Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Optical detection of spin-bath relaxation in Eu2 doped calcium fluoride Clarke, Thomas E. 1967

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1967 A67 C5.pdf [ 2.68MB ]
Metadata
JSON: 831-1.0085094.json
JSON-LD: 831-1.0085094-ld.json
RDF/XML (Pretty): 831-1.0085094-rdf.xml
RDF/JSON: 831-1.0085094-rdf.json
Turtle: 831-1.0085094-turtle.txt
N-Triples: 831-1.0085094-rdf-ntriples.txt
Original Record: 831-1.0085094-source.json
Full Text
831-1.0085094-fulltext.txt
Citation
831-1.0085094.ris

Full Text

OPTICAL DETECTION SPIN-BATH IN E u  2 +  OF  RELAXATION  DOPED  CALCIUM  FLUORIDE  by  THOMAS EDWARD B.Sc,  A  University  T H E S I S SUBMITTED  CLARKE  of B r i t i s h  Columbia,  I N PARTIAL FULFILMENT  THE REQUIREMENTS FOR  THE DEGREE  196h  OF  OF  MASTER OF S C I E N C E  in  the Department of Physics  We  accept  required  this  thesis  as conforming  to the  standard  THE U N I V E R S I T Y OF B R I T I S H COLUMBIA February,  1967  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements  f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a l ] a b l e f o r r e f e r e n c e and study.  I f u r t h e r agree t h a t p e r m i s s i o n f o r extensive  copying o f t h i s  t h e s i s f o r s c h o l a r l y purposes may be granted by the Head, o f my Department or by h i s representatives„  I t i s understood t h a t copying  or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed w i t h o u t my w r i t t e n p e r m i s s i o n .  Department o f p h y s i c s The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada  i ABSTRACT  The magneto-optical Faraday e f f e c t was used, to observe the spin-bath r e l a x a t i o n i n Europium doped CaF helium temperatures from 1.5 t o h.2° K.  2  crystals at  Theory shows t h a t the  magnitude of the Faraday r o t a t i o n i s p r o p o r t i o n a l  to the  d i f f e r e n c e i n p o p u l a t i o n of the ground s t a t e doublet. The experimental method used i n t h i s t h e s i s i s the same as that which was s u c c e s s f u l l y used by G l a t t l i and hy G r i f f i t h s .  Pulsed  microwave power a t X-band f r e q u e n c i e s was employed to d i s t u r b the e q u i l i b r i u m between the s p i n system and the bath. The observed r e l a x a t i o n time t  was expected t o have a T~  l  temperature dependence hut because of the o r i e n t a t i o n of the c r y s t a l i n our dc magnetic f i e l d which r e s u l t e d i n the seven t r a n s i t i o n l i n e s being c l o s e together, c r o s s - r e l a x a t i o n  effects  produced a temperature dependence of approximately T~ . I t i s p+ suggested that exchange coupled p a i r s of Eu and c l u s t e r s x  •3 +  i n v o l v i n g Eu  may account f o r t h i s temperature dependence  r a t h e r than there being a phonon b o t t l e n e c k present. The f i e l d dependence of the r e l a x a t i o n time was found not to he d i r e c t l y r e l a t e d to the resonance spectrum, p-t-  The Eu was .2%.  c o n c e n t r a t i o n of the c r y s t a l s used i n t h i s t h e s i s  ii  T A B L E OF  CONTENTS Page  Abstract List  of  • Illustrations  and  i  Graphs  Acknowledgments  v  Chapter  1.  INTRODUCTION  Chapter  2.  THEORETICAL BACKGROUND A)  1  Spin-lattice  Relaxation  3  a)  The  Direct  Process  b)  The  Raman P r o c e s s  6  c)  The  Orbach Process  6  B)  Phonon B o t t l e n e c k  C)  Europium  3  7  Doped C a l c i u m  a)  Crystal  b)  Ground  9  Fluoride  9  Structure S t a t e and  Paramagnetic 9  Resonance c) D) Chapter  3.  The  Magneto-Optical  EXPERIMENTAL A)  B)  The  10  Cross-Relaxation Faraday  Effect  ..  15  ARRANGEMENT  Apparatus  16  a)  The  Cryostat  16  b)  The  Magnet  17  c)  The  Microwave  d)  The  Optical  e)  Signal Detection  The  18  System  19  System  20  Experimental Procedures  a)  P r e p a r a t i o n s f o r the Measurements  b)  Faraday  d)  of the  .  26 26  Rotation  c) D e t e r m i n a t i o n  26  Resonance  Spectrum R e l a x a t i o n Time Measurements  27 29  iii  Page e) Temperature Measurements Chapter h.  EXPERIMENTAL RESULTS A) F a r a d a y R o t a t i o n  32  B) Resonance  33  Spectrum  C) R e l a x a t i o n Times  Chapter  5-  33  a) F i e l d Dependence  33  b) Temperature Dependence  33  DISCUSSION OF RESULTS A) F i e l d  Dependence o f I  B) Temperature Dependence o f I BIBLIOGRAPHY  30  39 39 hi  IV  LIST  OF  ILLUSTRATIONS  AND  GRAPHS Page  Figure 2.1  Crystal  2.2  Energy  2.3  Thermal  3.1  Block diagram  3.2  The c u r r e n t  3.3  Field  3.H-  Crystal  3.5  The d e w a r  3.6  R o t a t i o n due and  structure levels block  of CaF  of a s i n g l e diagram  Field  M-.3  Relaxation  cross-relaxation  .  ih  ...  I* 1  22 23  i n the microwave  cavity  2h  mechanism  2*+ 25  cap to diamagnetic effects  c r y s t a l a t room  h.2  of pair  of ions  regulation  adjusting  Resonance  i o n and a p a i r  f o r the apparatus  configuration  *+.l  8 2  spectrum  dependence o f rate  of  dewar 31  temperature of Eu  :CaF  35  2  36  I  o f Eu  :CaF  2  as a f u n c t i o n  of 37  temperature a)  Typical  relaxation  photograph  b)  Semi-logarithmic plot  of trace  of Eu ":CaF 2 +  i n a)  p  ....  38 38  V  ACKNOWLEDGEMENTS  The  research  for this  t h e s i s was s u p p o r t e d  Research Council  o f Canada  The  like  author  would  contributed  Dr.  throughout  (research  this  research  of this  supervisor)  H. G l a t t l i  f r o m whom I l e a r n e d  Miss  of the research  on t e c h n i c a l  the operation  without  n o t have been  stages.  of the  a n d a i d e d me a t a l l  program.  the l i q u i d helium  and f o r h i s  matters.  J . Gibb f o r her help  My p a r e n t s , could  i n the early  a n d who c o n s t a n t l y e n c o u r a g e d  R. W e i s s b a c h f o r p r o v i d i n g  advice  support  work.  Dr.  Mr.  who  f o rh i s continuous  J . B. Brown f o r h i s e n c o u r a g e m e n t  stages  t o D r . M. B l o o m .  work.  Dr.  equipment  grants  t o thank the f o l l o w i n g people  t o the success  M. B l o o m  through  by t h e N a t i o n a l  i n typing.  whose f i n a n c i a l undertaken.  and m o r a l  support  this  work  1 Chapter  One  INTRODUCTION  Spin-bath relaxation between a constant  system  spin  the  modulation  system  the  to of  the the  lattice  of  (195D  put  differences that  a  c r y s t a l and  could  of  spin-orbit  f o r t h the be  the  i n population  of  that hy  the  the  under which microwaves  of  the  change  d i s t r i b u t i o n of  effects i n general  developed  hy  Opeehowski  experimentally This  hy  thesis  of  over  the  and  the  of  spin hy  states.  oriented  Fluoride  i n an  external  magnetic  s e v e n t r a n s i t i o n l i n e s were as  levels.  dependence  in  Glattli's  c r y s t a l s the  effects  of  resonance  research  was  effects  i f any  relaxation  time  We  were  t o g e t h e r as  our  crystals.  