Dasgupta, D

Feller•, J

Hinks, D G

IACS Institutional Repository

Indian J. Phys. 7 5 A  (4 ), 2 9 3 -2 9 6  (2 0 0 1 )U P  Aan internationai journalVelocity measurements at the metamagnetic transition in UPt,J  Feller•■^ D  D asg u p ta* , D  G  H in k sS  J 0  K e tte r so n '’ a tid  B im a l K  S arm a-’”• Department of Physics, University of Wiscon^n-Milwuukee, Milwaukee WI 53201, USA Department of Physics, Northwestern |lniversity, Evanston IL 60208, USA Materials Science Division, Argonne Natiofial Laboratory, Argonne IL 60439, USA$E-mail • bksa^ma^^csd uwm.eduAbstract . The longitudinal ultrasonic attenuation and velocity were meiusurcd on a single crystal of UPt, in high magnetic fields up to a field of U Icsla Earlier measurements had reported a metamagnetic behavior in the vicinity of 20 Tesla, where a pronounced dip in velocity (softening of the lattice) is seen Simultaneous measurements at three frequencies during the same run were possible A small dispersion in the velocity is seen at the metamagnetic transition. An additional structure is seen at a slightly highci magnetic field at lower temperatures Also at temperatures below ItXlmK. quantum acoustic oscillations are seen in the ultrasonic velocityKeywords • UPt^, metamagnctisin, velocity dispersionPACS No. 75 30 kzL IntroductionThe h eav y  f e r m io n s  a re  r a r e  e a r th  o r  a c t in id e  in le rm c ta l l ic  co m p o u n d s th a t  s h o w  s t r o n g  e le c tr o n ic  c o r r e la t io n s  a t  lo w  lem peraiures. T h is  is m a n ife s te d  b y  a n  e n h a n c e d  e le c tro n ic  h e a t capacity a t lo w  te m p e ra tu re s  ( e q u iv a le n t  to  a  n a r ro w  b a n d  a t ihc lerm i le v e l) . T h e  r e n o r m a l iz e d  m a s s  m a y  b e  l(X) t im e s  la rg e r  than the  h a re -e le c tro n  m a s s , le a d in g  to  th e  c o n c e p t  o f  lo c a l iz e d  electron s ta te s , a n d  s t ro n g  m a g n e t ic  p ro p e r t ie s .  S o m e  o f  th e s e  arc su p e rc o n d u c tin g  a t te m p e ra tu re s  o f  th e  o rd e r  o f  1 K , a n d  in  these th e  h e a t c a p a c i ty  ju m p  a t  is  o f  th e  s a m e  o rd e r  a s  y  7  show ing th a t th e  C o o p e r  p a ir s  a ls o  in v o lv e  th e  h e a v y  m a ss .T he h eav y  f e n n io n  sy s te m s  (U P l3 , U R u 2S i2» U P d 2A l3 ,C e C u 2S i 2 , e t c . )  h a v e  v e r y  i n t e r e s t i n g  a n d  u n u s u a l  Jiuperconducting a n d  n o rm a l s ta te  p ro p e r tie s . U ltra so n ic  v e lo c ity  nicihods h a v e  p ro v e d  a n  im p o r ta n t  s e n s it iv e  to o l in  in v e s tig a tin g  these p ro p e r tie s  [1 ,2 J . T h e  b e s t  s tu d ie d  o f  th e s e  c o m p o u n d s  is It is n o w  b e lie v e d  th a t  th e  s u p e r c o n d u c tiv i ty  in  U P t^  is  o f  an u n c o n v e n tio n a l n a tu re , i.e . n o t th e  s im p le  s -w a v e  B C S  ty p e .sy m m etry  o f  th e  o rd e r  p a ra m e te r  is  lo w e r  th a n  th e  u n d e rly in g  Fermi su rfa c e . T h e re  a rc  m u lt ip le  s u p e r c o n d u c tin g  p h a s e s  [2 ,3 ] for all o r ie n ta tio n s  o f  th e  m a g n e t ic  f ie ld  w h ic h  c a n  b e  u n d e rs to o d  ‘n term s o f  a  tw o  c o m p o n e n t  o r d e r  p a r a m e te r  in  th e  G in z b u rg -  Landau fo rm a lism . A  w e a k  a n ti fe r ro m a g n e t ic  o rd e r in g  (a t -  5 K ) IS in s tru m en ta l in  r e m o v in g  th e  d e g e n e ra c y  a n d  th is  sh o w s  u pCorresponding A uthoras  a  s p l i t t in g  in  th e  s u p e r c o n d u c t in g  p h a s e  tr a n s i t io n ,  se e n  s im u l ta n e o u s ly  b y  u ltra s o n ic  a n d  h e a l c a p a c i ty  m e a s u re m e n ts . In  a d d itio n  th e  u ltra so n ic  a tte n u a tio n  in  U P l^  a t lo w  te m p e ra tu re s  in s tead  o f  fo llo w in g  an  e x p o n e n tia l d e c re a s e  a s  in  a  c o n v e n tio n a l s u p e r c o n d u c to r  (b e c a u s e  o f  th e  d e v e lo p n ie n l  o f  a n  e n e rg y  g a p , th e  n u m b e r  o f  q u a s ip a r t ic lc s  th a t  a t te n u a te  th e  s o u n d  w a v e s  d ro p  o f  e x p o n e n tia l ly )  sh o w s  a  p o w e r  la w  d e p e n d e n c e  w h e re  /? =  1 ,2 , o r  3. F o r  a n o n -c o n v e n tio n a l B C S  su p e rc o n d u c to r, th e  e n e rg y  g a p  g o e s  to  z e ro  e i th e r  a t p o in ts  o r  a lo n g  lin e s  a lo n g  th e  F e rm i su rfa c e . T h e re  is th u s  a lw a y s  so m e  b ro k e n  C o o p e r  p a i r s ,  a n d  th e i r  n u m b e r  h a s  a  m u c h  w e a k e r  te m p e r a tu r e  d e p e n d e n c e  g iv in g  r ise  to  a  p o w e r  la w  te m p e ra tu re  d e p e n d e n c e  fo r  th e  a t te n u a tio n  a n d  th e  h e a t  c a p a c i ty .  T h e  v a lu e  o f  th e  e x p o n e n t  s h o u ld  te ll th e  d if f e re n c e  b e tw e e n  a p o in t n o d e  o r  a  lin e  n o d e . H o w e v e r  th e  m e a s u re m e n ts  m u s t th e n  b e  d o n e  at v e ry  lo w  te m p e ra tu re s ,  a n d  th e re  s e e m s  to  b e  a la rg e  v a r ia tio n  b e tw e e n  s a m p le s . S h iv a ra m  etal. [4] m e a s u re d  th e  a tte n u a tio n  o f  s h e a r  w a v e s  p ro p a g a t in g  in  th e  b a sa l p la n e , w ith  th e  .sound p o la r iz a t io n  v e c to r  p a ra l le l  to  a n d  p e rp e n d ic u la r  to  th e  c -a x is . H e  o b ta in e d  tw o  d i f f e r e n t  v a lu e s  f o r  n (I a n d  2 ) , th e r e b y  c o n c lu d in g  th a t th e  s y m m e try  w a s  th a t  o f  a  d-wave.In  s t ro n g  m a g n e t ic  f ie ld s , s o m e  o f  th e s e  c o m p o u n d s  (U P t^ , U A l2P d 3 , C e R u 2S i2 . etc,) s h o w  a  m e ta m a g n e t ic  b e h a v io r  in  w h ic h  th e  v e lo c ity  s h o w s  a  r e m a rk a b le  d ip  (s o f te n in g  o f  th e  e la s t ic  c o n s ta n ts )  [5 ] . In  U P t , ,  th is  is a b o u t  3 %  a t 1 .5K  a n d© 2 0 0 1  lA C S294 J Feller, D Dasgupta, D G Hinks, J B Ketterson and Bintal K Sarniah ig h e r  a l lo w e r  te m p e ra tu re s . T h e  m e ta m a g n e t ic  t r a n s it io n  is  a t  2 0 .3  T  fo r  U P t3 , 8 T  fo r  C e R u 2S i2 a n d  17 .5 T  fo r  U P d 2A l 3 . T h e s e  tr a n s it io n s  a rc  s tro n g ly  re la te d  to  th e  fa c t th a t th e  h e a v y  fe rm io n  s ta te  s i ts  c lo s e  to  a  m a g n e t ic  in s ta b ili ty . S tu d y  o f  th is  e f f e c t w ith  v a r io u s  p ro b e s  w o u ld  th ro w  lig h t o n  th e  n a tu re  o f  th e  h e a v y  fe rm io n  s ta le .2. Experimental methodsP re lim in