Vijayaraghavan, R

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Indian J- Phys. 75A (4), 289-291 (2001)U P  Aan international journalNuclear magnetic resonance and bulk magnetismR  V ijayaraghiH van ’^SAMEER, IIT Campus, Muihbai-4(K) 076, India E-mail : rv(i!'ti|^.rcs.inAbstract : The paper reviews the power of nuclear magnetic resonance (|lMR) technique by giving few examples of studies in solids and their conelation with hulk magnetism. As illustration, the investigation in some traitifcition metal and rare earth alloys arc discussed NMR shift of specific nuclei from that of a diamagnetic solid are correlated to the nature of magnctiiiin in the solids In the ordered or paramagnetic state, the local field at ihe nucleus is proportional to the magnetic moment of the magnetic ion cither directly or through the polarization of the conduction electrons at different nuclear sites Examples in spin glass, and superconductors arc presentedKeywords NMR. magnetic materials, bulk magnetismPACS Nos, : 76 60 -k, 75.30.-m1. IntroductionT h e  m ag n e tic  re s o n a n c e  f r e q u e n c y  o f  a  n u c le u s  is  d ir e c t ly  proportional to  th e  e x te r n a lly  a p p lie d  m a g n e t ic  f ie ld  a n d  7  , the gym  m a g n e tic  r a t io  o f  th e  n u c le u s  {y  =  / i  /  Ih). In  a d d it io n  lu/ijj, local f ie ld s  w ill a l te r  th e  re s o n a n c e  f re q u e n c y  (Oq toCO.a) = r(Ho+H„„). ( 1 )T h e  local f ie ld s  c a n  b e  d u e  to  s e v e ra l re a s o n s ,  viz- c h e m ic a l ,  conduction e le c tro n  h y p e r f in e  in te ra c t io n  I .S . (I  =  n u c le a r  sp in , S = ionic sp in  s ta te ) , a n d  in te rn a l  m a g n e t ic  f ie ld s  w h ic h  m a y  b e  sialic o r t im e  v a ry in g  a n d  m a y  a d d  o r  s u b t r a c t  to  th e  e x te rn a l magnetic fie ld . In  th e  p a ra m a g n e tic  sy s te m s , is p ro p o r tio n a l to the m a g n e tis m  a n d  s u s c e p t ib i l i ty  X of th e  io n  a n d  in  th e  m agnetically  o rd e r e d  s y s te m s  to  o rd e r e d  m a g n e t ic  m o m e n t o f  the m ag n e tic  io n s , s u i ta b ly  m o d if ie d  a t  d i f f e re n t  n u c le a r  s i te s . In th is  s e n s e ,  b u lk  m a g n e t i s m  t h r o u g h  s u s c e p t i b i l i t y  o r  m agnetiza tion  a n d  N M R  a re  r e la te d  to  e a c h  o th e r  ; w ith  th e  former as m a c ro sc o p ic  p ro b e  a n d  th e  la t te r  a s  m ic ro sc o p ic  p ro b e . Since P ro fe s s o r  K . S . K r is h n a n  w a s  g re a t ly  in v o lv e d  in  th e  m agnetism  a n d  th e  m a g n e to  c h e m is t ry  o f  m a te r ia ls ,  th is  a r t ic le  IS d ed ica ted  to  h im  d u r in g  h is  b ir th  c e n te n a ry  y e a rs . T h e  a u th o r  ^ad a lso  th e  p r iv i le g e  o f  p e r s o n a lly  d is c u s s in g  w ith  P ro f . K . S . Krishnan th e  te c h n iq u e s  l ik e  N M R , M o s s b a u e r  e f f e c t  a n d  th e  neutron s c a t te r in g  w ith  s p e c ia l  r e f e re n c e  to  th e  m a g n e t is m  o f  materials.2. Transition m etal alloysP la tin u m  in a  tra n s it io n  m e ta l w ith  an  a to m ic  c o n fig u ra tio n  5d^6s a n d  h a s  Pt*^^ i s o to p e  w i th  s p in  /  =  1 /2 . T h e  te m p e r a tu r e  d e p e n d e n t p a ra m a g n e tis m  c o m e s  fro m  th e  u n f i lle d  d b a n d . (X =  1 X 1 (T^) e m u /g m  a t 3 0 0  K , . 