/2c 123 Data Analysis Our data analysis i s based on the same model employed f o r example by Rubinstein (123) and Stauss (122) . The cobalt impurity atoms are assumed to be i n substitutional s i t e s and to be distributed at random. The nucleus of a central cobalt atom w i l l experience a s h i f t i n i t s hyperfine f i e l d when a second cobalt atom i s brought into one of i t s near neighbor s h e l l s . These are assumed to be spherical. There-fore the s h i f t i n hyperfine f i e l d i s dependent on near neighbor distance only and a l l cobalt atoms i n a given s h e l l are equivalent. Moreover, the individual s h i f t s produced from different near neighbors to the same central cobalt atom are assumed to be additive and no cross terms e x i s t . The in t e n s i t y of each shifted component resonance l i n e i s proportional to the number o f nuclei experiencing that s h i f t . The width of a l l com-ponent lines are assumed to be the same. It i s given by the unbroadened central resonance l i n e as i t would be observed on the very d i l u t e a l l o y . As noted above, an impurity i n the i ^ s h e l l of a central co-balt atom produces a cha r a c t e r i s t i c s h i f t i n the hyperfine f i e l d of the central atom, AIL. Therefore the f i e l d , H(n^, n^, . ..,.n_.) experienced by a cobalt atom with n.. , n , n. impurity atoms i n the 1 s t , 2nc^, i z j . .., 3 " s h e l l i s H ( n r n 2 , n ) = £ (HQ + n^Hp 1 (1) The pr o b a b i l i t y p(n^, n..) for the near neighbor configuration given by n.,, ..., n_. to occur i s : 124 j w , n. N.-n. < p(n ,.n , . . . , n ) = n " i ' C 1 (1-C) 1 1 3 i = l n.! (N.-n.)' ( 2 ) Here N i s the t o t a l number of available sit e s i n the i t H s h e l l and-e C i s the atomic concentration of the cobalt i n the Co-Fe alloy.. For single occupancy i n one only of the near neighbor s h e l l s , the ex-pression reduces to: N. C N.+...+N. p(0, . . . , n = l , 0) = - i — (1-C) 1 3 (3) 1 1-C As expected those shells with a larger capacity w i l l have a greater pro-b a b i l i t y of containing an impurity and thus they contribute more to the signal than those embracing a smaller number of s i t e s . I f the l i n e shape of the component lines i s = S^H) then the t o t a l s i g n a l , S(H) i s given by: N i N j S(H) = I ...I j p(n., n )-S (H(n n )+H) n-1 n. = l ( i • • J • ^ 3 ) To evaluate t h i s equation i t i s necessary to define the component l i n e shape SQ(H) and estimate reasonable values for the s h i f t i n hyperfine • f i e l d , AH.. Different sets of AH. values are then tested i n order to l I f i n d that set which minimizes the discrepancy between the experimental and the predicted curve. As the present work i s intended as a p i l o t study, we have chosen to check our results against the set of AH^ parameters given by Stauss (122). These parameters are based on his own NMR spectra, but also take into account independent MBssbauer observations (130) 125 and neutron d i f f r a c t i o n measurements (131). These measurements give important information on the centroid p o s i t i o n , while the l a t t e r shows that only a few neighbor shells are of importance. The data used f o r the line shape computations are given i n Table VI/2. The position and r e l a t i v e i n t e n s i t i e s of the component' lines have been computed and are also given i n this table. We have f i t t e d our measured data by a computed spectrum. A Lorentzian l i n e • shape has been assumed and the height and width of the central l i n e have been adjusted such that a good f i t i s obtained over t h i s region of the spectrum. The computed spectrum are givert i n Figure VI/3'.along with the measured points. The apparent width (FWHM) of the central l i n e i s approximately 0.9 MHz corresponding to an approximate width of 0.8 MHz f o r the component l i n e s . S i m i l a r l y the height of t h i s l i n e i s approximately 15% lower than the maximum height observed. The theoretical spectrum and the measured points have been plotted by com-puter. In these computations we have neglected a l l atoms with more th two impurities i n the f i r s t four s h e l l s . This i s equivalent to neg-l e c t i n g 3r<^ and 4 ^ order terms and w i l l , cause only a very small devia tion from the exact model l i n e shape f o r the 1 atomic percent alloy. Discussion This experiment shows that the parameters, AH^ ,, deduced by Stauss (122)i y i e l d a moderately good f i t to the NMR/ON data when the height of the central l i n e and the l i n e width are f i t t e d parameters. Of course, a stringent test would require careful study over a range of concentrations and an independent analysis. The larger s a t e l l i t e 126 to fice page #127 Table VI/2 The f i r s t table gives the s h i f t s i n the hyperfine f i e l d Ah\ that have been estimated by Stauss (122) and Rubinstein (123) f o r a Co-Fe a l l o y For the bcc iron l a t t i c e the r e l a t i v e distance of these shells from the central atom are given i n terms of the l a t t i c e constant a^. The number of available sites, i s while p^ gives the p r o b a b i l i t y of th having one atom i n the i s h e l l . Based on the s h i f t s Ah\ given by Stauss we have computed the second table. Shells with more than two impurity atoms have been ignored. The p r o b a b i l i t y p(0, 0, 0, 0) f o r atoms with no s h i f t has been taken as unity. 127 i ^ * 1 s h e l l C a 0 ) 2 N. l P i ' 1% all o y Stauss(122) AH. kG l Rubinstein (123) A ^ kG 1 3/4 8 .08 -4.0 3.3 2 1 6 .06 3.6 3.7 3 2 12 .12- 3.6 0.6 4 11/4 24 .24 ^0.6 0.6 Shell n l n2 Population n 3 n4 4 AH = V n. AH. n . L . . I I i = l P ( n 1 , n 2 , n ff S(n 1, n 2 , 3' V 1 0 0 0 -4.0 .08. 0 1 0 0 3.6 .06 .18 0 0 1 0 3.6 .12 0 0 0 1 0.6' .24 2 0 0 0 -8.0 .0056 0 2 0 0 7.2 .0036 0 0 2 0 7.2 .0144 .0252 0 1 1 0 7.2 .0072 0 0 0 2 1.2 .0576 1 1 0 0 -0.4 .0048 ! .0144 1 0 1 0 -0.4 .0096 1 0 0 1 -3.4 .0192 0 1 0 1 4.2 .0144 .0432 0 0 1 1 4.2 .0288 0 0 0 0 0 1.0 Table VI/2 'XX ><*x xx 1 6 0 . 0 161.0 162 163.0 ~~I 164.0 1 6 5 . 0 1 6 6 . 0 ~I 1 6 7 . 0 1 6 8 . 0 1 6 9 . 0 170.0 MHz Figure VI/3a Based on the data given by Stauss. (122) a curve has been f i t t e d to our experimental-data given i n Figure VI/2b. Note the modulation width, Av, was 0.5 MHz. Counts 160.0 161.0 162.0 163.0 164.0 1 6 5 . 0 1 T 166.0 167.0 CD 1 6 8 . 0 169.0 170.0 MHz Figure- VI/3b A f i t to the spectrum given i n Figure Vl/2c i s shown. For this spectrum the modulation width was 0.3 MHz. 130 predicted on the low frequency side of the main resonance l i n e i s not apparent i n the experimental spectra. A s i m i l a r discrepancy i s also apparent i n the NMR data. A possible reason has been given by Le Dang Khoi et a l . (151). They suggest that there might be a repulsion be-tween nearest neighbour cobalt atoms so that the nearest neighbour configuration occurs with much smaller p r o b a b i l i t y than suggested by the random d i s t r i b u t i o n . This suggestion would also imply that the inte n s i t y of the high frequency s a t e l l i t e due to the second and t h i r d s h e l l would be greater than predicted by random d i s t r i b u t i o n , and th i s i s iimfact observed. The l i n e width used to f i t this data i s 1.0 MHz while i n the present case .8 MHz was used. A s l i g h t l y smaller l i n e width was obtained when we reduced both the p o l a r i z i n g f i e l d and modulation width of the radio frequency f i e l d . Although the l i n e width observed i n our experiments i s smaller than the one measured by NMR, i t i s s t i l l rather large when we compare i t with our measurements on the d i l u t e 6 0Co-Fe specimens. For the specimen of .01 and .2 atomic % cobalt concentra-tion we found a l i n e width of .42 and .52 respectively at H^=l kG (see Chapter V, i n p a r t i c u l a r Figure V/4). Thus considerable additional l i n e broadening i s present i n the spectrum of the all o y specimen. In our analysis only the 4 nearest shells are considered. This l i m i t a t i o n might provide the explanation for the rather large observed l i n e width. Alternately this width could be nearly explained i f the 1% Co-Fe all o y specimen did not show the marked narrowing of the resonance l i n e with reduction i n H^. In this case we have to comparejthe .8 MHz width with .7 MHz observed on the di l u t e specimens at high p o l a r i z i n g f i e l d s . 