apart  was  d o n e hy  found  Glattli  The  Europium  that  possible  to  interested  maximum c r o s s - r e l a x a t i o n of  magneto-  first  i n s u c h a way  l i n e s were f a r  cross-relaxation.  of  i n t h i s t h e s i s were c u t  field  close  resonance  (1958).  the  c r y s t a l s used  He  frequency  (1966) on E u r o p i u m d o p e d C a l c i u m F l u o r i d e c r y s t a l s . doped C a l c i u m  to  resonance  the  these  influence  Wesemeyer  extension  spin  appropriate  upon paramagnetic  (1953) a n d  Daniels i s an  electrons  treatment  due  magneto-optical  various  conditions  A quantum m e c h a n i c a l  from  vibrations  electron  influenced  the  place  lattice  he  optical  a  coupling.  idea  influenced  take  r o t a t i o n should  the  the  phonons  c r y s t a l f i e l d by  Faraday r o t a t i o n should  reasoned  ions  exchanged  bath.  interactions  Kastler  to  i n which energy i s  (1939) s u g g e s t e d t h a t a d i r e c t e n e r g y t r a n s f e r  the  due  way  of paramagnetic  temperature  Kronig  through  i s the  avoid to  would have  the while  possible  observe on  and  the  what  2  Chapter process  and  accompanying  arrangements discussion  2 g i v e s the background  and  effects.  procedures  are  t h e o r y about In Chapter  outlined  are presented In Chapter  h.  and  3  the the  relaxation experimental  the r e s u l t s  and  3 Chapter  Two  THEORETICAL BACKGROUND  A)  the to  Spin-Lattice  Relaxation  Spin-lattice  relaxation  process of the  field  There upper  of  three  the  in this  thesis  from a s i n g l e  phonons  v i b r a t i o n of  are  level  used  energy t r a n s f e r  surrounding l a t t i c e by the  is  to  describe  paramagnetic  by m o d u l a t i o n o f  the  spin crystal  lattice.  different  p r o c e s s e s by w h i c h a s p i n i n  a ground Kramers d o u b l e t  can r e l a x  to  the  the  lower  level. a)  The D i r e c t In this  Process  process,  a c t i o n w i t h the lattice on the upper  the  o r b i t a l moment  interaction) spin-phonon  state  to  fluctuating  a c t s as  system  the  lower  between the  two s t a t e s .  equilibrium value  a time dependent a spin f l i p  perturbation from  to  the  energy  number  given T  creates  charactwhose  by:  -i (2.1)  - 1 ) '  oscillators  b e t w e e n S a n d dS i s  the  difference  average phonon e x c i t a t i o n is  inter-  (orbit-  c a n be  0  of  electron  The p h o n o n s y s t e m  p ~(e* The n u m b e r  field  state which simultaneously  energy S , equal  b y p, , t h e  the  producing  a phonon of  erized  of  crystal  i n the  g i v e n by i t s  crystal  with  classical  energy  value:  (2.2) where 1 i s  the  sound i n the  crystal  crystal.  volume  and v i s  the  velocity  of  The t r a n s i t i o n p r o b a b i l i t y p e r  second  for  a spin f l i p  from  |b> t o ( a ) i s :  w „, = ^ i < b i H ; i > i > c s ) k  where H  a  i s the c r y s t a l  c  perturbation  i s that  due t o t h e t h e r m a l  (1962)  show t h a t  perturbation  field part  lattice  ( 2 - 3 )  Hamiltonian. o f H"  c  which i s time  strains £ .  f o r the d i r e c t  i s approximately  The r e l a x a t i o n  process  given  Scott  and  of  i s an operator  the t o t a l  The  matrix  angular  elements  Jeffries  the r e l a x a t i o n  i n form  and magnitude by:  He = £ l U " w h e r e UT  dependent  (2A) i n v o l v i n g combinations  o f components  momentum o p e r a t o r J_. of £  |<p.U)|€lM*W>|  are given  = - ^ - T -  b y : (Abragam  1961)  (2.5)  2  w h e r e M i s t h e mass o f t h e c r y s t a l . Therefore theory  from f i r s t  order  the t r a n s i t i o n  of  t h e combined  to  the f i n a l  time dependent  p r o b a b i l i t y p e r second f o r t r a n s i t i o n  spin-phonon system  state  perturbation  [ja> , p.($0  +  l\  from  initial  i s given  by:  W ..« ^^(F.c*)-i)|<b|ZU"*la>r b  where This  For  £  P - M/V equation  i s the c r y s t a l  b  (2.6)  density.  c a n be r e w r i t t e n a s :  the reverse  VvU  s t a t e [|h>,p.(^)j  process  = Kp,U)  the equation i s :  sec-'  (2.8)  5 The r a t e equation f o r the s p i n system can be w r i t t e n a s : -N  = N = - N W^  a  b  b  a  +NW. 3  a  b  (  where the three terms on the r i g h t represent emission,  spontaneous emission,  }  stimulated  and a b s o r p t i o n o f phonons  respectively. By i n t r o d u c i n g n = N a  value  n= Ntanh(iJr)  and i t s thermal e q u i l i b r i u m  where N i s the t o t a l number of  0  paramagnetic ions we o b t a i n : n = -Tj(n - n ) 0  where  (2.10)  T' d  K coth ( a i r )  Our measurements were performed a t X-band frequencies  thus  a l l o w i n g us t o make the approximation S^<-AT. Hence T^'  can  be r e w r i t t e n as: T  d  =  ^ T ~  =A  T  where  (2.11)  Scott and J e f f r i e s f i n a l l y a r r i v e d a t the equation f o r the r e l a x a t i o n r a t e f o r a Kramers s a l t t o be:  ( 0 1 1 f ( ^ f H < * i H • j u x i i t r i b>  TT'•  (2.12) +  <al^|i><i|H-J|b»r^4X - A T  where /3 i s the Bohr magneton, A I s the Lande g f a c t o r , |i> i s one of the s t a t e s f o r each higher Kramers doublet, H i s the dc magnetic f i e l d , and the sum %. i s over a l l the e x c i t e d doublets.  This can be w r i t t e n i n a form which shows the  6 temperature  and f i e l d  =  b)  a transition  difference The at  Process 6,  from  i s always  high temperatures, a t helium  relaxation  rate  inelastically  S i s the energy  |b> a n d l a ) w i t h  stronger than  hut the d i r e c t  temperatures.  into  t h e s p i n makes s i m u l -  l b ) t o |a) .  between t h e s t a t e s  Raman p r o c e s s  dominant  i s scattered  6^ w h i l e  phonon o f energy  taneously  process,  (2.13)  phonon o f energy  another  of the d i r e c t  H.*T  T h e Raman One  dependence  - %  +  the direct  process  S,. process  i s usually  F o r Kramers  s a l t s the  i s given by:  =C T ' c)  The O r b a c h In  less  Process  c a s e s where t h e c r y s t a l than  between  stage process developed Relaxation  Iii  proceeds  |c>.  to induce  with  splitting  A, ( e r g s ) i s  t h e maximum p h o n o n e n e r g y i e ( e = D e b y e  then r e l a x a t i o n  state  field  |a) a n d |b> may p r o c e e d hy F i n n , Orbach,  temperature) b y t h e two  and Wolf.  i.e.  v i a the intermediate occupation of  I t i s possible a spin f l i p  f o r the r e l a x a t i o n perturbation  from  |b) t o  |c) s i m u l t a n e o u s l y  t h e a b s o r p t i o n o f a p h o n o n o f e n e r g y A, , t h u s  conserving  energy. Scott such  and J e f f r i e s a process  given by:  (1962)  consider the rate  equations f o r  and deduce t h e Orbach r e l a x a t i o n ^  rate  t o he  7 B)  Phonon B o t t l e n e c k The  calculated  correct, spin  the  spin-phonon  to bath relaxation  process  present;  to helium short of  spin-lattice  i t may  be  the  spin-lattice  then  the  lattice  spin  that  spin  than  lattice  time.  