- Email: [email protected]
Neutron scattering study of the soft mode in the strongly anisotropic antiferromagnet RbFeCl3
Sohd State Commumcanons. Vol 38, pp 241 - 2 4 3 Pergamon Press Lid 1981 Printed m Great Bntaan
0 0 3 8 - 1 0 9 8 / 8 1 . 0 3 0 2 4 1 - 0 3 $02 00,:0
NEUTRON SCATTERING STUD~ OF THE SOFT MODE IN THE STRONGLh ,-LNISOTROPIC k N T I F E R R O M A G N E T RbFeCl3 H ~ osinzawa* Institute tot Sohd State Physics. The Um~erstt~ o ( T o k ) o . Roppong~. Mmato-ku, Tokyo 106. Japan and J D Axe and G Sinrane Brookha~en Nattonal Laborator', Upton, NY 119"3, U S 4. ( R e c e ~ ' e d 27 O c t o b e r 1980 by Y T o v o z a ' w a )
We report the softening o f the magnetic excitations in a strongly amso. trop,c S = 1 antlferromagnet RbFeCI~ As T is lowered towards T v , the softening occurs in a small region around q. = 0 and the gap energy vanishes according to the power law A ~ (T - T,,,)" We mterpret this effect using Lines" correlated-effective-field theor.,, applied to a stoner ground state ~.~stem
AN INTERESTING 4SPECT of spin d~rnamtcs m a smglet-ground-state s~stem is that, ~*hereas most theories [ l , 2] predict the softening of the magnetic excltons at the ordering temperature, this phenomenon has not been observed expermlentally ~o tar [3] In theearb, s e v e n t l e ~ . t h e s m g l e t - t n p l e t s ) s t e m Pr3TI [a]v, as studied intensively by neutron scattering but the exclton mode frequency showed little change around T c and it was later shov, n that an intra-trlplet mode is the appropr,ate soft mode tor this system [5 6] The latest attempt along tins hne ,s the neutron scattermgstud', o n P r S b [7] At low temperatures under high pressure, it behaves like a s m N e t - s m g l e t system, but although the tendency toward softening was found, there remains the finite gap even at Tv In tins letter we report the clear observation o f the complete softemng of the magneuc exmtatton around the ordenng temperature T,,, of a smglet-ground-state s~,stem Since, from the above mentioned results on Pr3T1. at appears that s m g l e t - t n p l e t systems show mtra-tnplet softening Isee also [8] }, ~ e thought it v, orth~,hde to stud,, instead a s t a g i e r - d o u b l e t system, ,alth expectation that different physics would emerge Consider the one-dimensional ferromagnet with the eftectwe spin S = I descr,bed b.~ the follow,ng Hamilton,an. 7C = V - - Dgs",): - ~v ~'"- J I { S , * .5,* ,. t + S , " S , Y . I) t
1
+ 2J,S~S~,. ,~, = "re + 7"fx~ + ~ z : ,
I1)
• Guest scientist at Brookhaven Nat,onal Laborator3,
241
~here d- and J~ denote amsotropzc exchangea perpendtcular or parallel to the chain direction respecuveb,, and Yz > d , Tile single-ion anlsotrop,, D > 0 represents effectively the crystal-field level spl,ttmg between the ground state 10~ and the excited states I+- I,~ Wltinn the scope of a mean-field theoD, the ratio d -- D , J d,stmgmshes three different magnetic types of behavior for the Hamlltoman equation I [ ) fl) The planar f e r r o m a ~ e t region d _< 1 the system behaves as a conventional planar terromagnet (10 The s m g l e t - d o u b l e t system regaon d >> 1 the effect of the exchange Js so small compared wzth D that the s.,,stem remains p a r a m a ~ e n c e,,en if T -+ 0 K The excitations are characterized as magnetic eXCltOns, t e the transit,on between the smglet and doublet levels (m) The intermediate regmn d Z [ the system also behaves as the ~mglet-doublet system tot T < D,k 8 ~hereas It has m a ~ e t l c long range order below TN In thereto perature re m,)n Tv < T < D ' / , 8 , the magnetic excitations are exclton-ltke, and ~t l~ materials ot tlus class which can be expected to show the softening near T,v Thus a spm 1 planar terromagnet wath strong s,ngle-ton amsotropy would be expected to show stron~v temperature dependent magnet,c excztattons One of the most suitable materials for this purpose is RbFeCI3 wh,ch Is known as a quast-one-dtmensmnal planar ferromagnet w l t h S = 1 [9 I0], whose onedtmens,onahty' IJ'l,'Jj. is estimated to be ~ 0 1, winle D 1~ I 0 meV) is sufficiently larger than J l ( ~ 0 4 meV) [I0. I1] It has been reported earher that RbFeCl3 shows an annferromagnetlc order below T,, = 2 55 K [9] Thus RbFeCI3 belongs to the region l m l In the prevmus paper [1 I] extendmg the Hamdton,an {1) to three dimensions we calculated the temperature
Vol 38. No 3
N E U T R O N S C ~ , T T E R I N G STUD~( OF THE S O F T MODE IN RbFeClx
_4_
RDFeI"
~
RbFeCI
200,
3 r
~0 10 I ~ 0 " " 0
L lag (00~) A E~ =13
O=(1
3
3Oc.
