Physica B 1658~166 (1990) 421-422 North-Holland

1.

ELASTIC PROPERTIES OF HEAVY-ELECTROW COHPWND CePdIn

Takashi SUZUKI, Minor" NOHARA. Toshizo FUJITA, Toshiro TAKABATAKE* and Hironobu FUJII*

Faculty of Science and *Faculty of Integrated Arts and Science, Hiroshima University, Hiroshima 730, Japan

The temperature dependence of the elastic constants C3 measured between 2 K and 150 K. All the elastic cons ants exhibi i?

, (Cl1 - Cl )/2 and C44 of CePdIn has been .e softening at low temperatures

due to the crystalline electric field and the antiferromagnetic ordering.

INTRODUCTION Rare earth compounds exhibit characteristic

dependences of the elastic constants on temperature and magnetic field reflecting a variety of 4f-electron states (1). Particularly, elastic softening at relatively higher tempera- tures T > TK, where TK is the Kondo temperature and 4f-electrons are well localized, is explained by crystalline electric field (CEF) effect mediating strain-quadrupole interaction since the localized state of 4f-electrons has an electric quadrupole (2.3).

Recently, equiatomic ternary compound CePdIn has been discovered as a new antiferromagnetic heavy-electron compound with TN = 1.8 K by our group (4-6). CePdIn crystallijes in the Fe2P- type hexagonal (space group-D3h) structure, in which the J = 5/2 sextet is expected to split into three Kramers-doublets. The magnetic sus- ceptibility follows the Curie-Weiss law at high temperatures above 100 K with an effective

which is very close to the ~,";l"e"tf~fC2e3'6%~e ion. Satoh et al. (6) esti- mated the Kondo temperature as TK = 3.3 K and the CEF energy separation as Al = 100 K between the ground state and the first excited doublet from the magnetic part of the specific heat.

In this paper we report the temperature dependence of the elastic constants (C C33 and C44 of CePdIn from 2 K to 1 propose a preliminary but new CEF level scheme estimated by a theoretical fit of strain suscep- tibility which is the linear response for the strain-quadrupole interaction against strain.

2. EXPERIMENTS Single crystals of CePdIn were grown by a

Czochralski method using a triarc furnace. Crystal axes were determined by an X-ray Laue camera. Temperature dependence of sound velocity v(T) was measured by a hand-made phase- comparison-type ultraionic apparatus .with a lia.-He crvostat. The elastic constant C(T) was calcylated"from v(T) with the density p = 8.605 g/cm . for which we ignore the thermal expansion (7) because the contribution is less than one- tenth of that from the velocity-change.

3. RESULTS AND DISCUSSION In Fig.1 (a), plotted with circles is the

temperature dependence of longitudinal C elastic stiffness with I1 symmetry in t e 0 h

y-mo;e point group. As temperature is reduced, t e characteristic softening due to the CEF effect is observed between 14 K and 150 K. The inset shows the lower temperature part of C 3, which exhibits a minimum around 14 K an a renews softening below 6 K. Shown in Figs. l(b) and (c) is the temperature dependence of transverse (Cll-C12)/2 with T symmetry and C44 with I6 symmetry, respective y. These elastic constants 51 of the transverse modes reveal also the softening due to the CEF effect and the renewed softening without minimum.

The renewed softening is likely to be related to the antiferromagnetic ordering and not to the formation of dense Kondo state (1) because the elastic anomaly arising from the formation of dense Kondo state should be expected only in the longitudinal mode mediating a large electronic Grt'neisen parameter.

