Schottky specific heat

The observed Schottky-specific heat is due to changes in internal energy that occur when nearly adjacent energy levels are occupied. The degenerate energy levels may be caused by external or internal magnetic fields. 

The electron spin-resonance parameters gi, gx. A, B, and one P for a number of rare earths in YVO4 have been reported (Ranon, 1968a, b). The Schottky specific heat, paramagnetic susceptibility, and quadrupole splitting have been calculated for Tm YV04 using results from optical measurements and sub-... 

Here k = is the compressibility, the averages are given by eq. (34) and y = -(din E /d In V) define electronic Griineisen parameters for a given CEF level. The close correspondence between )8 and the Schottky specific heat has been emphasized before (Ott et al. 1976, 1977, Liithi 1980a). The latter is described by a corresponding formula 1... 

As for elastic constants, the CEF effects in thermal expansion and the Schottky specific heat are especially pronounced in TmSb, see fig. 18. Equations (45) and (46) give a good fit to the data, (Ott and Liithi 1976, 1977) with y, = yj = -1.2 as seen from fig. 18. The CEF Griineisen parameters measuring the volume dependence of the CEF levels turn out to be of the order of one. In this way a number of cubic compounds have been studied so far TmSb, PrSb, SmSb, ErSb, CeTe and TmTe (Ott and Liithi 1977), and TmCu, TmZn and TmCd (Morin and Williamson 1984). 

The values of the 5 coefficient can be derived from experimental data obtained from the magnetic susceptibility, the Schottky specific heat, the hy-perfine structure, the magnetic form factor and the neutron inelastic scattering measurements. The S " values are shown in table 15. It can be seen that the coefficient is dominant since the others are smaller by an order of magnitude. 

An example of magnetic contributions to the specific heat is reported in Fig. 3.9 that shows the specific heat of FeCl24H20, drawn from data of ref. [35,36]. Here the Schottky anomaly, having its maximum at 3K, could be clearly resolved from the lattice specific heat as well as from the sharp peak at 1K, which is due to a transition to antiferromagnetic order (lambda peak). 

A special attention is to be devoted to copper, which is very often used in a cryogenic apparatus. The low-temperature specific heat of copper is usually considered as given by c = 10-5 T [J/g K], However, an excess of specific heat has been measured, as reported in the literature [59-69], For 0.03 K < T< 2K, this increase is due to hydrogen or oxygen impurities, magnetic impurities (usually Fe and Mn) and lattice defects [59-66], The increase of copper specific heat observed in the millikelvin temperature range is usually attributed to a Schottky contribution due to the nuclear quadrupole moment of copper [67,68],... 

The speeific heat of AU55 has been recently measured between 60 mK and 3 K, as a funetion of external magnetic field [54]. The increase in the specific heat at the lowest temperatures was attributed to a possible Schottky tail from Au nuclear quadrupole splitting. 

The coordination numbers based on this structure work extremely well for describing the microscopic physical properties of this material, including the Mossbauer I.S.s of the surface sites and of the specific heat of the clusters below about 65 K. No linear electronic term in the specific heat is seen down to 60 mK, due to the still significant T contribution from the center-of-mass motion still present at this temperature. The Schottky tail which develops below 300 mK in magnetic fields above 0.4 T has been quantitatively explained by nuclear quadrupole contributions. 

By measuring specific heat of a rare earth alloy, e.g., TmAb along with the Schottky contributions, the different levels can be identified. The specific heat per mole of rare earth ions may be written as... 

Schottky anomaly is determined from the difference between an RY compound and LaX or LuX compound. Then the crystal field parameters are deduced from the Schottky anomaly data. The accuracy of the method is limited by spin-phonon interactions and exchange effects in rare earth ions which affect the Schottky effect, ft is used to find crystal field parameters, W, x which fit the specific heat data as shown in Fig. 8.4. The figure refers to a plot of C/Rq vs. T for TmAF [19]. 

The cluster compounds [Ag6M4Pi2]Gc6 with = Ge, Sn show at low temperatures a valence fluctuation of the inner core Ag6" +, which can be seen in the elastic behavior " and vibrational anharmonicity as well as in the measurements of the specific heat. The valence fluctuations generate a pronounced schottky anomaly, which can be emphasized more clearly by the comparison and therefore possible normalisation of cluster compounds. 

The Schottky-like anomaly observed in the specific heat of the compounds discussed in this section can be derived phenomenologically using (a) the resonance-level model, (b) the spin glass behaviour, (c) the crystal field (Schottky) contribution or even (d) low-dimensional magnetic fluctuations. The cases where an HF behaviour is deduced from a large value will be discussed in sect. 9, in connection with the contribution to of the excited crystal field levels. It is clear that complementary techniques, such as NMR, AC susceptibility and electrical resistivity, can easily reveal the magnetic character of the microscopic interactions. In some of the HF compounds the ratio between the y term and the (( -> 0) = Xo value of the susceptibility, and between the / term and the coefficient of the resistivity. A, have values predicted by... 

Fig. 26. High-temperature specific heat of three Kondo eompounds with an abnormal Schottky anomaly, after de Boer et al. (1985) and Felten (1987). The continuous curve is a Schottky contribution for a F-j-Fg thermal promotion.

Fig. 16. Temperature dependence of 4f-derived specific heat, C, and entropy in units of the gas constant, SJR, for (a) CeRu j Gcj and (b) CeCu GCj (Felten et al. 1987). Solid curves in upper parts show Schottky anomalies corresponding to the CF splitting of Ce given in the text.

Fig. 69. The 5f-derived specific heat of URUjSij, AC, as a function of temperature (on a logarithmic scale) (Renker et al. 1987b). Thick line shows Schottky anomaly for doublet-doublet CF system with a sphtting of kg 75 K. Thin line is guide to the eye.

THE SCHOTTKY-TYPE ANOMALY IN THE SPECIFIC HEAT OF SOLID CH3D. 

U. Kohler, R. Demchyna, S. Paschen, U. Schwarz, F. Steglich, Schottky anomaly in the low-temperature specific heat of Bag.j,EUj,Ge43n3. Physica B 378-380, 263 (2006)... 

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