-01)
13~.i , , i ,
t
,
1
l
,
i
I
;,
,
i
I,
"rr,,~'v
t6Or" I
C
3~
C TN = Z 55~
~2OP c. E -4
/" q,
t
z60 O ,o
r,, :¢7" i
'\
]lO~
'r
os
"\ N'~i)~,
~ .~
5o
e l , ,
~oo
REDUCED IEMPEaATuRE ¢
.
0% ENERGY TRANSFER tm~V
Fig I C o n s t a n t Q s c ~ r s temperatures
forq~. = 0
)
ol L +
!
~
/
/ /
/
x
02
I
•
15 p
•
6~
a •
0
005
qc
01
O
,
5
IO 15 I EULPERATbRE r,~
20
Fig 3 Resolution-corrected integrated ,ntenslt~: for qc = 0 1 The inset shows the l o g - l o g plot o f the gap energ) at the zone center vs the reduced t e m p e r a t u r e
1 at t h r e e d t f l e r e n t
RbFeCI 3
'38
o
{ reducea
.5~ 35~
015 an,l]
Fig 2 Dispersion relations along ( 1. O, - - qe) hne d e p e n d e n c e of the m a g n e t l c - e x c t t o n m o d e with use of the correlated.eftecttve-field ( C E F ) theory de~eloped by Line> [12] Tins calculanon pred,cted that the wave vector ot the magnetic reflect,on (IO0)M is the s o t t e n m g point and that the e x c i t a t i o n gap will vanish at T = T,,, The RbFeCla sln~e cry. stal of an a p p r o x i m a t e size 10 × 15 ~ 17 mm ~ was grown by Brtdgman techniques, and its lattice constants ate a = 6 993,& and c = 5 954 (he,~agonal Pos/rnrnc ) The crystal ~as oriented >o as to w e the magnetic (hOl) scattermg plane and was m o u n t e d m the p u m p e d ~.r~ostat in winch the
temperature Ls easily controlled from I 2 to 20 K w~ttun the accurac.~ of 0 0 l degree All the inelastic m e a s u r e m e n t s were carried out on mple-axls spectrometers at the Brookhaven lugh-flux beam reactor Pyrolytic graphite cry stals were uaed as m o n o c h r o m a t e r , analyzer and tilter For large energy transfer the s p e c t r o m e t e r was operated in the constant O m o d e with fixed incident or analyzer e n e r ~ of 13 7 meV and various collm~at,ona, wlule for the small energy, transfer less than 0 S meV It was o p e r a t e d with 5 0 meV E, or E:. 2 0 - 4 0 - 4 0 - 4 . 0 c o l h m a t , o n s and Be filter As pred,cted b~, the CEF t h e o o , a m a r k e d temperature change was observed in a small region o f reciprocal ~pace around I 100),~t In Fig 1, we have plotted the typical results of constant O scana at Q = ( I. O. - 0 1 ) t o r tkree different temperatures %Veil-defined m a ~ e u c e x c l t a u o n s can be observed in the p a r a m a ~ e u c phaae The d,sperston relations observed along ( 1,0, - 4~ ) line at vanous t e m p e r a t u r e , a r e s h o ~ , n i n F l g 2 In ,.ontrast to the caae of PrSb [71 one can aee the clear s o t t e n m g the gap energy at the zone center seems to vanish as T - F,,,, = 2 55 K F,gure 3 sho,,,,s the resolution-corrected intensity tot qe =- 0 1, while m the inset the l o g - l o g plot of the gap energy ~ ~s the reduced temperature e - T -- T N g]ve~ a p o w e r l a w ..%le)-= 1 17e S w i t h 8 = 0 7 0 - 0 0 5 At the crmcal temperature T v . the m t e n s l D exJ'ubtts a peak and the gap vamshes The gap energy can be considered as a sort o f ( d,sJorder parameter which characterizes the paramagnetlc pha~e These results can be interpreted as features of a two.level s,,stem we ,nterpret well-defined e',.cttat|ons in the p a r a m a g n e n c pha>e a> a rnagneuc-e\c~ton m o d e b e t w e e n the ground s m g l e t a n d the exclted doublet At lower temperature~ the s c a t t e n n g intenslt.,, increases since the transluon