I f the  conducting the  spin-bath  relaxation  time.  There  time  energy  relaxation  time  time  we  oscillators  that  we  If ^  time  may  measure  want.  be  be i s the step  lattice  are  i s very-  incapable  shorter  i s short related  instead  This effect  two  time  i n a time  time  relaxation  a  then  relaxation  to the bath  relaxation  to bath  relaxation  lattice  and  i s , to measure  i s , therefore,  to l a t t i c e  the  T^  What we  s p i n v i a phonons t o l a t t i c e  bath.  then  relaxation  enough  to  of the  is called  the  spinthe  phonon b o t t l e n e c k . The  main e f f e c t  spin-bath relaxation  w h e r e AM  i s the  bath relaxation cubic is  a  time,  distinguished  sample  rate  ( S h u l z and  from  v  transfer  our v a l u e from  i s the  of sound.  p r o c e s s by  through  ions  per  bottleneck  i t s different possibly  Tp^. be  o f T-j_ i s v e r y l o n g .  spins to l a t t i c e  phonon-  The  c o n c e n t r a t i o n d e p e n d e n c e , and  A phonon b o t t l e n e c k would not because  Tp^  the  1966)  of paramagnetic  i s the v e l o c i t y  the d i r e c t  dependence  Jeffries,  linewidth,  c i s t h e number  dependence,  size  to:  spin resonance  c e n t i m e t e r , and  temperature  of the phonon b o t t l e n e c k i s t o change  expected i . e . The  i s v e r y slow.  i n our rate  Glattli  crystals of  energy  (1966)  8  9 C)  Europium a)  Doped C a l c i u m  Crystal The  Structure  p o s i t i o n of  crystal  lattice  Crystal  Structure)  ions.  The  a lattice face  of  3.86  has  6  i n CaF  crystal  lattice 2  A.  cubic  symmetry.  The field  State  Eu  degenerate  first  ground  of  be  and  ions  be  found  a °S  7/5L  only  transitions  of  the  ±5/2,  microwave r a d i a t i o n as Am = 3 .  The  a..  distance E a c h F~  ion  nearest calcium to  the  of  lower  than  Resonance state.  split  of 7/i  the  and  The  P  7/l  through  multiplet in  o f a few  the  can  induced  forbidden  order.  the levels  magnetic  Magnetic  seven paramagnetic  KOe,  equidistant  i l / 2 .  the  the  ^D,/,. i n s e c o n d  by  be  cubic  8-fold  order  the  approximately  w e l l as  the  a  Trivalent rare  sites  i n higher  =1  2 +  of  distortion  into eight nearly  f o r m &m  a  A. Ca  Ca  ions form  at  cubic.  at  can  *3/2,  h  2  with  constant  replace  a magnetic f i e l d  described  and  ground  m u l t i p l e t s ^D  is split  calcium  noticeable  lattice  state  In  ^7/2,  - 2 and  Eu  A  Paramagnetic  the  n u m b e r s : M=  Am  2.72  at  h  and  lattice  a t 2.36  neighbors  CaF  Wykoff:  cubic  lattice  in a  8 F~  neighbors  spin-orbit coupling  1957)  state  which can  can  fluoride  ground  order  (Lacroix,  and  a  I t remains  f r e e i o n has  of the  interplay  The  symmetry.  i o n s , however,  Ground  ions  (from  The  with  causing  earth  b)  2.1.  A.  1  nearest  without  field  calcium  simple  Ca " " n e a r e s t  neighbors  2.36  2  a  3  8 F"  at  form  o f -g-a. 2.72  12  nearest  neighbors ions  ions  cubic  and  and  Each u n i t c e l l contains  i o n has  A  fluorine  i s shown i n F i g u r e  constant  2 +  F"  the  fluorine  centered  Each C a  Fluoride  quantum  dipole by  our  X-band  transitions  resonance  lines  10  resulting to  from  these  the c r y s t a l f i e l d  relative respect  This  within  splitting  c)  directions.  our magnetic f i e l d  direction  the single  gives  spin  i s a t a minimum.  to G l a t t l i  field Our  since  to a  the Cooi]  t h e maximum  system  with  crystals  was p a r a l l e l  3 0 ° from  w h i c h was a p p r o x i m a t e l y  direction.  a r e s e p a r a t e d due  of the e x t e r n a l magnetic  to the crystallographic  direction  refer  transitions  h y a n amount w h i c h d e p e n d s u p o n t h e  orientation  were c u t so t h a t  ation  1  Am--  cross-relax-  the c r y s t a l  field  treatment  of this  For a complete  ( 1 9 6 6 ) .  Gross-Relaxation At  high  concentrations  an  important  role  of  the different  to  cross-relaxation  spin-spin  interactions  i n the redistribution levels  i n the spin  effects.  relaxation  mechanisms which  relaxation  times  can play  of the populations  system which c a n l e a d  The t h r e e  different  c a n have an e f f e c t  cross-  on t h e  2+  i)  o f our Eu  :CaF  2  crystals are:  C r o s s - r e l a x a t i o n between d i f f e r e n t of  an e l e c t r o n i c  The  hyperfine  splitting compared This  structure  i s not resolved  electronic  t o the d i p o l a r  width  o c c u r s when t h e r e s o n a n c e  saturating  This  components  transition  of a given  broadened.  hyperfine  can result  only parts  transition  excitation  to diffuse  hy:  (Bloemhergen e t a l ,  i s not large  of the single line  components.  microwave  The t i m e  pulse  i t takes f o r  through t h e whole l i n e 1 9 5 9 )  as  i s inhomogeneously  i n a short  of the l i n e .  the  i fthe hyperfine  i s given  11 where A V * i s is  thewidth  the width  ii)  components.  between d i f f e r e n t e l e c t r o n i c  are several  possibilities  for multiple  between t h e d i f f e r e n t e l e c t r o n i c  levels  processes which conserve  momentum w h i l e  the  a  t o the other  l i n e s a r e a quadruple  double  flip  with f l i p s  a double  spin  flip  and  3/2 — 5 / 2 .  not  conserve The  due  of theline  triple  cause  ation  shapes  i nthe spin  n  A  Two  spreading  flip  involving  spin  from flips  +• 1/2— - 1 / 2 w h i c h do  without the  be v e r y  i n v o l v e d due  spin  systems spins  interactions  systems which  i n calculating  between spins c a n  can lead  of the d i f f e r e n t to cross-relax-  effects. two d i f f e r e n t s p i n  and e x c i t e d  doublet  total  2  structure.  pairs.  s y s t e m s made u p o f s i n g l e  I f we assume t h a t  have a s p i n - l a t t i c e r e l a x a t i o n , time  from  flip  and would  t o other  and exchange  Consider ions  spin  a r e d i s t r i b u t i o n i nthe populations  levels  :GaP .  transition  i snot possible  We h a v e a s s u m e d n o n - i n t e r a c t i n g Dipolar  flips  momentum.  hyperfine  Gross-relaxation  T^.  1/2  spin  calculation of thet r a n s i t i o n p r o b a b i l i t i e s  the complicated  iii)  a single  arealso  t o t h e above mechanisms  knowledge to  angular  of Eu  transitions  - 3 / 2 — - 1 / 2 and 1/2—3/2 and  from  involving  There  actual  angular  t h e c e n t e r + 1/2 — * -  e x c i t a t i o n from  line  a n d &\J  line  o f i t s homogeneously broadened  Gross-relaxation There  o f t h e whole r e s o n a n c e  a spin-lattice relaxation  Shulz rate  and J e f f r i e s equations  given by:  the single  ions  o f T^ a n d t h e e x c i t e d  time  o f T , t h e n we h a v e 2  1966 f o r t h e c a s e  f o rthepopulation  of N,»N  1  differences  the n, a n d  12  n,=  -W (N*n,  h =  -W (N, n, - N > , ) - T ; ' ( n - n l )  t  and N  system,  pair  doublet,  is  are the populations  a  i s the t o t a l a n d n ' ^ nl  differences.  