Anomalous crystal field effects in the specific heat of Ce-heavy fermion compounds

Journal of MagneUsm and Magnetic Matermls 63 & 64 (1987) 101-103 North-Holland, Amsterdam

101

A N O M A L O U S C R Y S T A L F I E L D E F F E C T S IN T H E S P E C I F I C H E A T O F C e - - H E A V Y FERMION C O M P O U N D S J G S E R E N I *+, G N I E V A * and J P K A P P L E R * * * Centro At6mtco Bardoche, 8400 Bardoche, Argentina ** L M S E S U A 306, lnsntut de Physique 67084 Strasbourg, France

Specific heat anomahes due to the F7---, Fx thermal promotion were measured for CePd~Bo 6 and CePd3Slo ~ For the heavy-fermlon compound CePd~B. ~ one observes a quasl-hnear C(T) dependence, instead of the expected exponential one This behavmor ~s discussed m terms of the &fferent hybndlzatmn of the conduction electron states with the ground (I 7) and excited (1"~) crystal field levels

1. Introduction T h e n u m b e r of reported Ce and U heavy fermlon (HF) c o m p o u n d s has Increased very rapidly during the last years T h e y usually show a low t e m p e r a t u r e specific heat (C) anomaly, which m the case of Ce has a m a x i m u m in C vs T at temperatures between 1 and 4 K with a characteristic high C / T ratio of 0 3 J/mol K 2 ~< C / T ~< 3 5 J/mol K 2 as T---~ 0 K [1,2] At higher temperature, where the full expected entropy of S = R In 2 is r e c o v e r e d by the anomaly, a high value of the C~ T ratio is systematically observed in a n u m b e r of C e - H F c o m p o u n d s (table 1) They show a small value dispersion (120 mJ/moi K 2 < C/T < 250 mJ/mol K 2) c o m pared with those of the T--->0 K region T h e most striking feature is that the C [ T ratto behaves quasl-mdependent of temperature, within a certain t e m p e r a t u r e range m all cases, excepted for CeCu2Sl2 Facing the quasl-hnear C vs T dependence, In this t e m p e r a t u r e range, two questmns arise 1) Is it due to a stmflar m e c h a m s m as the T--~ 0 K limit (Fermi hqmd, with very high electron e l I e c t w e mass)9 or 2) IS tt connected with the expected Schottky anomaly of the F7 ~ F8 thermal promotion9 We have measured the specific heat of CePdaBo6 which shows the largest measured C/T ratio at T ~ O (C/T~>33J/molK 2) T h e + Alexander von Humboldt Fellow

Table 1 C / T ratio m mJ/mol K 2 of C e - H F compounds and the range of hneanty for the C vs T plot Compounds

C/T

Range (K)

Ref

CeAI2 CeAI3 Ce3AI11 CeCu6 CePb3 Celn 3 CelnAu2 Ce0 tYo 9lnAu2 CePd3B Ceo lLao 9Pd3B CePd3Bo 6

130 250 120 x 3 230 225 140 130 120/10 160 160/10 170

10--15 8-12 12-14 12-17 8-12 11-13 7-12 5-12 7-12 5-13 6-10

[3] [3,4] [3] [1] [5] [3] [6] [6] [2] [2] [2]

system CePd3Slo3 was also measured as a reference c o m p o u n d , because it orders m a g netmally at TN = 2 44 K without any evidence of K o n d o or H F behaviour and with an entropy gain of AS = 0 94 R In 2 within the transition In the case of the cubic c o m p o u n d CeAI2 an anomalous Schottky specific heat was already observed, which does fit neither a F7 ~ ['8 nor a F8 ~ F7 thermal p r o m o t i o n [7]

2. Experimental and results In fig 1 we show the specific heat measurements for both CePd3Bo 6 and CePd3Slo 3 up to 4 0 K m a C / T vs T 2 plot T h e latUce contrtbutlon was evaluated as the D e b y e function for

0304-8853/87/$03 50 O Elsevier Science Pubhshers B V (North-Holland Physics Pubhshmg Dwlslon)

J G Serem et al / Crystal field effects m Ce-heavy fermzon compounds

102

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I

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i

i

I

i

I

t

I

t

I

Ce Pd3Sto.~ ....

0.6

•"

CePd3B06

t9 O

1-

r.S(_)

O2

4

L

°o

°

2I

I

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1

f

l ooo T a [K2]

Fig 1 Phgh temperature C / T vs T dependence of CePd~B06 and CePd~Sl(>~ The reset shows the low temperature C vs T anomaly of CePd3Bo 6 and the magnetm order of CePd3Slo 3, after lattice subtraction

0o = 2 4 1 K , which is the D e b y e t e m p e r a t u r e extracted from the LaPd3B m e a s u r e m e n t [2] T h e high t e m p e r a t u r e C/T ratio (at T ~ 10 K) was obtained from a linear extrapolation to T-*0K, using the C/T=3"+/3 T2 function, where /3 accounts for phonons but the 3' term does not necessarily represent a density of states as In the case of free electrons T h e extrapolation for 3" Is 170 mJ/mol K 2 for CePd3Bo6 and less than 30 mJ/mol K 2 for CePd3Sto 3 In the inset of fig 1, the low t e m p e r a t u r e C vs T behavior is &splayed for both c o m p o u n d s under study (after lattice subtraction) to show the characteristic H F behavior of CePd3Bo6 and the magnetic transition of CePdaSlo a In fig 2, we show the Schottky anomaly for the Fv--* F8 thermal promotion of these systems In the abscissa the reduced t e m p e r a t u r e T/8 was used (8 = F7-F8 sphttmg) m order to c o m p a r e their behavior with that of CeAl2 [7], the archetype of K o n d o systems Only CePd3Slo 3 follows roughly the c o m p u t e d Schottky anomaly, with the expected m a x i m u m of Cmax=6 4 J / m o l K Both CePd3Bo 6 and CeAI2, show spread and reduced maxima with Cmax of 4 8 and 4 2 J / m o l K , respectively T h e F7-F8 crystal field splitting is evaluated as 6 = Tm~x/O377, which gives 6 ~66 K for CePd3Bo 6 (ln good a g r e e m e n t with our magnetic m e a s u r e m e n t s [10]) and 6 ~ 120 K for

