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accordance with Eq according to Eq anisotropy antiferromagnetic applied assume atoms ators average value axis Bose operators calculations coefficients commutation relationships configurations Consequently consider correlation functions crystal lattice Curie point Curie temperature denote density matrix dependence eigenfunctions eigenvalues electrons elementary excitations exchange integral expansion external field ferromagnetic resonance field H form of Eq formulas free energy given by Eq Green's functions Haar Hamiltonian Heisenberg interaction isotropic ferromagnet Izyumov magnetic field magnetic substances mass operator matrix molecular field neutron notation number of particles obtain the following occupation numbers parameter perturbation theory Phys Phys.Rev problem quadratic form quantities quantum reciprocal lattice represents scattering second quantization series in powers solution spectral density spectrum spin operators spin system spin waves SSSR sublattices Substituting Eq system of equations theory of magnetism tion Tyablikov unit cell variables Vonsovskii wave function wave vector zero