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Gamma ray anisotropies in antiferromagnetic crystals of MnSiF₆.6H₂0 and CoC1₂.6H₂0 Griffiths, David J. 1960

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GAMMA  RAY  ANISOTROPIES  ANTIFERROMAGNETIC MnSiF -6H 0 6  2  AND  IN  CRYSTALS  OF  CoCl '6H 0 2  2  by David B.A.,  J.  University  of B r i t i s h  A THESIS SUBMITTED THE  Griffiths  IN P A R T I A L  REQUIREMENTS  FOR  MASTER O F  in  Columbia,  THE  1959  FULFILMENT DEGREE  OF  SCIENCE  the Department of PHYSICS  We  accept  this the  THE  thesis  required  UNIVERSITY  OF  as conforming standard  B R I T I S H COLUMBIA  September,  I960  to  OF  In presenting the  this thesis  r e q u i r e m e n t s f o r an  in partial  advanced degree at  of B r i t i s h Columbia, I agree that it  freely available  agree that  the  f o r r e f e r e n c e and  permission for extensive  f o r s c h o l a r l y p u r p o s e s may D e p a r t m e n t o r by  be  the  of  University  Library  s h a l l make  study.  I  copying of  g r a n t e d by  his representatives.  fulfilment  the  It is  further this  Head o f  thesis my  understood  that  copying or p u b l i c a t i o n of t h i s thesis, f o r f i n a n c i a l  gain  s h a l l not  Department of  be  a l l o w e d w i t h o u t my  7*1-/2$ICS  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a . Date  S£f*T£ria&r  Columbia,  So ftbo. (  written  permission.  (i)  ABSTRACT  By  the  magnetic . 1°K.  technique  salts  By  good  paramagnetic and  may  of  be  cooled  thermal  salts,  to  contact  the  C0CI2.6H2O were  adiabatic  demagnetization,  temperatures between  crystals  antiferromagnetics  cooled  to  less  parathan  and  MnSiFg.6H20  temperatures  at  which  the  54  hyperfine impurity  interaction was  ferential  comparable  population  energy  states.  by  crystalline  the  impurity, of  was  the / - r a y s  data  led  acting  to  on  fication  a  the of  anisotropy  of  field  given  by  off  impurity  by  axes  CoCl .6H 0. 2  by  ion  Y-emission  2  of  the  of  the  the  of  in a  spin, active  induced Mn  distribution  r a d i o a c t i v e Mn  .  the  field  crystalline  i n MnSiFg.SH^O  and  to  calculations representing a  means o f  pre-  available  nuclear at  Mn  resulted  anisotropic  the  as  of  introduced  This  present  determination  the  an  kT.  alignment  measured  Also  made o f  netic,  The  to  of  distribution  theoretical  temperature. was  energy  function such  alignment  in  of  data, the  This  verithe  absolute a  determination  antiferromag-  TABLE ®F CONTENTS  Page ABSTRACT LIST OF  i ILLUSTRATIONS  i i  ACKNOWLEDGEMENTS  i i i  CHAPTER, I II  INTRODUCTION  1  DESCRIPTION OF APPARATUS AND  TECHNIQUES  A. The Apparatus  4 4  ( i ) Apparatus f o r * A d i a b a t i c Demagnetization ( i i ) C r y s t a l , P i l l s and Sample Holder ( i i i ) S u s c e p t i b i l i t y C o i l s and  4 4  D.C.  Inductance B r i d g e  6  (iv) Electronics  7  (v ) Vacuum System and Pumps B. B r i e f D e s c r i p t i o n of Experiment  9 10  C. Note on Thermal Contact between Pill  and C r y s t a l  D. A Magnetic to Absolute  12 Temperature  Determination III  12  MnSiF -6H 0 6  2  A. S t r u c t u r e I  Data on MnSiFg^HgO and  Growing of C r y s t a l s  B. T h e o r e t i c a l C o n s i d e r a t i o n s  15 15 16  CHAPTER  IV  Page C. R e s u l t s  24  D. Magnetic I n t e r a c t i o n s i n Alignment Work  27  CoCl -6H 0  29  2  2  A. S t r u c t u r e Data on CoCl2'6H20 and Growing of. C r y s t a l s  V  29  B. T h e o r e t i c a l C o n s i d e r a t i o n s  31  C. R e s u l t s  37  SUMMARY AND CONCLUSIONS  42  BIBLIOGRAPHY  4 5  (ii)  LIST OF ILLUSTRATIONS To f o l l o w Page  Figure 1  Photograph of Magnet  4  2  Dewar and Contents  7  3  D.C.  7  4  Photograph of D.C.  Mutual Inductance B r i d g e Mutual Inductance  7  Bridge 5  Block Diagram of E l e c t r o n i c s  7  54 6  Spectrum of Mn  Gamma E n e r g i e s  8  7  Photograph of E l e c t r o n i c s  9  8  Photograph of Counters  9  9  Vacuum System  9  10  Galvanometer C a l i b r a t i o n  12  11  T-T* R e l a t i o n  13  12  U n i t C e l l o f MnSiF -6H 0  15  13  A n i s o t r o p y v e r s u s Temperature I  23  14  A n i s o t r o p y versus Temperature II  23  15  Log  I  24  II  24  g  versus Log T  2  / 16  Log fe v e r s u s Log T  17  Photograph of Three Dimensional Model  30  of C r y s t a l S t r u c t u r e of CoClg'GHgO 18  Counts along a, b and c Axes of  34  CoCl *6H20 as F u n c t i o n s of Temperature I 2  19  Counts along a, b and c Axes of CoClg-GHgO as F u n c t i o n s of Temperature II  34  (iii)  Figure  20  To  Proposed R e l a t i v e D i r e c t i o n s f o r Alignment Axes i n C o C l 2 * 6 H 0 2  follow Page 35  (iv)  ACKNOWLEDGEMENTS  I would f i r s t  l i k e to thank Dr.  J . M. D a n i e l s , who  suggested the problems attempted i n t h i s t h e s i s , f o r h i s s u p e r v i s i o n and a l s o f o r h i s i n v e s t i g a t i o n s o f the t h e o r e t i c a l aspects of t h i s work. I would a l s o l i k e to express my thanks to Dr. J . C. G i l e s f o r a l l the experimental  knowledge he  c o n t r i b u t e d and f o r h i s a s s i s t a n c e throughout most of the long experiments.  ^My thanks go a l s o to Miss Maria  Elena Porta f o r the h e l p she a f f o r d e d i n some o f the experiments.  T h i s work c o u l d not have been c a r r i e d out  without the h e l p o f Mr„ R. Weissbach who i s r e s p o n s i b l e f o r the p r o d u c t i o n  o f the l i q u i d helium and a l l matters  of equipment i n the low temperature l a b o r a t o r y .  I am  a l s o g r a t e f u l f o r the h e l p given by Mr. J . Lees, the department glassblower,  p a r t i c u l a r l y r e l a t i n g t o work  on sample h o l d e r s , dewars and the vacuum system. Finally,  I wish to acknowledge g r a t e f u l l y the  f i n a n c i a l a s s i s t a n c e given me by the N a t i o n a l Research C o u n c i l i n the form of a bursary.  CHAPTER I  INTRODUCTION  In t h i s t h e s i s , the alignment o f the nuclear manganese 54 s i t u a t e d i n a n t i f e r r o m a g n e t i c MnSiFg.6H20 and CoCl .6H20 was s t u d i e d . 2  had  a c t i v e Mn  being  deposited  spin of  c r y s t a l s of  The above c r y s t a l s  i n t h e i r surface  l a y e r s and upon  cooled s u f f i c i e n t l y by the w e l l known process of  a d i a b a t i c demagnetization, the alignment o f the manganese 54 n u c l e i was s t u d i e d by means of the / - r a y d i s t r i b u t i o n of the decaying n u c l e i .  In the absence of any e x t e r n a l l y  a p p l i e d magnetic f i e l d ,  the alignment i s achieved  by means o f the h y p e r f i n e field.  entirely  i n t e r a c t i o n and the c r y s t a l l i n e  This c r y s t a l l i n e f i e l d  i s g e n e r a l l y thought to be  c l o s e l y a l l i e d with the d i p o l e f i e l d s o f the waters of crystallization.  Since  the atoms w i t h i n the c r y s t a l are  i n r e g u l a r a r r a y s , i t i s reasonably expected that the c r y s t a l l i n e f i e l d has d i r e c t i o n a l p r o p e r t i e s . Energy l e v e l s of the e l e c t r o n i c c o n f i g u r a t i o n s o f the Mn^  which are normally degenerate are d i f f e r e n t i a t e d due  to the e x i s t e n c e  of the c r y s t a l l i n e f i e l d ,  and a t the low  temperatures experienced by the manganese impurity the energy d i f f e r e n c e between the v a r i o u s p e r m i s s i b l e i s of the order  of kT.  states  This r e s u l t s i n a p r e f e r e n t i a l  -2-  d i s t r i b u t i o n of the p o s s i b l e energy s t a t e s v/ith the r e c e i v i n g the g r e a t e s t p o p u l a t i o n . r e s u l t s from the h y p e r f i n e already  The  nuclear  alignment  i n t e r a c t i o n coupling  the  a l i g n e d e l e c t r o n i c s p i n s with that of the  The  nucleus.  54 * i n the  form of the s p i n Harailtonian f o r Mn  (L  complexes presented by the manganese f l u o r o s i l i c a t e the c o b a l t c h l o r i d e i s given  e l e c t r o n i c and component along  case, any  s p i n s and  that D i s zero  r e s u l t i n g nuclear  f o r S = 1/2,  hyperfine  s t r u c t u r e may  ground s t a t e and The sent  hyperfine  higher  to Abragam and be due  The  to an admixture of  -  we  5 4  t i o n of the value  the  the  may  repre-  form,  B(S,I, + S lJ. y  study of the a n i s o t r o p i c e m i s s i o n of  the o r i e n t e d M n  and  s-electrons.  i n s t e a d of the more g e n e r a l  Z  T h i s need  S = 5/2  s t a t e s w i t h unpaired  ASJ  by a  Pryce* (1951),  s t r u c t u r e i s i s o t r o p i c , i.e„  i t by A S~.T  be  i n which  alignment i s achieved  not concern us d i r e c t l y as manganese 54 has According  I the  I t might  d i f f e r e n t mechanism than that o u t l i n e d above.  