131 The center frequency of the main l i n e as well as that of the resolved s a t e l l i t e l i n e are given i n Table VI/3. Our values represent the average from 4 recorded spectra. These values are i n good agree-ment with those obtained.from the spectra given by Stauss. Agreement with NMR results i s also found for the r e l a t i v e i n t e n s i t i e s of the s a t e l l i t e s and for the normalized centroid s h i f t . A summary of a l l spectra measured i s given i n Table VI/4. In conclusions, we have shown that NMR/ON i s a viable tech-nique for investigating hyperfine f i e l d d i s t r i b u t i o n s i n di l u t e a l l o y s , combining the attractive features of NMR andMMtfssbauer methods. In the p a r t i c u l a r experiment performed on a 1% Co-Fe a l l o y , results were obtained i n agreement with those determined by NMR and with better re-solution. Relaxation Measurements on the.Al_loy Specimen For comparison with our previous work the spin l a t t i c e re-relaxation rate of the 6 0Co impurity nuclei i n the 60Co-Fe_ all o y speci-men was measured. The specimen was cooled to approximately 10 mK. This temperature was estimated from the anisotropy.of .the y-radiation. A p o l a r i z i n g f i e l d of ,1.0 kG corresponding to a saturation parameter of .61 was applied and the relaxation observed by NMR/ON. The Korringa constants were computed under the spin temperature assumption. Results are shown together with some of those obtained from the 6 0Co -Fe and 6 0Co , 0-Fe specimen i n Table VI/5. Those from spectrum #26 indicate a shorter relaxation time,, the s t a t i s t i c s of At f - f Av f\ Af„ L 0 a z 0 1 0 1 c Spectrum # sec mK KG; WCH0,TL) MHz MHz MHz MHz MHz MHz counts u s o 9 Ax 10 11.5 1,0 .741 160-170 .5 165.82 167.77 1.3 .53 35.800 .208 .231 12 Ax 60 11.7 1.0 .754 160-170 .5 165.67 167.62 .90 .31 214.000 .230 .250 12 Eq 60 11.7 1.0 1.100 160-170 .5 165.64 167.82 .81 148.700 .267 .333 15 Ax 60 12.0 1.0 .760 160-170 .3 165.68 167.65 .87 .59 214.600 .178 .383 15 Eq 60 12.0 1.0 160-170 .3 165.74 167.82 .81 147.900 .428 33 Ax 30 13.0 .5 .895 164-179 .3 165.79 167.91 .75 125.600 .143 .238 • INJ Table VI/4: The results of our NMR/ON measurements on the 1% Co-Fe,alloy are given. In a l l cases the radio frequency f i e l d was ^ 5 mG and i t was modulated at 100 Hz. The frequency band f - f was divided into 126 increments. 3. Z Each frequency was applied for the dwelltime At. Af^ and Af^ are the FWHM l i n e width as measured of the spectrum. The counts given were taken over a time in t e r v a l At and correspond to W(Hn-, T ), the anisotropy S^ U L of the magnetically non-saturated specimen at temperature T . ^— i s the r a t i o of the s a t e l l i t e height over 0 the height of the mainline as measured d i r e c t l y from the spectrum. 133 this record, however, are r e l a t i v e l y poor and the difference i s not expected to be s i g n i f i c a n t . There appears to be no appreciably d i f -ference between the results from the 1% allo y specimen and the more di l u t e specimens investigated i n Chapter IV. Thus the spin l a t t i c e re-laxation time of the 6 0Co nuclei appears to be independent of the concentration of the 5 9Co-Fe all o y system. We note that the 5 9Co nuclei do not contribute to the spin-spin interaction, between the 6 0Co nuclei due to t h e i r different resonance frequencies. 134 NMR (ref . 122) 5 9 C o ( 6 0 Co) NMR/ON (th is work) 6 0 C o f 0 MHz 288 .3 ± .3 C165.7) 165.72±.05 MHz 291 .8 ± .3 (167.7 ± .2) 167.75i.05 flfQ MHz 2.0 ± . 3 (1.15 ± .2) .87 ±.1 f Q - ^ MHz 3.5 ± .4 (2.01 + .3) 2.03 ±.07 .15 ( ref . 123) .19 ±.02 Table VI/3 The center frequency o f the mainl ine and o f the s a t e l l i t e f j as measured by NMR and NMR/ON on 1% Co-Fe specimens are given. The ob-served l i n e width i s A f Q and S Q and S x are the s i gna l height of the main and s a t e l l i t e l i n e re spect i ve ly . (S^ does not include the con-t r i b u t i o n from the main l i n e ) . Specimen 1% , Spectrum #25 a l loy Spectrum #26 .1% f i gure IV/2 .02% f igure IV/2 TjT Ax TjT Eq 1.28±,1 1.18±.2 .90±.15 1.03±.3 1.15±.l .85±.l Table VT/5 The Korringa constants f o r the 1%, .1% and .02% Co-Fe specimens. The measurements were made by NMR/ON at a p o l a r i z i n g f i e l d o f 1 kG. 135 CHAPTER VII SOME COMMENTS ON THE SPIN TEMPERATURE QUESTION AND THE DIFFERENT METHODS OF MEASURING THE RELAXATION TIME BY NUCLEAR ORIENTATION As pointed out previously, a spin temperature f o r the relax-ing impurity nuclei exists i f the coupling between them i s much stronger than between the nuclei and the l a t t i c e . In terms of the relaxation times this means In nuclear orientation experiments T^ normally i s very long due to. the low temperature employed. However, at the same time, T^. i s also com- < paratively large as the concentration of the impurity nuclei i s usually small. The Suhl-Nak'amura r e l a t i o n predicts that T^  i s independent of temperature and inversely proportional to concentration (50, 51) and thus an estimate can be obtained i n some cases. Assuming that t h i s i s a spin-spin coupling due to the Suhl-Nakamura inter a c t i o n , this gives f o r our 6 0Co 19,-Fe_ specimen: R.L. Streever and P.J; Caplan (68) measured a transverse re-laxation time of 0.0048 seconds i n a 5 9 C o l 0 -Fe specimentatt4<?2°iG; T 60 = 2 Y59, 2 C59 T 59 2 Y60 C60 T 6 0 _ 2 146 sec. 136 Here Crn and C,. denotes the concentrations of the 5 9Co-Feand the 6 0Co-Fe specimens respectively. Our measurements give for the "Korringa con- , stant' of 5 0Co-Fe C = T -60T = .50 to 2.90 [sec °K] Employing the r e l a t i o n T = tanh i ^ r ) with T = .010 K, f = 165.8 MHz we have T^ 0 = 53.1 to 307.7 sec This indicates c l e a r l y that T^ 6 0 << T^ 5 0 . Thus the spin temperature theory should be applicable at least for some of our specimens. In p r i n c i p l e the assumption T^  << T^  can be tested experimentally by determining: 1) which of the two models (e.g.. spin temperature or non-spin temperature) provides the better f i t , i . e . , the smaller value, between the measured and the computed relaxation curves and •2), which model produces relaxation times that are more consistent with independent relaxation measurements obtained by NMR, f o r example. For our 60Co-Fe_ specimens consideration of both the above points indicates that a nuclear spin temperature can be defined. How-ever, on r e f e r r i n g to Table IV/1 and Table IV/2 i t should be noted' that assuming a spin temperature gives only s l i g h t l y better agreement to experiment than the non-spin temperature theory. In addition there are reasons to be discussed below, which cast some further doubt on the conclusion that a common-spin temperature exists throughout the sample. The problem of inadequate knowledge of the i n i t i a l state i s 137 obviated i n an experiment described by R.A.: Fox (132) and N.J. Stone et a l . (34, 77, 133) measuring the relaxation of the isomeric state of 1 0 9Ag. This non-resonant relaxation measurement makes use of the 40 sec intermediate state i n the decay: 1 0 9 G d ^ 1 0 9 " l A g % 1 0 9 A g A 1 0 9Cd-Fe specimen i s prepared. The hyperfine f i e l d o f ' 1 0 9 m A g , i s measured by NMR/ON on l l o m A g to within the hyperfine anomaly (77). A l l other parameters, i n p a r t i c u l a r the i n i t i a l condition, are known and the anisotropy which i s a function of the relaxation during the 40 sec intermediate state i s studied for various temperatures. These measurements confirm fhe low temperature r e l a t i o n f o r ^1' = C (j^) tanh (^p^) • However, the difference between the theo-r e t i c a l prediction from the spin temperature relaxation