Thermal Properties of Itinerant Magnets
This chapter is concerned with the effect of spin fluctuations on magnetic entropy and specific heat. To be consistent with treatments in preceding chapters, we first introduce a free energy of spin fluctuations, which is consistent with the total spin am
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Thermal Properties of Itinerant Magnets
5.1 Difficulties Involved in the Spin Fluctuation Theory of Specific Heat Temperature dependence of the specific heat of weak itinerant electron ferromagnets in a wide range of temperature was treated by Makoshi and Moriya [1]. The free energy used by them is written by F(M, T ) = FSW (M, T ) + Fsf (M, T, χ −1 (T )).
(5.1)
It consists of the Stoner-Wohlfarth free energy FSW and the contribution Fsf from thermal spin fluctuations. At low temperatures for exchange-enhanced paramagnets, it reduces to that of paramagnon theories for them. Moreover for ferromagnets, it can also be applied to properties at higher temperatures in the paramagnetic phase where the Curie-Weiss law temperature dependence of magnetic susceptibility is observed. Nevertheless, there exist the following difficulties: 1. As shown in the left figure of Fig. 5.1, a curious negative steep decrease of the specific heat appears just above the critical temperature with decreasing temperature. 2. It is based on the free energy that violates rotational invariance in the spin space. This is because only the transverse components of spin fluctuations are included in their treatment. Otherwise, spontaneous magnetic moment shows discontinuous change at the critical temperature. 3. Effects of zero-point spin fluctuations are neglected from the beginning. 4. The effect of the external magnetic field has not been treated by them. Their theory was later simply extended by Takeuchi and Masuda [2] to include the external magnetic field effect. Their numerically estimated changes of specific heat under the presence of magnetic fields of Sc3 In are compared with their experiments in Fig. 5.1.
Y. Takahashi, Spin Fluctuation Theory of Itinerant Electron Magnetism, Springer Tracts in Modern Physics 253, DOI: 10.1007/978-3-642-36666-6_5, © Springer-Verlag Berlin Heidelberg 2013
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5 Thermal Properties of Itinerant Magnets 4.0
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(CH-CH=0)/T (mJ/K g-atom)
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T/Tc
Fig. 5.1 Temperature dependence of the specific heat by Makoshi and Moriya derived from the SCR theory (left) and the effect of magnetic field on the specific heat of Sc3 In by Takeuchi and Masuda (right)
We will show in the following, how the temperature dependence and the external field effects of entropy and specific heat are derived based on our spin fluctuation theory presented in Chaps. 3 and 4.
5.2 Free Energy of Spin Fluctuations In order to be consistent with our treatments of various magnetic properties, it will be better for the free energy to satisfy the following requirements: • It is consistent with the total spin amplitude conservation (TAC). Then, the effect of zero-point spin fluctuations has to be included. • The rotationally invariant treatment in the spin space has to be made. Thus, both the effects of transverse and the perpendicular components of spin fluctuations have to be included in t
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