hence D ^ 0.  and  the e l e c t r o n i c s p i n  the a x i s of q u a n t i z a t i o n .  s t a t e d i n passing  and  splitting  i n t e r a c t i o n s r e s p e c t i v e l y ; S and  nuclear  two  by  where A and D are a measure of the h y p e r f i n e crystalline field  lowest  y - r a y s from  i n MnSiFg^R^O r e s u l t e d i n a determinaof D given above i n the s p i n H a m i l t o n i a n  -3-  and r e p r e s e n t a t i v e of the c r y s t a l l i n e f i e l d present at the manganese impurity.  For t h i s work, i t was necessary to  measure a parameter, c h a r a c t e r i s t i c of the 7*-ray p o l a r diagram and known as the a n i s o t r o p y of the  y -emission.  T h i s i s d e f i n e d as the r a t i o of the d i f f e r e n c e i n i n t e n s i t i e s of the emission of T'-rays along the a x i s of alignment and some d i r e c t i o n i n the plane p e r p e n d i c u l a r to t h i s a x i s to the i n t e n s i t y of e m i s s i o n i n the l a t t e r direction, i.e.  In p a r t i c u l a r , the experimental dependence of the a n i s o tropy so d e f i n e d upon temperature was c a r e f u l l y  ascer-  t a i n e d over a range of temperatures i n g e n e r a l extending from beldw 0.045°K to 0.120°K with the a c t u a l c a l c u l a t i o n s being made with the r e s u l t s from the " h i g h " temperature s e c t i o n of t h i s i n t e r v a l .  The reasons f o r doing t h i s are  given i n the t h e o r e t i c a l d i s c u s s i o n of Chapter I I I . R e s u l t s o b t a i n e d show a f u n c t i o n a l dependence of a n i s o tropy upon temperature which i s i n agreement with that 2  a r r i v e d at by J . H. D a n i e l s  from p u r e l y t h e o r e t i c a l con-  siderations.  ^ 54  The experiments of Mn  i n CoClg'Gl^O were done to  o b t a i n i n f o r m a t i o n about the a x i s or axes of alignment i n CoCl2*6H 0 by means of a three counter system 2  measuring  the 7* -ray count as a f u n c t i o n of temperature along three crystallographic  axes.  -4-  CHAPTER II  THE EXPERIMENTAL APPARATUS  A.  The  Apparatus  ( i ) Apparatus  for Adiabatic  Demagnetization.  The magnetization and subsequent the paramagnetic  demagnetization of  s a l t , potassium chrome alum, used to  a t t a i n temperatures  below 1°K was  p r o v i d e d by a water  c o o l e d electromagnet capable of producing the necessary f i e l d s of between 10-20 set of was  at 2 1/4  kilogauss.  i n . when the f i e l d  The magnet gap  s t r e n g t h was  20 kg. f o r a magnet c u r r e n t of 230 amps.  was  of the order The magnet  mounted on t r a c k s e n a b l i n g i t to be withdrawn from  the apparatus a f t e r demagnetization.  A photograph of the  magnet with i t s c o o l i n g c o i l s i s shown i n f i g u r e ( i i ) Crystal, P i l l s  1.  (K Cr Alum) and Sample Holder.  The c r y s t a l s i n which the alignment was observed were mounted between two copper  to be  impregnated  K Cr Alum c y l i n d e r s , r e f e r r e d to as p i l l s .  These  K Cr Alum p i l l s were made i n the f o l l o w i n g manner: a s o l u t i o n of C r ( S 0 4 ) g ' K 2 S O 4 • 24H 0 was 2  to evaporate to s a t u r a t i o n .  2  prepared and allowed  The c r y s t a l s which  formed  were then d r i e d and s t o r e d i n a d e s s i c a t o r c o n t a i n i n g a s a t u r a t e d vapour of K Cr Alum.  When ready f o r use,  these  F i g u r e 1.  Photograph of Magnet to f o l l o w page 4-  I  ~5-r  s m a l l c r y s t a l s were ground About 200 turns of No.  to a powder. 36 B and S enamelled  copper  wire w i t h a t o t a l s u r f a c e area of approximately 60  cm  2  were s o f t s o l d e r e d to a copper d i s c of 1 cm, diameter^. The space between the s t r a n d s was  then f i l l e d with the  KCr Alum powder and Apiezon o i l B and the assembly pressed i n t o a " p i l l " at about was  2  pressure.  done by housing the powder, s t r a n d s and copper  in a p i l l  This disc  press and by the use of a h y d r a u l i c ram.  r e s u l t was led  5 tons/cm  was  a c y l i n d e r of KCr Alum impregnated  copper wire and having a f l a t  The  by enamel-  copper d i s c at one  end.  The c r y s t a l s to be used were then p l a c e d between two  such  pills.  A t h i n f i l m of Apiezon grease was  added to ensure  a good thermal c o n t a c t between the c r y s t a l and the copper impregnated due  pills.  H e a t i n g of the p i l l - c r y s t a l  system  to induced eddy c u r r e n t s upon demagnetizatiou  found to be l e s s s e r i o u s f o r the case of enamelled  was copper  / wire than f o r that of bare wire. A g l a s s sample h o l d e r or tube of approximately 1.5 diameter and 17 cm. and p i l l  system.  l e n g t h was  used to house the c r y s t a l  The c r y s t a l and p i l l s were put i n a  l u c i t e sheath which was  suspended  by nylong threads from  g l a s s hooks extending from the top and bottom of the sample tube. ing  The a c t u a l mounting was  achieved by  break-  the bottom end of the tube and remoulding again with  a flame.  The  thread extending from the bottom of the  cm.  -6-  lucite turn  sheath  was  sample to  holder.  with The  copper This of  so that  sample  (iii)  holder  ported  was  d i d n o t make  f o r easy  t o a pumping  Susceptibility former,  Coils  coils  during  the course  of a run.  sample  tube  was  wrapped daries 1  insulated  i n black wound  lite in  length.  opposition  S.S.C. ance  S±  copper  wire  which  o f 1600 ohms. D.S.C.  copper  The  secondary  h a s a room  was u s e d  Bridge.  tube,  2  i n the system  susceptibility  influx  by  being  o f two  secon-  by a gap o f  l e n g t h o f the bake1 i n . and 1 3620,  1/4^in.  o f No. 40  temperature  had about  with  sup-  of the glass  and s e p a r a t e d  t u r n s , and S  wire  used  consisted  the f u l l  The p r i m a r y  No. 3 6 B&S longer  by t h e  two s e c o n d a r i e s w e r e  had 3200  were  Any p o r t i o n  i n series  The  by  o f the c r y s t a l - p i l l  The c o i l s  seal.  attachment  Inductance  the sample  which  not covered  extending  and  i n t h e dewar  a n d D.C.  tape.  former.  con-  of the holder.  against radiation  i n . and a primary  lateral  a t t o p e n d by a  removal  p l a c e d around  the s u s c e p t i b i l i t y  was  of the  v i a a copper-glass  line  tube  determination^ o f the temperature  coils  which i n  the tension of the suspension  to the holder  provided  which  a t the bottom  terminated  to the copper  bakelite  spring,  tube.  holder  soldering  hook  the sheath  connected  the sample  A  to a glass  the sample  tube  to a tungsten  This enabled  arrangement  soft  connected  connected  be v a r i e d  tact  was  B&S  d.c. r e s i s t -  570 t u r n s o f  a resistance  t o compensate  o f 70 ohms.  the e f f e c t  of  -7-  the  first;  that i s , i t was wound i n o p p o s i t i o n and was of  such a magnitude  as to y i e l d no d e f l e x i o n on the galvano-  meter when the r e v e r s i n g s w t i c h was and KCr Alum at room temperature. compensators  thrown with the c o i l s Also there were o t h e r  i n the mutual d.c. inductance bridge  circuit  which c o u l d be v a r i e d over a range from approximately 0-4 millihenries.  These l a t t e r compensators were kept at room  temperature and allowed easy adjustment of the d e f l e x i o n s before c a l i b r a t i o n to be made. The sample was  p l a c e d i n s i d e the s h o r t e r secondary,  s i t u a t e d near the c e n t r e of the b a k e l i t e former. ing  switch , as shown i n f i g u r e 3, was  opened  which  the c i r c u i t c o n s i s t i n g of the primary windings of the  susceptibility coil. circuit  thrown,  A revers-  i s dependent  The e.m.f. induced i n the secondary upon the s u s c e p t i b i l i t y of the  KCr Alum p i l l housed w i t h i n the b a k e l i t e former. ing  a C u r i e law dependence of the paramagnetic  By assum-  susceptibility  on temperature, the galvanometer d e f l e x i o n s were c a l i b r a t e d to  give the temperature of the c r y s t a l - p i l l system at any  time. Drawings  illustrating  the dewar and c o n t e n t s , and the  d.c. mutual inductance bridge c i r c u i t with i t s s u s c e p t i b i l i t y c o i l s appear as f i g u r e s 2 and 3.  A l s o a photograph of the  d.c. mutual inductance bridge appears i n f i g u r e (iv)  Electronics  4.  (Counting System).  The block diagram shown i n f i g u r e 5 i l l u s t r a t e s the  ^ C A P  RUBBER  RING  S E A L  R E T U R N  LINE  L E A D  4"  PUMPING  LEAD  CALORIMETER PUMPING  LINE  VAPOUR  P R E S S U R E  LINE  LIQUID  HELIUM  KCr A L U M  PILLS  S A M P L E  SUSCEPTIBILITY  FIGURE DEWAR8r  2.  S A M P L E  HOLDER  C O N T E N T S to  follow  page  7  COILS  « V  5.6  \  • W W — 4 6  |  -WWV 175  f  -WW 7 l 0 f  A  A M M E T E R 5.00  A.  2 - 2 4  V  WITH  0 . 