theory and the non-spin-temperature theory are too small to be distinguishable. This very elegant method i s limited to systems which have an intermediate state with a h a l f - l i f e ^1/2^1" Two additional methods f o r the investigation of relaxation phenomena or the spin temperature question are available. These are: the method of fast magnetization of the p o l a r i z i n g solenoid f i r s t des-cribed by Turrell(134) and Reid et a l . (135) and the fast p a r t i a l de-magnetization (F.P.D.) employed by C h i l a s k v i l i et a l . (136) and Bar-clay et a l . (137). In either method the magnetization or demagnetiza-ti o n has to be performed i n a time short compared to the relaxation time. Chaplin et a l . (138) show that for a very short thermal time constant the f i r s t method w i l l result i n adiabatic magnetization of 138 the nuclei and hence no relaxation effects are observed. Increasing the eddy current heating or the thermal time constant leads to s i g n i f i c a n t relaxation e f f e c t s , but only under favorable conditions w i l l the res-ponse s t i l l be fast enough for the equilibrium l a t t i c e temperature to be established s u f f i c i e n t l y rapidly. In either case the i n i t i a l con-ditions are not known. This method of quickly bringing the p o l a r i z i n g f i e l d from zero to i t s maximum value has been employed by Fox (139) and Spanjaard et a l . (140).. The relaxation of 6 0Co-Fe from an i n i t i a l temperature T(t=0) = .00538 K to T(t=«>) = .0222 K i s examined. When the results are f i t t e d by a single exponential curve an apparent T^=105 sec i s measured, while the non-exponential f i t gives: T^  = 520 sec cor- '. responding to a high temperature 'Korringa constant' T^T = 2.8 sec °K. The exponential f i t , of course, i s not r e a l i s t i c . Unfortunately both the exact theories produce an almost equally good f i t f o r T^ T = ,2.8 (actually T^T computed with, a spin temperature should be a l i t t l e , shorter) and i t i s not possible to distinguish between these. The no-spin temperature theory i s preferred f o r t h i s analysis.ofSihee for concentrations of the impurity nuclei i n the host material below 10 6 a spin temperature i s very unl i k e l y . When preparing the i n i t i a l condition by the method of fast p a r t i a l demagnetization, the p o l a r i z i n g f i e l d i s applied and remains constant. The demagnetizing f i e l d on the paramagnetic cooling s a l t i s reduced almost to.zero.corresponding, for example, to a temperature of 20 mK of the s a l t p i l l s , heat l i n k and specimen. The remaining f i e l d i s reduced quickly as compared to the relaxation time to be measured. To simplify the analysis the l a t t i c e should reach i t s f i n a l 139 temperature, e.g. 10 mK, i n a time short as compared to the relaxation time to be measured. This can f o r example be monitored with 54Mn-Cu which has a very short T^ (3.37). In t h i s method both the i n i t i a l and the f i n a l conditions are known and therefore accurate relaxation mea-surements are possible. This method has been: applied to 6 5Zn-Fe (136) for which the spin temperature question was studied (140) and to 60Co-Fe_ (137) . The 60Co-Fe_ measurements are compared with NMR/ON results i n which the i n i t i a l state i s prepared by a single passage. , The i n i t i a l conditions are probably also known i n th i s case and the Korringa con-stant i s computed to be C = 1.75 ± .15 ssecKK i n both eases. A spin temperature was not assumed to exist i n the analysis (141). It appears that the det-erminationxofithemipe-laxat'ion in,the long l i v e d intermediate state, the fast p a r t i a l demagnetization method or the single passage NMR/ON are the most promising tools f o r relaxa-tion measurements as well as for the investigation of the spin tempera-ture question, since the i n i t i a l conditions are known. In an attempt to explain the discrepancy i n the Korringa constants obtained by the different methods of relaxation measurement on 6 0Co-Fe we have carried out independent nuclear orientation relaxa-t i o n experiments employing the fast p a r t i a l demagnetization method. The 6 0Co 2%-Fe_ specimen was used. I n i t i a l specimen temperatures as high as 50 mK are produced by p a r t i a l l y magnetizing the solenoids.' As the photo-multiplier of the Nal-detector loses most of i t s gain i n the f i e l d from the solenoids, the count rate corresponding to the i n i t i a l condition i s either inferred from the equatorial counts taken 1 4 0 with a Ge(Li)-detector or from a graph of specimen temperature versus solenoid f i e l d that was obtained i n an e a r l i e r run. The time constant of the Nal-detector system was less than one second, ,while the magnetic f i e l d i s reduced to zero, i n less than 8 seconds. Figure VII/1 shows two t y p i c a l relaxation records. The observed relaxation times computed from our experimental data under the spin temperature assumption are given i n Table VII/1. The high f i e l d value f o r the Korringa constant i s C = 1.75 sec K. In a low p o l a r i z i n g f i e l d a much smaller T^ T i s measured. Thus the strong f i e l d dependence of the relaxation time i s also shown by t h i s method of relaxation measurement, confirming t h i s aspect of our NMR/ON measurements represented i n Chapter IV. A study '(et42;)iKerf thfe'ffr.igftii _ . Co-Fe shows that rather large systematic differences exist between the values obtained by the various methods. The different results, published i n the l i t e r a t u r e are compiled i n Table VII/2. The i n i t i a l condition i s believed to be known i n only three cases. These y i e l d C =1.75 sec K. In a l l other measurements C "V 2.5 sec K i s obtained indicating that the unknown i n i t i a l condition has the effect of overestimating the relaxa-t i o n time. In our relaxation experiments the i n i t i a l condition i s de-fined by the observed anisotropy and the assumption that- an i n i t i a l temperature does ex i s t . When th i s assumption i s dropped the i n i t i a l condition i s undefined. In t h i s case we can choose any i n i t i a l state that w i l l produce the observed anisotropy and the general shape of the relaxation curve. We have attempted to construct i n i t i a l conditions, 141 to face page #142 Figure VII/1 Two a x i a l relaxation records obtained by the fast p a r t i a l demagnetization method are shown (15 August 1973, Spectrum #19 and 31). The number of counts collected from the 6 0Co Q^-Fe specimen i n 5 second time i n t e r -vals are plotted against time. At time t = 40 sec the solenoids which gener,at'.ad the magnetic f i e l d at the sa l t p i l l assembly were demagnetized from a current of .5 A to 0 A i n less than .8 seconds. The r e l a t i v e l y small counts obtained for t < 40 sec. are due to the strong f i e l d de-pendence of the photomultiplier. The anisotropy before relaxation starts corresponds to the highest point. A l i s t of the r e l a t i v e para-meters i s given below: Spec* lb 'ho mK wcivp CT,. LO V mK W(T0) V mag. saturation Spin temp. C sec. k 19 3.2 11 .568 5990 24 .846 8910 1.0 1.75 31 1.3 11 .606 6490 27 .83511 9350 .91 .88 142 COUNTS 9 0 0 0 8 0 0 0 + 7 0 0 0 + 6 0 0 0 + • ° „ o o o ° o f ° o oo H 0=3.2 kG ° 0 ° o 0 o - O , . 5 A 0 9 0 0 0 +°° 8 0 0 0 + 7 0 0 0 + OA H 1 h — h 100 2 0 0 o o o o o o < ' o o ° < o - h — I — I — h — f -3 0 0 sec 6 0 0 0 -O o" o o H a =l .3 k G .5A b o o o 0 o „ ° o o o o o ° o o 0 ° o ° o o _ . o o o o o „ ° o o o o OA o ° ° ° o ° O o H 1 1 r-—I f — r -100 2 0 0 4 1——r 3 0 0 sec Figure VII/1 143 T T Date H KG T mK spin temp. 15 Aug. 73 1.25 15 Aug. 73 1V25 15 Aug. 73 3.15 15 Aug. 73 3715 15 Aug. 73 3715 15 Dec; 73 3.00 11.0 .87±.15 ll'.O .98±.15 l'l'vO 1.681.2 l'l.O 1.75±.2 M.O 1.751.2 19.0 1.,85±.4 Table VII/1 The spin l a t t i c e relaxation time has been measured by nuclear orientation i n small and large p o l a r i z i n g f i e l d s . The 6 0Co Fe specimen has been employed and the i n i t i a l state was pre-pared by r a i s i n g the temperature of the specimen. A strong de-pendence of the Korringa constant on the p o l a r i z i n g f i e l d i s evident. 