Vol 38, No 3
NEUTRON SC-~TTERING STUDY OF THE SOFT MODE IN RbFeClx
probabthty ts proporttonal to the populanon difference between two levels This temperature dependence ~s different than would be e,:pected from spin waves propagating m quasl-one-dtmensmnal magnets above T,v [ 11 ] The peak shaft corresponds to the temperature dependence of the single-,on level scheme, m other words, to that of the etgentuncttons and etgenlevels winch describe wave vector dependent propagating exmtattons [ 131 A hmtted number of scans were made to observe the temperature dependence of the whole dispersion relanon The excltatton e n e r ~ around the zone boundary, at T = 15 K ex.l'ublts a shght decrease. winch Js also consistent with the rnagnet~c e,ccKton ptcture [12] Recently lanes [13] has calculated exactlF the temperature dependence of the smgle-~on e,cc~tat,on m the model Hamtltoman J(" = J('c + X'~z The calculatton shows that the de~,elopment of amsotropl~. spin correlattons modifies an effect,re.field bas~s and causes the temperature dependence of the propagating mode He has predicted the presence of such tempera. ture dependence m all an,sotroptc m a ~ e t s The occurrence of the sottenmg m RbFeCI3 supports the correctness of has predict,on Finally, ,ae discuss an addmonal exastence--condmon for softening M t h o u ~ , accord,ng to lanes [13]. the effect should be present m antfferromagnets with ~trong.lF uma',dal an~otrop.,,, the laing anttterromagnets with half-integer spins seem not to sho~, such softemng For example. CoF~. [14] ~s a t~,p~cal [smg annferromagnet wtth S = } , a n d ~ts magnetic exmtattons have been observed above and belov, T,v, but no smular anotnal3, was reported on the temperature dependence throughT.vlseeF~g 10of[141} Thusempmcallytt appears that the sotten,ng occurs only m the strongb an~sotroptc planar magnet with integer spm In conclusmn, we have found that RbFeCI3 has the well-defined magnettc exc~tattons m the paramagnettc phase, and ~ts excitation spectrum reveals the clear softening around the zone center ,.,,'hen T "* T,v The gap enerD' at q = 0 vanishes accord,rig to the power lay, w~th the cnttcal exponent 8 = 0 70 ,- 0 05 The s m g l e t - d o u b l e t model ga~,es the l n t u , m e phystcal
243
picture for this behavtour, v, hde Lines CEF theory Js vet) useful to treat deta.tled temperature dependences of the magnetic e',.cltatlons -~fter tlus Letter was written, v,e learned that Grand et al bneflv reported the obseo, atmn of the softening m RbFeCI3 [15]