Rannestad  rate  saturation  equations  o f n,  i n t h e two l e v e l s  population  a n d Wagner and have  population  (1963) h a v e s o l v e d  the  following  difference  of the s i n g l e  the s i g n a l recovers  at the rate  I"' w h i c h  by:  T-^is  "the c r o s s - r e l a x a t i o n  There  are several  relative  1)  magnitudes  Tj»  T  and  l x  2  .  (2  where t h e r a t e  v a l u e s X"' c a n t a k e d e p e n d i n g o f T-^, T , a n d 2  2)  T  1  2  » T  2  T^.  to  i s the case  f  pairs  rate  T-'  (2.21)  of strong  relaxation  relaxation rate be e q u a l  relaxation  » |vTi  spin-lattice the  (2.20)  ions.  I"'= This  on  T ^ T g  i s the s p i n - l a t t i c e  the single  19)  time.  .'. Z" - X"'  of  these  shown t h a t  i " * x" • [T.-(IT- T-)/(T» • -ir - x-f] (#) where  of  of the excited  are the e q u i l i b r i u m  the population  and t h e r e f o r e  given  (2.18)  t  each  ions  - T,"(n, - n? )  U  w h e r e N,  coupled  - N, n j  lt  cross-relaxation  of the s i n g l e  f o r the s i n g l e  to the s p i n - l a t t i c e  reduced  by t h e f a c t o r  ions,  ions  rate  a n d weak therefore  i s observed  of the excited  N*/ N, , w h i c h  i s the  13  s p e c i f i c heat r a t i o of the two systems.  (2.22)  Here we have strong s p i n - l a t t i c e r e l a x a t i o n of the e x c i t e d p a i r which r e s u l t s i n an observed r e l a x a t i o n r a t e equal t o the c r o s s - r e l a x a t i o n r a t e m u l t i p l i e d by the  reducing f a c t o r N*/N, .  Shulz and J e f f r i e s evaluate case 2 to a r r i v e a t the r e s u l t : (2.23)  for  the c o n c e n t r a t i o n and temperature dependence and (2.2*f)  f o r case 3•  The r e s u l t f o r case 3 i s the same temperature  dependence as i n the Orbach process i n the l i m i t A'»AT. Because of the p o s s i b i l i t y of p a i r s or c l u s t e r s w i t h a d i s t r i b u t i o n of values of A', the value of I'may d i f f e r from t h a t c a l c u l a t e d . the  form I ^ T  2  The temperature dependence may be of  as was found by G i l l ( 1 9 6 2 ) , Shulz and  J e f f r i e s ( 1 9 6 6 ) , and G l a t t l i  (1966).  I t w i l l be noted that  t h i s temperature dependence i s s i m i l i a r to that found when a phonon b o t t l e n e c k i s present.  From equation ( 2 . 1 9 ) i t  can be seen that c r o s s - r e l a x a t i o n can l e a d to a wide v a r i e t y of c o n c e n t r a t i o n and temperature dependences,  i . e . N*/N,  depends on the r e l a t i v e concentrations of the two systems.  Single  Pairs  Ions  |a> N  a  +•  a  =  N,  b b  IL +  1a>  and  lb) o f a  of a p a i r  i o n and  ions.  2  Excited Pairs  Helium  Bath  Figure block  of  single  N  Single Ions  Thermal  2  2.2  "1  I  N  M, - N - n  n-,  l/3>, I  -  N|  1  levels  levels  N,  N-|  Figure Energy  N„ +  diagram  2.3  of the  system  of Figure  2.2  15 D)  The M a g n e t o - O p t i c a l  Faraday  Effect  The  Faraday  effect  magneto-optical  direction passing  t h r o u g h a medium  magnetic It the M  of polarization  has been  plane  is  the Faraday r o t a t i o n P  c e r t a i n general  intensity  the only  limit  on t h e t i m e  redistribution  paramagnetic  time  ions  of the l i g h t  i n population  Glattli for  Eu "doped 2 1  9  crystals  of  dipole  transitions  e f f e c t s the  the Faraday r o t a t i o n .  ( 1 9 6 6 ) shows t h a t CaF  levels  c e r t a i n c o n d i t i o n s , by  between v a r i o u s  and t h e r e f o r e  system  method.  i n the energy  magnetic  A change  is  the p r o p o r t i o n -  resolution of this  c a n be c a u s e d , u n d e r  c a n be  1(P)  detection  microwave r a d i a t i o n which induces  magnetization  The d e p e n d e n c e  law of the analyser  of the populations  levels.  magnetization  by an a n a l y s e r  c a n be c a l c u l a t e d f r o m  The r e s p o n s e  ( r o t a t i o n of  conditions.  I(t) transmitted  and i f t h e t r a n s m i s s i o n  P °< M.  A  after  as a f u n c t i o n o f an e x t e r n a l l y a p p l i e d  shown t h a t  known t h e m a g n e t i z a t i o n ality  polarized light  o f p o l a r i z a t i o n ) i s p r o p o r t i o n a l to the  the l i g h t  measured  i n the  field.  of the c r y s t a l under  of  of l i n e a r l y  i s t h e change  t h e p r o p o r t i o n a l i t y P <* M  at the l i g h t  frequencies  used  holds here.  16 Chapter EXPERIMENTAL  A)  Three ARRANGEMENT  The A p p a r a t u s The  apparatus used  i n the o p t i c a l  resonance  and r e l a x a t i o n  identical  to that used  Rieckhoff  (1962).  features  therefore  our experiments  by  Griffiths  (1965).  shown i n F i g u r e  review,  which  and r e f e r  i n this  (1966),  by G l a t t l i  and t h e few changes  of  a)  We  described  large  thesis  i s nearly-  Griffiths  only b r i e f l y ,  w e r e made d u r i n g  you to the d e t a i l e d  A b l o c k diagram  (1965), and the general  the course  description  of the apparatus i s  3«1«  inner  dewar w h i c h  enough t o f i t over  adjusting  rods.  This  n i t r o g e n dewar w h i c h filling and  during  strip  light  the microwave  dewar  Both  site  t h e number  resulted Except  i n eliminating  line,  noise from  which  c o n t a i n s the openings rods  plastic a t oppo-  sleeve.  This  signal.  o f t h e dewars I s  (1965).  Our cap  the connections to the helium  and t h e manometers e n t e r i n g  from  the side.  f o rwaveguide,  i s screwed  glass  out of the  of black  our l i g h t  by G r i f f i t h s  line,  adjusting  i t requires  secured i n place  dewar b y a c o p p e r  t o t h e method u s e d  t h e pumping  of times  layers  f o r a new d e w a r c a p t h e m o u n t i n g  identical  i n an o v e r s i z e d  To k e e p n i t r o g e n b u b b l e s  of the inner  and the  d e w a r s a r e made o f p y r e x  p a t h w i n d o w s made o f s e v e r a l  sides  cavity  i s then placed  reduces  a run.  silvered.  c o n t a i n s the helium has a diameter  t a p e w e r e c u t o u t a n d t h e s e were  and  of paramagnetic  The C r y o s t a t The  has  detection  return  The c o v e r  transfer  syphon,  on t o p o f t h e b r a s s c a p .  A  17  combination used  of  t o pump  fig-diffusion  out the t r a n s f e r  siphon  m e r c u r y manometers, and t h e " s o f t " to via  a hard  vacuum.  a pumping  pressure  above  b)  The Magnet  of  3*6Si)  speed  the l i q u i d  helium  t h e o i l and  o f t h e i n n e r dewar pump was  employed  t o reduce the  surface i n order  to obtain  description  o f t h e pumping  system  core watercooled  was e s p e c i a l l y  Daniels  and b u i l t  Japan.  