144 to face page #145 Table VII/2 Summary of relaxation measurements on 60Co-Fe_. Except f o r the f i r s t two measurements nuclear orientation methods have been applied. For. these the ' f o i l ' specimens employ a host material several tenths of a millimeter thick. The a c t i v i t y i s 'diffused into the host to a depth of approximately! ym. Those results marked•'1 ym foil',employ a specimen approximately 1 ym thick. 'Fast HQ * implies that the i n i -t i a l state i s prepared by quickly increasing the p o l a r i z i n g f i e l d from zero to at time t=0. An analysis employing a single expon-e n t i a l i s not r e a l l y applicable at low temperatures, the values com-puted, by th i s method are given for reference purposes. 'Multi ex-ponential' analysis implies that either a spin temperature was assumed or that i t was not assumed. Analysis under the former assumption generally produces results that are shorter than those obtained under the l a t t e r assumption (143), (the difference i s approximately 15% for our NMR/ON measurements on Co-Fe). A l l measurements (ignoring those analysed by a single exponential) y i e l d C = 2.3 to 2.8 sec. K, except for those methods where the i n i t i a l condition i s known. In these cases we have: C = 1.75 sec. K. This does indicate that the assumption of an i n i t i a l temperature might be erronious and results i n a Korringa constant that i s much too large. Table VII/2 Co-Fe Method Type of Theory T K H Q kG C sec K i n i t i a l condition known? reference comment 1%, powder 1%, f o i l NMR NMR multi exp. multi exp. 4 to 77 4.2 16 7 . 5 2.8 2.6 68 57 l O ' H , f o i l 10~H, f o i l -vlO"t,%, f o i l ^10"'*%, f o i l 10 " H , f o i l fast H„ fast H„ fast H 0 fast H. fast H 0 single exp. single exp. single exp. multi exp. multi exp. .0053 .0053 .005 to .03 1.01.3 1.0±.l .91 2.8 2.6 NO NO NO NO NO 134 135 139 139 140 ^10~ 2%, single crystal ^10~ 2%, f o i l F.P.D. F.P.D. multi exp. multi exp. spin temp. .0065 to.03 ^.012 >3.0 1.751.15 1.751.2 YES YES 137 this work ^10 "2s-single crystal NMR/ON single pas. multi exp. .005 to .03 1.751.15 YES 137 ^10~ 2%, f o i l -vl0" 2%, f o i l ^10" 2%, 1 ym f o i l ^10~ 2%, 1 ym f o i l -\>10~2%, 1 ym f o i l -vl0" 2%, 1 ym f o i l 56Co-Fe_ 5 0Co-Fe 60 Co-Fe NMR/ON NMR/ON NMR/ON NMR/ON NMR/ON NMR/ON NMR/ON NMR/ON NMR/ON multi exp. Spin Temp, multi exp. no spin temp. single exp? single exp. single exp. multi exp. multi exp. multi exp. multi exp. V012 ^.012 ^.025 .017 .0067 to .04 .0067 to .04 .007 to .035 >3.0 >3.0 9.4 .68 2.31.15 2.61.15 2.0 .87 1.0 1.8 2.41 2.5 1.761.1 NO NO NO NO NO NO NO NO 143 this work 143 this, work 115 144 145 73 73 73 73 The data from reference 145 are reanalysed Final slope analysed I n i t i a l slope analysed 146 given by non-Boltzmann distri b u t i o n s of the level populations, that meet . these c r i t e r i a . The d i f f i c u l t i e s encountered i n producing the correct i n i t i a l anisotropy have lead us to an alternate approach. In t h i s we have assumed that not a l l of ;the impurity nuclei are excited by the applied radio frequency f i e l d , and that those which are excited are at a uniform spin temperature, i . e . there jmtgftte&feDiregrSresi:6:ife:dir:£fe.rent spin temperature i n the specimen. With these assumptions an i n i t i a l aniso-tropy can be represented by a temperature T(t=0) that iselargerror equal to a certain minimum temperature, T . . (T . corresponds to a n mm mm uniform excitation of a l l nuclei.) A number of these i n i t i a l conditions are i l l u s t r a t e d i n Figure VII/2. The relaxation of 6 0Co-Fe has been computed under the spin temperature assumption with T(t=0) = Tm^n=20 mK, T =10 mK and C=2.50 sec. K and i s taken as a reference curve. These points have been f i t t e d assuming that various fractions of nuclei are excited by the resonant radio frequency f i e l d . A summary i s given i n Table VII/3. Two points emerge c l e a r l y from t h i s study: .the f i t be-comes poor only for i n i t i a l temperatures that are considerably higher than T^ n. For these, the anisotropy changes very l i t t l e during the f i r s t part of relaxation. Secondly, as higher i n i t i a l temperatures are assumed the computed relaxation time becomes progressively shorter. This i s summarized i n Figure VII/3. Table VII/2 indicates that i n those nuclear orientation experiments where the i n i t i a l condition i s known, the Korringa constant for 6 0Co-Fe i s 1.75 sec K. Figure VII/3 shows that t h i s value i s obtained from the present simulated data i f the i n i -t i a l temperature of the excited nuclei i s taken as T(t=0) ^ 60 mK. For t h i s i n i t i a l condition the f i t i s s t i l l quite good (see Table VII/3). 147 to.face page #148 Figure VI1/2 The dots indicate a relaxation curve that has been computed f o r 6 0Co-Fe with C = 2.5 sec K, T 2 « T . T(t=0) = 20 mK and T^ = 10 mK. This curve has been f i t t e d by relaxation curves that assume that only a fraction of the impurity nuclei i s excited by the radio frequency f i e l d . The f i r s t graph shows the case where these nuclei relax from T s(t=0) =20 or 30 mK (the difference between both curves i s beyond.the resolution of our graph). The second graph shows the case where Tg(t=0) = .1 or 1 K." Only f o r these higher temperatures we f i n d that the re s u l t i n g points d i f f e r appreciably from the dots representing the o r i g i n a l relaxation curve. The Korringa constants and other parameters are given i n Table VI1/3. 148 W(o) Co-Fe T (t=0)=20 or 30 mK j\ § o SPIN TEMP. .6-.51 .8, * .v 60Co-Fe .71 .61 .5-W(o) x NO SPIN TEMP. © x •0 iSo 200 t sec T(t=0)=.l o r I K ° SPIN TEMR * NO SPIN TEMR x •9, * * * o 1 1 1 1 1 0 100 200 t sec Figure VII/2 149 2+ 1 + I«T sec-K X 60, Co-Fe °SPIN TEMP" xNO SPIN TEMP • EXP —I f- 1 1 1 H 1— 2 0 4 0 6 0 8 0 -v-100 -Ar- + 10 10 T i,(-t-o) mK Figure VII/3 The dependence of the Korringa constant C = T^T on the assumed i n i t i a l , temperature i s \[lt=Oj),.. Note the break i n the temperature axis. The model i s explained i n the text. 150 T(t=0) mK 20 30 50 110 1000 10 5 W!(0) .7906 .8903 .9566 .9905 .9999 1.0 Z . 1.0 . .635 .623 .577 .576 .576 C sec K (spin"temp.) 2.50 2.13 1.83 1.63 1.45; 1.43 X 2 (spin temp.) .5 .10"3 4.91 28.9 67.8 155 .0 94.3 C sec K (non-spin temp) 2.88 2.43 2.08 1.83 i :63 1.60 X 2 (non-spin temp.) 5.94 3.16 1.69 15.3 79.2 51.0 Table VII/3 The results demonstrated i n Figure VII/2 are summarized'., Z i s the fract fraction of nuclei that i s excited by the radio frequency f i e l d . 151 This oversimplified model indicates that the discrepancy be-tween the Korringa constants shown i n Table VII/2 could be explained i f we assume i n those experiments where the i n i t i a l conditions are probably not known that instead of a uniform excitation of the nuclei a prefer-e n t i a l excitation occurs. This sit u a t i o n might occur i f the resonance li n e i s unusually broad at i t s base, such that a f r a c t i o n of the nuclei i s not excited as i t i s outside the frequency band covered by the f r e -quency modulated radio frequency f i e l d . Alternately d i f f u s i o n of the active nuclei to a depth greater than the skin depth would have a simi-l a r e f f e c t , t h i s of course i s not applicable to very t h i n f o i l specimens which are completely penetrated by the radio frequency f i e l d . A simi-l a r result i s expected i n a s i t u a t i o n where a l l impurity n u c l e i are uniformly excited by the radio, frequency f i e l d and the i n i t i a l state i s erroneously described by a spin temperature. The above model i n d i -cates that an incorrect assumption of a Boitzmann d i s t r i b u t i o n f o r the i n i t i a l state of the nuclei just before relaxation w i l l produce a relax-ation time that i s too long., The above discussion i s offered as a possible explanation for the observed differences i n the Korringa (constant measured by various methods. NMR/ON experiments designed to study the resonance signal as a function of the applied radio frequency f i e l d or designed to measure the Korringa constant as a function of the frequency, modulation width might illuminate the s i t u a t i o n . 