Spin waves at low temperatures in two-sublattice Heisenberg ferromagnets and ferrimagnets with different sublattice anisotropies

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The Hamiltonian for two-sublattice Heisenberg ferromagnets and ferrimagnets with different sublattice anisotropies, which is applicable for rare-earth - transition-metal (R - T) intermetallics, is established. In order to study spin-waves in easy plane or easy cone configuration, a transformation of spin-vector coordinates is performed by rotating the quantization axis frame by Eulerian angles and accordingly the Hamiltonian. Spin-wave spectra at low temperatures of the present system are determined by performing the standard Holstein - Primakoff transformation and a four-step diagonalizing procedure consisting of two coupled Cullen transformations, an extended Bogoliubov transformation, two independent Bogoliubov transformations and two independent Holstein - Primakoff transformations. The results for the ground states of the easy axis, the easy plane and the easy cone configurations are compared with those obtained by the mean-field theory. The border lines between the different spin structures are derived in either the pure classical limit or the large-exchange limit. Continuous transitions, accompanied with the continuous change of the angle between the averaged sublattice magnetizations, are found in both cases. It is found that splittings of the spin-wave spectra of the two-sublattice Heisenberg ferromagnets or ferrimagnets exist. A gap can appear in the spin-wave spectra, depending on the competition among the exchange and the anisotropies. Other physical properties, such as sublattice magnetization and specific heat, are discussed also.