Acknowledgements - We gratefull,, acknot,,'ledge useful discussions wtth K Hlrakawa and ~,1 Sterner VCe are thankful to K Ubukosin for preparing the samples rtus research was supported by the Dt,,lslon of Bas,c Energ) Sctence~, U S Department of Energ',, under Contract No DE-ACO2-76chO0016
REFERENCES I 2 3 4
B Grover, Ph3s. Rev 140, 4.1944(1965) Y W a n g & B R Cooper. Phvs Re~' 172,539 1196S) For re~,mw's see R J Blrgeneau, 4IP Conf Proc 10, 1664 (1973) W J L Bu,,ers, 4lPCon/ Proc 24, 27 11975J R J Birgeneau. J Als-Ntelsen & E Bucher Ph.vs Rev Lett 27, 153011971J,Ph),s Rev B 6 , 2 " 2 4
(197')
5 t)
8 9 10 II
12 13 1..115
S R P S m l t h , J Phvs C5 L15711~'72) .1 ,.Ms-Nwlsen, J K Klems, ~a,, J L Bu~,ers ,.v,. R J Birgeneau J Ph),s CIO 26"3 I 19 "7'7) D B McWhan C Vetoer R '~oun_~blood & G Sinrane, P f l ~ Rev B20,4o12 {lt-}7 O) M E L m e s , J Ptlw C7, L287 ( l'-)741 G R Da,,idson, ~,l E,bschutz, D E Co~ & V J Mmklewlcz. 4IP Con] Proc 5 , 4 3 0 ( 19 .7'l ) M E l a n e s & M Eibschutz Ph)~Re~' B I I 45S3 (1975) RbFeCI3 is m an'~ e',ent a p o o r " quasl-ld materml See H Y o s i n z a ~ a . W Kozukue & K H l r a k a w a , J Ph)'s. Soc Japan 49. 144 ( 10"30~ ME lanes,Ph)'s Rer B I I , 113411975) M E Lmes, Phvs Rev Lets 42 533 (19"7'9) P Mattel R-~ Cowie3, & R W H Ste,,enson, Can J Ph)'s 46, 1355119o'31 D P Grand, P R Krlschna, B Hermlon& C Escnbe, .knne',, to The -~nnual Report ILL p 104 119791
0 0 3 8 - 1 0 9 8 / 8 1 . 0 3 0 2 4 1 - 0 3 $02 00,:0
NEUTRON SCATTERING STUD~ OF THE SOFT MODE IN THE STRONGLh ,-LNISOTROPIC k N T I F E R R O M A G N E T RbFeCl3 H ~ osinzawa* Institute tot Sohd State Physics. The Um~erstt~ o ( T o k ) o . Roppong~. Mmato-ku, Tokyo 106. Japan and J D Axe and G Sinrane Brookha~en Nattonal Laborator', Upton, NY 119"3, U S 4. ( R e c e ~ ' e d 27 O c t o b e r 1980 by Y T o v o z a ' w a )
We report the softening o f the magnetic excitations in a strongly amso. trop,c S = 1 antlferromagnet RbFeCI~ As T is lowered towards T v , the softening occurs in a small region around q. = 0 and the gap energy vanishes according to the power law A ~ (T - T,,,)" We mterpret this effect using Lines" correlated-effective-field theor.,, applied to a stoner ground state ~.~stem
AN INTERESTING 4SPECT of spin d~rnamtcs m a smglet-ground-state s~stem is that, ~*hereas most theories [ l , 2] predict the softening of the magnetic excltons at the ordering temperature, this phenomenon has not been observed expermlentally ~o tar [3] In theearb, s e v e n t l e ~ . t h e s m g l e t - t n p l e t s ) s t e m Pr3TI [a]v, as studied intensively by neutron scattering but the exclton mode frequency showed little change around T c and it was later shov, n that an intra-trlplet mode is the appropr,ate soft mode tor this system [5 6] The latest attempt along tins hne ,s the neutron scattermgstud', o n P r S b [7] At low temperatures under high pressure, it behaves like a s m N e t - s m g l e t system, but although the tendency toward softening was found, there remains the finite gap even at Tv In tins letter we