152 CONCLUSION Our low temperature nuclear orientation studies of the spin-l a t t i c e relaxation time of d i l u t e impurities i n a ferromagnetic host show that the relaxation time of those impurity nuclei located' in. the domains depends on the degree, of magnetic saturation of the host mat-e r i a l . This dependence was f i r s t observed by NMR measurements, but an independent study was desirable due to the uncertainties i n the i n t e r -pretation of these results. No f i e l d dependence of the relaxation times i s predicted by the exi s t i n g theories and thus the need f o r a de-t a i l e d theoretical study i s evident. In a second experimental study we have carried out the f i r s t measurements of the hyperfine f i e l d d i s t r i b u t i o n i n an allo y system by NMR/ON. We have shown that NMR/ON i s p o t e n t i a l l y a very useful tool for these investigations and can supplement s i m i l a r nuclear mag-netic resonance and Mo'ssbauer measurements. F i n a l l y we fi n d a discrepency between the rates f o r spin-l a t t i c e relaxation measured by various methods. A possible explanation for t h i s discrepency i s presented. 153 REFERENCES 1. R.J. Blin-Stoyle, M.A. Grace, Handbuch der Physik, (Springer Ver-lag, Berlin) , 42_, 555, (1958) . 2. A, Simon, M.E. Rose, J.M. Jauch, Phys. Rev. 84, 1155, (1951). 3. D.A. Shirley, Annual Review of Nuclear Science, (Emilio Segre, e d i t o r ) , 16_, 89, (1966). 4. H.A. Tolhoek, J.A.M. Cox, Physica, 19, 101, (1953). 5. S.R. de Groot, H.A. Tolhoek, W.J. Huiskamp, Alpha-, Beta- and Gamma-Ray Spectroscopy, (K. :Siegbahn, editor, North Holland, Amsterdam), 2_, 1199, (1966). 6. M. Ferentz, M. Rosenzweig, Tables of F-Coefficients, Argonne National Laboratory Report' #5324", (1955). 7. T. Yamazaki, Nuclear Data, A3.i,l, (1967). 8. H. Frauenfelder, R.M. Steffen, ref. 5, 2_, 1196, (1966). 9. CM. Lederer, J.M. Hollander, I. Perlman, Tables of Isotopes, (John Wiley and Sons, New York 1968). 10. A. Abragam, M.H.L. Pryce, Proc. Roy. Soc. London, A205, 135, (1951). 11. N. K u r t i , Nuovo Cimento, Supplement 3, 6, 1101, (1957). 12. B.N. Samoilov, V.V. Skl y a r e v s k i i , E.P. Stepafljov, Zh. Eksperim, Soviet Physics JETP, 9, 448, (1959). 13. B.N. Samoilov, Soviet Physics JETP, 1_1, 261, (1960). 14. E. Fermi, Z. Physik, 60, 320, (1930).' 15. W. Marshall, Phys. Rev. 110_, 1280, (1958). 16. R.A. Fox, Thesis, (Oxford, 1971). 17. P.T. Callaghan, P.D. Johnston, N.J. Stone, to be published. P.T. Callaghan, P.D. Johnston, N.J. Stone, Hyperfine Interactions Studied i n Nuclear Reaction and Decay, (K. Karlsson, R. Wap-p l i n g , editors, Uppsala, Sweden, 1974), p. 202. P.T. Callaghan, P.D. Johnston, W.M. Lattimer, N.J. Stone, i b i d . , p. 250. 154 18. P.T. Callaghan, N.J. Stone, R.B. Alexander, i b i d . , p. 72. P.D. Johnston, M. Kaplan, P. K i t t e l , N.J. Stone, i b i d . , p. 78. 19. D.R. Hartree, Proc. Cambridge Phil.Soc. 24, 89, (1928). V. Fock, Z. Physik, 61_, 126, (1930). . J.C. Slater, Phys. Rev. 35_, 210, (1930). 20. E. Fermi, E. Segre, Z. Physik, _§2_, 729, (1933). 21. A. Abragam, J. Horowitz, M.H.L. Pryce, Proc. Roy. Soc. London, A230, 169, (1955). 22. R.M. Sternheimer, Phys. Rev. 86_, 316, (1952). 23. A.J. Freeman, R.E. Watson, Magnetism, (G.T. Rado, H. Suhl, editors, Academic Press, New York ), 11A, 167, (1965). 24. R.E. Watson, A.J. Freeman, Phys. Rev. 123, 2027, (1961). 25. P.W. Anderson, Phys. Rev. 124, 41, (1961). P.W. Anderson, A.M. Clogston, B u l l . Am. Phys. Soc. 6, 124, (1961). 26. E. Daniel, J. F r i e d e l , J . Phys. Chem. Solids, 24_, 1601, (1963). 27. I.A. 'Campbell, J . Phys. C2_, 1338, (1969). 28. D.A. Shirley, CA. Westenbarger, Phys. Rev. A138, 170, (1965). 29. D.A. Shirley, S.S. Rosenblum, E. Matthias, Phys. Rev. 170, 363, (1968). 30. CP. S l i c h t e r , Principles of Magnetic Resonance, (Harper and Row, New York 1963). 31. A. Abragam, The Principles of Nuclear Magnetism, (Clarendon Press, Oxford 1962) . 32. D.A. Shirley, Hyperfine Structure and Nuclear Radiations, (E. Matthias, D.A. Shirley, editors, North Holland, Amsterdam 1968),.P. 843. 33. E. Matthias, B. Olsen, D.A. Shirley, Ji.E. Templeton, Phys. Rev. A4, 1626, (1971). 34. F. Hartmann-Boutron, D. Spanjaard, J . Physique, 33, 285, (1972). D. Spanjaard, F. Hartmann-Boutron, J. Physique, 33, 565, (1972). 35. GiVlH; Wilson, Phys. Rev. 177, 629, (1969). G.V.H. Wilson, J.A. Barclay, CG. Don, Phys. Rev. B6_,, 729, (1972). 36. J.A. Barclay, C.G. Don, P. Lloyd, C F . Osborne, G.V.H. Wilson, J. Phys. Fl_, 960, (1971) . J.A. Barclay, D.H. Chaplin, C C Don, G.V.H. Wilson, Phys. Rev. B6, 2565, (1972) . 155 37. A.M. P o r t i s , R.H. Lindquist, Magnetism, (G.T. Rado, H. Suhl, edi-t o r s , Academic Press, New York) 11A, 357,.(1965). 38. A.C. Gossard, A.M. P o r t i s , Phys. Rev. Let. 3, 164, (1959). 39. J . I . Budnick, L.J. Banmer, R.J. Blume, E.L. Boyd, J . Appl. Phys. 32, 120S, (1961). S. Ogawa, S. Morimoto, J . Phys. Soc. Japan, 16/ 2065, (1961). 40. R.L. Streeyer, L.H. Bennett, Phys. Rev. 131, 2000, (1963). 41. For example: B.II Bleaney, B. Bleaney, E l e c t r i c i t y and Magnetism, (Clarendon Press, Oxford, 1957, 2nd edition) p. 267. 42. J.D. Jackson, C l a s s i c a l Electrodynamics, (John Wiley and Sons, New York 1962) . 43. For example: Ref. 41, p. 269. 44. A.M. P o r t i s , A.C. Gossard, J. Appl. Phys. 31, 205 S, !(1960) . 45. H. Suhl, Phys. Rev. 109, 606, (1958). . H. Suhl, J . Phys. Radium, 20_, 333, (1959). 46. T. Nakamura, Progr. Theor. Phys. (Koyoto), 20_, 542, (1958). 47. P.G. de Gennes, J. Phys.• Radium, 2_3, 510, (1962).. P.G. de Gennes, P.A. Pincus, F. Hartmanri-Boutrori, J.M. Winter, Phys. Rev. 129, 1105, (1963). 48. A.M. P o r t i s , J. Phys. Soc. Japan, Supplement B-1, 17_, 81, (1962). 49. J. Barak, N. Kaplan, Phys. Rev. Let. 23_,. 925, (1969)., 50. M. Weger, E1L. Hahn, A.M. P o r t i s , J. Appl. Phys., 32, 124S, (1961). 51. A. Narath, Hyperfine Interactions, (A.J. Freeman, R.B. Frankel, editors, Academic Press, New York 1967), p. 287. 52. E.D. Shaw, B u l l . Am. Phys. Soc. 14, 540, (1969). . 53. P. Pincus, V. Jaccarino, D. Hone, T\ Ngwe, Phys. Let. 27_, 54, (1968). 54. D. Hone, V. Jaccarino, T. Ngwe, P. Pincus, Phys. Rev. 186, 291, (1969) 55. T. Moriya, Prog. Theor. Phys. (Koyoto), 16, 23, (1956). see also: T. Moriya, Prog. Theor. Phys. 28, 371, (1962). T. Moriya, J. Phys. Soc. Japan, 18,'516, (1963). 56. T. Moriya, J . Phys. Soc. Japan, 19,, 681, (1964). 57. M. Kontani, T. Hi o k i , Y. Masuda, J . Phys. Soc. , Japan, 32_, 416, (1972). 156 58. J . iKorringa, Physica, 16,. 601, (I960). 59. Y. Yafet, V. Jaccarino, Phys. Rev. A133, 1630, (1964). 60. Y. Obata, J . Phys. Soc. Japan, 18., 1020, (1963). 61. M. Weger, Phys. Rev. 128, 1505, (1962). 62. i N. Kaplan, V. Jaccarino, J.'H. Wernick, Phys. Rev. Let. 16, 1142, (1966) 63. R.E. Walstedt, V. Jaccarino, N. Kaplan, J. Phys.. Soc. Japan, 21, 1843, (1966). . . 64. V. Jaccarino, N. Kaplan, R.E. Walstedt, J.H. Wernick, Phys. Let. 23_, 514, (1966) . 65. M.B. Salomon, J. Phys. Soc. Japan, 21, 2746, (1966). . 66. N. Kaplan, V. Jaccarino, R.T. Lewis, J. Appl. Phys. 39_, 500, (1968). 67. M. Kontani, J . Itoh, J. Phys. Soc. Japan, 2_3, 646, (1967). 68. R.L. Streever, P.J; Caplan, Phys. Let. A38, 439, (1972). 69. A. Abragam, ref. 31, Chapter 5, p. 133. 70. A. Abragam, W.G. Proctor, Phys. Rev. 109, 1441, (1958). N.F. Ramsey, Phys. Rev. 103, 20, (1956). 71. CP. S l i c h t e r , r ef. 30, p. 120. 72. CP. S l i c h t e r , ref. 30, p. 118. 73. F. Bacon, J.A. Barclay, W.D. Brewer, D.A. Shirley, J.E. Templeton., Phys. Rev. B5_, 2397, (1972). Further references pertaining to the low temperature relaxation theory are: M. Sott, Czech. J. Phys. B19, 1044, (1969). M. Odehnal, J . Low Temp. Phys. 1_, 477, (1969). H. Gabriel, Phys. Rev. 181_, 506, (1969). D. Spanjaard, F. Hartmann-Boutron, Le Journal de Physique, 30, 975, (1969) . D. Spanjaard, F. Hartmann-Boutron, Sol. State Com. 8_, 323, (1970). P. Jaucho, P . V . P i r i l a , Phys. Rev. Bl_, 21, (1970). F. Hartman-Boutron, D. Spanjaard ref. 34. 