Since the elastic constant is the second derivative of the free energy of the system with respect to the strain, the strain susceptibility X includes both contributions of van Vleck-type and Curie-type on the analogy of the magnetic :usceptibilitv. In case of CePdIn. the van Vleck 'erm contributes only to the transverse modes of (Cl,-Cl whereas the Curie term contribu z

)/2 and C44. es only to the longitudinal mode of C33,

The strain susceptibility for the transverse modes exhibits a saturating behavior without minimum at low temperatures. In contrast with the transverse modes, the appreciable minimum is observed in the strain susceptibility for the longitudinal mode at low temperatures. The tem- perature dependences of elastic constants shown in Fig. 1 are in qualitative agreement with the theory. In order to estimate the CEF level scheme, we took account of only the strain- quadrupole interaction and tried a0 non-line r least squares fitting to C(T) = C 6T) - 9 Ng X for the softening above 10 K, where C , N, g and X are the elastic conj+tant without the CEF effect, the number of Ce ion per unit volume,

0921-4526/90/$03.50 @ 1990 - Elsevier Science Publishers B.V. (North-Holland)

422 T. Suzuki, M. Nohara, T. Fujita, T. Takabatake, H. fijii

(a) 2 e $ =o R

”

23.050 150 T (K)

1 b 1 3.08 ; 1 I CePdln 1

3.04 ' I I I 0 50 100 150

T (K)

9.68 1 I I I 0 50 100 150

T IK)

FIGURE 1 Temperature dependences of the elastic constants (a) for C (c) for P

mode, (b) for (Cl,-$2)/Z mode and mode. The inset 1s the low

temperature4p\rt of each elastic constant.

coupling constant between the quadrupole and the strain, and the strain susceptibility, respectively. The quadrupole-quadrupole exchange interaction is not taken into consideration since

% uadrupolar ordering is hardly expected

for Ce ground state in hexagonal symmetry. In Figs. l(a), (b) and (c), a theoretical fit is indicated by a solid curve for Al = 56 K and

A2 = 128 K. where Al and A2 are the energy separations from the ground-state doublet )*5/Z> to the first excited doublet 1*1/Z> and from 1?5/2> to the second excited doublet 1?3/2> by assuming a temperature-linear dependence of

CL33 (cl’-Cl2)/2 c44

Igl (K) --

__ 625 128 152

a (107 erg/cm3 .K) -24.98 -4.371 -10.52

b ‘(10” erghd) 24.583 3.1692 9.8881

TABLE I The fitted values of lgl, a and b for C33, (Cll-Cl2)/2 and C44 mode.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Co(T) = aT t b. The values of lg], a and b are tabulated in Table I. The calculated curves are in good agreement with the experimental results above 30 K. The discrepancy between the calcula- tion and the experiment at low temperatures is caused by the appearance of the renewed soften- ing due to the antiferromagnetic order and/or by the formation of dense Kondo state, even if it is unsuitable for the fitting to assume the linear temperature dependence of background elastic constant Co at low temperatures. The coupling constant lgl for the C

z3 mode is extra-

ordinarily large comparing wit that for other modes. This suggests anisotropic c-f mixing in CePdIn which is also expected from the anisotropy of resistivity and magnetic suscepti- bility of single crystal (7).

In summary, we present the temperature dependence of the elastic constants fj; CePdIn, and propose a CEF level scheme for Ce in this compound determined by means of the strain susceptibility.

ACKNOWLEDGMENTS The authors would like to thank Dr.Y.Maeno

for valuable discussion. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan.

REFERENCES T.Goto. T.Suzuki. Y.Ohe. T.Fuiimura and A.Tamaii, J. Magn..Magn. Mat. 76 i 77 (1988) 305. B.Ltithi, "Dynamical Properties of Solids", ~01.3, eds. G.K.Horton and A.A.Maradudin (North-Holland, Amsterdam, 1980) p.245. P.Fulde, "Handbook on the Physics and Chemistry of Rare Earths", eds. K.A.Gshneider and L.Eyring (North-Holland, Amsterdam, 1978) chap.17. H.Fujii, Y.Uwatoko. M.Akayama, K.Satoh, Y.Maeno, T.Fujita, J.Sakurai, H.Kamimura and T.Okamoto, Jpn. J. Appl. Phys. 26-3 (1987) 549. Y.Maeno, M.Takahashi. T.Fujita, Y.Uwatoko, H.Fujii and T.Okamoto. Jpn. J. Appl. Phys. 26-3 (1987) 545. K.Satoh, T.Fujita, Y.Maeno, Y.Uwatoko and H.Fujii. J. Phys. Sot. Jpn. 2 (1990) 692. H.Fujii et al., this issue.