0 5 0  S H U N T S  E X T E R N A L  C  TINSLEY  G  WITH  C O M P E N S A T O R  G A L V A N O M E T E R  T E L E S C O P E  AND  PARAMAGNETIC  P  Si  S2  TO  S C A L E  S A M P L E  S E C O N D A R Y  SURROUNDING  T H E  IN  S A M P L E  S E C O N D A R Y  B A T H  P A R T I A L L Y  C O M P E N S A T I N G HELIUM  T H E  Si  IN  T H E  B A T H  LIQUID H E L I U M  R E V E R S I N G  FIGURE  S W I T C H  B A T H  3.  M U T U A L  I N D U C T A N C E  BRIDGE  to  follow page "J  Photograph of D.C.  Mutual Inductance Bridge to f o l l o w page 7  LIQUID  HELIUM  AND  CALORIMETER COILS,  NITROGEN  AND  DEWARS,  SUSCEPTIBILITY  SOURCE  CATHODE FOLLOWER i  CATHODE FOLLOWER  LINEAR  LINEAR  AMPLIFIER  AMPLIFIER  L . . .  PULSE  AMPLITUDE DISCRIMINATOR!  HEIGHT  ANALYZER  1  PULSE H-EJGHT  AMPLITUDE DISCRIMINATOR  ANALYZER  i SCALER Co  SCALER  PLANE  FIGURE  Mn  PLANE  <  SCALER  SCALER  Co  Mn  AXIS  AXIS  5.  BLOCK  DIAGRAM  OF  THE  COUNTER to  ARRAY  folio**  page 7  -8-  c o u n t i n g arrangement used  to measure the Mn°  manganese f l u o r o s i l / L c a t e .  During the a c t u a l  Mn** and Co**®  alignments were observed.  4  alignment i n experiment,  For t h i s work, the  54 Mn  counts are c o n s i d e r e d ; the p u l s e s leave the  l a t i o n counters v i a a cathode linear amplifier.  scintil-  f o l l o w e r and are f e d i n t o a  From here they pass i n t o a pulse h e i g h t  a n a l y z e r which accepts any p u l s e s of magnitude g r e a t e r than the gate s e t t i n g .  F i n a l l y , the pulse i s recorded on a  scaler. Prior  to each experiment,  e n e r g i e s was  a spectrum of the  taken by sweeping the base l i n e of a p.h.a.  at f i x e d channel width over the energy band. base l i n e was  peak.  taken i n t h i s manner i s shown i n f i g u r e  evitable  the p.h.a. enabled one drift  The p.h.a.'s  then set at the energy value of the minimum  f o l l o w i n g the Compton s c a t t e r i n g  setting  7*-ray  A typical 6.  T h i s method of  to best minimize  i n the e l e c t r o n i c s  spectrum  the i n -  d u r i n g the course of an  \  experiment. In  the work on CoClg'^HgO, a t h i r d counter was  fixed  i n space along the a - a x i s of the c r y s t a l a t the same d i s tance from i t as the f i r s t  two c o u n t e r s .  The counts r e c o r d -  ed by these three counters were then used to determine orientation  of the alignment axes w i t h i n the c r y s t a l .  The Nal ( T i ) s c i n t i l l a t i o n c r y s t a l was diameter, 1 i n . l o n g and was RCA  the  1 1/2  in. in  h e l d i n o p t i c a l c o n t a c t on an  6342 p h o t o m u l t i p l i e r by Dow  Corning F l u i d 200.  The  t COUNTS/MIN. - 6 0 0  160  2 0 0  2 4 0  280  3 2 0  P.H.A.  FIGURE  3 6 0  SETTING  4 0 0  —  6.  S P E C T R U M  OF  M n  5  4  G A M M A  ENERGIES.  to  follow  page  &  -9-  phototubes mu  metal  were  shielded  tubing.  The  photomultipliers at  900  high voltage  b y TMC  amplifiers  commercially Instrument Schmidt  Model  Co.  The  trigger were  Company.  The  and  were  available  analyzers  a  stray was  HV4A  magnetic  fields  supplied  to the  high voltage  built  Linear  Models  The  single  were  Berkeley Decimal  1 kilowatt  power  R e g u l a t o r made of  the e l e c t r o n i c s  Vacuum  A diagram shows  how  System  used  siphon and  the s a l t  ducing  jacket,  Instrument  Scalers  supply  (Models  operated  on  (Stabiline Corp.).  counters appear  Photo-  as f i g u r e s  7  reduce  a  tube.  four  may  fore  system  be  This  thermally  parts  pair  Kinney  The  of  mm.  mechanical  the helium  p r e s s u r e on  bath  the bath  9,  before  diffusion  the apparatus  manometers,  o f 10  i n figure  insulated  o f pumps was  of the order inch  appears  pump a n d a m e r c u r y  such  t h e p r e s s u r e on  temperature.  Pumps.  o i land mercury  a vacuum  addition  A  to evacuate  sample  and  o f t h e vacuum  demagnetization. were  and  Atomic  pulse height  was  Electric  Superior  the  8. (v)  and  by  218 o f  by A t o m i c  standard regulated  with  i s the usual  channel  equipment  Voltage  2001).  discriminator  510 m a n u f a c t u r e d  scalers  Model  electronic  and  units set  agreement  Amplifier  amplitude  circuit.  i n close  The  graphs  by  volts.  The  2105  against  inner  capable  pump  as the dewar  of pro-  o f mercury.  pump was and hence was  wall  used  In to  lower i t s  observed  by  F i g u r e 7.  Photograph of  E l e c t r o n .sc s to f o l l o w page  9  F i g u r e 8.  Photograph of Counters to f o l l o w page 9  0  PIRANI  GAUGE  TO  SIPHON  J A C K E T TO  S A M P L E  — T U B E  {)  OUT  PHILLIPS GAUGE  45  -»~  LITRE  OUT  RESERVOIR  HELIUM  M  B A T H  LIQUID AIR  0  T R A P  M E R C U R Y DIFFUSION  PUMP OUT D: M . -  ROTARY  DISCHARGE  '  TUBE  M A N O M E T E R  M  M  PUMP  FIGURE  Hg  9.  120 cm. V A C U U M  Oil lOOon.  S Y S T E M to  follow  page  9  -10-  means o f the mercury and o i l manometers. l i n e s l e a d i n g back to the helium storage  There were r e t u r n from both the  inner dewar and the Kinney 4 i n . pump. For much o f t h i s experimental d e s c r i p t i o n i n more q 4 d e t a i l see LaMarche and LeBlanc . 0  B.  B r i e f D e s c r i p t i o n of the Course of an Experiment Firstly,  soldered  the sample holder was p r o p e r l y a l i g n e d and  to i t s pumping l i n e .  Next, the s u s c e p t i b i l i t y  c o i l was c o r r e c t l y p o s i t i o n e d about the sample and the dewars brought i n t o p l a c e . was  The w a l l o f the inner dewar  pumped t o a few c e n t i m e t e r s  and the space between the  inner and outer dewars was f i l l e d with The  liquid  nitrogen.  r e s i s t a n c e of the secondary windings o f ttte s u s c e p t i -  b i l i t y c o i l s was then checked and when s u f f i c i e n t l y low, i n d i c a t i n g that the inner dewar had been c o o l e d ,  clean  helium was f l u s h e d through the inner dewar and about 5 cm. admitted to the sample h o l d e r .  The i n n e r dewar was l e f t  with c l e a n helium a t atmospheric pressure  and once the  inner dewar was a t the temperature o f l i q u i d n i t r o g e n , the w a l l of the inner dewar was pumped hard on the f o r e - d i f f u s ion pump system. During pumping o f the inner w a l l the spectrum of the 2* -ray emission  i n the a c t i v e sample was taken and the  e l e c t r o n i c s , properly adjusted. hard along with the s i p h o n j a c k e t .  The manometers were pumped When t h i s was completed  the  t r a n s p o r t dewar was  brought up and the t r a n s f e r of  l i q u i d helium to the inner dewar took p l a c e . p l e t i o n of the t r a n s f e r , a check was 5-10  made to ensure about  microns pressure of helium being present i n the sample  holder.  T h i s was  charge tube. set  Upon the com-  done by menas o f a s u i t a b l y s i t u a t e d  The d.c. mutual  dis-  inductance b r i d g e c i r c u i t  was  up and the mutual inductance a d j u s t e d to ensure s u i t a b l e  galvanometer d e f l e x i o n s .  While the 4 i n . pump was r e d u c i n g  the  pressure over the l i q u i d helium bath, a c a l i b r a t i o n of  the  galvanometer was made f o r d e f l e x i o n versus temperature. About  der  one micron of helium was  left  i n the"sample  hol-  as an exchange gas to c a r r y away the heat of magnetiza-  t i o n from the paramagnetic s a l t ' the magnet was, then brought up and the f i e l d exchange gas was  applied.  A f t e r 7-10  minutes, the  pumped out of the sample h o l d e r which  then l e f t open to the f o r c e and d i f f u s i o n .  was  Demagnetization  took place about one h a l f hour l a t e r and as soon as p o s s i b l e a f t e r t h i s the counters were s t a r t e d . I t might  be noted i n p a s s i n g that the r a t e at which  demagnetization o c c u r s i s very important. too  I f the r a t e i s  r a p i d , then eddy c u r r e n t h e a t i n g r e s u l t s i n the copper  wires permeating the KCr Alum p i l l s ; cess i s not a d i a b a t i c .  The speed adopted i n t h i s s e r i e s o f  experiments always gave an i n i t i a l 0.045°K.  i f , too slow, the pro-  temperature w e l l below  /  During the subsequent warm up, counts were taken f o r  -12-  ten  minute i n t e r v a l s a l o n g with temperature  r e a d i n g s which  were recorded as d e f l e x i o n s on the galvanometer. completion of the warm up, helium was  Upon the  introduced into  the  sample h o l d e r and when the a n i s o t r o p y had vanished (at s u f f i c i e n t l y h i g h temperatures,d e f l e x i o n on the galvanometer), taken to determine of  i n d i c a t e d by almost n i l n o r m a l i z a t i o n counts were  the 7 * - r a y d i s t r i b u t i o n i n the absence  any a n i s o t r o p y . F i g u r e 10 shows a t y p i c a l galvanometer  calibration,  g i v i n g the d e f l e x i o n s as a f u n c t i o n of T~*J T, being the a b s o l u t e temperature  of the helium bath determined  from  the vapor pressure t a b l e s of helium by H. Van D i j k M. Durieux C.  (the Tgg  temperature  and  scale).  Note on Thermal Contact between C r y s t a l and  Pills  The same method of thermal c o n t a c t between c r y s t a l and KCr Alum , p i l l was  used by M. LeBlanc  (1959) on  Co(NH4) (S04Jg'GHgO and a warm up r e l a t i o n was 2  which was  obtained  i n good agreement (10-15%) with the p r e v i o u s l y  known data on the s a l t .  A l l runs done on the C o C l ' 6 H 0 2  2  and MnSiF6'6H20 were thus assured of at l e a s t as good a thermal c o n t a c t between s a l t and c r y s t a l as that achieved on the C o ( N H 4 ) ( S 0 ) ' 6 H 0 . 2  D.  A Magnetic  4  2  2  to Absolute Temperature D e t e r m i n a t i o n  As mentioned p r e v i o u s l y , C u r i e ' s law was for  the KCr Alum p i l l s  over the temperature  assumed v a l i d  range, w i t h i n  FIGURE  10.  CALIBRATION DEFLEXION  OF VS.  G A L V A N O M E T E R I . to  follow  page  12.  -13-  which the a n i s o t r o p y was  to be s t u d i e d .  Hence, the  d e f l e x i o n r e g i s t e r e d on the galvanometer was i n t o a magnetic  temperature, T*.  One would  translated l i k e to  i n v e s t i g a t e the r e l a t i o n s h i p between t h i s magnetic t u r e and the thermodynamic or K e l v i n temperature the  tempera-  throughout  range of o b s e r v a t i o n . Twelve demagnetizations were performed upon KCr Alum  pills  of l e n g t h 3.75  i n . , diameter 0.50  i n . , and by  o b s e r v i n g the warm up of the s a l t the i n i t i a l  magnetic  temperatures a t t a i n e d were determined by e x t r a p o l a t i o n . The r a t i o o f the e x t e r n a l magnetic f i e l d temperature  — ^  to the helium bath  was r e c o r d e d f o r each of the twelve de-  m a g n e t i z a t i o n s , and v a l u e s of S/R  where S i s the entropy s  were o b t a i n e d f o r the v a r i o u s v a l u e s of -J|2L from the t a b l e s compiled by H u l l and H u l l P h y s i c s (1941).  T  .  % i n the J o u r n a l of Chemical ^  The amount of entropy (S/R) a s s o c i a t e d  w i t h the KCr Alum was ing  5  then assumed to remain c o n s t a n t dur-  the subsequent a d i a b a t i c demagnetization.  graph r e l a t i n g S/R D a n i e l s , American  the  to T°K o b t a i n e d f o r KCr Alum by I n s t i t u t e of P h y s i c s Handbook, page  was  examined.  the  corresponding i n i t i a l  tained.  Next,  Knowing S/R  f o r the s a l t now  i n zero  a b s o l u t e temperature was  4-16,  field, ascer-  Hence, f o r the twelve demagnetizations, p o i n t s  were o b t a i n e d f o r a p l o t of magnetic versus thermodynamic temperatures.  The r e s u l t i n g graph appears as f i g u r e  on the f o l l o w i n g page.  11,  0 . 2 4  0 . 2 2  -  0 . 2 0  -  0.18  -  0.16  -  0.14  _ /  O.I2  -  O.IO  -  0 . 0 8  -  0 . 0 6  -  0 . 0 4  _  0.02  -  0 . 0 0  (PROC.  ROY.  to  0.02  0.04  . 0.06  0.08  O.IO  0.12  O.I4  0.16  O.I8  SOC.  follow  O  2 0  2 Q 4  page  A .  218,  (1950-51))  13  0 . 2 2  0 . 2 4  i.  0 . 2 6  -14-  Agreeraent between T* and T was found a t the low temp e r a t u r e end to lower temperatures than had been shown by g  Bleaney  i n Proc. Roy. Soc. 2C-4A, 218 (1950-1951),  though  t h i s was not thought s i g n i f i c a n t s i n c e Bleaney's v a l u e s for  the shape f a c t o r o f the p i l l s had been used without  correction.  CHAPTER I I I  MnSiF -6H 0 6  A.  2  S t r u c t u r e Data on MnSiFg-6H2Q and Growing o f C r y s t a l s MnSiFg.6H20 c r y s t a l l i z e s i n the C 2 ( R 3 ) space group. 3 i  It  belongs to the CoCl type c r y s t a l group, the l a r g e s t o f  which i s NiSuClg«6H20  ( n i c k e l c h l o r o s t a n n a t e hexahydrate). o  MnSiF6'6H20 has a rhombohedral u n i t c e l l with a and a  Q  OL = 96°53'.  Q  = 6.45 A  I t s hexagonal p s e u d o c e l l i s d e f i n e d by  = 9.71 A and CQ = 9.73 A. The u n i t c e l l has S i i o n s a t each o f the c o r n e r s o f  the  c e l l , enveloped by a f l u o r i n e octahedron. The  Mn.6H 0 octahedron appears a t the c e n t r e of the c e l l . 2  accompanying  An  diagram, f i g u r e 12, i l l u s t r a t e s the r e l a t i v e  p o s i t i o n s of the i o n s forming the u n i t c e l l of MnSiF6*6H20. MnSiFg'6H20 i s an a n t i f e r r o r n a g n e t i c w i t h a Neel temp e r a t u r e , given by Ohtsubo e t a l , 7  1958, o f 0.10°K.  c r y s t a l s a r e t r i g o n a l and grow i n hexagonal p a r a l l e l to the t r i g o n a l a x i s ( G r o t h  8  1906).  The  pillars The p r e f e r r e d  a x i s i s along the hexagonal a x i s (Ohtsubo e t a l , 1958). Work i n dynamic n u c l e a r p o l a r i z a t i o n by R. W. Kedzie and C. D. J e f f r i e s  9  has shown the s p i n o f M n ^ t o be I » 3, 54 4.  and the magnetic momentfX = 3.30 - 0.06 n.m. The c r y s t a l used was approximately 0.15 mm.,in t h i c k -  FIGURE  12.  DIAGRAM  (showing  UNIT  only  OF  UNIT  one  of  S T R U C T U R E  O  Mn  at  centre  of  C E L L  the  fluorine  OF  MnSiF  MnSiFf-6H,0  octahedra).  6 ^ 0 -  F  O  H  •  S i  O  M n  unit  OF  x  cell,  0  M n :  ('/fe^/a^'A) to  follow  page  I  -16-  ness with an e f f e c t i v e s u r f a c e of about 0.8 cm . 2  The growing of the MnSiFg'61*20 c r y s t a l s "was  achieved  by adding manganous carbonate t o h y d r o f l u o s c i l i c i c a c i d and s t i r r i n g u n t i l a l l CO2 was d r i v e n o f f .  The straw  c o l o u r e d s o l u t i o n obtained was then allowed  t o s i t or was  heated to s a t u r a t i o n with  the r e s u l t that c r y s t a l s of  MnSiF6-61120 were formed.  The c r y s t a l s were then sub-  merged i n an a c t i v e s o l u t i o n o f M n C l i 2  r a d i o a c t i v e Mn ' . 1  4  the manganese  being  T h i s r e s u l t e d i n some o f the i n a c t i v e  Mn ions of the s u r f a c e l a y e r s being r e p l a c e d by the a c t i v e 54 Mn  from the s o l u t i o n .  When t h i s r e s u l t i n g  i n the c r y s t a l was s u f f i c i e n t l y  radioactivity  i n t e n s e , the c r y s t a l was  mounted, as p r e v i o u s l y d e s c r i b e d , and ready f o r use.  /  B.  Theoretical Considerations The form of the s p i n Hamiltonian  Mn  ++  r e p r e s e n t i n g the  i o n i n a magnetic complex i s g i v e n , i n g e n e r a l , as  follows:  where any c o n t r i b u t i o n due t o the i n t e r a c t i o n of the quadrupole moment of the nucleus present  and the e l e c t r i c f i e l d  a t the p o s i t i o n of^ the nucleus  i s omitted  gradient as i s the  i n t e r a c t i o n o f the n u c l e a r magnetic moment with any magnetic  fields.  -17-  For our case, there i s no e x t e r n a l f i e l d , and A = B f o r i s o t r o p i c h y p e r f i n e s p l i t t i n g . a r e s u l t a n t s p i n Hamiltonian Mn  2+  i . e . , H = 0, This yields  f o r our i n v e s t i g a t i o n s of  i n MnSiF6'6H20 of the f o l l o w i n g form:  ft = A S - I + D[s2-iS(s 0 ) . +  The  following theoretical calculations follow closely  those due  to D a n i e l s ( p r i v a t e communication) and show the  d e r i v a t i o n of the dependence of the a n i s o t r o p y upon temperature. Consider  the  y'-ray d i s t r i b u t i o n to be r e p r e s e n t e d  an o p e r a t o r P,  and  g i v e n by Trace  (Pp)  the a c t u a l d i s t r i b u t i o n , F  by  , to be  where p i s the s t a t i s t i c a l  matrix  g i v e n by  where E^,..., E  n  are the e i g e n v a l u e s of the  Hamiltonian  o p e r a t o r ; i . e . the allowed energy v a l u e s . The of  procedure i s that of f i n d i n g the e x p e c t a t i o n value  a parameter-operator  existence states.  To i l l u s t r a t e  following: a statistical  which has a number of p o s s i b l e  matrix  the p o i n t , c o n s i d e r the  -18-  and an operator  ("""'; then we may  'OJPJ^  i n s t a t e 1 by  and  represent  the value of  the e x p e c t a t i o n value of  P  P  by * . < ' |  r  l > l  +  n  i  <  Z  i  r  l  )  2  /  "  < ^ | P l  +  n  >  which i s simply  Tr Hence we  (rjO.  see the a c t u a l d i s t r i b u t i o n i s i d e n t i c a l to the  e x p e c t a t i o n value of the operator P Y  , repi'esenting the  -distribution. " */fcT In our case  p _  &  , and  hence  TV  ( 1  where T r ( p ) ^ 0 and i s i n f a c t = 4~J7". I t i s t h e r e f o r e convenient  to d e f i n e P =  4^7"  +  ^  where of course, T r ( p ' ) = 0. Hence  Tr(rj>)  = _ i — +  1<T  ^ _  fck'T*  T r ( . ) + ^ T r ( ^ ) - - .  wherein we  have s u b s t i t u t e d  4^"  a high temperature approximation represent  +P  forP  to e " ^ /  k T  and have used e n a b l i n g us to  the e x p o n e n t i a l f u n c t i o n by i t s corresponding  power s e r i e s , t e r m i n a t i n g a f t e r the f i r s t  few  terms.  