report the clear observation o f the complete softemng of the magneuc exmtatton around the ordenng temperature T,,, of a smglet-ground-state s~,stem Since, from the above mentioned results on Pr3T1. at appears that s m g l e t - t n p l e t systems show mtra-tnplet softening Isee also [8] }, ~ e thought it v, orth~,hde to stud,, instead a s t a g i e r - d o u b l e t system, ,alth expectation that different physics would emerge Consider the one-dimensional ferromagnet with the eftectwe spin S = I descr,bed b.~ the follow,ng Hamilton,an. 7C = V - - Dgs",): - ~v ~'"- J I { S , * .5,* ,. t + S , " S , Y . I) t
1
+ 2J,S~S~,. ,~, = "re + 7"fx~ + ~ z : ,
I1)
• Guest scientist at Brookhaven Nat,onal Laborator3,
241
~here d- and J~ denote amsotropzc exchangea perpendtcular or parallel to the chain direction respecuveb,, and Yz > d , Tile single-ion anlsotrop,, D > 0 represents effectively the crystal-field level spl,ttmg between the ground state 10~ and the excited states I+- I,~ Wltinn the scope of a mean-field theoD, the ratio d -- D , J d,stmgmshes three different magnetic types of behavior for the Hamlltoman equation I [ ) fl) The planar f e r r o m a ~ e t region d _< 1 the system behaves as a conventional planar terromagnet (10 The s m g l e t - d o u b l e t system regaon d >> 1 the effect of the exchange Js so small compared wzth D that the s.,,stem remains p a r a m a ~ e n c e,,en if T -+ 0 K The excitations are characterized as magnetic eXCltOns, t e the transit,on between the smglet and doublet levels (m) The intermediate regmn d Z [ the system also behaves as the ~mglet-doublet system tot T < D,k 8 ~hereas It has m a ~ e t l c long range order below TN In thereto perature re m,)n Tv < T < D ' / , 8 , the magnetic excitations are exclton-ltke, and ~t l~ materials ot tlus class which can be expected to show the softening near T,v Thus a spm 1 planar terromagnet wath strong s,ngle-ton amsotropy would be expected to show stron~v temperature dependent magnet,c excztattons One of the most suitable materials for this purpose is RbFeCI3 wh,ch Is known as a quast-one-dtmensmnal planar ferromagnet w l t h S = 1 [9 I0], whose onedtmens,onahty' IJ'l,'Jj. is estimated to be ~ 0 1, winle D 1~ I 0 meV) is sufficiently larger than J l ( ~ 0 4 meV) [I0. I1] It has been reported earher that RbFeCl3 shows an annferromagnetlc order below T,, = 2 55 K [9] Thus RbFeCI3 belongs to the region l m l In the prevmus paper [1 I] extendmg the Hamdton,an {1) to three dimensions we calculated the temperature
Vol 38. No 3
N E U T R O N S C ~ , T T E R I N G STUD~( OF THE S O F T MODE IN RbFeClx
_4_
RDFeI"
~
RbFeCI
200,
3 r
~0 10 I ~ 0 " " 0
L lag (00~) A E~ =13
O=(1
3
3Oc.
-01)
13~.i , , i ,
t
,
1
l
,
i
I
;,
,
i
I,
"rr,,~'v
t6Or" I
C
3~
C TN = Z 55~
~2OP c. E -4
/" q,
t
z60 O ,o
r,, :¢7" i
'\
]lO~
'r
os
"\ N'~i)~,
~ .~
5o
e l , ,
~oo
REDUCED IEMPEaATuRE ¢
.
0% ENERGY TRANSFER tm~V
Fig I C o n s t a n t Q s c ~ r s temperatures
forq~. = 0
)
ol L +
!
