Handbook on the Physics and

Zuckermann, Transport properties (electrical resistance, thermoelectric power and thermal conductivity) of rare earth intermetallic compounds 117. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and silicon 52.

Introduction

Temperature dependence of the specific heat of the impurity (or magnetic) for N = 6 and different values of nf in NCA. Sketch of the dispersion relation e(k) for quasi-particle bands, as derived from the periodic Anderson model in a mean-field approach (Millis and Lee 1987).

Fig. 2. Temperature dependence of the 4f-electron density of states in NCA

ENERGY TRANSFER hw{meV} ENERGY TRANSFERhw {meV}

The shaded areas mark magnetic scattering (Severing and Murani 1990). the inelastic line at 50 meV with a linewidth of 40 meV alone is responsible for a static susceptibility of 1.4 x 10-3 emu/mol. The temperature dependence of the quasi-elastic line width of CeSn 3 is shown in fig.

Fig. 24. Q-dependence of the inelastic magnetic scattering in C e P d a deduced from the intensity in the energy window f i o m 1 to - 6 meV at T = 240 K (Holland-Moritz et al

T T4!cesn3T42 K

CeSn3_xlnx and Celn3

The temperature dependence of the quasi-elastic C e C u i S i 2 line width was investigated by H o r n et al. Temperature dependence of the quasi-elastic linewidth of CeA13 plotted against T and T 1/a (Murani et al. 1980). The temperature dependence of the quasi-elastic line width was measured by Murani et al.

Temperature dependence of the linewidths for the one-site quasi-elastic contributions (open squares, Fs_~) and for the inter-site inelastic contributions (open circles, Fs) obtained on a CeRu2Si 2 single crystal (Regnault et al. 1990). The evolution of the quasi-elastic linewidth with temperature was reported by H o r n et al. The temperature dependence of the quasi-elastic line width appears to follow a law of T 1/2 (D7 data, H o r n et al.

The temperature dependence of the Lorentzian quasi-elastic line width was reported by Balakrishnan et al. The temperature dependence of the quasi-elastic line width for both pressures is shown in fig. For an explanation of the inelastic neutron spectra of YbPdzSi2 (and YbAgCu4), see also Polatsek and Bonville (1992).

Temperature dependence of the quasi-elastic Lorentz linewidth of YbPdCu 4 (filled squares), YbAuCu 4 (filled triangles) and YbAgCu4 (filled circles). Temperature dependence of the quasi-elastic magnetic line width (filled circles) and of the position A of the inelastic line (open circles) in EuNi 2 P2 (Holland-Moritz et al. 1989b).

Fig. 44. S p i n - o r b i t transition in CeSn 3 ~In~ m e a s u r e d at 7 ' = 20 K with E0 = 600 meV on the H E T spectrometer (redrawn from M u r a n i et al

Summary

Thermal conductivity of rare earth compounds at high temperatures 206 10.1. Phonon Spectrum Peculiarities and ~L of Rare Earth Compounds 206. Rare earth compounds (RECs) comprise a broad set of new classes of materials with unusual and sometimes unique properties. Fortunately for the authors, thermal conductivity has now been measured in no more than a hundred RECs.

However, due to the specificity of the charging and behavior of the 4f shells (see Table 4), not all RECs are magnetic. All the non-standard classes of lanthanide materials listed above show their specificity in the non-standard behavior of physical parameters. From the history of research on thermal conductivity 0c) in solid bodies, it is clear that tc always "reacted" to the appearance of new effects.

There is only one previous review devoted to ~c and other thermal properties of rare earth chalcogenides (Smirnov . 1972), in which data were collected up to 1972. Of course, due to the limited scope of this review, we could not analyze all literature data on tc REC. This should help readers understand what new features are added to the overall picture of thermal conductivity behavior by the results at ~c REC.

Brief summary of thermal conductivity of solids

Currently, the most important theoretical theorems of the thermal conductivity K of solids are obtained, understood and described in Oskotski and Smirnov (1972), Berman (1976), Smirnov and Tamarchenko (1977) and other monographs, and many reviews. At low and medium temperatures, the acoustic phonons of the spectrum participate in the heat transport and scattering processes. Sometimes some of the constants can be evaluated by independent theoretical calculations or measured experimentally.

In this review we will try to use this method of analysis as rarely as possible and limit ourselves only to the physical nature of the behavior of ICL(T). Here B and D are constants, eV is the Fermi energy, and 15 and I7 are integrals of type. In the intermediate temperature range, L is determined by the temperature and the purity of the sample.

Bipolar thermal conductivity, tCblp, appears in s e m i c o n d u c t o r s in the region of the intrinsic c o n d u c t i t y due to diffusion of electron-hole pairs fi'om the h o t to the cold end of a sample. The electron component of the thermal conductivity contains information about the scattering mechanism and its character (elastic or inelastic), and enables one to determine the type of energy band structure (parabolic, non-parabolic), the presence of additional subbands with light and heavy carriers , to determine, and the nature of the electron interaction with phonons and other electrons. By analyzing data on the thermal conductivity of RECs, in this review we will try to draw more attention to non n s t and d a r d effects characteristic of the solids containing ions with f-electrons.

Fig. 5. The dependences L/(ko/e) 2 - f(ll*) calculated by eq.(13) (curve 1) and eq.(15) (curves 2 and 3) for r = -0.5

Influence of the magnetic structure on the thermal conductivity of lanthanide compounds

The influence of the dispersion of electron spin perturbations of i% in the paramagnetic region (i.e. the magnetic contribution to the thermal conductivity) is estimated by comparing ~qot -~ three of the magnetic and non-magnetic compounds of the RA12 family . It is interesting to note that in EuO a strong decrease in the thermal diffusivity, D, is observed at Tc (Salamon et al. 1974). In a S OPT, the orientation of the magnetic m o m e n t s relative to the crystallographic axes changes under the influence of external parameters (temperature, magnetic field, pressure) (Belov et al. Belov 1972).