a ry  m e a s u re m e n ts  w e re  d o n e  a t th e  H ig h  F ie ld  M a g n e t  L a b o ra to ry  a t th e  M a x  P la n c k  In s ti tu te  in  G re n o b le . R e c e n t m e a s u re m e n ts  w e re  d o n e  a t th e  N a tio n a l H ig h  M a g n e tic  F ie ld  L a b o ra to ry  (N H M F L )  a t T a lla h a s se e  u s in g  th e  3 2 m m  b o re  3 0 T  a n d  3 3 T  r e s i s t i v e  m a g n e t s  a n d  v a r io u s  c r y o g e n ic  in s e r t s  in c lu d in g  a  d i lu t io n  r e f r ig e r a to r  th a t  p e rm it te d  te m p e ra tu re  v a r ia tio n  b e tw e e n  4 0 m K  to  7 7 K . A  n e w  p u ls e d  h e te r o d y n e  u ltra so n ic  s p e c tro m e te r  w a s  b u ilt fo r  th e se  m e a s u re m e n ts , w h ic h  a llo w e d  s im u l ta n e o u s  m e a s u re m e n t a t v a r io u s  f r e q u e n c ie s  in  th e  s a m e  ru n . T h u s  th e re  is  n o  a m b ig u ity  in  th e  te m p e ra tu re  as  w a s  in  a n  e a r l ie r  m e a s u re m e n t  [6 J. T h e  s in g le  c ry s ta l  o f  U P t^  w a s  o f  h ig h  q u a li ty  (4  x  4  x  7 m m ) a s  e v id e n c e d  b y  a sh a rp  s u p e rc o n d u c tin g  tr a n s i t io n  (~  15 m K )  a n d  a  re la t iv e ly  h ig h  T .^ ( - 5 3 0  m K ). O v e rto n e  -  p o lish e d  L iN b O ^ tran sd u ce rs  w ere  a ff ix ed  w ith  e p o x y  to  th e  e n d  f a c e s  o f  th e  c r y s ta l .  V e lo c ity  a n d  a tte n u a tio n  c h a n g e s  w e re  m e a s u re d  u s in g  a c u s to m -b u i l t  p u ls e  s u p e r h e t e r o d y n e  p h a s e - s e n s i t i v e  s p e c t r o m e te r .  A  s p e c ia l  fe a tu re  w a s  th e  p o s s ib il i ty  o f  s im u l ta n e o u s ly  m e a s u r in g  v a r io u s  f r e q u e n c ie s , in  th e  s a m e  f ie ld  ru n . T h is  re m o v e d  a n y  a m b ig u ity  in  sm a ll  te m p e ra tu re  v a r ia tio n s  fro m  o n e  f ie ld  s w e e p  to  a n o th e r . R e la tiv e  velcK ity  an d  a tte n u a tio n  m e a s u re m e n ts  w e re  p e rfo rm e d  a t  f r e q u e n c ie s  3 0 ,8 6  a n d  140  M H z  w h ile  th e  m a g n e tic  f ie ld  w a s  sw e p t a t  a  co n .s tan t ra te . T h e  m a in  fe a tu re s  w e re  o b s e rv e d  w ith  s o u n d  p ro p a g a t in g  in  th e  b a s a l  p la n e , a n d  th e  f ie ld  a ls o  in  th e  b a sa l p la n e  ( U P t ,  is  a  h e x a g o n a l  c ry s ta l) .  T h e  e a s y  a x is  fo r  m a g n e t iz a t io n  is  in  th e  b a sa l p la n e .3* Experimental resultsO n e  o f  th e  e a r ly  s ig n s  th a t  u l t ra s o n ic s  is a  p o w e r fu l p ro b e  o f  th e  h e a v y  fe rm io n  s ta te  w a s  th e  o b s e r v a tio n  o f  a n  a s s o c ia te d  p e a k[7 ] in  th e  z e ro  f ie ld  lo n g i tu d in a l  so u n d  a tte n u a tio n  n e a r  12K . T h is  a t te n u a tio n  p e a k  c a n  b e  d e s c r ib e d  in  te rm s  o f  a  n a r ro w  re s o n a n c e  p e a k  w ith  a  w id th  o f  -  2  m e V  in  th e  d e n s i ty  o f  s ta te s  -  1 m e V  a b o v e  th e  fe rm i s u r fa c e ,  p re s u m a b ly  re s u lt in g  fro m  a  h y b r id iz a t io n  o f  th e  /  l e v e l s  ( o r  n a r r o w  /  b a n d s )  a n d  th e  c o n d u c tio n  b a n d . A  m a g n e t ic  f ie ld  o f  a b o u