~
/
/ /
/
x
02
I
•
15 p
•
6~
a •
0
005
qc
01
O
,
5
IO 15 I EULPERATbRE r,~
20
Fig 3 Resolution-corrected integrated ,ntenslt~: for qc = 0 1 The inset shows the l o g - l o g plot o f the gap energ) at the zone center vs the reduced t e m p e r a t u r e
1 at t h r e e d t f l e r e n t
RbFeCI 3
'38
o
{ reducea
.5~ 35~
015 an,l]
Fig 2 Dispersion relations along ( 1. O, - - qe) hne d e p e n d e n c e of the m a g n e t l c - e x c t t o n m o d e with use of the correlated.eftecttve-field ( C E F ) theory de~eloped by Line> [12] Tins calculanon pred,cted that the wave vector ot the magnetic reflect,on (IO0)M is the s o t t e n m g point and that the e x c i t a t i o n gap will vanish at T = T,,, The RbFeCla sln~e cry. stal of an a p p r o x i m a t e size 10 × 15 ~ 17 mm ~ was grown by Brtdgman techniques, and its lattice constants ate a = 6 993,& and c = 5 954 (he,~agonal Pos/rnrnc ) The crystal ~as oriented >o as to w e the magnetic (hOl) scattermg plane and was m o u n t e d m the p u m p e d ~.r~ostat in winch the
temperature Ls easily controlled from I 2 to 20 K w~ttun the accurac.~ of 0 0 l degree All the inelastic m e a s u r e m e n t s were carried out on mple-axls spectrometers at the Brookhaven lugh-flux beam reactor Pyrolytic graphite cry stals were uaed as m o n o c h r o m a t e r , analyzer and tilter For large energy transfer the s p e c t r o m e t e r was operated in the constant O m o d e with fixed incident or analyzer e n e r ~ of 13 7 meV and various collm~at,ona, wlule for the small energy, transfer less than 0 S meV It was o p e r a t e d with 5 0 meV E, or E:. 2 0 - 4 0 - 4 0 - 4 . 0 c o l h m a t , o n s and Be filter As pred,cted b~, the CEF t h e o o , a m a r k e d temperature change was observed in a small region o f reciprocal ~pace around I 100),~t In Fig 1, we have plotted the typical results of constant O scana at Q = ( I. O. - 0 1 ) t o r tkree different temperatures %Veil-defined m a ~ e u c e x c l t a u o n s can be observed in the p a r a m a ~ e u c phaae The d,sperston relations observed along ( 1,0, - 4~ ) line at vanous t e m p e r a t u r e , a r e s h o ~ , n i n F l g 2 In ,.ontrast to the caae of PrSb [71 one can aee the clear s o t t e n m g the gap energy at the zone center seems to vanish as T - F,,,, = 2 55 K F,gure 3 sho,,,,s the resolution-corrected intensity tot qe =- 0 1, while m the inset the l o g - l o g plot of the gap energy ~ ~s the reduced temperature e - T -- T N g]ve~ a p o w e r l a w ..%le)-= 1 17e S w i t h 8 = 0 7 0 - 0 0 5 At the crmcal temperature T v . the m t e n s l D exJ'ubtts a peak and the gap vamshes The gap energy can be considered as a sort o f ( d,sJorder parameter which characterizes the paramagnetlc pha~e These results can be interpreted as features of a two.level s,,stem we ,nterpret well-defined e',.cttat|ons in the p a r a m a g n e n c pha>e a> a rnagneuc-e\c~ton m o d e b e t w e e n the ground s m g l e t a n d the exclted doublet At lower temperature~ the s c a t t e n n g intenslt.,, increases since the transluon
Vol 38, No 3
NEUTRON SC-~TTERING STUDY OF THE SOFT MODE IN RbFeClx
