Isotropic ferromagnet

Similar studies have been carried out for AT (Landau et al., 1989) and Heisenberg ferromagnets with free surfaces (Binder and Hohenberg, 1974), yielding a somewhat larger value of fi (ft 0.84). This result is compatible with an experimental determination of fi for the isotropic ferromagnet Ni, fii 0.82 (Alvarado et al., 1982). 

When speaking of kinematic interaction, it should be noted that the problem of its separation in connection with the transition from Pauli operators to Bose operators is far from new. This problem arises, in particular, for the Heisenberg Hamiltonian, which corresponds, for example, to an isotropic ferromagnet with spin a = 1/2 when spin waves whose creation and annihilation operators obey Bose commutation relations are introduced. This problem was dealt with by many people, including Dyson (6), who obtained the low-temperature expansion for the magnetization. However, even before Dyson s paper, Van Kranendonk (7) proposed to take into account of the kinetic interaction by starting from a picture where one spin wave produces an obstacle for the passage of another spin wave, since two flipped spins cannot be located at the same site (for Frenkel excitons this means that two excitons cannot be localized simultaneously on one and the same molecule). 

Let us consider the simplest case of an optically isotropic ferromagnet. The presence of magnetization reduces the symmetry to the single-axis one. The e tensor can be represented as a sum of symmetric and asymmetric tensors, which is given by [26]... 

The EMD of a magnetostrictive film is directly related to the film s stress. The change of the orientation of the film s EMD can be determined by considering the minimum of the magnetoelastic energy for an isotropic ferromagnet (du Tremolet de Lacheisserie 1993) ... 

By means of this thermodynamic model the internal friction for an isotropic ferromagnet near Tq was calculated by Belov et al. (1960) and Peqioular (1965). The internal friction characterizes the damping of the sample s sound vibrations with time and is defined as a ratio of the mechanical energy dissipated over a period of time to the fill mechanical energy of the sample. It is related to the sound attenuation coefficient as... 

The second term in expansion (86), squared in mechanical stress, was taken into accoimt by Kataev (1961). For an isotropic ferromagnet the following formula was derived ... 

Isotropic ferromagnets , (with P. Pincus) Solid State Commun.. I, 339 (1969). 

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