t  2 0 T , c o m p a r a b le  to  1 m e V  in  th e  e le c tro n ic  e n e rg y  s c a le , m a y  th e re fo re  p ro d u c e  s ig n if ic a n t  e f f e c ts  o n  th e  a t te n u a tio n  p e a k  by , e .g . s h if t in g  a n d  sp lit t in g  th e  p o s i t io n  o f  th e  F e rm i su r fa c e  re la tiv e  to  th e  re s o n a n t p e a k  in  th e  d e n s i ty  o f  s ta te s .The effect of a high magnetic field (up to 23T) on sound velocity and magnetic susceptibility for UPt^ , was studied by Kouroudis et a l [5] ; a soft longitudinal acoustic mode and oscillatory behaviors in some shear modes were observed. These observations have been interpreted as a metamagnetic transitionin  w h ic h  th e  sp e c im e n  a c q u ir e s  an  e n h a n c e d  m a g n e t ic  m om ent w ith in  a  sm a ll  f ie ld  in te rv a l  : a  s o f te n in g  o f  th e  la ttic e , the p h e n o m e n a  o b s e r v e d  in  a c o u s t ic  m e a s u re m e n ts ,  a cco m p an ies  th is  tr a n s it io n . C le a r ly  th is  is n o t a  tru e  p h a s e  tra n s it io n , in that th e  th e r m o d y n a m ic  p ro p e r t ie s  a re  n o t s in g u la r  (o n ly  rapidly v a ry in g ) ;  it w o u ld  b e  w o r th w h ile  to  c a r ry  o u t th e  m easu rc rn en is  to  th e  lo w e s t  p o s s ib le  t e m p e r a tu r e  a v a i l a b le ,  to  se e  if  the p h e n o m e n a  e v o lv e s  in to  a  tru e  pha.se tr a n s i t io n  a t T  =  0 . With th is  in  m in d  m e a s u re m e n ts  a re  b e in g  c a r r ie d  o u t  a t  th e  N ational H ig h  M a g n e t ic  F ie ld  L a b o ra to ry  in  T a lla h a s s e e  on  a  dilu tion  r e f r ig e r a to r  a n d  a  3 3 T  m a g n e t .In  an  e a r l ie r  s e t  o f  m e a s u re m e n ts  a t th e  H ig h  F ie ld  M ag n ti F a c ility  a t th e  M a x  P la n c k  In s ti tu te  in  G re n o b le , th e  v e lo c ity  and a tte n u a tio n  o f  so u n d  w e re  m e a s u re d  a t f ie ld s  u p  to  2 6 T  and te m p e ra tu re s  d o w n  to  2 K . T h e  ‘K o n d o '-  p e a k  se e n  e a r l ie r  in the so u n d  a tte n u a tio n  a t z e ro  f ie ld  [7 ] is  e n h a n c e d  as  th e  m agnciK  fie ld  is  in c re a s e d , a n d  s h if ts  to  lo w e r  te m p e ra tu re s .  H ow cvci a b o v e  17 T , th e  p e a k  w a s  n o t  o b s e r v e d .  T h e  a ttc n u a lio n  in c rea .sed  r a p id ly  a s  th e  te m p e ra tu re  is  lo w e re d  a n d  th e  field in c re a s e d  to  2 0  T. A l a b o u t  2 0  T  th e re  is  a  s tro n g  v e lo c ity  dip (e la s tic  s o f te n in g  d u e  to  th e  e n h a n c e d  m a g n e t iz a t io n )  at the m e ta m a g n e t ic  t r a n s i t io n  w ith  an  a s s o c ia te d  in c r e a s e  in the a t t e n u a t i o n .  I t  is  i n t e r e s t i n g  to  s p e c u l a t e  w h e th e r  the d is a p p e a ra n c e  o f  th e  p e a k  in  th e  te m p e ra tu re  d e p e n d e n c e  ol th e  a t te n u a tio n  a b o v e  17 T  a n d  th e  o n s e t o f  th e  m etam ag n c iR  p e a k  in  th e  f ie ld  d e p e n d e n c e  a t lo w  te m p e r a tu r e s  m ay In in te rp re te d  a s  a  m e r g in g  o f  th e  tw o  p h e n o m e n a .A t th e  m e ta m a g n e t ic  t r a n s i t io n  th e  lo n g i tu d in a l  sound v e lo c ity  (a  