An a x i a l  investigations  electromagnet  designed  by the Tateno hole through  with a l i g h t  (series  for this  Electric  t h e magnet  impedance  work by D r . J .  allows  beam p a r a l l e l  optical  t o the magnetic  o f u p t o 12 KOe a t hO a m p e r e s i n a p o l e p i e c e  ation  o f 7.27  as 0 . 5 . dc  cm.  This f i e l d  to investigate  substances  The c u r r e n t t h r o u g h  generator  rheostats.  i s large  from  was  stabilized  was  r e g u l a t e d by a combination  b y power t r a n s i s t o r s ,  A l o n g term  was a c h i e v e d , w h i c h  width  o f t h e h y p e r f i n e components than  watercooled  The m a g n e t c u r r e n t whose b a s e c u r r e n t  stability  i s certainly  the r e s o l u t i o n  by  has been d e s c r i b e d by  gauss  better  by a  o f v o l t a g e and c u r r e n t f e e d -  This s t a b i l i z a t i o n  G a r w i n e_t a l ( 1 9 5 9 ) .  g values as low  t h e g e n e r a t o r was m i n i m i z e d  5600 M f d . c a p a c i t o r s i n p a r a l l e l .  is  with  t h e magnet was p r o d u c e d  two  back l o o p s .  separ-  enough a t X-band  a n d r e g u l a t e d b y means o f f o u r The r i p p l e  M.  M f g . Co., Tokyo,  field  frequencies  refer  (1965).  Griffiths  iron  wall  o f one i n c h d i a m e t e r  a detailed  to  The  high  jacket,  was  down t o 1 . 5 ° K .  temperatures For  A Kinney  line  2 forepump  pump a n d H y v a c  less  of at least than  the l i n e  o f the Europium  limit  s e t by t h e  ±1  l i n e s and  inhomogeneity  18  of  the magnetic  was  taken  value  around  The v a l u e  a calibration  of the current  mounted  or  from  field.  on a d o l l y  curve  through  The magnet  could  c)  Gyroscope  oscillator)  w h i c h was c a p a b l e  a 6 volt  from  supply.  A ferrite  the c a v i t y  power.  T.  monitored stub  250  used  t o measure  mW  a t X-  c u r r e n t was  provided  b y a home  line  protected  reaching  by a v a r i a b l e the k l y s t r o n  t h e sample  power p a s s e d  crystal  t h r o u g h a 3 0 db  two v a r i a b l e p r e c i s i o n a t t e n u a t o r s , a n d power f r o m  by a c r y s t a l  system w i t h  after  guide  of delivering  reflex  T h e k l y s t r o n was m a t c h e d t o  Before  and a c r y s t a l  just  gears.  klystron (  modulated  the c a v i t y  i n t h e f o u r t h arm o f t h e magic  meter f o l l o w e d  The  velocity  isolator  The r e f l e c t e d  tuner  microwave  by a r e f l e x  transmission  t h e microwave  attenuator,  a magic  a  power  reflected  flap  v i a a s e t o f worm  The k l y s t r o n h e a t e r  r e c t a n g u l a r waveguide  susceptance.  place  a l s o be r a i s e d , l o w e r e d ,  c a r b a t t e r y and t h e h i g h v o l t a g e s  made r e g u l a t e d the  2K39  Go. L t d . ,  band f r e q u e n c i e s . by  into  was  System  M i c r o w a v e p o w e r was p r o d u c e d Sperry  The magnet  i s shown i n F i g u r e 3 « 2 .  of the c i r c u i t  The M i c r o w a v e  field  t h e measured  i t t o be r o l l e d  r o t a t e d i n the h o r i z o n t a l plane  A diagram  in  H vs I using  t h e magnet.  which allowed  t h e dewar.  of the magnetic  the f e r r i t e  detector  isolator.  by a c i r c u l a r  sample  cavity  iris.  Two s c r e w s  waveguide above t h e c a v i t y  were u s e d  3 « D  inserted I t was  o f t h e sample  was c o u p l e d  wave-  to the  coupler  (See F i g u r e  frequency  contained  A cavity  was c o u p l e d  a 2 0 db d i r e c t i o n a l  the resonance  cylindrical  T, w h i c h  (1N23).  detector  was  cavity.  t o t h e wave-  extending  into the  t o match t h e l o a d e d  19  cavity  to the  cavity  was  operated  figuration This  transmission line  which  the  can  half  of  the to  as  the  was  a  cap  to  the  are  induced  the  wave g u i d e  gear  Pa.  cavity.  was  to the  drive  Since  and  i n the  A  not  33. of  ad-  teflon  the  i t was  plug  lower  found  also  nec-  to t i l t  i t  crystals.  obtained  from  Superior  dewar f r o m  the magnetic-dipole  a microwave magnetic was  problem  fills  ethylsuphate  used  con-  i s shown i n F i g u r e  crystal  f o r Cerium  The  field  temperatures.  s t e e l waveguide  by  The  W i t h CaF2 c r y s t a l s  only r o t a t e the  Morristown,  mode.  solution  at helium  cavity.  case  112  plane  simple  turned using  Stainless Co.,  a  crystal  be  essary  TE  i n a horizontal  mode p e r m i t s  justing  i n the  a t room t e m p e r a t u r e .  field,  brass  transitions  the  set p e r p e n d i c u l a r to the  the  Tube  H-plane  dc  of  magnetic  field. Pulse applying the  modulation  a pulse  reflector  capacitor.  from  The  relaxation  taken  place before system,  generator  the k l y s t r o n resonance. 160A  d)  a T e k t r o n i x 161  repetition  the  form  a  time  was  pulse•  t o be  generators  To  (10)  tune  had  the  T e k t r o n i x 162  through  were powered by  This  the a  to  Mfd.  recovery  reflector.  swept  by  generator  at least  t h a t complete  a p p l i e d to the  frequency  micwave-  allowed  cavity Tektronix  supply.  The  Optical  System  The  optical  system  attached  pulse  sawtooth v o l t a g e from  was  Both  r a t e used so  achieved  klystron via a 1  a p p l y i n g a new  r e g u l a t e d power  rigidly  m i c r o w a v e s was  e l e c t r o d e of the  times  rowave  of the  t o the  including magnet b y  t h e Hg  light  source  means o f s h e e t s  was  of 7  ply  20  w h i c h were b o l t e d turn  bolted  system  by f o r c e d  air.  and p a s s e d  a current  regulator  the l i g h t  glass  parallel  with  t h e magnet.  H100  AVT  cylinder  housing  was t a k e n f r o m  through f i l t e r  capacitors,  tube  10-^+0)  (Amperite  single  and f r e e  a  a choke,  i n order from  lines  from  light  intensity  just  of arc.  source so t h a t  before  A camera i r i s  and t h e f i r s t  The  lens  region.  to  ripple  t o a narrow and  from  A  Corning  wavelengths  was u s e d  to select  analyser  and  and were  mounted  angle  readings  was i n s t a l l e d to adjust  A second  the photomultiplier  between  the l i g h t  would...always b e fixed iris  to allow  of  through  the c a v i t y and thus  was only  operplaced light  shut out  light.  Detection  light  R.C.A. 6217  batteries  Both  the photomultiplier  w h i c h h a d come d i r e c t l y  Signal  thickness  w h i c h made p o s s i b l e  i n i t ' s linear  scattered  transmitted  t h e Hg s p e c t r u m .  circle  minutes  ating  with  were o f t h e Glan-Thompson t y p e  a divided  the  the l i g h t  beam a t t h e c r y s t a l ' s p o s i t i o n .  *+300 - UAfOO A a n d 7 mm.  polarizer  five  collimated  C.S. No. 7-?h  filter  between  an  The c u r r e n t  i n t e n s i t y as constant  series of lenses  nearly  e)  or rotated  the optical  possible. A  in  allowed  s o u r c e was a G e n e r a l E l e c t r i c  generator  keep  This  a r c lamp w h i c h was i n s i d e a b r a s s  cooled  and  as  t o t h e magnet's y o l k .  