1 . 1 0  x  1 0 ^  e m u /g m  a t 8 0 K ) (1 ). TTic K n ig h t S h if t  (K S ) , w h ic h  is  th e  N M R  f re q u e n c y  s h if t  o f  Pt*^^ in m e ta l f ro m  th a t o f  a  r e f e re n c e  c o m p o u n d  is ~ 3 %  a t 3 0 0 K  a n d  ~  3 .5 %  a t 8 0 K , a r is e s  fro m  th e  c o re  p o la r iz a t io n  o f  s e le c tro n s  d u e  to  u n f i l le d  d  e le c tro n  sp in s  a n d  n o rm a l I S in te ra c t io n  fro m  c o n d u c tio n  e le c tro n s . T h e  p a ra m a g n e tis m  a r is in g  f ro m  d  b a n d  c a n  b e  m o d if ie d  by  su ita b le  a l lo y in g  w ith  m e ta ls  lik e  tin , le a d  o r  m e r c u r y  [ I j .  T h e  la rg e  n e g a t iv e  K n ig h t  S h if t  g e ts  r e d u c e d  c o n s i d e r a b l y  o n  a l l o y i n g  w i th  w e a k  o r  n o  t e m p e r a t u r e  d e p e n d e n c e  a n d  e v e n  b e c o m e s  p o s i t iv e  d u e  to  th e  a b se n c e  o f  J  e le c tro n s . T h e  s u s c e p tib i l i ty  o f  th e  a llo y  th e n  b e h a v e s  lik e  a  p a u li p a ra m a g n e t [ 1 ]. T h e  K n ig h t sh if t d a ta  is i l lu s tra te d  in  T ab le  1 in  th e  te m p e ra tu re  ra n g e  o f  1 1 0  K  to  3CX)K (1 ).Table 1. Knight shift in platinum alloys.INSa  Senior Scientist.Alloy Pt% K.S.at 300KK.S.at ItOKPt metal 100 -3% -3  5%Pt,Sn 75 --0.32% -0.44%PtSn 50 -^0.37% -1-0.37%Pt,Pb 75 -0.29% -0.46%PtHg, 33 -1-0.3% -1-0.3%© 2 0 0 1  lA C S290 R Vijayaraghavan3« NMR in ferromagnetsT h e  o b se rv a tio n  o f  N M R  in fe r ro m a g n e tic  c o b a lt  m e ta l w a s  firs t m a d e  b y  G o s s a rd  a n d  P o r t is  [2 ] w ith o u t  a n y  e x te rn a l f ie ld  (z e ro  f ie ld  N M R ) a t a  h ig h  f r e q u e n c y  o f  2 13.1 M H z , c o r re s p o n d in g  to  an  in te rn a l f ie ld  o f  2 1 .3  te s la  a t Co'^^ n u c le u s  a t  3 0 0 K , w h ic h  is  la rg e ly  te m p e ra tu re  d e p e n d e n t .  S o o n  th e  re s o n a n c e  o f  th e  Fe^^ a n d  Ni*^* w a s  o b s e r v e d  w ith o u t  e x te rn a l f ie ld s  in  fe r ro m a g n e t ic  iro n  a n d  n ic k e l c o rre s p o n d in g  n e g a tiv e  in te rn a l f ie ld s  o f  33  te s la  a n d  10 te s la  re s p e c tiv e ly . T h e  r e s o n a n c e  f ie ld s  fo l lo w  th e  b u lk  m a g n e t iz a t io n  a n d  a re  r e la te d  to  th e  m o m e n t o f  th e  m a g n e t ic  io n s  in  th e s e  c a s e s .4. NMR in rare earth alloysT h e  p ro b le m  o f  th e  p o la r iz a t io n  o f  th e  c o n d u c tio n  e le c tro n s  in  a  m e ta l b y  a  lo c a l iz e d  s p in  is  v e ry  c ru c ia l  to  th e  u n d e rs ta n d in g  o f  fe r ro m a g n e t is m  in  3d a n d  4 /m e ta l s .  