The nature and characteristic features of the S O P Ts have been studied most completely in the orthoferrites RFeO3. The nature of the transitions changes significantly in (ac) reorientation in an external magnetic field H. Anomalous behavior of to(T) of Smo.6Gdo.4FeO 3 in the S O P T region is associated with unusual behavior of the sound speed (Fig. 18c ).

As a result, the contribution to the heat transfer of phonons decreases with the energy of the junction. At low temperatures in a magnetic field H = H~ one observes in GdC13 an increase (+AK) and in D y A 1 G a decrease (-A~c) of the thermal conductivity. In principle, the magnetic field can also affect t%, but due to the low mobility of carriers in the lanthanide metals, it is practically impossible to achieve a sufficiently high magnetic field (H~0) for the suppression of carriers (H~0 ) ~o > H~).

Fig. 8 ~:,oUTas a function of Tin YAl~ (Bauer et al.

Thermal conductivity of spin glasses

Schematic view of magnetic momcnt in ferromagnetic (FM), antiferromagnetic (AM) and spin glass (SG) systems. The thermal conductivity of the EuxSrl_~S system in the temperature region 0.06-30 K and in magnetic fields up to 7 T has been measured by Arzoumanian et al. The effect of a giant increase in t h e r m a l conductivity in a m a g n e t i c field in the spin-glass region requires special explanation.

Schematic form of the electron band structure (a, b, c) and p(T) (a', b', c') for metals with Kond o impurities (a,a'), concentrated Kondo systems (including systems with heavy fermions) at T < TK (b, b') and for compounds with a homogeneous intermediate valence of rare earth ions (c, c'). The latter case is close to the situation in the class of materials considered in this section and is reminiscent of the situation shown in Fig. Two peaks are clearly seen in the temperature dependence of the heat capacity of CeB6: a large peak at TN and a small one at T1 (Fig. 56) (Peysson et al. 1985).

The temperature dependence of the heat capacity (C) of CeB 6 at two magnetic fields (Peysson et al. 1985). The contribution of ~L to Kto t is taken into account in the calculation of L(T)/Lo as in the previous case (Bauer et al. 1987). In the classical compounds with an intermediate valence of the tantanide atoms (SmB6, TmSe) ~c L >> ~co (especially in the low temperature range).

Figure 27 shows a scheme of the formation of metallic spin glasses (Mydosh 1978)

Influence of paramagnetic lanthanide ions on the thermal conductivity of ordered and disordered systems

Both theoretical approaches give more or less the same result - essentially a decrease in the thermal conductivity of crystals containing paramagnetic ions. Let us consider the two-level scheme (fig. 60) (Smirnov et al. 1989) and a phonon energy distribution function which is a product of the Planck function and the p h o n o n density function (phonon spectrum) (fig. 61). Phones can also be scattered by the planes of the d-shell that are split by the crystal field.

A is the distribution through the lattice crystal field, ~ is the distribution of the levels with temperature, ~ oc T - L/2 (Oskotski et al. These levels are degenerate according to the orientations of the total spin of the d-shell. This leads to the splitting of states with a total momentum Y = L + S and into a simpler level structure than in the case of the d elements.

Temperature dependence of - AGEs - reduction of thermal conductivity due to p h o n o n scattering due to PLnIs has a resonance form (fig. 62) in the two-level model (fig. 60) (Oskotski and Smirnov 1971, Oskotski et al. Dependence from the temperature of - AKro ~ in the high temperature region from the concentrations and arrangements of PLnIs in the lattice Theoretically - A G , ~ is defined in the Callaway model as the difference of ~CL(1) and ~ Ce(2), where XL(1) is calculated taking into account the p h o n o n scattering by sample boundaries, defects and phonons (N and U processes), and tce(2) is calculated taking into account the same processes plus phonon resonance scattering from the split paramagnetic levels of lanthanide ions (Oskotski et al.

Thermal conductivity of rare earth superconductors 1. Main principles

At T < T~, ~c~ first decreases (as in the previous case) and then may increase slightly due to a weakening of the electron phonon scattering. Schematic form of the temperature dependence of l<[. c~ and K~ for a metal when electron-impurity interaction is the m a i n electron scattering mechanism. One can indirectly obtain information about the behavior of the gap, A, from the temperature dependences of the heat capacity and the thermal conductivity of HFS systems (see table 6 and fig. 105) (Varma 1985).

Schematic form of the superconducting gap A(k) in momentum space (Buzdin and Moshchalkov 1986) (a) in a standard superconductor; and in a heavy-fermion superconductor with (b) vanishing gaps at some points and (c) on lines on the Fermi surface. At present there is no clear understanding of the nature of the linear term in ~c~. Since then, extensive investigations into the physical properties of systems with the coexistence of superconductivity and magnetism have been carried out.

The latter interval has been fixed only by precise measurements of magnetic susceptibility and linear expansion coefficient (Ot t e t al. 1978, Woolf et al. 1979). The temperature dependence of the electrical resistance, R, for ErRh4B~ without a magnetic field and in a longitudinal magnetic field H = 12 kOe (Ott et al. The temperature dependence of the electrical resistance, R, for SmRh4B 4 without a magnetic field and in a longitudinal magnetic field.