light  mercury  dc  aluminum f r a m e s w h i c h were i n  t o be r a i s e d , l o w e r e d ,  The  and  to angle  passing  through  the analyser  photomultiplier  each g i v i n g  90 v o l t s .  t h r o u g h a 10 K A r e s i s t o r .  was d e t e c t e d  powered by t w e l v e r a d i o The p h o t o c u r r e n t  The r e s u l t i n g p h o t o  by B  was f e d  signal V  h  21 was  found  t o be p r o p o r t i o n a l t o t h e l i g h t  Vpk= 700 mV intensity signals time but  and so c a r e  s o t h a t Y^  were  constant short The  never  filtered long  with  enough  s i g n a l s were  The  opposite  10  exceeded  the  600 mV.  a v a r i a b l e RC  light  The r e l a x a t i o n  network with  so as n o t t o d i s t o r t  then d i s p l a y e d  oscilloscope using  a  taken to adjust  to  a  the s i g n a l s  e n o u g h t o c u t down t h e n o i s e .  502  photo  was  i n t e n s i t y up  a built  taken from  KJl h e l i p o t .  photographed using  The image  on a  in differential  b i a s needed t o c a n c e l  s i g n a l was  directly  a No.  Tektronix  dc a m p l i f i e r .  t h e dc component 6 dry c e l l  regulated  o n t h e o s c i l l o s c o p e was  a Polaroid Tektronix  scope  of the by  then  camera.  A~V/JC yc^ej-Q /vr  Ge*tc<-a Aor  I J-L  XK 33  \  C rys +,l / c/e /c cvfe-  /  delays cle/ec/or  G£"  /-//oo//tv y  i fi in:  Tic:A £2/7  fi((~er poferi.  O H O fyt^rK<J  Figure  c/  7c kfro^i'x ~77~^—  3-1  Block  diagram  for* t h e  f.tfe  apparatus ro ro  23  Figure  3. > 1  Crystal adjusting  mechanism  Figure  3.5  The d e w a r  cap  26 B)  The a)  experimental Procedures P r e p a r a t i o n s f o r the The  Europium  oriented  from  polished  by  The  Optovac  the  by  s t a n d a r d low  in  detail  desired  low  rotating  good  with  b)  were c o o l e d temperature  critical  the  After  crystal  and  were  as  a t low magnetic  temperatures are  i n Cerium  fields  described  having reached i s aligned  transmission.  of the proper alignment  v i a the  This  align-  ethylsulphate. i s the  which  the  (Glattli)  Faraday  s h o u l d be  linear  field.  Faraday  Rotation  To d e t e r m i n e adjusted If  cut  and  helium  techniques which  r o d f o r maximum l i g h t as  were b o u g h t  to l i q u i d  (1965).  Griffiths  check  rotation  crystals  2  Inc., North Brookfield  temperature,  ment i s n o t A  GaF  author.  crystals  by  doped  Measurements  the Faraday  t o minimum l i g h t  rotation,  t r a n s m i s s i o n for. a g i v e n  the angle o f the a n a l y s e r  Faraday  rotation  i s given  the a n a l y s e r  i s (f^ (H), t h e n t h e  was field.  total  in  by:  /° . (H) = <JU (H) - <fU(H = o) T  t  E a c h v a l u e o f cj) was  averaged  must be  the Faraday  walls the  corrected  by  o f t h e dewar P%  s a m p l e Pi .  respect  and  several  rotation  of the  d  are of opposite sign  To  of  with  gives:  (3.2)  l/op) = i/^tl + l/M*!/ -) fa  1 }  glass  3  where  3. pt  readings.  f o r the diamagnetic r o t a t i o n  S i n c e /o, +/o  t o p, , t h i s  from  (  i s independent  of temperature  and  has  been  27  determined is  also  Faraday  c)  a t room  where P  temperatures  independent  ?  down t o 1 . 5 °  of temperature  r o t a t i o n o f our dewar  r e l a t i v e change  two  level  spin  is  usually  system  c a l l e d the  t o a microwave  saturation  3.5.  difference radiation  of  S.  (3.3)  An  the  two  An.  spin be  are the p o p u l a t i o n  l e v e l s i n the presence  respectively. system  The  population  i s proportional  and  differences  absence  difference  of  between  microwaves  o f a two  to the magnetization M  level and  - r j  M.  M  (3A)  0  the magnetization i s i n turn  Faraday  r o t a t i o n , the  saturation  proportional c a n be  put  to  the  i n the  form:  5 -  w h e r e /> a n d /0„ the  can  written:  5 =  If  a  field  An.  and  y  The  S = IT- ' where A n  /o  Spectrum  i n the p o p u l a t i o n  due  K.  i s shown i n F i g u r e  D e t e r m i n a t i o n o f the Resonance The  is negligible.  presence  (3.5)  are the paramagnetic  and  absence  Faraday  of the microwave  rotations  in  radiation  respectively. In define general as t h e  a m u l t i l e v e l system, the  saturation  hold.  The  S  equation 3.^  since  saturation  r e l a t i v e change  c a n be u s e d  e q u a t i o n 3.3 of a spin  does  system  i n m a g n e t i z a t i o n due  to  not, i n is  defined  t o microwave  28 radiation.  S i s a measure o f the microwave a b s o r p t i o n .  To o b t a i n the paramagnetic resonance spectrum S i s p l o t t e d a g a i n s t t h e a p p l i e d dc magnetic f i e l d  E q u a t i o n 3 * 5 has  H.  been used t o determine the resonance spectrum f o r Eu It  r e q u i r e s r e a d i n g t h e a n g l e s o f minimum l i g h t  w i t h microwaves  Pi-  :CaF . 2  transmission  on and then o f f f o r each f i e l d v a l u e .  method i s s u f f i c i e n t  This  t o determine t h e s p e c t r a found i n  u n d i l u t e d r a r e e a r t h s a l t s which e x h i b i t broad resonance lines.  I f the microwave power r e q u i r e d t o produce a  measurable  s a t u r a t i o n heats the sample  be used t o determine t h e s a t u r a t i o n .  a p u l s e method c a n The l i g h t  intensity  I t r a n s m i t t e d by the a n a l y s e r i s g i v e n by:  I(<P) = (I. - I-/Jcos <p * Iv, l  ( 3 > 6 )  where (j) i s the a n g l e o f the a n a l y s e r w i t h r e s p e c t t o t h e p l a n e o f p o l a r i z a t i o n o f the l i g h t . transmitted l i g h t  .  i s the minimum  A s m a l l change  around t h e  g i v e s from e q u a t i o n 3 * 6 :  a n g l e s <p="% , ^  =  i s the maximum  i n t e n s i t y a t <p= o and  l i g h t i n t e n s i t y a t <p= \  U l l  I  (I -l-r/x)b$-0  s i n c e |A<f>l = IA/a)  (X-I-/JA/°  (3.7)  i f &p i s the change i n F a r a d a y r o t a t i o n  due t o a microwave p u l s e . The s a t u r a t i o n due t o a microwave p u l s e u s i n g e q u a t i o n 3*7 is:  ^  " ^ a - i v j  where AI-^ i s the i n t e n s i t y a t h5° t o the minimum. E q u a t i o n 3 . 8 was used t o determine the s a t u r a t i o n .  (3.8)  29  The  dc p h o t o s i g n a l V  minimum  light  intensity into  was r e c o r d e d .  heating  A V k  w  a  d)  Relaxation  from  We  (1966).  always kept  pulse  point  semi-log  graph paper.  Figure A  i n magnetization  i s a linear  and  time  t o observe  height zero  of the recovery  analysis refer to of the  a n d t h e t r a c e was  the values  The s l o p e s  being  p l o t t e d on  of the r e s u l t i n g  of n i n the equation  then  f o r the  straight observed  g i v e n by:  scope  match t h e s l o w l y  A  screen  sec  n  (3.9)  - 1  h.h f o r a n e x a m p l e .  