0

02

04

T /d

0

Fag 2 Crystal field Schottky (Clv_Fr) anomaly vs reduced temperature (T/8) of CePd3Bo 6 (O) and CePd3Slo 3 (A) with 8 = 66 K and CeAI2 (O) with 8 = 1 2 0 K The continuous curve is the computed one for the Fv-F8 thermal promotion

CeAI2 [7,9] T h e entropy change observed is about 90% of the expected AS = R In 3 for this transition

3. Discussion T h e measured C vs T dependence, at T > 8/10 was tried to be fitted by a normal Schottky curve, with a hypothetical 6 = 6(T) d e p e n d e n c e and supposing a symmetry reduction (1 e the F8 quadruplet split into two doublets) T h e experimental results can be a p p r o a c h e d only with a drastic reduction of the baricenter (by a factor three), which seems unlikely because of the unphysical distortion requested to the crystal structure of these two different cubic systems Anyway the two questions In the introduction seem to have a c o m m o n answer i e the quasilinear C vs T d e p e n d e n c e and the Cmax reduction resemble an effect raising from a similar mechanism which Involves the ground state, but with a different energy scale We have to n o n c e here that the pure trIvalent CePd3SIo 3 does not show these anomahes in the ground nor in the excited states Recently, the possibility of an independent InterconfiguratIonal Mixing (IM) for each crystal field sub-level was proposed on the basis of the analysis of neutron scattering m e a s u r e m e n t s per-

J G Serem et al / Crystal field effects m Ce-heavy fermton compounds

103

formed In Intermediate Valence systems [11] Within this picture the linear C term (T) is related to the entropy through a characteristic temperature Tf, I e TTf -- S(Tf), for each crystal field sub-level For the CePd3Bo 6 ground state we have AS(F7) = 0 83 R In 2 and 3' ~ 3 3 J/mol K 2 [2], therefore Tf(FT)= 1 4 K, this value can be related to the low t e m p e r a t u r e m a x i m u m Tmax

perturbed because of the IM Such a mixing leads to an e n l a r g e m e n t of the F8 level width, which can be responsible for the e n h a n c e m e n t of the measured entropic contribution at the low temperature side of the Schottky anomaly

1 K [2]

[1] See G R Stewart, Rev Mod Phys 56 (1984) 755 and references therem [2] J G Serem, G Nleva, J P Kappler, M J Besnus and A Meyer, J Phys F 16 (1986) 435 [3] J Peyrard, Ph D Thesis, Umverslt6 de Grenoble (1980), unpubhshed [4] J V Mahoney, V U S Rao, W E Wallace, R S Craig and N G Nereson, Phys Rev B9 (1974) 154 [5] J R Cooper, C Rlzzuto and G Olcese, J de Phys 32 (1971) C1-1136 [6] M J Besnus, J P Kappler, A Meyer, J Serem, E Slaud and R Lahlouel, Physlca 130B (1985) 240 [7] C Deenadas, A Thompson, R Craig and W E Wallace, J Phys Chem Sohds 32 (1971) 1853 [8] M Loewenhaupt and F Steghch, Physlca 86-88B (1977) 187 [9] J P Kappler, M J Besnus, E Beaurepalre, A Meyer, J Serenl and G Nleva, J Magn Magn Mat 47&48 (1985) 111 [10] D Wohlleben and B Wlttershagen, J Magn Magn Mat 52 (1985) 32 [11] J P Kappler, M J Besnus, A Meyer, J G Serem and G Nleva, Proc of the 6~mes Journ de la RCP 520 sur les "Compos6s de Terres Rares et AcUmdes /l Valence Anormale", Strasbourg (1983) p 23 [12] M N Francdlon, A Percheron, J C Achard, O Gorochov and B Cornut, Sohd State Commun 11 (1972)

Now, for the excited level Fa we expect AS(F8) = R In 3, because the total entropy of the C e - - 5 / 2 multlplet is R In 6, with the measured quasl-hnear terms T(CePdaBo 6) = 170 mJ/mol K 2 and T(CeAI2) -- 130 mJ/mol K 2, we obtain. T f ( F s ) = 53 and 70 K, respecUvely, We want to note that for both systems the electrical reslstlwty mcreases for decreasing T with a In T d e p e n d e n c e at those Tf temperatures [12,13] Such an effect is usually attributed to a K o n d o scattering which TK t e m p e r a t u r e should be similar to the c o m p u t e d Tf For both systems, the high t e m p e r a t u r e magnetic susceptibility (4 K < T < 300 K) is not well fitted taking into account the sole crystalhne field effect [12,14] In the case of CeAI2, It was found to be higher than the expected value at T < 8 and lower at T > 8, in coincidence with the specific heat tendency Furthermore, neutron scattering m e a s u r e m e n t s give a quasi-elastic hne associated with the F8 excited level, f r o m which a TK of the order of 30 K was estimated [9] In terms of the speofic heat contribution, the meaning of these large Tf values is that the thermal F7--~ F8 p r o m o t i o n has to be strongly

Relerences

845 [13] J A Wtute, H J Wflhams, J H Wermck and R C Sherwood, Phys Rev 131 (1969) 1039