of the Less-Common
Metals, 88 (1982)
L3 - L6
Thermal conductivity of LaB, at low temperatures
and s. JANOh
Institute of Experimental Physics, Slovak Academy 041 54 Kofice (Czechoslovakia) Yu. B. PADERNO,
V. I. LAZORENKO
Institute of lateral ~oblems, Str. 3, 152 152 Kiev (U.S.S.R.) (Received
ndm. Febr. vit’azstva 9,
and E. S. KONOVALOVA
The rare earth hexaborides REB, form an interesting group of CaB,type compounds characterized by strong covalent bonds between the B, octahedra and the RE atoms which form two interpenetrating cubic lattices. The compound LaB, is a high conductivity metallic boride which has recently attracted much attention mainly because of its practical application as an electron beam source with a low work function and a high brightness [l, 21. Many experimental and theoretical studies of the energy bands 13 - 51, the Fermi surface [6,7] and the optical [IS], electrical [9 - 111 and superconducting properties 112, 131 of this material have been performed. However, the thermal transport properties of this compound have received little attention, p~icul~ly at low temperatures. The results of experimen~l ~vestigations of the thermal conductivity of LaB, are reported in this paper. The observed temperature dependences are discussed in terms of the electronic and lattice thermal conduetivities of metals and alloys. Electrical resistivity data obtained on the same sample are utilized in the analysis of thermal conductivity. A single crystal grown using the floating zone technique was used in this work. The sample had dimensions of 2.5 mm X 2.5 mm X 25 mm with a residual resistance ratio of 175. The thermal conductivity was determined using a steady state axial heat flow method. The carbon resistors used as thermometers were calibrated against the helium vapour pressure in the temperature range below 4.2 K and against a calibrated germanium thermometer at temperatures above 4.2 K. The absolute error in the determination of the thermal conductivity did not exceed 5%. The electrical resistance was measured potentiometric~y using the four-probe method. The thermal conductivity data obtained for LaB6 between 0.7 and 25 I( are plotted in Fig. 1. The most significant feature of this curve is the nonlinear behaviour of the thermal conductivity at temperatures below 15 K, i.e. 0022-5088/82/0000-0000/$02.75
0 Elsevier Sequoia/Printed
in The Netherlands
Fig. 1. The thermal conductivity field of 3 T; -, the electronic
of LaB6: l, in zero magnetic field; +, in a magnetic thermal conductivity according to eqn. (1).
below the thermal conductivity maximum. The electrical resistivity of LaB, shows a metallic behaviour (Fig. 2) and hence, by the Wiedemann-Franz law K/s,
where K, is the electronic thermal conductivity, Lo is the Lorenz number and p. is the residual electrical resistivity, a linear dependence of the thermal conductivity (represented by the full line in Fig. 1) is expected in this temperature region. The non-linearity of the thermal conductivity of LaB6 is surprising as such behaviour at low temperatures is not observed in other metals and alloys with electrical conductivities comparable with that of LaB,. A detailed analysis of the observed thermal conductivity curve in zero magnetic field shows that in the temperature range between 4 and 12 K K = T* and below 3 K K = T3. This suggests that the phonon thermal conductivity Kg is the dominant component of the heat transport since at such temperatures the phonon thermal resistivity W, = l/K, of metals and alloys can be expressed in the form 
: . IO0
. . . . . . . . . . .... . *
T [Kl Fig. 2. The electrical resistivity of LaB6.