the c a v i t y .  pulse  and so t h e d e c a y  measure  For a detailed  by p o i n t w i t h  the value  second  employed  6 0 0 mV  the Faraday r o t a t i o n i s  I"= AT  See  height  of the p h o t o m u l t i p l i e r .  A p o l a r o i d p h o t o g r a p h was t a k e n  measured  relaxation  (two s e c o n d s ) t o  t h e maximum V ^  range  image on t h e o s c i l l o s c o p e s c r e e n  give  pulsed  d i s p l a y e d on t h e o s c i l l o s c o p e  the magnetization.  lines  light  a p o l a r o i d p i c t u r e of the  t o a change  a microwave  Glattli  rates  then  The s a t u r a t i o n s i g n a l  crystals  2  the photosignal  after  f o r minimum  Time Measurements  :CaF  proportional  of  repetition  stay w e l l w i t h i n the l i n e a r  In Eu  of  and the angle  the c r y s t a l .  trace.  f o r maximum a n d  The m i c r o w a v e s w e r e  a t long  determined  s  saturation to  transmission  the cavity  avoid  was m e a s u r e d  h  (Tektronix the pulse  This  enabled  changing  5^5A  with  response  cavity  the klystron to  resonance  of the experimental  i n ) was  o f t h e wavemeter  us t o tune  applied t o the r e f l e c t o r  line  a CA p l u g  by a d j u s t i n g t h e  electrode.  t r a c e was o b t a i n e d  by  30 5 +5A t o t r i g g e r t h e 502 o s c i l l o s c o p e  using  the  time  after  e)  the  F r o m 1.5  the  and  refer  2  was  highest  still  less  could  be  pressures from  1.5  2.3  t o h.2°  (1966). than  rapidly  as  was  k.2°  K  by  immersed  calculated  in by  the  explanation  the  signal  change  of t h i s  to noise  the temperature at which K.  liquid measuring  t o 2 . 3 ° K w i t h an o i l i n Faraday procedure  Since the c o n c e n t r a t i o n  .2%  temperature  obtainable  out.  t h e c r y s t a l was  For a d e t a i l e d  deteriorated the  from  to G l a t t l i  CaF  K  the temperature  helium vapour  rotation.  died  second  Measurements  t o ^.2°  m a n o m e t e r and  the  p u l s e had  Temperature  helium  a  l  was  of Eu  in  ratio  raised  meaningful r e s u l t s  and  so  were  Rotation (Degrees)  Figure  3.6  R o t a t i o n due t o d i a m a g n e t i c e f f e c t s o f dewar and c r y s t a l a t room t e m p e r a t u r e  32 Chapter  Four  EXPERIMENTAL  A)  Faraday The  tional in  Rotation  change  measured  i n t h e angle  i n order  t o check  case  dewar  was  plotted i nthe third  and  the Faraday  The measured  and f o r t h e diamagnetic  paramagnetic 7/z  that  with  field  was  r o t a t i o n was  propor-  r o t a t i o n was c o r r e c t e d  f o r t h e F a r a d a y r o t a t i o n due t o t h e g l a s s w a l l s o f  the  B  of polarization  t o themagnetization.  each  RESULTS  r o t a t i o n of the c r y s t a l  chapter.  r o t a t i o n was c o m p a r e d  confirmed  3.6)  (Figure  which  The r e s u l t i n g  t o theB r i l l o u i n  function  t h e p r o p o r t i o n a l i t y between r o t a t i o n and  magnetization. The  t h i c k n e s s /o (s6 /mm  s a t u r a t i o n r o t a t i o n p e r mm.  0  oo  f o r our  2+ crystals) of  i s p r o p o r t i o n a l t o t h e Eu  concentration  Faraday for  frequencies  that  depend  of p  theratio  on t h e l i g h t  close  It both  spectrum  effect  to the o p t i c a l  frequency  i s known t h a t  This  for different  M  measure f o r t h e r e l a t i v e  in  of the o p t i c a l  rotation is negligible.  light  found  dependence  concentration,  for CaF  2  concentrations  Europium  ions  t h e d i v a l e n t and t r i v a l e n t  would  i f the effect on t h e  be s t r o n g e s t  transitions.  Glattli  concentrations  does n o t  crystals  and i s a d i r e c t  of the d i f f e r e n t  enter state.  thefluoride (Shen,  specimens.  lattice  196*+)  The E u ^  +  7 i o n has a  F  contribution is  very  0  singlet  groundstate  t o the Faraday  and g i v e s  rotation.  s e n s i t i v e t o t h e growing  no p a r a m a g n e t i c  The r a t i o  conditions.  of E u  Europium  2 +  t o Eu3  +  added i n  2+ the than  form  of Eu 0 2  3  will  i f i t was a d d e d  result  i n the form  ct ahna n be ss tahte o uar Eu um e dc o tn hc ae tn t r iE ou n a +  i n a higher  3 +  of EuFy  ncentration o fc o.2%.  Eu  concentration  I n our c r y s t a l s i s as great  i t  or greater  33  B)  Resonance The  external in  Spectrum  saturation magnetic  Chapter 3.  individual ever, The  field  The 3°  approximately  of the  gauss  points  an  was  C)  several  we  w i t h our cannot  = 1,  are from  Field The  field  dependence h.2.  i n region A  C; Am = 3 .  of the r e l a x a t i o n  The  r e a d i n g s were  B e t w e e n t h e Am  Temperature The  points  the  the  curvea  results  1.5°  shown i n F i g u r e  K  time  electronic relaxations  The = 1,  K  relaxation Am = 2 ,  B;  the s i g n a l s  As  was  temperature  to the highest  were  and too  *+.3  are averages  explained  earlier  to the d i r e c t i o n which  This  results  transitions  i n minimum  and  therefore  between d i f f e r e n t  dependence  temperature  field was  1  from the  measurements the  light  o f f the[lQO]  separation maximizes  transition  The  several  and 30  which  ( +.2°K).  to n o i s e r a t i o  were done w i t h b o t h t h e dc m a g n e t i c  direction.  as  data.  gave a r e a s o n a b l e s i g n a l  path p a r a l l e l  are  Dependence  from  measurements.  times  t a k e n a t 1.58°  Mc/s.  transitions  spin-bath relaxation  measured  still  how-  transitions.  on  a r e f o r t r a n s i t i o n s Am  weak t o e v a l u a t e a n y  was  do  Dependence  w i t h a m i c r o w a v e f r e q u e n c y o f 8591  b)  the  We  run but  based  is  Times  shown i n F i g u r e  times  rheostat  resolve  3  and  one  i s a composite  outlined  structure.  2,  the  runs.  Relaxation a)  ^.1  of  i n t h e manner  or h y p e r f i n e  o f t h e Am  drawn t h r o u g h the p o i n t s of  therefore  lines  shown i n F i g u r e  as a f u n c t i o n  step possible  and  envelope  systems  determined  minimum  transition  obtain  spin  lines.  between cross-  3h The  experimental  points  c a n be f i t t e d  T"'= where  the value  semi-log Our  i s observed  dependence  crystal.  This  concentration values  that  Slope  Runs  No.  2  the  B  2.12  E  1.99  F  1.88  the absolute  value  i s due t o a s l i g h t  between the c r y s t a l s .  i n crystal  identical  p o s i t i o n each time  in  fact  the degree  At quite  these high  temperatures  (good  field  effecting  to the  the l i n e  separ-  Line  E is  runs which d i d agree i n  dependence. the accuracy  signal to noise  measurement does n o t exceed in  i s due t o o u r  of cross-relaxation.  made u p o f two s e p a r a t e  magnitude and temperature  I"'depends o n  The d i f f e r e n c e s i n  t o o r i e n t the e x t e r n a l magnetic  and hence  as the  d i f f e r e n c e i n Eu  2 f o r the E and F runs  thus  (n)  as w e l l  of the r e l a x a t i o n rate  inability  ation  drawn on  were a s f o l l o w s :  1  functional  of the l i n e  paper.  