To c a l c u l a t e the e x p e c t a t i o n value of the operator  i t i s necessary  to s u b s t i t u t e f o r ^  distribution  , the s p i n a  -19-  Hamiltonian  54  r e p r e s e n t i n g the a c t i v e Mn  nucleus  in i t s  magnetic complex; as we saw p r e v i o u s l y ,  Let us c o n s i d e r the decay scheme o f  Mn^.  / Examining T r ( T f );  T r ( r ' ) - 0 and T r ( ^ ' ) = 0, the l a t t e r  being a property of the Hamiltonian.  By u s i n g  these  2  p r o p e r t i e s and o t h e r s l i s t e d by D a n i e l s that T r ( V  tl  %  ) and T r (  2  c o n t r i b u t e nothing  to T r ( P p )  value of P ,  or the e x p e c t a t i o n The  r'tl )  i t can be shown  f i r s t term which does c o n t r i b u t e to the d i s t r i -  bution f u n c t i o n i s the one i n  Tr(r'*^^).  Upon examining  , i t i s noted that such terms as Tr( Vfir  (S-xV"  w i l l contribute.  D(s£- V  S  s(s-hrt}  }  However, ( S - l ) * x s(s-»-/) i s a p l a i n number  and so w i l l g i v e A ( S - I ' ) l > V S(S-t-\) 2  t  3  Notice  + a l l permutations  T r ( r O = O.  that,  * 3> T v [ r ' ( s - x y - S j ] l  now  T r ( S * ) = T V 5 r s+ 0(2S + O ( 3 S * * 3 S - 0 -TrlS^Sx ) = — 1  30  S(S+'0C2S + i H 2 S  l  +  Z S i - 0  f  "  -20-  and s i m i l a r  permutations.  T r [r'lS-lY S^]  Then  + permutations  +[Tr(r'l )+ T r l r ' I ^ ] Vo S('s-r)VzS+l)C2S - ZS-+ 0 l  l  x  +  S(S + 0 ( 2 S + 0 C * + S 4 «+S-3^  =  l  s(s<-«)Us+0(2sVi.s+iV T r l r ' i ^ + T r f r ' i ^ ) + T r t r ' i r ) | the l a t t e r term vanishes s i n c e Tr(P'lJ)+Trfr I^4Trfr'l^ = Tr[r'(l* * I j + X j ^ ,  -  Trfrid+rt]  =  l(i4.^TrCr^  = o.  Hence  and /o  x  as a r e s u l t  Tr(rp)- J -  -  TJL-^'^ ) . 1  where 77(0  -  (15 + I H 2 1 + ^  T (r?)=-1- - - J r  £ ± - - H -  •  S  *  £  Trfr'll)  , X = 3  for  S=|  -21-  Now, T r C r ' l J ) = l%<3)r'|3> + * < z l r » W > + 2 < i l r ' b >  <wlr'\u> = <-l< Ir'l-k")  since  r  <±3|r'|i3> =• J L - (-±= - cos+G}  and  <±z|r']iz>=  ^ [ i - z ^ e ^ o o i ' e )  <±l ] r ' l * l >  + ± cos^G -± cos** Q \  where e i s the angle between the a x i s of q u a n t i z a t i o n ( z - a x i s ) and the d i r e c t i o n of emission of the Y -ray. A note as to the o r i g i n of Let p^, p ,  ^>-i be e i g e n f u n c t i o n s forming  o  set,  follows.  which represent  an orthonormal  the fi-V decay of the parent  nucleus.  Then the wave f u n c t i o n s r e p r e s e n t i n g the o v e r a l l decay and i t s i n t e r a c t i o n s w i l l be ^j? , which w i l l be c o n s t r u c t e d as f o l l o w s :  A 1 j  j jo  \ *  7  where & and *P r e p r e s e n t the i n t e r m e d i a t e and f i n a l s t a t e s r e s p e c t i v e l y of the decaying nucleus.  f u n c t i o n s f o r these s t a t e s and  form closed orthonormal sets,  where  They a r e the wave  \ 7 - j . U j * 1 3"+J-\.  The  L.  M m i r r  ,  are the Wigner or Clebach-Jordan  t  coeffi-  c i e n t s that are e v a l u a t e d i n the t a b l e s g i v e n by Condon and S h o r t l e y (1953J.  We  can e v a l u a t e f o r a l l mi that  appear i n the summation o  o  where  a  r e the components of the normalized wave  f u n c t i o n s f o r the photons of m u l t i p o l e order  ,  whence o o  In our  case  and so f o r  < l ' | > = VV,*  we o b t a i n  |3,*^*p,^  3  r  3  %  and by o r t h o n o r m a l i t y of the j j ' s , t h i s reduces  Also,  < |r'| > l  l  4jfp ^j) 0  t  to  -23-  and  \ <>ir-i.>- i<t:i*:> + ^<*:i^v*73=^:i*:> upon i n s e r t i n g the a p p r o p r i a t e s p h e r i c a l harmonic f u n c t i o n s V j i  for  one  o b t a i n s the r e l a t i o n s o b t a i n e d above f o r  Tr(r'lJ). Thus  hence  T  r  ( r p  )  .  . £1.  . _ i _  2 ». i  . ^ l  f. -  T h i s then i s the d i s t r i b u t i o n f u n c t i o n f o r the Let us denote i t by 1(6),  Ke)«^  J  remember t h a t € , the a n i s o t r o p y was 1  d e f i n e d by  (*M  and upon s u b s t i t u t i o n f o r these angles we  i - M-A'D/WST  Here we  5  W T S  find  The  that  3  have the p r e d i c t e d i n v e r s e c u b i c dependence  of a n i s o t r o p y upon temperature i n the "high region.  t -emission.  henceforth.  k*T3  6  W e )  temperature"  r e s u l t s show good agreement w i t h t h i s as  be seen i n f i g u r e s 13 and  14 where the a n i s o t r o p y i s  can  FIGURE 0 . 2 2 0  _  1  M n  5  4  IN  I  MnSiF  impregnated  6  6Hjp.  L  KCrAlum  1  III  1  t  OF  Copper  0 . 2 0 0  0.180  ANISOTROPY  13.  pills.  E X P E R I M E N T A L  RESULTS  THEORETICAL  T  CURVE  1i i\  0.160  2 2 21  0 . 1 4 0 2 0  >T  a, o cr  0 . 1 2 0  W  O.IOO  H O  z  19 18  16 15  0 . 0 8 0 ,  14  0 . 0 6 0  13  a-. .045°*  'ill  050*K0 . 0 4 0  0 6 0  0  K  070°K 0 . 0 2 0  to . 0 8 0  0  IO  follow  page  K  3 0 0  2 3  9 8  .100 2 0 0  II  K . 0 9 0  IOO  12  MINUTES  °K  J  .lto K. 0  4 0 0 A F T E R D E M A G N E T I Z A T I O N  I 5 0 0  7  FIGURE 14.  ANISOTROPY Copper  0 . 2 0 0 T  T  9  $  0  O F  M n  5  impregnated  4  IN  MnSiF  K C r Alum  f c  -6H 0. x  TI.  pills.  2 81 0 - 5 9  T  —6  O. 1 8 0  E X P E R I M E N T A L 0 . I 6 0  R E S U L T S  \  \  I  •  T H E O R E T I C A L  T ~  3  C U R V E 2 2  O. 1 4 0 21  9\  2 0  0 . 1 2 0  SO  1  O. l O O  19  f  18  T *  17  >  16  a. o  ac 0 . 0 8 0  to  O  follow  15  page 2.3  14  z 0.060  13  0.045°K  0 . 0 4 0  0 . 0 5 0  12  K 0 . 0 6 0  0 . 0 2 0  J. i  K 0 . 0 7 O  O  ti-l  K 0 . 0 8 0  K 0 . 0 9 0 ° K  3 0 0  O.IIO° K  A F T E R  10  11  0.120  9  K  8 7  4 0 0 M I N U T E S  11  DEMAGNETIZATION  -24-  p l o t t e d as a f u n c t i o n of temperature  with a t h e o r e t i c a l  i n v e r s e cube curve p l o t t e d f o r comparison,  and  in figures  15 and 16 where the power dependence of a n i s o t r o p y upon temperature C.  i s c a l c u l a t e d from  the experimental  results.  Results R e p r e s e n t a t i v e p o i n t s from  the a n i s o t r o p y versus tem-  perature p l o t of the experimental r e s u l t s were taken  and  t r e a t e d as f o l l o w s : TABLE I (from f i g u r e T^K  T^  6 T  0.165  .070  34.3  x IO  0.122  .080  51.2  x 10"  0.090  .090  72.9  x 10~  0.069  .100  100 x I O  0.052  .110  133  (£ T )  = A = 6.46  3  m  I£T  3  - (6T ) 3  13)  1  - (ST )mean 3  5.66  x 10~  5  6.25  x IO  5  6.56  x 10"  5  -0.10  - 5  6.90  x IO"  5  +0.44  6.92  x 10~  5  +0.46  and  the corresponding  - 5  x 10~ x IO" /  6T3  3  5  5  5  -0.80  - 5  -0.21  °K. - t  0.40.  mean Using t h i s value of A  , then £ = -0— <p3  ( a n i s o t r o p y ) v a l u e s were found l i s t e d i n t a b l e 1 above. t h e o r e t i c a l T~  3  f o r the  temperatures  T h i s set of p o i n t s gave the  curve which appears  in figure  13.  FIGURES  15 8 16.  LOG  6  VS.  LOG  T.  to  I I I I  0.2  follow  page  2-4  •25-  \  TABLE II (from f i g u r e 14)  1 0.148  0.070  34.3  i i x 10"  0.107  0.080  51.2  0.077  0.090  72.9  0.054  6 T  3 €T  3  _  (€T ) 3  5.08 x I O "  5  x 10~  5  5.48 x I O "  5  x IO"  5  5.61 x 1 0 ~ .  + 0.29  0.100  100 x I O "  5  5.40 x I O "  + 0.08  0.040  0.110  133 x 1 0 ~  5  5.32 x I O "  5  0.00  0.029  0.120  173 x I O "  5  5.01 x I O "  5  - 0.31  It i s noted here that a p l o t o f l o g 6  versus l o g T  3  U T L  3  &  =  an  - 0.24  5  (6 T )mean  m e  + 0.16  5  5  ft  = 5.32 x 10" 5  - (raeauj feT )^^] 3  mean m  e  a  = ± 0.18.  n  was done f o r the two s e t s o f data and the r e s u l t i n g are shown i n f i g u r e s 15 and 16.  I t i s to be noted  graphs also  that the s l o p e s of these l i n e s are -2.77 f o r the data of t a b l e I and -2.91 f o r the data o f t a b l e II*.  Both  these  r e s u l t s i n d i c a t e an i n v e r s e c u b i c dependence of a n i s o t r o p y upon temperature  w i t h i n experimental accuracy.  The agree-  ment between the data and the t h e o r e t i c a l work o f J . M. D a n i e l s c o n c l u s i v e l y demonstrate the r e l a t i o n  ^  cC  \  54 f o r the case of Mn  i n a magnetic complex where i t s s p i n  H a m i l t o n i a n may be g i v e n as  AST.  + 3>^S^- ^ S f S + O J  A d e t e r m i n a t i o n o f the c r y s t a l l i n e f i e l d may be c a r r i e d out as f o l l o w s .  s t r e n g t h , D,  -26-  Theoretically £ = -  \X  f\ J> x  W T3 3  f r o a the experimental r e s u l t s e -  for  we have S. ?*f  *  IO~ s  the theory to be compatible w i t h experiment as  it  would appear from the above to be - \Z \?  *9 *  5".  -  to'*  ' V . I *  Let  us take A to be the same as that f o r the d i l u t e  i.e.  salt,  one i n which the paramagnetic i o n s have been r e -  p l a c e d to a great extent by diamagnetic i o n s , ZnSiFg«6H 0. 2  A word about t h i s procedure  e.g.  follows.  