T h e  e s s e n tia l  p o in t  is  th a t th e  d o r / s p i n s  im p re s s e d  a  u n if o rm  o r  o s c i l la to ry  p o la r iz a t io n  u p o n  th e  c o n d u c tio n  e le c tro n s ,  w h ic h  th e n  c o u p le  th e  ra re  e a r th  o r  t r a n s i t io n  m e ta l  io n s  to  o r d e r  m a g n e tic a l ly . N M R  c a n  p ro b e  th is  a t th e  n u c le a r  s i te  th r o u g h  z e ro  f ie ld  N M R  te c h n iq u e  a t n u c le a r  s i te s  o f  m a g n e t ic  io n  o r  a t  th e  a l lo y in g  s i te  d u e  to  re so n a n c e  sh if t w h ic h  c a n  b e  c o rre la te d  to  th e  b u lk  su sc e p tib ility . (KjOt )• T w o  e x a m p le s  a rc  g iv e n  b e lo w : (a )  R a ree a r th  P t2 ( R P t j )  a n d  (b )  R a re  e a r th  P t ,  ( R P t , )  a llo y s  w h e re  P t a to m s  a re  in  tw o  in e q u iv a le n t  c ry s ta l lo g ra p h ic  s ite s .T h e  R P t^  c o m p o u n d s  h a v e  c u b ic  L a v e s  s t ru c tu re  ( M g C u 2 ) w ith  a ll th e  p la t in u m  a to m s  e q u iv a le n t .  T h e  a llo y s  L a P t2» C c P t2 » P rP t2 a n d  N d P t2 h a v e  in c r e a s in g  ra re  e a r th  m a g n e t ic  m o m e n t. L a P t2 » w ith  n o / e l e c t r o n ,  is  a  r e f e re n c e  c o m p o u n d  [3 ].(i) L a P l2 : K  =  0.75% a t  a ll te m p e ra tu re s ,(ii) C e P t2 : =  3 x  10^^ e m u /m o lc  K  =  +  1 %  a t 4 0 0 Ks= 5  X e m u /m o le  K  =  +  1 .4%  a t 8 0 K ,(iii) P r P t j : jj; =  6  x  I (T^ e m u /m o lc  K  =  2 .2 %  a t 4 0 0 K=  10 X 10--^ e m u /m o le  K  =  -k 2 .8 %  a t 8 0 K ,(iv) N d P t2 ; t  =  8  X e m u /m o le  K  =  +  2 .9 %  a t 4 0 0 KX  - 1 2 x \ 0 r ^ c m u /m o le  K  = + 4 .2 % at 8 0 K .( ; f  is  m o s tly  in f lu e n c e d  b y  4 f  e le c tro n s )T h e  R P lj  c o m p o u n d s  ( C a C u j  s t ru c tu r e ) ,  P t a to m s  e x is t  in  tw o  in e q u iv ^ e n t  s i te s  P tj a n d  Pt^^ in  2 :3  ra t io  a n d  th e  p o la r iz a t io n  a t th e  tw o  s i te s  is  fo u n d  to  b e  o s c i l la to ry , n o t u n ifo rm  b e c a u s e  tw o  d is t in c t  r e s o n a n c e s  a re  o b s e r v e d  w ith  d if f e re n t  te m p e ra tu re  d e p e n d e n t  s lo p e s  [3 ] .(i) LaPtj: Pt, K%==0.1% Pt„s:+l%at400K(R e fe re n c ec o m p o u n d ) ,(ii) CePtj: Pt, K% =  +  0.3% Pl,,=:+L2%at400K+0.4% +L6%at80K,(iii) P rP t^ : P t, K %  =  +  0 .7 %  P tn  =+1.3% at4(K )K+  1 .3 %  + 1.5 % a iS 0 K(iv ) N d P t , ;  P i, K%> =  + 1 .2 %  P ti, =  + 1 .8 % a i4 W K+  1 .8 %  + 2 .3 % a tK 0 K5. NMR and " Antiferromagnetic" Cu^Sb alloyC u 2S b  h a s  tw o  in c q u iv a le n t c o p p e r  s ite s  w ith  C u , a n d  CUj, havn,i- te tra g o n a l s i te  sy m m e try . O n e  o b s e r v e s  q u a d ru p o la r  sp in  N M k  lin e s  fro m  th e  tw o  site s  fro m  4 2 0 K  to  7 7 K  w ith o u t any  apprcciahiL c h a n g e  in  th e  K n ig h t S h if t  a n d  l in e w id th .  H o w e v e r  th is  alh)\ js f ro m  m a g n e t ic  s u s c e p tib i l i ty  a n d  s p e c if ic  h e a t m easurem cin re p o r te d  a s  an  a n ti f e r ro m a g n e t  w ith  T,^ =  3 7 3 K  w ith  as 2 (^ B o h r m a g n e tro n  [4]. H o w e v e r, N M R  sh ifts  a rc  sm a ll, about 0  I ^  I t  is c le a r  th a t i f  a n t ife r ro m a g n e tis m  c o m e s  f ro m  c o p p e r  ions, iIil N M R  lin e s  w o u ld  h a v e  d ra s t ic a l ly  c h a n g e d  o n  p a ss in g  througn th e  m a g n e t ic a l ly  o rd e r in g  te m p e ra tu re .  