probabthty ts proporttonal to the populanon difference between two levels This temperature dependence ~s different than would be e,:pected from spin waves propagating m quasl-one-dtmensmnal magnets above T,v [ 11 ] The peak shaft corresponds to the temperature dependence of the single-,on level scheme, m other words, to that of the etgentuncttons and etgenlevels winch describe wave vector dependent propagating exmtattons [ 131 A hmtted number of scans were made to observe the temperature dependence of the whole dispersion relanon The excltatton e n e r ~ around the zone boundary, at T = 15 K ex.l'ublts a shght decrease. winch Js also consistent with the rnagnet~c e,ccKton ptcture [12] Recently lanes [13] has calculated exactlF the temperature dependence of the smgle-~on e,cc~tat,on m the model Hamtltoman J(" = J('c + X'~z The calculatton shows that the de~,elopment of amsotropl~. spin correlattons modifies an effect,re.field bas~s and causes the temperature dependence of the propagating mode He has predicted the presence of such tempera. ture dependence m all an,sotroptc m a ~ e t s The occurrence of the sottenmg m RbFeCI3 supports the correctness of has predict,on Finally, ,ae discuss an addmonal exastence--condmon for softening M t h o u ~ , accord,ng to lanes [13]. the effect should be present m antfferromagnets with ~trong.lF uma',dal an~otrop.,,, the laing anttterromagnets with half-integer spins seem not to sho~, such softemng For example. CoF~. [14] ~s a t~,p~cal [smg annferromagnet wtth S = } , a n d ~ts magnetic exmtattons have been observed above and belov, T,v, but no smular anotnal3, was reported on the temperature dependence throughT.vlseeF~g 10of[141} Thusempmcallytt appears that the sotten,ng occurs only m the strongb an~sotroptc planar magnet with integer spm In conclusmn, we have found that RbFeCI3 has the well-defined magnettc exc~tattons m the paramagnettc phase, and ~ts excitation spectrum reveals the clear softening around the zone center ,.,,'hen T "* T,v The gap enerD' at q = 0 vanishes accord,rig to the power lay, w~th the cnttcal exponent 8 = 0 70 ,- 0 05 The s m g l e t - d o u b l e t model ga~,es the l n t u , m e phystcal
243
picture for this behavtour, v, hde Lines CEF theory Js vet) useful to treat deta.tled temperature dependences of the magnetic e',.cltatlons -~fter tlus Letter was written, v,e learned that Grand et al bneflv reported the obseo, atmn of the softening m RbFeCI3 [15]
Acknowledgements - We gratefull,, acknot,,'ledge useful discussions wtth K Hlrakawa and ~,1 Sterner VCe are thankful to K Ubukosin for preparing the samples rtus research was supported by the Dt,,lslon of Bas,c Energ) Sctence~, U S Department of Energ',, under Contract No DE-ACO2-76chO0016
REFERENCES I 2 3 4
B Grover, Ph3s. Rev 140, 4.1944(1965) Y W a n g & B R Cooper. Phvs Re~' 172,539 1196S) For re~,mw's see R J Blrgeneau, 4IP Conf Proc 10, 1664 (1973) W J L Bu,,ers, 4lPCon/ Proc 24, 27 11975J R J Birgeneau. J Als-Ntelsen & E Bucher Ph.vs Rev Lett 27, 153011971J,Ph),s Rev B 6 , 2 " 2 4
(197')
5 t)
8 9 10 II
12 13 1..115
S R P S m l t h , J Phvs C5 L15711~'72) .1 ,.Ms-Nwlsen, J K Klems, ~a,, J L Bu~,ers ,.v,. R J Birgeneau J Ph),s CIO 26"3 I 19 "7'7) D B McWhan C Vetoer R '~oun_~blood & G Sinrane, P f l ~ Rev B20,4o12 {lt-}7 O) M E L m e s , J Ptlw C7, L287 ( l'-)741 G R Da,,idson, ~,l E,bschutz, D E Co~ & V J Mmklewlcz. 4IP Con] Proc 5 , 4 3 0 ( 19 .7'l ) M E l a n e s & M Eibschutz Ph)~Re~' B I I 45S3 (1975) RbFeCI3 is m an'~ e',ent a p o o r " quasl-ld materml See H Y o s i n z a ~ a . W Kozukue & K H l r a k a w a , J Ph)'s. Soc Japan 49. 144 ( 10"30~ ME lanes,Ph)'s Rer B I I , 113411975) M E Lmes, Phvs Rev Lets 42 533 (19"7'9) P Mattel R-~ Cowie3, & R W H Ste,,enson, Can J Ph)'s 46, 1355119o'31 D P Grand, P R Krlschna, B Hermlon& C Escnbe, .knne',, to The -~nnual Report ILL p 104 119791