Assuming the value o f A , given by D a n i e l s  as  -0.0072 cm~* f o r the s t r e n g t h of the h y p e r f i n e i n t e r a c t i o n to be the same f o r MnSiFg*6H 0 as that of  the d i l u t e  2  salt  Z n S i F g ' 6 H 0 , we can proceed to a d e t e r m i n a t i o n o f D, the 2  c r y s t a l l i n e f i e l d strength,  in MnSiFg.6H 0. 2  c a t i o n f o r t h i s procedure a r i s e s  The j u s t i f i -  from the f a c t  s p i n i n t e r a c t i o n i s a p r o p e r t y of  the a c t i v e  that the s p i n -  i o n , i n our  case Ban*** and should not be too g r e a t l y a f f e c t e d  by  c r y s t a l f i e l d c o n d i t i o n s which of course d i f f e r between the d i l u t e s a l t magnetic  ion.  and our M n S i F g « 6 H 0 , 2  However, i t  which l a c k s the  i s worth making the  that the A value has been taken as that f o r the salt.  dia-  reservation dilute  -27-  <  Given  A = - 0.0072 cm  and we  k = 1.38  x IO ®  ergs/degree  - 1  can s o l v e f o r D 5.89  D =  D.  A  x 10~ 12A  2  5  k —  3  -1 = - 0.032 cm . n  M  n  Magnetic I n t e r a c t i o n s i n Alignment Work Alignment experiments u s i n g M n  5 4  i n Ce Mgg(NQg )±2~^^2^  7*-ray p o l a r diagram was  showed that the  affected  magnetic i n t e r a c t i o n s between the manganese and T h i s phenomenon has state e f f e c t .  i n the absence of a magnetic f i e l d , a r r i v e d at t h e o r e t i c a l l y . f i e l d of the order i s increased. along  cerium i o n s .  s i n c e been r e f e r r e d to as the  T h i s produces a net decrease i n  of a few  from the  by  solid  anisotropy,  value  Upon a p p l i c a t i o n of a magnetic hundred gauss, the  T h i s e x t e r n a l magnetic f i e l d  the t r i g o n a l a x i s of the c r y s t a l ,  anisotropy  i s applied  i . e . along  the  axis  of alignment. T h i s e f f e c t i s important to r e c a l l s i n c e i t has made the v a l i d i t y of the determination moments by means of nuclear Daniels  1 0  i n 1957  (Can.  o f nuclear  magnetic  alignment open to  J o u r n a l of P h y s i c s 35,  question. 1133J  examined t h i s s o l i d s t a t e e f f e c t i n a q u a n t i t a t i v e manner. H i s i n v e s t i g a t i o n s have shown that i n alignment e f f e c t e d hyperfine  s p l i t t i n g i n zero e x t e r n a l magnetic f i e l d ,  our case, any  as i n  i n t e r a c t i o n between the i o n i m p u r i t i e s or  between the i m p u r i t i e s and  the host i o n (determined  by  by  -28-  whether the s a l t i s d i l u t e or not) a f f e c t s the ¥ -ray d i s 1 tribution f i r s t l y  i n the "^T" term w i t h i n  the high tempera-  ture approximation r e g i o n , where the 9* -ray d i s t r i b u t i o n f u n c t i o n i s expanded i n a s e r i e s of ^. Since i n our case the a n i s o t r o p i c emission o f 7 * - r a y s 1 has e x h i b i t e d a — r r - dependence, i t i s p e r m i s s i b l e neglect  to  the p o s s i b i l i t y of any magnetic i n t e r a c t i o n s i n -  v o l v i n g the impurity  and hence i n v a l i d a t i n g our r e s u l t s .  As our r e s u l t s are a p p l i c a b l e to "high temperatures", the i n v e r s e cube r e l a t i o n between a n i s o t r o p y j u s t i f i e s i g n o r i n g e f f e c t s which enter approximation.  and temperature  only  i n the  -29-  CHAPTER IV  CoCl *6H 0 2  A.  2  S t r u c t u r e Data on CoCl9'6HgO and Growing of C r y s t a l s Many experiments have been c a r r i e d out i n which  a c t i v e n u c l e i have been o r i e n t e d and t h e i r ¥-ray  d i s t r i b u t i o n determined.  radio-  resultant  In many cases, the  a c t i v e n u c l e i were p l a c e d i n environments which were w e l l e s t a b l i s h e d and about which the c r y s t a l s t r u c t u r e data was  known.  There are now  some n u c l e i whose p r o p e r t i e s  are so w e l l known that the r e v e r s e procedure may ted.  be  attemp-  That i s , the angular d i s t r i b u t i o n o f f - r a y s from  these n u c l e i might be used to o b t a i n i n f o r m a t i o n about the environment i n which they are a l i g n e d .  I t i s the  o b j e c t of t h i s chapter of the t h e s i s to attempt to d e f i n e an a x i s or axes of alignment i n C o C l * 6 H 0 from measure2  2  ments of the ¥ -ray d i s t r i b u t i o n of a c t i v e manganese 54 a l o n g the three c r y s t a l l o g r a p h i c  axes.  C o C l * 6 H 0 c r y s t a l l i z e s i n the m o n o c l i n i c system, and 2  2  i t s e x t e r n a l morphology The s a l t was  has been d e s c r i b e d by G r o t h *  1  (1906).  found to become a n t i f e r r o m a g n e t i c at about  3°K from s u s c e p t i b i l i t y measurements on the powder  (Haseda  12 and Kanda  1957).  the u n i t c e l l of  The f o l l o w i n g i s a resume of data on  CoCl *6H 0. 2  2  -30-  CoCl^'GHgO i s o f m o n o c l i n i c p r i s m a t i c type; a : b : » 1.4788 : 1 : 0.9452 with d e f i n i n g parameters  (3 » 1 2 2 ° 1 9 '  The c | 001^  l i s t e d by Groth.  i s one o f p e r f e c t c l e a v a g e .  are the face  X-ray a n a l y s i s o f the c r y s t a l  13  as done by Mizuno e t a l  r e v e a l e d two formula u n i t s per  u n i t c e l l w i t h space group t a b l e l i s t s the atomic  - C^ .  The f o l l o w i n g  m  positions.  Kind o f Atom  Position  x  y_  Co  origin  0  0  0  0  0.175  to.221  0.255  0  0.700  CI  4(i)  0.278  0  8(j)  0.0288  4(j)  0.275  T  On  z_  14  Date  lists  the g f a c t o r s from paramagnetic  ance as g t = 2 . 9 , / g ^ = 5.0 and g a  c  reson-  = 4.0 where a' i s  i n c l i n e d to the d i r e c t i o n o f the a - a x i s by about 3 2 ° because of the m o n o c l i n i c s t r u c t u r e A photograph  ( JJ = 1 2 2 ° 1 9 ' ) .  o f a three dimensional model o f the  crystal structure i n unit c e l l  i s shown i n f i g u r e 17 with  the k i n d p e r m i s s i o n o f Mr. E. Sawatzky, o f t h i s Department, Mizuno e t a i s t a t e that the two c h l o r i n e i o n s and f o u r water molecules a r e arranged o c t a h e d r a l l y about the Co""" i o n s forming the group CoC^'^HjjO and that the o t h e r 1  1  two waters  r e q u i r e d f o r the formula SHgO a r e l o c a t e d a t  somewhat g r e a t e r d i s t a n c e s from the C o  + +  ions.  The c r y s t a l used was approximately 3 mm. t h i c k with  -31-  an e f f e c t i v e s u r f a c e area of about 1.0 cm . The  growing o f the CoCl2'6H 0 c r y s t a l s was achieved 2  i n the f o l l o w i n g manner.  Commercial c r y s t a l s of  CoCl2*6H20 were d i s s o l v e d i n water to form an unsaturated aqueous s o l u t i o n .  T h i s s o l u t i o n was then allowed to  s a t u r a t e and any r e g u l a r c r y s t a l s which p r e c i p i t a t e d were taken from i t .  These c r y s t a l s were g e n e r a l l y too s m a l l  and were allowed to i n c r e a s e i n s i z e , i n a c r y s t a l grower which c o n s i s t e d of an i s o t h e r m a l s a t u r a t e d aqueous s o l u t i o n of CoCl2 6H20. ,  C r y s t a l s of proper s i z e and shape  were then submerged i n an a c t i v e s o l u t i o n of MnCl2*4H20 with the r e s u l t that some C o  + +  ions of the s u r f a c e l a y e r s  were r e p l a c e d with the r a d i o a c t i v e Mn  i o n whose  subsequent a n i s o t r o p y i n CoCl2'6H20 was to be observed i n the attempt  to determine  an alignment  a x i s or axes.  It should be noted that the e l e c t r o n i c s were the same as f o r the work on MnSiFg-SH^O .except f o r the a d d i t i o n o f a t h i r d counter along the a - a x i s of the CoC^'GH^O crystal. B.  Theoretical Considerations In the p r e v i o u s chapter we saw that the 7* -ray  d i s t r i b u t i o n was g i v e n by Tr(r*j>), where F was an o p e r a t o r r e p r e s e n t i n g the y -ray d i s t r i b u t i o n and p was the s t a t i s t i c a l matrix.  For the case of p r e f e r r i n g to a  s i n g l e n u c l e a r s p e c i e s of s p i n I, i t i s necessary (21+1)  to know  r e a l constants i n order to u n i q u e l y s p e c i f y i t .  -32-  In what f o l l o w s , i t i s convenient  to d e s c r i b e p not 2  i t s matrix elements but r a t h e r by the the d i s t r i b u t i o n up to order 21.  (21+1)  ^M^^  .  \-  The  first  Ix I*, I x T ' X ' X  and permutations term;  statis-  Tr(MJj p ) or  few of these o p e r a t o r s are given  • 3lx-Id+rt J l * of I , I , I x  y  z  by  L.I^M*  I«-I*? W l * '  vTsX'-  i n the form of the  last  .... The moments^ *CM , > s  of  moments of  These are the  t i c a l averages of a s e t of o p e r a t o r s M^,  by  the o p e r a t o r s  are p r o p o r t i o n a l to the c o e f f i c i e n t s  ,  i n the expansion  of p  as a s e r i e s of  such o p e r a t o r s ; they are chosen to transform a c c o r d i n g to the f i r s t  21 i r r e d u c i b l e r e p r e s e n t a t i o n s of the r o t a t i o n  group and are the same as Fano's i r r e d u c i b l e tensors.  