S o  it is  c le a r  th a t Cu ,S! is n o t a n  a n ti f e r ro m a g n e t  b u t a  s im p le  P a u li  p a ra m a g n e l I’ln , e x a m p le  sh o w s  th e  p o w e r  o f  a  m ic ro sc o p ic  p ro b e  lik e  N M R  ova b u lk  p ro b e s  lik e  m a g n e t iz a t io n , s p e c i f ic  h e a t e tc .6 . S p in  g la s s  C o - G a  s y s te m sC o b a lt G a lliu m  a llo y s  (C o^G a, x -  0 . 3 5  <  a <  0 .7 5  )h av cC \( i s tru c tu re . In  a  w e ll- o rd e re d  c q u ia to m ic  a llo y  (x -  0 .5 0 ), coba!? h a s  n o  m a g n e t ic  m o m e n t a n d  c a n  b e  re g a rd e d  a s  a  noninagncih m atrix . F o r x > 0 .5 0 , th e  e x c e s s  C o  a to m s  g o  to  G a  site , giving ris^  to  sp in  g la s s  l ik e  m a g n e t ic  p ro p e r t ie s .  B a s ic a l ly  excess cobalt g o e s  to  g a l l iu m  (a n t is t ru c tu re )  s i te  s u r ro u n d e d  by  e ig h t cobalt a to m s , fo n n in g  a  m a g n e t ic  c lu s te r  in  a  n o n m a g n e tic  m atrix . One c a n  o b s e r v e  s p in  g la s s  f e a tu r e s  in  a .c  s u s c e p t ib i l i ty  up ic X =  0 .6 3  (x > 0 .6 3  b e c o m e s  fe r ro m a g n e t) . N M R  o f  Co"’*^ (zero 1 tcU c o n f ig u ra t io n )  f ro m  c lu s te r  c o b a lt  a to m s  a n d  n o rm a l field  N M K  f ro m  th e  re s t  o f  th e  n o n m a g n e t ic  C o G a  s y s te m  c an  be seen m o d if ie d  b y  th e  p re s e n c e  o f  C o  c lu s te r s  w ith  d if fe r in g  sizes and d if fe r in g  sp in  f re e z in g  te m p e ra tu re  [5 ].In  th e  p a ra m a g n e tic  s ta te , K n ig h t  S h if t  C o^^ a n d  Ga^*  ^ arc0 .2 5 %  a n d  0 .0 5 % ,  in d e p e n d e n t  o f  te m p e r a t u r e  a n d  x. I( p re s u m a b ly  c o m e s  f ro m  th e  g e n e ra l  C o G a  sy s te m , unaffected b y  a n ti s t ru c tu r e  c o b a l t  a to m s . In  a d d it io n  a s a te ll i te  C o^ ‘^ was o b s e rv e d  fo r  0 .5 0  ^  jc ^  0 .5 6  w ith  K n ig h t S h if t  c h a n g in g  from - 1.5 %  to  - 2 .5 %  in  a  te m p e ra tu re  ra n g e  o f 4 0 0  to  2 0 0 K , w ith  large c h a n g e s  in  th e  l in e w id th .  T h is  s h o w s  th e  p o w e r  o f  N M R  " s e c ” b o th  m a g n e t ic  a n d  n o n m a g n e t ic  a to m s  a t  th e  sam e  time. O n  g o in g  to  l iq u id  h e l iu m  te m p e r a tu r e ,  th e  s p in s  o f  these a n ti s t ru c tu r e  c o b a l t  a to m s  f r e e z e  to  g iv e  z e ro  f ie ld  N M R  linc> w ith  d if f e r in g  lo c a l in te rn a l  f ie ld s  f ro m  4  te s la  o n w a rd s  from " m a g n e tic "  c o b a lt  in  th e s e  c lu s te r  sp in  gla.ss sy s te m , w h ile  NMR f r o m  ’* n o r m a r '  c o b a l t  f r o m  C o - G a  m a t r i x  c a n  a ls o  be s im u l ta n e o u s ly  o b s e r v e d  u s in g  e x te r n a l  f ie ld  [S ].7. Borocarbide superconductorsT h e  d is c o v e ry  o f  s u p e r c o n d u c t iv i ty  in  q u a te r n a ry  ra re  earth U -ansition m e ta l b o ro c a r b id e  ( R E N i jB jC )  ra is e s  so m e  im porianiNuclear magnetic resonance and bulk magnetism 291questions regarding superconductivity and magnetism [6]. The transition metal like Nickel and rare earth atoms like, Dy, Ho, Er, Xm have large magnetic moments. Still in RENi^B^C, superconductivity is seen at fairly high temperatures, while magnetic ordering due to rare earth moments also takes place |6].DyNi^BjC HoNi2B 2C  ErNijBjC Tm N ijBjCYNi2B2CT.