Crystal  It  line:  (^.1)  n  of n i s the slope  graph  results  A T  to the straight  o f measurements i s  r a t i o ) and t h e e r r o r o f  the size  of the c i r c l e s  drawn  Figure No c h a n g e  Earlier  i n 1 was o b s e r v e d  by v a r y i n g  the pulse  work showed no c h a n g e i n I when t h e p u l s e  was c h a n g e d  by a f a c t o r o f 3 0 .  length.  length  37  39  Chapter  Five  D I S C U S S I O N OF RESULTS  A)  Field  Dependence  From appears to  the graph  that  effects  which there  B)  than  a s were  This  could  the d i r e c t  Temperature A  The f i e l d  i s an energy  system.  faster  dependence  a s was t h e c a s e  1965)  (Griffiths,  spin  of X vs the external  the f i e l d  the spectrum  relaxation  of X  of T i s not d i r e c t l y related  f o r Neodymium  ethylsulphate.  d e p e n d e n c e may be due t o c r o s s -  outlined  transfer lead  by Bloembergen  (1961) i n  between d i f f e r e n t p a r t s  to a cross-relaxation  spin-lattice relaxation  Dependence  comparison  magnetic f i e l d i t  of the  process  process.  of X  o f our r e s u l t s with those  of G l a t t l i ' s f o r  2+ Eu  :CaFg  shows t h a t  than h i s .  This  different crystals field.  our values  c a n be e x p l a i n e d  electronic  of relaxation  i n our e x t e r n a l  c r y s t a l s were c u t so t h a t  the spins  to transmit  Our after  t o take method  the  This  t h e i r energy  h a v i n g more t r a n s i t i o n l i n e s a v a i l a b l e process  dc magnetic  separation  cross-relaxation  t o t h e b a t h f a s t e r by  f o r the d i r e c t  of observing  t h e change  microwave p u l s e  i n paramagnetic  o f t h e m a g n e t i z a t i o n due t o t h e E u ^  the  only  The  occurrence  seems t o i n d i c a t e  they of a T  contribute  t o the Faraday  temperature  the presence  rotation  e n a b l e s us t o measure t h e  time dependence that  relaxation  place.  a saturating  extent  between  t r a n s i t i o n s w h i c h i s a t a maximum i n o u r  b e t w e e n t r a n s i t i o n l i n e s was a maximum. allows  are faster  by the c r o s s - r e l a x a t i o n  due t o t h e i r o r i e n t a t i o n s Glattli's  times  dependence  ions (to rotation). at f i r s t  o f a phonon b o t t l e n e c k ,  however  the values of T are much f a s t e r than they should be i f a b o t t l e neck were present.  I t has been shown t h a t p a i r s of ions might  be coupled together through exchange i n t e r a c t i o n t o form paramagnetic systems w i t h energy l e v e l s which d i f f e r from those of s i n g l e i o n s .  C r o s s - r e l a x a t i o n from s i n g l e ions t o exchange  coupled p a i r s (or l a r g e r c l u s t e r s ) has been proposed by many authors t o e x p l a i n the T~  2  dependence; V a n Vleck (1959 and 1961)  ,  G i l l (1961), G i l l and E l l i o t t (1961), Bloembergen and Pershan (1961), S t a t z e t a l (1961), Ramestad and Wagner (1963), and J e f f r i e s (1966), and G l a t t l i  Shulz  (1966).  S t a t z e t a l (1961) and G i l l (1961) measured r e l a x a t i o n times of t r a n s i t i o n s xn the Cr  p a i r spectrum i n ruby.  The paxr  r e l a x a t i o n r a t e s were found t o be about three orders of magnitude f a s t e r than the s i n g l e i o n r e l a x a t i o n r a t e s .  The above authors  q u a l i t a t i v e l y explained the strong s p i n - l a t t i c e coupling of p a i r s as due t o modulation of the exchange i n t e r a c t i o n by the l a t t i c e vibrations.  I n our c r y s t a l s as i n two of G l a t t l i * s there i s an  a p p r e c i a b l e c o n c e n t r a t i o n of E u ^ i o n s . +  These ions have a  ground s t a t e s i n g l e t 'F . Since the exchange i n t e r a c t i o n acts on the e l e c t r o n i c s p i n r a t h e r than on the t o t a l angular momentum, Eu^  ions could be coupled t o nearby Eu  pairs.  I t i s possible  t h e r e f o r e , f o r e i t h e r exchange coupled p a i r s and/or c l u s t e r s made up of Eu  p a i r s and E u  J  ions t o have a steeper i- vs T  dependence and thus account f o r the T~^ temperature dependence. Since we only had one s e t of c r y s t a l s w i t h the same E u  2 +  and  Eu3  c o n c e n t r a t i o n i t was not p o s s i b l e t o check as t o which mechanism was  responsible. Q u a n t i t a t i v e or even s e m i - q u a n t i t a t i v e explanations are  i m p o s s i b l e , due t o the very complicated s t r u c t u r e of our system.  +  1+1 BIBLIOGRAPHY  (1961) The P r i n c i p l e s o f N u c l e a r M a g n e t i s m  A b r a g a m , A.  University Bloerabergen,  (1961) P r o c . o f t h e Y l l t h I n t . G o n f . on Low  N.  Physics Bloembergen,  N.,  Shapiro,  (Univ. S.,  of Toronto  Pershan,  N. a n d P e r s h a n ,  Daniels,  J.M.  and  G a r w i n , R.L.,  (1961)  Gill,  J.C.  and  Proc.  Phys.  J.O.  Press)  J.  Singer  ed.  (1958) C a n . J . P h y s . 365 ^05  Soc.  22,  Shapiro,  G.  (1959)  58  E l l i o t t , R . J . (1961) A d v a n c e s i n Quantum E l e c t r o n i c s (Columbia Univ. P r e s s ) J . S i n g e r ed.  (1966) P h . D.  H.  Univ.  H u t c h i n s o n , D., Penman, S., a n d Rev. S c i . I n s t r . 3 0 , 105  J.C.  Glattli,  (Columbia  W e s e m e y e r , H.  Gill,  Artman,  M+5  (1961) A d v a n c e s i n Quantum  P.S.  Electronics  and  Temp.  1961)  Press,  P.S.,  (1959) P h y s . Rev. 11}+, Bloembergen,  (Oxford  Press)  Thesis, Univ.  of B r i t i s h  Columbia  (Unpublished) Griffiths, Kastler, Kronig,  (1965) P h . D. T h e s i s , U n i v . o f B r i t i s h  D.J.  A. R.  (195D  C. R.  Acad. S c i . , P a r i s ,  (1939) P h y s i c a 6,  deL.  2^2,  953  33  (1957) H e l v . P h y s . A c t a . 3 0 ,  37^  Lacroix,  R.  Low,  Paramagnetic Resonance i n S o l i d s , Suppl. 2 P h y s i c s , S e i t z and T u r n b u l l e d .  W.  (1953) R e v .  O p e c h o w s k i , W. R a n n e s t a d , A. Rieckhoff,  K.E.  S c h u l z , M.B. Scott,  and  P.L.  Wagner, P . E .  Jeffries, Jeffries,  CD.  (196*+) P h y s . Rev.  Statz,  Rimai,  Van  Vleck,  J.H.  L.,  (1962) 133,  State  26^  (1966) P h y s . Rev.  Weber, M.J.,  131,  P h y s . Rev.  1953 Columbia  1^9,  270  122?  32  A5-11 De  M a r s , G.A.,  and  Koster,  G.F.  (1961) J . A p p l . P h y s i c s 32 S u p p l . , 218 S (1959) Quantum E l e c t r o n i c s C H . Townes e d . (Columbia  Wyckoff,  25,  (1963) P h y s . Rev.  CD.  S h e n , Y.R. H.,  Physics  Solid  (1962) P h . D. T h e s i s , U n i v . o f B r i t i s h  and and  Mod.  Columbia  Crystal  Univ.  Press)  p.391  S t r u c t u r e s , I n t e r s c i e n c e P u b l i s h e r s , New  York  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0085094/manifest

Comment

Related Items