The matrix elements of V are f u n c t i o n s of the  s p h e r i c a l p o l a r c o o r d i n a t e angles 0, <f . p as a s e r i e s o f o p e r a t o r s for  statistical  the angular  i n t o TriTp  By  substituting  ) one  obtains  distribution.  s where F  r  (6,^  ) i s a f u n c t i o n of the angles 6 and <4? and i s  so f a r undetermined. If  the o p e r a t o r s M  are normalized  z o n a l harmonics,  r the f u n c t i o n s F  r  (9, o? ) are a l s o normalized z o n a l harmonics  m u l t i p l i e d by a constant A Hence,  xi  wte,<f) = £ L r-o  which depends on r but not on  r  *r  < i>ArY*(e.<p). M  s= -r  s.  -33-  The constants A *  g  depend on the s p i n s and the s p i n changes  i n the decay cascade which produces the r a d i a t i o n .  It  v might be added that f o r some symmetries, the s t a t i s t i c a l matrix  i s g r e a t l y s i m p l i f i e d due to v a r i o u s ordered  moments v a n i s h i n g . D a n i e l s has d e r i v e d e x p r e s s i o n s f o r the d i s t r i b u t i o n of  y-rays  along the three c r y s t a l l o g r a p h i c axes.  Con-  s i d e r the three c r y s t a l l o g r a p h i c axes, a, b, c f o r CoCl2'6H20.  The b a x i s i s p e r p e n d i c u l a r to the a-c plane:  a,c and K, the alignment  a x i s , l i e i n afe,plane.  i s one a x i s of alignment  then by c r y s t a l symmetry i t must  be i n the a-c plane.  I f there  L e t us c a l l t h i s a x i s K.  At the high temperature r e g i o n e x p e r i m e n t a l l y  observed,  the p o l a r diagram i s o f the form W(0) = 1  +  { ( T )  ^(cos  where 0 i s the angle between the d i r e c t i o n of o b s e r v a t i o n and the a x i s K, and f ( T ) i s a f u n c t i o n o f  temperature.  w(a)= l + W P ^ s e ) ^ i - U *|Tco -e  H e n c e  5  Since W(a), W(b) and W(c) are measured q u a n t i t i e s , i . e . the normalized  counts,  and s i n c e  that we have three equations and 6.  V = 122°19', i t remains  i n two unknowns, i . e . f ( T )  Hence we may f i n d f ( T ) and 6 from any two and use  -34the  third  results  as  for  a  check  the  case  Considering solve  Hence  we  ©  The  =  values of  for  have  cos  plus  -  and  the  7T  defines  f ( T ) we  £  1  with  axis of  experimental  alignment.  equations  above  we  can  the  same  temperature,  W(c)  the  mental  our  values  of  18  the 0  will  then  i s one  W(a),  Also  showing  agreement  19,  we  W(b)  inserted  and  are  to w i t h i n  alignment.  then  a  2  insert  various  for  values  0  2  the  -  plot  should  W(c).  lt  (V  ©  x  of  as  given  following  2  ).  the  experi-  functions of  calculated  statistical  these  values  alignment,  = G  0  W(c ) a s  the  essentially  f o r W(c),  cos  possibility  calculated  values  have  and  The  For  have  acceptable  i t  can  a x i s of  3 ^l-W(b)]  and  6.  axis of we  obtain  |  two  since  f o r W(c).  2 ^ 1-W(b)j  +  perature. no  for  us  *  7  imply = ~K -  2  f ( T j and  a b o v e we  « w(b)  figures  0  experimental  f(T) =  expression  W(c) In  concern  i f there  with  Inserting our  not  we  - Wf a) j  i n cos"^  expression  which,  agree  ^wCb^  and  calculated  of  the  2[l-W(b)j  direction  into  1  0^=0  need  W(b)-Wfall wCb^) - » J  Cos © =  obtain  signs  say,  values  by  theory  two  ± O.Slli'  minus  + ©  Having  then  one  first  f ( T ) '-  f o r 0, =  for  of  the  for,  inserting  and  for  values error.  of  temW(c)  This  FIGURE  18. NORMALIZED  COUNTS  A L O N G  C R Y S T A L LOGRAPHIC  1.100  A X E S  'DURING  WARM-UP.  o  R E S U L T S  •  C A L C U L A T E D  c AXIS  1.  COUNT.  b axis  1.050  •  o  ooo o o o  o  o  0 . 9 5 0  o  o  o o  a axis  in Z D  8  0 . 9 0 0  Q UJ N  _J 2  0 . 8 5 0  CE  c axis  O Z  o  v  \  o  (  0 . 8 0 0  t  0 . 0 4 5 4 0  8 0  t  0 . 0 5 0  "T~ 120  K  \  0 . 0 6 0  K. 160  t  „  0 . 0 7 0 °O K .  T  T  2 0 0 MINUTES  t .K .  0 . 0 8 0  2 4 0 A F T E R  t  0_ . 0J 9 0 °£3K .  t  0 . •1 0 0  _  T  2 8 0  DEMAGNETIZATION.  0  K  ~\  3 2 0 +•  to  3 6 O follow  —I 4 0 0  page  3*+  F I G U R E  19.  N O R M A L I Z E D  C O U N T S  A L O N G  C R Y S T A L L O G R A P H I C  A X E S  DURING  W A R M - U P  R E S U L T S .  o I.IOO  •  o 1  O  o  1.05O  C A L C U L A T E D  o  b axis  D  0 . 9 5 0  O IJ N  • <  0 . 8 5 0  C O U N T S .  I  o  o  o  {II  II  I'I I  1  o  o  o  O  o  a axis  0 . 9 0 0  ct o Z  I  AXIS  o  I.OOO  2 O °  c  o  1  w  JL.  I  0 . 8 0 0  c axis. o  o  o  o  t  0 . 0 4 5  0 . 7 5 0  J  I  4 0  8 0  t  0 . 0 5 0 " K .  L 1 2 0  160  2 0 0  t  0 . 0 6 0  J  2 4 0  K.  I  2 8 0  t  0 . 0 7 0  L_  3 2 0 MINUTES  t  K.  0 . 0 8 0  I  3 6 0 A F T E R  K .  I  4 0 0  0 . 0 9 0  I  440  D E M A G N E T I Z A T I Z  t  K.  0 . 1 0 0  I  °K.  L  4 8 0  5 2 0  —*-  ATION ro  follow  page  3 ^  -35-  d i s c r e d i t s the p o s s i b i l i t y of there being one a x i s of alignment  i n CoC^'GE^O.  As a r e s u l t ,  there are two pos-  s i b i l i t i e s , one that there are two axes of alignment and the o t h e r , that the s p i n H a m i l t o n i a n i s such that i t does not possess a x i a l symmetry.  FigureV20 shows the proposed  d i r e c t i o n s o f the axes of alignment i.e.  f o r the f i r s t  case,  of two axes o f alignment. By c r y s t a l symmetry, s i n c e there are two ions per  unit c e l l ,  the axes of alignment  c o n t a i n i n g b and an a x i s K.  (T,T* J l i e i n a plane  Then by s p h e r i c a l  the angle between T and a, 9  trigonometry,  i s g i v e n by cos 6  = cos^pcosdT.  Hence, W f o . ) = I- ^  (T)+ I^(T)  COS^COSV \  Note that although the angle between T and b i s not the same as that between T' and b, the squares of the c o s i n e s are the same.  Here we have three equations i n three  unknowns, i . e . f (T), ^ and o( and hence we can d e f i n e them without arobiguityi however, i t i s not p o s s i b l e w i t h i n t h i s framework alone to check the v a l i d i t y o f the v a l u e s obtained.  This s t i l l  l e a v e s .the p o s s i b i l i t y that the  s p i n H a m i l t o n i a n may not possess the r e q u i r e d a x i a l symmetry. What f o l l o w s i s a sketch of the s o l u t i o n o f the above  /  FIGURE  20.  PROPOSED  RELATIVE  ALIGNMENT  A X E S  DIRECTIONS IN  CoCI  6H  FOR O.  «r-=/Za° 19'  PERSPECTIVE (K  LIES  IN  VIEW. a c  PLANE!)  K  (SECTION  IN  b-K  PLANE.) to  follow  page  35  -36-  three equations f o r f ( T ) , C|) and <K. From the f i r s t e q u a t i o n  i f we put t h i s i n t o the second and t h i r d e q u a t i o n s , u s i n g sin <x" = 1 - cos C* , e 2  obtain  2  W  = I- i  W(<0  Cos**?  and = 1+ f  W(b}  J  L  - [\W<0-1  *\$]  C c o s f V- l l f  hence  W  (a)  -1  +• i-Jf  cos*  a?  and w ( b ) -1 -  f  -  _  W(a)-\+i£  l  2  d'-tp)  W (ai  -  I +  <^  cos c?  substituting for cos "? cos  1  from (2) i n t o  and c o l l e c t i n g  terms  (1) and e x p a n d i n g  yields,  -i- C  7* I  substituting  2 sin V  w C O- I +- i f 2  = 1 - cos <f> and s i m p l i f y i n g  an e x p r e s s i o n f o r f ( T j o f the f o l l o w i n g  where IcosYsi^H'  v  form:  yields  -37-  S=  122°19',  and  3  /  = 3W(aJ - W(a)W(b) + W(b)  - [w(a)]  2  Knowing f ( T ) , i t i s e a s i l y shown that sin a  =  t J^JL. t w ( b ) - \ i + ^  and  1  j_ _  r-  ~1 •> - I  COS  One  c o u l d express s i n t t  W(a),  W(b)  and W(c);  and cos 4> d i r e c t l y i n terms of  however, t h i s i s unnecessary  and q u i t e  complicated.  C.  Results The f o l l o w i n g t a b l e s l i s t  a l l mathematically  accept-  able s o l u t i o n s to our three equations i n v o l v i n g f ( T ) , <P and OC .  Although some of the s o l u t i o n s w i l l vary f o r d i f -  f e r e n t s e t s of experimental data, i f there are two  alignment and U  axes present then we should expect the parameters  necessary f o r t h e i r d e f i n i t i o n to appear c o n s i s t e n t l y i n the data gathered from a l l experiments  c a r r i e d out f o r  54  Mn  i n CoClg'Gi^O.  T h i s data shows a d i f f e r e n t  function  f o r f ( T ) f o r the two runs, but an examination of the values of  and OC shows some agreement between the two  runs,  c e r t a i n s o l u t i o n s being more c o n s i s t e n t than o t h e r s . t h i r d experiment  which was  stopped because of  failure indicated quite similar along the three c r y s t a l l o g r a p h i c  A  apparatus  trends i n the count r a t e s axes.  -38-  TABLE I I I  T°K  DC  0.070  39° 9'  30°13'  0.080  38°44'  30°55'  0.090  40°17'  28° 6'  f (TJ +0.2315  50° 50' ,129°10'  -0.1865  30°7' , 149°53'  +0.2315  55 29' ,124°31'  -0.1865  39° 4', 140°56'  +0.1598  50°37', 129°23'  -0.1322  31°34•, 148° 26'  +0.1598  54*49', 125°11'  -0.1322  39°17', 140°43'  +0.0899  5lV47' ,128° 13'  -0.0673  24°30', 155°30'  +0.0899  57°39', 122°21'  -0.0673  37°57', 142° 3'  9  TABLE IV  T°K 0.030  f (T) 42°15'  23° 0'  0.090  4l°56'  23°58'  0.100  4l°55'  24° 0'  +0.2500  46°50' ,133°10'  -0.1620  24°38* ,155°22'  +0.2500  56°35' ,123°25'  -0.1620  43° 2' ,136°58'  +0.2113  47° 20',132°40'  -0.1403  25°11' ,154°49'  +0.2113  56°25' ,123°35'  j0.1403  42°31 ',137°29'  +0.1570  48°29* ,131°31*  -0.1044  23° 0' ,157° 0*  +0.1570  57°16' ,122°44»  -0.1044  41° 20' ,138°40'  -40-  These t a b l e s show the r e s u l t s c a l c u l a t e d from separate experiments. appears  I t should be noted  to be a d i f f e r e n t  two  that f,(T)  f u n c t i o n f o r the two  experiments.  