„ =6K t .  =11KT..„, =11K,lied=8K, =6.5K, = 1.5K,T ,  =15.5KS.CAs an example, the NMR of B' ‘ nucleus in YNi2B2C where there IS no/elcctrons but only d electrons from Nickel atoms is briclly pre.senled here. It has ThCr2Si2 structure and boron atoms have uniaxial symmetry. NMR of B" shows quadrupolar broadened line (I=3/2) with = 0.7 MHz and a small Knight shift of + 0.06% which decreases to + 0.05% in the superconducting state [71. Though cryslallographically. all boron atoms are equivalent, two NMR lines arc seen, with one of them moving to higher fields as temperature is lowered through T^ .^ and the other signal is nearly constant with the change of icniperatures. It is speculated that the former belongs to the regions of the superconducting stale, while due to chemical disorder between carbon and boron atoms, the latter stays in normal region. From the relaxation time studies, it is inferred that nickel atoms may carry magnetic moments. YNi2B2C may be con.sidcred as itinerant antiferromagnetic spin lluctualing material where electronic correlations play an important role [7]. N M R  of boron nucleus in other borocarbides will be very inicrc.sting in view of the coexistence of magnetism and superconductivity.8. ConclusionThe technique of NMR in understanding bulk magnetism is shown with examples from transition metal and rare earth alloys. Due to the brief nature of this article, NMR of rare earth nuclei in rare earth alloys and transition metal based Hcusler alloys are not mentioned. The example of spin glass shows how NMR can be used to probe microscopically the presence of magnetic and non magnetic regions. In .some ca.ses, this technique is unique in deciding the magnetic nature of the material. NMR can throw a lot of insight in understanding the nature of cooperative .phenomena like magnetism and superconductivity.'Acknowledgment?Thc author expresses his gratitude to his colleagues in the Condensed Matter Physics group at the Tala Institute of Fundamental Re.scarch, Mumbai for their collaboration and cooperation during his tenure at TIFR.References[ 11 S S Dharinalti. V U S Rao ami R Vijayaraghavan Ptoc hit. Coni on Mnjinetism (Nollinghain, U K ) (1964)12] AC Gossard and A M Poin.s PIm Rev Uit. 11 164 (1959)[3) R Vijayaraghavan, S K Malik and V U S Rao Pliy.s. Rev Lett 20 106(1968)(4) L C Gupla, S K Malik and R Vijayaraghavan PIm Utt 28A 255 (1968)15| A K Grover, L C Gupta, R Vijayaraghavan, M Matsumara, M Nakano and K Asayama Solid State Comniun 30 457 (1979) and relcrcntcs therein[6 ] R Nagarajan and L C Gupta Studies in Hi}*h Temperatute Supeuvnductors Vol. 26 (cd) A V Narlikar (New York . Nova vScience) (1997)[71 T Kohara, T Oda, K Ueda, Y Yamada, A Mahajan, K Elankuinaran, Zakir Hos.sam, L C Gupta, R Nagarajan, R Vijayaraghavan and Chandan Ma/umdar Ph\s Rev B51 3985 (1995)

Nuclear Magnetic Resonance and Bulk Magnetism

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Nuclear Magnetic Resonance and Bulk Magnetism

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