74. R.A. Fox, Thesis, (Oxford 1971), Chapter 6, Section 3, p. 76. 75. R.A. Fox, Thesis, (Oxford 1971), p. 88, equations (6.15), (6.17). 76. P.G.E. Reid, M. Sott, N.J. Stone, Hyperfine Structure and Nuclear Radiations, (E. Matthias, D.A. Shirley, editors, North Hol-land, Amsterdam 1968), p. 799. 157 77. N.J. Stone, Hyperfine Interaction i n Excited Nuclei, (G. Goldring, R. Kali s h , editors, Gordon and Breach), 1_, 273, (1971). 78. R.A. Fox, Thesis, (Oxford 19.71) p. 86 and Appendix A. 79. CP;. S l i c h t e r , ref. 30, p. 269. 80. G.K. White, Experimental Techniques i n Low Temperature Physics, (Oxford University Press 1968, 2. edition) p. 259. 81. : G.K. White, ref. 80, p. 315. 82. G.K. White, ref. 80, p. 341. 83.. G.K. White, ref. 80, p. 217. 84. G.K. White, ref. -80, p. 328. T. Ashworth, H. Steeple, Cryogenics ,i>5_,22-67, (. (1965) . 85, 85. G.K. White, ref. 80, p. 209, 213. 86. G.K. White, ref. 80, p. 224. J.A. Barclay, Thesis, (University of C a l i f o r n i a , Berkely 1969), UCRL - 18986, p. 52. 87. G.K. White, ref. 80, p. 285. 88. G.K. White, ref.. 80, p. 287. 89. J . Lammeraner, M. S t a t l , Eddy Currents (Prague S.N.T.L. 1966), p.88, 90. M.W. Garrett, J . Appl. Phys. 22, 1091, (1951). D.B. Montgomery, Magnet Design, (Wiley-Inter-Science 1969) . A. Echarri, M. Sacchetti, M. Spadoni, Rev. S c i . Inst. 42, 801, (1971) 91. J.E.C. Williams,, Adv.. Cry, Eng. 17, 93, (1971). Z.J.J. Stekly, J . Appl. Phys. 42_, 65, (1971). P.F. Chester, Reports on Progress i n Physics, 30_, 561, (1967). 92. Supercon, Superconducting wire Type M, T48 B Nb-Ti, Core .254 mm 0, Copper Sheeth .406 mm 0. Formvar insulated, 9 Erie Drive, Natick, Mass. 01760. 93. E.J. Lucas, Z.J.J. Stekley, C. Laverick, G. Pewitt, Adv. Cry. Eng. 10, 113, (1964). 94. P.F. Smith, M.N. Wilson, A.H. Spurway, Appl. Phys. 3_, 61, (1970). B. Colyer, Rutherford Laboratory Reports, RHEL/R 264. A.J. Middleton, P.D. Hey, B. Colyer, Rutherford Laboratory Reports, RHEL/R265. P.F. Smith, 8th International Conference on High Energy Accelera-t o r s , Cern Geneva, Sept. 20-24, (1971). 15.8 P. Clee, Rutherford Laboratory Memorandum, RHEL/M/E4 (1971). P.F. Smith (Rutherford High Energy Laboratory, Chilton Didcdt, Birk s h i r e , England), private communication. 95. G.R. White, ref. 80, p.228. Mc Fee, Rev. S c i . Inst., 30, 98, (1959). W. Mercouroff, Cryogenics, 3_, 171, (1.963). • S. Deiness, Cryogenics, 5_, 269, (1965). F. Lange,, Cryogenics, 10_, 368, (1970). 96. G.K. White, ref. 80, p.140. J.R. Clement, E.H. Quinell, Rev. S c i . Inst. 2_3,. 213, (1952). W.C. Black, W.R. Roack, J.C. Wheatley, Rev. S c i . Inst... 35, 587, (1964). F.C. Koppp T. Ashworth, Rev. Sci. Inst. 4_3, 327, (1972). 97. R.L. Rosenbaum, Rev. S c i . Inst. 4J_, 37, (-1970). L.G. Rubin, Cryogenics 10,• 1£, (1970). W. Weyhmann, So l i d State Physics, Methods of Experimental Physics, Series, Volume I I , (R.V. Coleman, editor, Academic Press 1974). 98. Oxford Instruments, Cryospares, Feed through L4 10 p i n , Osney Mead, Oxford 0X2 0DX, England. 99. C.L. Ruthroff, Proc. IRE, 47_, 1337, (1959). 100.. R.I. Sarbacher, W.A. Edson, Hyper and Ultrahigh Frequency Engineering, (John Wiley,1 New York, 1943), p. 319. F.E. Terman, Radio Engineers Handbook, (McGraw H i l l , New York 1943), p. 124. W.C. Johnson, Transmission lines and networks, (McGraw H i l l , New York, 1950). F.E. Terman, J.M. Pet-tit, Electronic Measurement, (McGraw H i l l , New York 1952), Chapter 4. 101. *RDPTP i s a "UBC-computer program' that i s used to read paper punch tape to a preliminary disc f i l e . The computer program INTERP has been written to interprete the papertape code produced by the Kicksort analyser i n connection with the Teletype punch, i The interpreted data are arranged i n a set of 256 numbers for each 'spectrum'. This i s placed i n a d i s c f i l e along with some information for i d e n t i f i c a t i o n . 102. ' This computer program i s a modified version of SPECTAN as described by P.W. Daly Thesis, (UBC 1973) p. 49. 103. < R.M. Bozorth, Ferromagnetism, (Van Nostrand, New York 1951). 104. A. Aharoni, Phys. Rev. Let. 22, 856, (1969). A. Aharoni, Phys. Rev. B2^ , 3794, (1970). 159 105. E. Karlsson, B. Lindgren, B. Jonsson, Hyperfine Interactions Studied i n Nuclear Reaction and Decay, (K. Karlsson, R. Wappling, editors, Uppsala, Sweden, 1974) p. 146. 106. J.A. Cameron, I.A. Campbell, J.P. Compton, R.A.G. Lines, G.V.H. Wilson, Proc. Phys. Soc. 90_,, 1077, (1967). . 107. I. Ben-Zvi, P. Gilad, G. Goldring, P. Hillman, A. Schwarzschild, Z. Vager, Phys. Rev. Let. 19_, 373, (1967). 108. K.S. Krane, B.T. Murdock, W.A. Stey/ert, Phys.. Rev. Let. 30_, 321, (1973). 109. Jl:6hns:on^ Ma$heW'S3. Ltd., 110 Industry Street, Toronto 15. 110. New England Nuclear Corp., 575 Albany Street, Boston, Mass. 02118. 111. C. K i t t l e ^ Introduction to So l i d State Physics, (John Wiley, New York 1968) Chapter 18, p. 568. R.M. Barrer, Diffusion i n and Through Solids, (Cambridge Univer-s i t y Press, 1941). R.J. Borg, D.Y.F. L a i , Acta Metal, 11_, 861, (1963). R.J. Borg, D.Y.F. L a i , . P h i l . Mag. 18/55, (1968). CRC-Tables, Handbook of Chemistry and Physics, (Chemical Rubber Co., 112. CRC-T?je¥elandjy.d0hio .i97i% e5Jnd redition)iysEt.4:73, (EhiMc? Cleveland, Ohio 1971, 52nd e d i t i o n ) , F-47, F-71. 112. C.J. Smithells, Metals Reference Book (Butterworth, 4th edition) 2_, 649, (1967) . J. A s k i l l , Tracer Diffusion Data f o r Metals, Alloys and Simple Oxides, (IFI, Plenum, New York, 1970). • 113. C.J. Smithells, Metal Reference Book, (Butterworth, 4th e d i t i o n , New York, 1967), Vol. 1, p. 328. W.J. Mc G. Tegart, E l e c t r i c a l and Chemical Polishing of metals i n research and industry (Pergamon Press, New York, 1959). 114. J.A. Cameron, R.A.G. Lines, B.G. T u r r e l l , P.J. Wilson, Phys. Let. 4, 323, (1963). J.A. Cameron, I.A. Campbell, J.P. Campbell, J.P. Compton, R.A.G. Lines, G.V.H. Wilson, Proc. ,Phys.. Soc. 90, 1077, (1967). 115. S. Kohzuki, Y. Aoki, N. Yamashita, J. Itoch, J . Phys. Soc. Japan, 32_, 1678, (1972). 116. M. Butler, Y. Yafet, private communication. 117. W. Gotze, P. WOlfe, J . Low Temp. Phys. 5_, 575, (1971). 118. E. Hagn, G. Eska, International Conference on Hyperfine Inter-actions Studied i n Nuclear Reaction and Decay. (K. Karlsson, R. Wappling, editors, Uppsala, Sweden, 1974) p. 148. ) 160 119. E. Simanek, Z. Sroubek, Check. J. Phys. B12, 202, (1962). 120. Y. Koi, A. Tsujimura, H. Tadamiki, T. Kushida, J . Phys. S o c , Japan, 16, 1040, (1961). 121. N.J. Stone, Hyperfine Interactions i n Excited Nuclei, (G. Goldring, R. Kali s h , editors, Gordon and Bre.ack, 1971), Volume 1, p. 237 arid p. 264. 122. G.H. Stauss, Phys. Rev. IH, 3106, (1971). 123. M. Rubinstein, Phys. Rev. 172, 277, (1968). 124. Y. Koi, A. Tzujimura, T. Hihara, T.' Kushida, J . Phys. Soc. Japan, 16_,. 1040, (1961) . 125. R.C. La Force, S.F. Ravitz, G.F. Day, J. Phys. Soc. Japan Sup-plement B-1, 17, 99, (1962). 126. R.F. Jackson, R.G. Scurlock, D.B^  Utton, T.H. Wilmshurst, Phys. Let. 12, 168, (1964) . 127. M.B. Sterns, Phys., Rev. 146, 439, (1966). 128. C E . Johnson, M.S. Ridout, T.E. Cranshaw, Proc. Phys. Soc. (London) 81_, 1079, (1963) 129. G.K. Wertheim, V. Jaccarino, J.H. Wernick, D.N.E. Buchanan, Phys. Rev. Let. 12_, 24, (1964). 130. G.K. Wertheim, D.N.E. Buchanan, J.H. Wernick, J . Appl. Phys. 42_, 1602, (1971). 131. M.F. C o l l i n s , G.G. Low, Proc. Phys [ Soc. (London), 86_, 535, (1965). I.A. Campbell, Proc. Phys. Soc. (London), 89_, 71, (1966). 132. R.A. Fox, Thesis, (Oxford 1971) p. 96. 133. N.J. Stone, R.A. Fox, F. Hartmann-Boutron, D. Spanjaard, Hyper-fine Interaction i n Excited Nuclei, (G. Goldring, R. Kali s h , editors, Gordon and Breach), 1_, 351, (1971). 134. B.G. T u r r e l l , Phys. Let. A24, 669, (1967). B.G. T u r r e l l , Hyperfine Structure and Nuclear Radiation, (E. Mat-th i a s , D.A. Shirley, editors, North Holland, Amsterdam, 1968), p. 803. 