where B and C do not depend on the temperature. The first term in eqn. (2) represents the scattering of phonons by electrons and the second term represents the scattering of phonons by the boundaries of the sample. The latter mechanism becomes important as the phonon mean free path approaches the smallest dimension of the sample. In such a case the electrons are not expected to contribute to the heat transport, but subsequent thermal conductivity measurements in a longitudinal magnetic field indicated a substantial magnetic field effect on the thermal conductivity (Fig. 1) which suggests that the electronic thermal conductivity has a major role in heat transport. However, the contribution of the phonon thermal conductivity to K cannot be excluded absolutely. The effect of the magnetic field on the thermal conductivity at 4.2 K is similar to the effect of a longitudinal magnetic field of 3 T on the electrical resistivity at the same temperature (a ApIp value of 0.75 was observed). These results suggest that the non-linearity of the thermal conductivity at temperatures below 15 K is probably due to a mechanism (in addition to point defect scattering) that leads to a decrease in the electronic contribution to the thermal conductivity. This mechanism may be related to the scattering of electrons by certain types of lattice vibrations (phonon modes). The analysis of REB, lattice vibrations [ 13, 151 shows that low energy peaks with a high phonon density appear in the
phonon density of states. These peaks are related to the translational and torsional modes (represented by the rotational motion of B6 molecules). The torsional modes are responsible for the main part of the specific heat, which is much larger than that expected from the acoustic phonons, in REB6 at temperatures below 10 K. Moreover the conduction electrons in LaB, are strongly coupled to the boron sublattice, with the main contributions coming from the low frequency modes [5, 131. The presence of the low frequency phonons and their interactions with electrons can lead to small angle inelastic electron scattering at low temperatures. This scattering may be quite effective in reducing the thermal current for it can change a “hot” electron outside the Fermi surface into a “cold” electron inside it. Small angle scattering produces only a small change in the electric current, and therefore serious deviations from the Wiedemann-Franz law may occur . This explanation of the origin of the thermal conductivity anomaly in LaB6 is only qualitative, however, and other explanations are not excluded. The decrease in the thermal conductivity at temperatures above the thermal conductivity maximum shows a K = T-‘” relation which can be ascribed to a combination of electron scattering by acoustic and optical phonons, which becomes important, and to the increase in the phonon conductivity which is sometimes observed at these temperatures. A more detailed analysis of the heat transport in this temperature range is limited because of the small extent of this region. The temperature dependence of the electrical resistivity of LaB, (Fig. 2) is similar to that obtained by Tanaka et al. [lo] and supports their conclusions regarding the role of optical phonon scattering in the electrical resistivity of LaB, at temperatures above 20 K. 1 P. H. Schmidt, L. D. Longinotti, D. C. Joy, S. D. Ferris, H. J. Leamy and Z. Fisk, J. Vat. Sci. Technol., 15 (1978) 1554. 2 M. Futamoto, M. Nakazawa and U. Kawabe, Surf. Sci., 100 (1980) 470. 3 A. J. Arko, G. Crabtree, D. Karim, F. M. Mueller, L. R. Windmiller, J. B. Ketterson and Z. Fisk, Phys. Rev. B, 13 (1976) 5240. 4 A. Hasegawa and A. Yanase, J. Phys. F, 7 (1977) 1245. 5 P. F. Walch, D. E. Ellis and F. M. Mueller,Phys. Rev. B, 15 (1977) 1859. 6 Y. Ishizawa, H. Nozaki, T. Tanaka and T. Nakajima, J. Phys. SOC. Jpn., 48 (1980) 1439. 7 Y. Ishizawa, T. Tanaka and E. Bannai, J. Phys. Sot. Jpn., 49 (1980) 557. 8 A. I. Shelykh, K. K. Sidorin, M. G. Karin, V. N. Bobrikov, M. M. Korsukova, V. N. Gurin and I. A. Smirnov, J. Less-Common Met., 82 (1981) 291. 9 Yu. B. Paderno, V. I. Novikov and E. S. Garf, Sov. Powder Metall. Met. Ceram., 11 (1969) 70 (in Russian). 10 T. Tanaka, T. Akahane, E. Bannai, S. Kawai, N. Tsuda and Y. Ishizawa, J. Phys. C, 9 (1976) 1235. 11 I. Frankowski and P. Wachter,Solid State Commun., 41 (1982) 577. 12 R. J. Sobczak and M. J. Sienko, J. Less-Common Met., 67 (1979) 167. 13 G. Shell, H. Winter and H. Rietschel, in Superconductivity in d- and f-band Metals, Academic Press, New York, 1980, pp. 465 - 471. 14 J. M. Ziman, Electrons and Phonons, Clarendon, Oxford, 1960. 15 T. Kasuya, K. Takegahara, T. Fujita, T. Tanaka and E. Bannai, J. Phys. (Paris), Colloq. C5,40 (5, Suppl.) (1979) 308.