m e a s u re  o f  th e  e la s t ic  b u lk  m o d u lu s )  sh o w s  a dip (s o f te n in g )  w h ic h  b e c o m e s  la rg e r  as  th e  te m p e ra tu re  is low ered T h is  d ip  is a b o u t  1%  a t 2 K  a n d  b e c o m e s  m o re  th a n  57r ai te m p e ra tu re s  b e lo w  0 .5 K . T h e re  is  a lso  a  sm a ll v e lo c ity  dispcision ( th e  s o u n d  v e lo c ity  c h a n g e  a t  th e  tr a n s i t io n  is  m o re  fo r  sound w a v e s  w ith  a  lo w e r  f r e q u e n c y ) . F ig u re  1 s h o w s  th e  la rg e  changeF ig u r e  1 . V e lo c ity  m ea su rem en ts  at th e  m e ta m a g n e tic  transinon  at tem p era tu res 2 .4 K , I .6 K , 0 .5 5 0 K  and 0 .0 7 0 K . T h e  in se t  sh ow s the d isp ersion  for the m easurem ents at 2 .4K .Velocity measurements at the metamagnetic transition in UPt, 295jp the vel(x:ity a t th e  m e ta m a g n e tic  tran s itio n , th e  v e lo c ity  d ip  [Yccoming la rg e r a s  th e  te m p e ra tu re  is lo w ered . T h e  in se t sh o w s a small velocity d isp e rs io n , th e  m easu re m e n ts  b e in g  d o n e  at the  Tallahassee m a g n e t fac ility . In  th e  e a r l ie r  m e a su re m e n ts  a t Grenoble, the d if fe re n t fre q u e n c y  ru n s  w ere  d o n e  as sep ara te  runs, and it w as n o t c le a r  w h e th e r  th e  d isp e rs io n  seen  w as rea l, or due to slig h t v a r ia tio n s  in  th e  te m p e ra tu re  fo r th e  d iffe ren t runs With the n ew  sp e c tro m e te r, s im u lta n e o u s  m easu rem en ts  were done at th e  d if fe re n t f re q u e n c ie s , in th e  sam e  fie ld  sw eep , so that there is no  a m b ig u ity  in  th e  tem p era tu re . F ig u re  2  sho w s the attenuation o f  th e  u ltra so n ic  s ig n a l as  th e  f ie ld  is sw ep t. T h e  measurements at d if fe re n t fre q u e n c ie s  .scale as  the  sq u are  o f  the frequency. A tten u a tio n  m easu rem en ts  cou ld  be reliab ly  m ade only at the lo w er h a rm o n ic s .2510 15 20Applied Magnetic Field (T)25 30Fu •60 .At m uch lo w e r te m p e ra tu re  (b e lo w  IK ), th ere  seem s to  be structure in  th e  v e lo c ity  d ip  (a  sh o u ld e r on  th e  h ig h  fie ld  ’"‘dc) possibly in d ica tin g  a  seco n d  p h en o m en o n  (F ig u re  4). T h is  has now been seen  o n  tw o  d if fe re n t c ry s ta ls  o f  U P t, (g ro w n  *^nder d if fe re n t  c o n d i t io n s ) ,  a n d  th e r e  m a y  b e  a  s e c o n d  '^ ’^^ ceptibility p e a k  a t th e  h ig h e r  fie ld  s id e  o f  th e  m e tam ag n e tic  ^^^nsiiion. S u scep tib ility  m e a su re m e n ts  a t lo w er tem p era tu res  awaited. A t s til l lo w e r  te m p e ra tu re s , b e lo w  -  3 0 0  m K , hubnikov-de H aas-lik e  q u an tu m  o sc illa tio n s  b eco m e visib le  inthe  velocity . To a m u ch  le s se r  ex ten t, o sc illa to ry  b eh av io u r is a lso  o b se rv ed  in the a tten u a tio n . A  d e ta iled  an a ly s is  o f  the d a ta  is p re sen ted  in  a recen t p a p e r [8 ].ht;ure 2. Attenuation at the metamagnetic transition at T I.IK for Iriquencics 30, 84 and 140 MHz. The inset shows the temperature ilcpcndcticc of the attenuation measured at 140 MHzThe m agnetization  w as a lso  m easu red  w ith  a  v ibrating  sam ple magnetometer. T h e re  is  an  