135. P.G.E. Reid, M. Sott, N.J. Stone, Phys. Let. A25, 456, (1967). P.G.E. Reid, M. Sott,•N.J. Stone, Hyperfine Structure and Nuclear Radiation, (E. Matthias, D.A. Shirley, editors, North Hol-land, Amsterdam, 1968), p. 799. 161 136. O.A. C h i l a s k v i l i , C.J. Sanctuary, N.J. Stone, 11th International Conference on Low Temp. Phys., (J.F. A l l e n , D.M. Finlayson, D.M. McCall, editors, University of St. Andrews, Scotland, 1968), 137. J.A. Barclay, D.H. Chaplin, C.G. Don^ G.V.H. Wilson, Phys. Rev. B6, 2565, (1972) '. 138. D.H. Chaplin, C.G. Don, G.V.H. Wilson, Phys. Let. A32, 137, (1970). 139. R.A. Fox, Thesis, (Oxford, 1971), p. 94. 140. D. Spanjaard, R.A. Fox, I.R. Williams, N.J. Stone, Hyperfine Inter-actions i n Excited Nuclei, (G. Goldring, R. Kali s h , editors, Gordon and Breach), 1_, 345, (1971). 141. J.A. Barclay, H. Gabriel, J . Low. Temp. Phys. 4_, 459, (1971). 142. R. Kieser, B.G. T u r r e l l , P.W. Martin, Internation Conference on Hyperfine Interactions Studied i n Nuclear Reaction and De-cay (Uppsala, Sweden, 1974) p. 10. 143. R. Kieser, N. Kaplan, B.G. T u r r e l l , Phys. Rev. B9_, 2165, (1974). 144. J.E. Terapleton, D.A. Sh i r l e y , Phys. Rev. Let. 18^ , 240, (1967). 145. W.D. Brewer, D.A. Shirley, J.E. Templeton, Phys. Let. A27,- 81, (1968) 146. R.W. Landee, D.C. Davis, A.P. Albrecht, Electronics Designers Handbook, (McGraw H i l l , New York 1957) p. 16-20. 147. R. Morrison, Grounding and Shielding Techniques i n Instrumentation, (J. Wiley, New York, 1967). 148. R.W. Streater (Department of Chemistry and Lawrence Radiation Laboratory, University of C a l i f o r n i a , Berkeley, C a l i f o r n i a , 94720), private communication., 149. Airco Speer Electronics, Bradford, Pennsylvania 16701. 150. P.M. Berglund, H.K. Collan, G.J. Ehnholm, R.G. Gy l l i n g , O.V. Lon-nasmaa, J . of Low Temp. Phys. 6_, 357, (1972). T5a... Le Dang Khoi, P. V e i l l e r and I.A. Campbell, J. Phys. F4_, 2310 (1974). 162 APPENDIX I RELAXATION UNDER THE ASSUMPTION THAT A SPIN TEMPERATURE DOES EXIST We start from the master equation (.73) , +1 a p n = I (p W - p W ) (1) LT v m mn - K n nm dt m = - r p denotes the diagonal elements of the density matrix and W , W are n 6 ' • mn' nm the up and down t r a n s i t i o n p r o b a b i l i t i e s . The mean energy E of the nuclei with energy levels E^ i s : E- = I p n E n (2) n=-I. Under the 'spin-temperature' assumption p ^ i s given by the Boltzmann d i s t r i b u t i o n : exp (-3 QEJ 'S n P n I exp (-BsEi) 2^.«) where: B g = • and T g i s the nuclear spin temperature, s .> i s Boltzmann's conbtaut. Consider: dE d E ' ^ S . dt dB s dt (3) 163 As E = n«'(-V4' = n(hf) = n»AE i s independent of g„ we have n I 5 dE d +1 d exp (-O ) _ = I p E = I E 1= ^ _n_ dB s d3 s n=-I n n n n d3 s I exp (-SgE.) i 'Afit-e.-r d i f f e r e n t i a t i o n and s l i g h t rearrangement this yields dE E 2 exp (-3CE ) E exp (-g„E ) E exp (-3 QEJ ^ m r S m + m r S m < £ , n . S n dB s m ' I exp (-BgE^ m I exp (-Bg^ ) n J exp (-BgE^ with E = m • AE thi s gives m dE dt3c = -(AE) 2 (<m2> - <m>2) (4) (3) and (4) y i e l d ^. = - (AE) 2 (<m2> -, <m>2) dt dt (3') We now 'find find. dE _ d +1 +1 dp — = j - I P E = I (m AE) -dt dt m=^ I m=-I dt m with (1) dE +1 +1 w = l m AE I (PFT,W > - P m I f J dt m=-I n=-I 164 Assuming that only t r a n s i t i o n s with Am = ±1 take place we can write the summation over n = m ± 1 e x p l i c i t l y + I ( m=-I.( dE 1 dt m p - .W , - m p W . m+1 m+lm m mm-1 + m p , W i - m p* W . m-1 m-lm pm mm+1 dE ( +1+1 +1 — ' = AE I Y (m-1) p W- -} - I m p W . 3j_ j % J mm-1 Lr m mm-1 dt i -1+1 -I +1 +1+1 + J m p , W , - y (m-1) p , W . ^ m-1 m-lm ^ J m-1 m-lm dE t +1+1 +1+1 AE '| y - p W T + f m p W .) | T \ ht , Km mm-1 m mm-1 '-I dt ( -1+1 j +1*1 -I Lht , Km-1 m-lm m-1 m-lm '+1+1 -1+1 As the 2nc* and 4*^ term are zero and s h i f t i n g the 1 s t and 3r<^ term back to a summation from -I to +1 we have: dE +1 -AE y [p W . - p W .] L ^ L m+lm+lm m mm+1 dt 165 Assuming an interaction of the form A«I«S between the nuclei and the conduction electrons we w i l l have for the up and down t r a n s i t i o n pro-b a b i l i t i e s : AE exp(-AE3L) W , = — [1(1+1) - m(m+l)] nnn+'1 2KC l-exp(-AE-eLD) (6) AE W m+lm 2 k- c [1(1+1) - m(m+l)] l-exp(-AEg L) where C = T^T i s the high temperature value.of the Korringa constant, (2-), (5), (6) with p m + 1 = p m exp (-BgAE) andlW.: ^  = ^  m exp C-eLAE) y i e l d ; dE +1 — = -AE I (P m W m + l m) [exp (-3sAE)-exp(-3LAE)] dt -I dE (AE) 2 exp (-ggAE - exp(-3LAE) [1(1+1) - <m2>-<m>] dt 2k'C 1 - exp(-BjAE) (7) (7) into (3)') gives dB s _11 I(I+-1) - <m2>-<m> exp(-BgAE) - exp (-3^AE) dt 2kC <m2> - <m>2 1 - exp(-g AE) (8) Equation (8) can be solved numerically and describes the relaxation of the nuclear spin temperature as a function of time. 166 APPENDIX I I RELAXATION IN THE REGIME WHERE A SPIN TEMPERATURE IS NOT VALID and As i n appendix I we have: dp +1 — = I (Pffl W - Pm W .) (1) ^ .,. m nm m mn dt . n=-I iWdtfh Am = ±1 AE exp(-B AE) r T / * T . - i " \ . / ' . ^ ^ ^ A-1 Wmm +1 = - [ I ( I + 1 > " m C m + 1 ) J 2kC l-exp(-B LAE) AE 1 V l m = - [ I C I + 1 ) " m C m + 1 ) ] 2kC 1 - exp(-3LAE) (2) D P M m dt m-1 m-1 m m+1 m+1 m m m m-1 m m m+1, (3) or i n matrix notation (denoted by the lower bar): d — p(t) = - F • p(t) dt _ _ _ (4) 167 The matrix elements are F = W .+W , = W{[I(I+l)-m(m-l)] + [I(I+l)-mCnn-l)].. mm m m+1 m m-1 ; J L < . exp(-3LAE)} F m = W . ==-W[I(I+l)-mCm-l)] m m-1 m m m-1 L J l^J F . = W . =-W[I(I+l)-m(m-l)]exp(-3TAE) m m-1 m-1 m L - , J r v L / where: W = 2kC l-exp(-B LAE) The solution of the matrix equation (4) i s : p_(t) = exp(-Fp_) • p_C0) (6) To diagonalize the matrix F_ we l e f t and right multiply with the trans-formation matrices U 1 and U respectively.- U has the eigenvectors of F_ as columns. Thus U"1 p_(t)U = U'1' exp(-Ft)U • U"1 p_C0) U U"1 p_(t)U =, exp(-Kt)-U" 1 p_(0) U where the elements of K are k, = k, 6, with k, the eigenvalues of F. — Am A Xm A • — We have i n matrix and component notation: 168 P_(t) = U exp (-Kt) U 1 • p(0) pm C t ) = I \x e^~h^ I Uxn P n ^ ™ A n That t h i s equation s a t i s f i e s the boundary conditions given by the i n i -t i a l and f i n a l states Pm(0) and PMC°°) respectively can be seen by considering: lima t+!0 p Ct) = 7.U - l ' T u : 1 p CO) = T 5 p CO) = p (0) nr X mX L An r n v L mn K n ^ ' H n r 1 A n n ( 8 ) lime i and t-*» p Ct) = I U ,- 6V. y U*1 p (0) = Y U .U71 p (0) = p C°0 nr x m A A 1 A n n mi i n n J m A n n st where the 1 l i n e r e l i e s on the orthogonality of the eigenvectors nd while the 2 l i n e r e l i e s on the facts that only one of the eigenvalues k.. = k. = 0 and on a detailed analysis of U . t O . p CO). The density X I 7 mi i n n v 7 matrix elements as computed v i a (W) can be substituted into the ex-pression for the orientation parameters Bv and these i n turn w i l l de-termine the time dependence of the anisotropy WC6,t). Alternately equation (.4) could be solved numerically: d l i m e p_Ct+At)-p,Ct) — p_(t) = At+0 — = -F-p_Ct) C9) 169 APPENDIX I I I THE PERSISTENT MODE SWITCH AND MAGNET CONTACTS The persistent mode switch employed i n the 22 kG magnet and the p o l a r i z i n g solenoid u t i l i z e s the superconducting-to-normal t r a n s i -t i o n that occurs i n a superconductor when i t i s warmed above i t s c r i -t i c a l temperature. Two 1.7 m long strands of wire were taken from the same batch as used i n the construction of the superconducting c o i l . The ins u l a -t i o n was removed with 'Stripex' and the copper mantle was etched away with a 50% n i t r i c acid solution from a i m long center section. Both wires were now pushed through a single piece of t e f l o n 'spaghetti' 1.1 m long. The insulated section was coiled into a ri n g of approxi-mately 2.2 cm diameter and secured with thread. The heating element was made up by winding a length of thin insulated constantan wire of approxi-mately 12 Q around the ri n g . F i n a l l y , approximately 10 layers of 1 cm wide cloth tape were wrapped over