T h i s d i f f e r e n c e might p o s s i b l y o r i g i n a t e i n the nature of the warm up encountered  i n a g i v e n experiment.  From the  r e s u l t s above, i t would appear that a value f o r OC of about 40° to  i s ^consistent throughout both.  f o r <K  each experiment  and common  I f one assumes that t h i s i s the c o r r e c t  , then the most c o n s i s t e n t value f o r  separate runs i s i n the neighborhood these values of ct and axes of alignment  of 50°.  value  f o r the I f we  <p to be the ones d e f i n i n g the  two  assume two  i n the c r y s t a l with r e s p e c t to the a - a x i s  as shown i n f i g u r e 20 by v i r t u e of t h e i r c o n s i s t e n c y throughout the two separate experiments  and average  t h ^ values  we  o b t a i n the f o l l o w i n g mean v a l u e s : for  OC - 40°43'  and  <f = 49° 19' or 130°4l'.  An important c o n c l u s i o n to be made i s that these two of  alignment  axes  are c o n t a i n e d on the s u r f a c e s of cones making  an angle of 40°43' with r e s p e c t to the a-c plane;  one,  above, and the other below. C o n s i s t e n t data f o r <f and a  i s a necessary but not  s u f f i c i e n t c o n d i t i o n f o r the two axes case.  Hence,  although our r e s u l t s g i v e to a f a i r degree c o n s i s t e n t values for  c e r t a i n c h o i c e s of  and CL  t  there s t i l l , e x i s t s  a l t e r n a t i v e p r i c t u r e which i m p l i e s that the s p i n  the  Hamiltonian  t  -41-  does not possess  axial  symmetry.  It i s i n t e r e s t i n g at t h i s p o i n t to give r e f e r e n c e 15  to a recent paper of Moriya  i n which a new  mechanism of  the a n i s o t r o p i c superexchange i n t e r a c t i o n i s o u t l i n e d . T h i s work, i n essence,  proposes a c o u p l i n g between the  ions of some f e r r o - and a n t i f e r r o m a g n e t i c s of low such that i n the case of the a n t i f e r r o m a g n e t i c a r i s e s a s p i n arrangement which i s d i f f e r e n t accepted  at present,  there  from the  i . e . a l t e r n a t i n g ferromagnetic  i n the c r y s t a l planes. i s an  symmetry  In t h i s new  layers  s p i n arrangement, there  a p p r e c i a b l e s p i n c o n t r i b u t i o n from a d i r e c t i o n  i n the plane of the t r a d i t i o n a l ferromagnetic would appear that our proposal of two would be compatible  one  axes of  not  layers.  It  alignment  with such a scheme of s p i n a r r a y s i n  the a n t i f erromagnetic,  i n our case  /  CoC^'^I^Oo  -42-  CHAPTER V /  SUMMARY  By the techniques of a d i a b a t i c demagnetization, the temperature of the a n t i f e r r o m a g n e t i c , MnSiFg-BH^O, was lowered u n t i l the h y p e r f i n e with  i n t e r a c t i o n energy a s s o c i a t e d  the Mn*''* impurity was comparable  to kT. T h i s r e -  d u c t i o n i n temperature produced a p r e f e r e n t i a l  distribu-  t i o n of the Mn * n u c l e i throughout t h e i r allowed 5  energy  s t a t e s , the lowest energy s t a t e s r e c e i v i n g the g r e a t e s t population.  T h i s i s the a c t u a l mechanism commonly  r e f e r r e d to as n u c l e a r alignment.  I t should  be kept i n  mind that i n t h i s p a r t i c u l a r magnetic complex i n which the Mn * i o n was s i t u a t e d , i . e . i n the MnSiF6'6H 0 c r y s t a l , 5  2  the e l e c t r o n i c s p i n s were f i r s t  a l i g n e d i n the presence  of 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 and the r e s u l t i n g  align-  ment o f the Mn * n u c l e i was r e a l i z e d as a r e s u l t of the 5  hyperfine  i n t e r a c t i o n c o u p l i n g the e l e c t r o n i c and n u c l e a r  spins. In the experiments r e p o r t e d i n t h i s t h e s i s , the 7*-ray p o l a r diagram was c a l c u l a t e d as a f u n c t i o n of temperature over t h a t temperature range w i t h i n which the alignment was present. c h a r a c t e r i z e d a t a given  The Y-ray  p o l a r diagram was  temperature by a parameter known  - 4 3 -  as the a n i s o t r o p y of  9* -ray e m i s s i o n and d e f i n e d i n the  i n t r o d u c t i o n to the t h e s i s .  T h i s parameter was  calculated  as a f u n c t i o n of temperature  and over the "high  temperature  r e g i o n " as d e f i n e d i n chapter I I I , showed a dependence 1  1  g i v e n by, £oC  .  T h i s was  i n agreement with the depend-  <j<3  ence c a l c u l a t e d from theory. of p r o p o r t i o n a l i t y from € OC T~  3  By a s c e r t a i n i n g the constant  the experimental r e s u l t s f o r  and equating i t to  —, the constant of prok , -12A D i n the t h e o r e t i c a l r e l a t i o n fc = ^3^,3 » 3  portionality was  found that D,  s t r e n g t h was was  2  i n d i c a t i v e of the c r y s t a l l i n e  g i v e n by D = - 0.032 cm" . 1  field  This calculation  made with the value of A, known f o r the d i l u t e The  same procedure  was  salt.  f o l l o w e d i n the work done on  the CoCl2*6H20 with the a d d i t i o n of a t h i r d counter r e c o r d the y - e m i s s i o n  to  along the a - a x i s of the c r y s t a l .  As before i n MnSiFg«6H 0, the a c t i v e i o n was 2  Mn^.  By  r e c o r d i n g the 7*-ray d i s t r i b u t i o n along the three c r y s t a l l o g r a p h i c axes of CoCl2* H20 as f u n c t i o n s of tem6  p e r a t u r e , i t was  hoped that the o r i e n t a t i o n of the a x i s  or axes of alignment Experimental  and  w i t h i n the c r y s t a l c o u l d be  t h e o r e t i c a l r e s u l t s were not  with the assumption  show a l l the mathematically tf and  compatible  of the e x i s t e n c e of a s i n g l e  ment a x i s w i t h i n the c r y s t a l .  The  determined.  align-  r e s u l t s t a b l e s I I I and  acceptable solutions for f ( T ) ,  d e f i n e d i n the t h e o r e t i c a l s e c t i o n o f chapter  IV.  It would appear that the c h o i c e of any one s e t of f i g u r e s  IV  -44-  for  f C T ^ t p and Oi would at best be q u i t e u n c e r t a i n , although  statistical  c o n s i d e r a t i o n s would f a v o r those values  listed  f o r ^ a n d 01 as 49° 19' or 130°4' and 4o°43' r e s p e c t i v e l y . Since the counts were taken along the three b a s i c axes of the C O C ^ ' G H J J O of  c r y s t a l i t would seem that r e o r i e n t a t i o n  the three counters or the a d d i t i o n of more would not y i e l d  any b e t t e r method f o r s e l e c t i n g for  the a c t u a l p h y s i c a l values  f ( T ) , <f and « from the mathematically  accepted  ones.  The g r e a t e s t a i d to t h i s s e l e c t i o n o f the p h y s i c a l values should be expected  from the theory governing  the nature of  the f u n c t i o n s y i e l d i n g the 7* ~ Y d i s t r i b u t i o n . rSL  For  example, i f f ( T j c o u l d assume only p o s i t i v e or negative v a l u e s , the c h o i c e f o r <f and Oi would then be unique to w i t h i n * f o r TT - up f o r the angle o f o r i e n t a t i o n i n the a-c plane.  At present  there appears to be no p h y s i c a l j u s t i f i -  c a t i o n f o r l i m i t i n g the range of values assumed by f ( T ) .  -45BIBLIOGRAPHY  1.  A. Abragam and M.H.L. Pryce, Proc. Roy. S o c London, A 205, 135 (1951 J.  2.  J.M. D a n i e l s , Notes on Low Temperature U.B.C.  Physics,  (1959-60).  3.  G. Lamarche, T h e s i s f o r Ph.D., U.B.C. December 1956.  4.  M.A.R. LaBlanc, T h e s i s f o r Ph.D., U.B.C. January 1959.  5.  J.R. H u l l and R.A. H u l l , J o u r n a l of Chemical Vol.  9, p.465 (1941),  6.  B. Bleaney, Proc. Roy. Soc. A 204, 218  7.  A. Ohtsubo e t a l , Kamerlingh Onnes Conference p.49  8.  Physics,  (1950-1951).  (1958).  P. Groth, Chemische K r y s t a l l o g r a p h i e , 1 T e i l , (1906).  9.  R.W.  Prog.  p.558, \  Kedzie and C D . J e f f r i e s , B u l l . Am. Phys. S o c ,  3, 415, (1958). 10.  J.M. D a n i e l s , Can. J o u r n a l o f P h y s i c s 35, 1133 (1957).  11.  P. Groth, Chemische K r y s t a l l o g r a p h i e , 1 T e i l ,  p.248,  (1906). 12.  T. Haseda, E. Kanda, J . Phys. Soc. Japan, 1£, 1051 (1957)  13.  J . Mizuno, K. Ukai, T, Sugawara, J . Phys. Soc. Japan, 14, 383 (1959).  14.  M. Date, J . Pnys. S o c Japan, 1_4, 1244 (1959).  15.  T. Moriya, Phys. Rev. L e t t e r s , V o l . 4, No. 5, p.228  

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