e n h a n c e d  m a g n e tiz a t io n  a t th e  niciamagnetic tra n s itio n , th e  fea tu re  b e co m in g  sh a rp e r as the  temperature is lo w e re d  (see  F ig u re  3). B y  d if fe ren tia tin g , th e  'susceptibility m ay  be o b ta in e d  : th is  sh o w s up  as a  p eak  a t the  transition that c o rre sp o n d s  to  th e  v e lo c ity  d ip , the  tw o  b e in g  related therm odynam ica lly  th ro u g h  th e  re la tion  where Ac is the c h a n g e  in  th e  b u lk  m o d u lu s , X th e  m ag n e tic  ''uscepiibility, B th e  m a g n e t ic  f ie ld  an d  F th e  m a g n e tic  Oruenisen p aram eter. A  fit to  th e  d a ta  ag ree s  w ith  a value  o fFigure 3. Magnetization measurements (upper curve) on a sample of UPt, with a vibrating sample magnetometer The susceptibility (lower curve) IS obtained by differentiatingiFigure 4. Velocity measurements at the metamagnetic transition at very low temperatures A second dip is visible at lower temperatutes.4. ConclusionU ltraso n ics  h as been  a p o w erfu l p ro b e  fo r th e  s tu d y  o f  p h ase  tr a n s i t io n s ; b o th  su p e rco n d u c tin g  an d  m ag n e tic . T h e  ve lo c ity296 J Feller, D Dasgupta, D G Hinks, J B Ketterson and Bimal K Sarmawhich is a measure of the elastic constants show remarkable features when one goes through either types of phase transition. Most of the striking features were seen with longitudinal sound (the elastic constant involved is the bulk modulus). In the metamagnetic transition, the velocity data agrees with the susceptibility measurements. The added advantage is the much higher sensitivity and the frequency dependence (dispersion). For pure samples and at low temperatures, oscillations in the velocity show that the metamagnetic instability is close to the Fermi surface, and mapping of the Fermi surface may be possible.AcknowiedgnieiitWc thank the staff at NHMFL Tallahassee for their help during the experiment. This work was supported by the National Science Foundation (NSF Grant D M R -9704020 and DMR-9971123) and NH M R (NSF grant DMR-9527035).References[ t ] B K Sarma, M Levy, S Adcnwalla and J B Ketterson inAcoustics, Vol. XX (ed) M Levy (New York : Academic) p inn(1992)[2] S W Lin Ph. D. Thesis (University of Wisconsin-Milwaukcr(1993)[3] S Adenwalla, S W Lin, Q Z Ran, Z Zhao, J B Kettetson, J a .Sank L Taillefer, D G Hinks, M Levy and B K Sarma Phys Rev leu 2298 (1990) :  G Bruls, D Weber, B Wolf, P Thalmeicr, B l .u H „  A deVisscr and A A Mcnovsky Phys. Rev. Lett. W 2294 ( l<)gii[4J B S Shivaram, Y H Jeong, T P Rosenbaum and D G Hinki Pin, Rev Uil. 56 1078 (1986)(5) 1 Kouroudis, D Weber, M Yoshizawa, B Luthi, L Pucch, P tijj,, J Flouquet, G Bails, U Welp, J J M Franse, A Menovsky, E Huchoi and J HufnagI Phys. Rev Utt. 58 820 (1987)(61 S W Lin, I Kouroudis, AGM Jansen, P Wyder, B Luthi, D Ci Him., J B Ketterson, M Levy and B K Sarma Physwa B 223 & 224(1996)[7] V Muller. I) Maurer, K de Groot, E Bucher and H H Bomiiiel Phu Rev Utt. 56 248 (1986)[8] JR Feller, D Dasgupta, D G Hinks, J B Ketterson and B K .Sainu (preprint)

Velocity Measurements at the Metamagnetic Transition in UPt3

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Velocity Measurements at the Metamagnetic Transition in UPt3

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