the entire unit. The switch i s i l l u -strated i n Figure III/A. The contact between the superconducting wire of the magnet winding, the persistent switch and the f l e x i b l e copper mag-net leads (gauge 16, t e f l o n insulated) was made on a binding post con-s i s t i n g of a piece of 1/8" diameter copper tubing which was insulated with an inner t e f l o n sleeve and two large t e f l o n washers. This was bolted to the magnet flange. Approximately 30 cm of each of the superconduct-170 ing wires were wound on to the post and secured. Then a 15 cm long section of the magnet lead was wound on top. I n i t i a l l y pure indium was used to solder the contacts. However, we found l a t e r that ordinary 50/50 radio solder performed equally we'll. After a l l the. contacts were made the entire unit was vacuum-impregnated with p a r a f f i n wax. This not only s t a b i l i z e d the c o i l windings but also provided the persistent mode switch with the appropriate degree of thermal insulation_to ensure both stable superconducting operation and normal operation with l i t t l e power input. The switch was driven normal when the heater current ex-ceeded approximately 75 mA. I t i s clear that i n th i s arrangement the contacts to the superconducting wires depends v i t a l l y on the metallur-g i c a l quality of the bond between the copper and Nb-Ti core i n the superconducting wire. An equally good bond can be expected f o r f i l a -mentary superconducting wire. Since no direct contact between the Nb-Ti metal was made, filamentary wire could be readily employed f o r the c o i l windings., 171 BINDING POST: to p e r s i s t e n t switch r e t a i n i n g b o l t t e f l o n washer copper tubing magnet flange to c o i l PERSISTENT SWITCH: constantan wire superconducti wire 2.2 cm bare Cu bare Nb-Ti bare Cu .35 m 1.0m .35 m ' , , ' t e f l o n s p a g h e t t i 1.1m r Figure I I I / a Construction details of the superconducting solenoids are shown. 172 APPENDIX IV RESISTANCE BRIDGE The 33 Hz resistance bridge has been designed with the f o l -lowing objectives i n mind: i) extremely low power dissipation i n the sensing r e s i s t o r i i ) good precision and s t a b i l i t y . The block diagram of the bridge i s given i n Chapter III Figure III/5 and the c i r c u i t diagram i s given i n Figure IV/A. A 33 Hz sine wave generator drives the Wheatstone bridge and supplies, v i a a phase s h i f t e r , the reference signal for the m u l t i p l i e r c i r c u i t . This sine wave i s obtained by dividing the output from a _ W, cry s t a l controlled o s c i l -l a t o r . The harmonics are removed i n a narrow band twin T f i l t e r (146). This i s important as any voltage at a frequency other than 33 Hz would caus:e additional power input into the sensing r e s i s t o r and additional noise output from the m u l t i p l i e r . The signal from the Wheatstone bridge i s amplified i n a mat-ched low-noise preamplifier followed by a narrow band stage. The out-put i s fed into a m u l t i p l i e r c i r c u i t which provides optimum phase-sen-s i t i v e detection. The last stage i s an amplifier with long time cons-tant swhich drives the n u l l - i n d i c a t i n g meter. The design r e l i e s as f a r as possible on integrated c i r c u i t s . The f i e l d - e f f e c t t r a n s i s t o r i n the low-noise preamplifier was selected s p e c i f i c a l l y for i t s excellent noise characteristics at low frequencies. 173 The power supply i s decoupled from the a.c.-line with an i s o l a t i o n transformer to avoid the p o s s i b i l i t y of a 60 Hz stray voltage i n the sensing r e s i s t o r . Shielding and grounding (147) were c a r e f u l l y con-sidered. Figure IV/A shows the complete c i r c u i t diagram. The less common components are i n d i v i d u a l l y l i s t e d . As a sensing r e s i s t o r we have chos en 100 f2, 220 Q and 470 fi Speer grade 1002 carbon r e s i s t o r s (149). 174 to face page #175 Figure IV/A Ci r c u i t diagram of the resistance bridge. The power dissipation i n the sensing r e s i s t o r can be kept well below 10~ 1 0 W. Some of the less common components are l i s t e d below. Pvp = Sensing r e s i s t o r 100, 220 or 470 £2 Sp.eer grade 1002. A 1000 pF p a r a l l e l capacitor and a 300 yH series inductance are employ-ed to decouple Rj, from stray radio frequency f i e l d s . R = 0 to 10 kl] i n 0.1 8 steps, 1% metal f i l m r e s i s t o r s . C = 0 to 5.5 nF s i l v e r mica capacitors. . T = Audio transformer, Hammond #585, 20.K : 80 K T 2 = Audio transformer, Hammond #818, 80 K : 200 Q Transistors 2N 5225 unless otherwise noted. A l l r e s i s t o r s i n Kfi unless otherwise noted. A l l capacitors i n yF unless otherwise noted. , 175 13 Hx TROM T a Figure IV/Aa The Wheatstone bridge, narrow band amplifier (2N5556, 2N5210, 2X MC 1456), m u l t i p l i e r (MC 1494L) and the meter amplifier (MC 1456) are shown. 176 Figure IV/Ab The cr y s t a l controlled oscillator(0.540672 MHz), frequency divider (CD 4020 E), narrow band f i l t e r (MC 1456), voltage divider and phase s h i f t e r are shown. .' 177 APPENDIX V EQUIPMENT LIST Block I: Radio frequency generator: Wavetek model 2001 sweep signal, generator (modified) Radio frequency amplifier: ' IFI model 2500 Radio frequency mV-meter: HP model 411A and model 11025 A probe Multimeter; Conway•Masterranger . Oscilloscope: Telequiment Model S 51A Frequency sweep i n t e r f a c e : operation a m p l i f i e r with, adjustable gain, adjustable d.c. o f f s e t and long time constant f i l t e r . Block I I : Ge(Li) detector and preamplifier: Nuclear diode model LGCC-13.2-3. Power supply: HP model 6516 A Nal detector: Harshaw N a l ( T l ) , matched window, Type 20 MB 20/5 A, 5" x 5" Power,supply: Fluke model 412 B Preamplifier:- W. Malakoff, U.B.C. Thesis, (1969), p. 37 Linear a m p l i f i e r : Tennelec model TC 203 SCA: Ortec model 416 Scaler: Ortec model 775 (and time 719) 178 Block I I I : Multi-input multiscaling interface: see appendix VI Mult i channel analyser: Kicksort model 705/706 Address read out: Kicksort-model 870 N Paper tape punch: Kicksort model 857 N BRPE S e r i a l read and Teletype model BRPE 11 / 179 APPENDIX VI MULTI-INPUT MULTI-SCALING AND CLOCK UNIT This unit was designed to extend the single-input, multi-scaling c a p a b i l i t i e s of a multi-channel analyser to a multi-input multi-scaling capability. As shown i n the block diagram Figure VI/A, a maximum of four independent count inputs can be used. The counting period f o r a l l four channels i s synchronous and the unit introduces a dead time of less than 0.3 ysec. The data from the different inputs are transferred at the end of a counting period. This i s accomplished by sequential count-down of the buffer-stages. The count-down clock rate i s 1 MHz. In order not to exceed the maximum multi-scaling clock (channel advance) input rate of the Kicksort analyser a 10 ysec delay was used between counting down the individual stages.. This implies that ifche added count input rates has to be less than 1 MHz. The maximum number of counts that can be stored per channel i s (16)4I*= 65536. The 1 MHz reference signal i s derived from a c r y s t a l o s c i l l a t o r . This frequency can be divided by 1, 1,0, 10 2, 10 9 and by 1, 2, 3, 16. Two indepen-dent clock outputs are available. Clock II i s normally used for the multi-scaling clock input. Clock I i n connection with i t s j-k f l i p -flop can be used, for example, to turn o f f a radio frequency signal after a preset time. This i s useful i n the NMR/ON experiments. 180 I M i X - t a t OSC. • cLi'v! jLt by a i , l , . . . ,16 divide by i , l p . . . , i t 3.K. S U O T f t . ' , . - ( t « P eiocfc J out-/»•-*• ciocfc iL out f>~i~ sunt iv»p«»+ X c l o c k | .ftHi c l o c k COIIKI IV|»U-F JIT c o u n t .V|on+ mr u p Cou'vt-tr c l o u * . C o u u-p 0(0 CO »-teu.i .+ t r -h> awaits 4. ( M s c-r Figure VI/A Block diagram of the clock and multi-input multi-scaling unit. 

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