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accordance with Eq according to Eq anisotropy antiferromagnetic applied assume atoms ators average value Bogolyubov 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 Fourier free energy func given by Eq Green's functions Haar Hamiltonian Heisenberg interaction isotropic ferromagnet Izyumov magnetic field magnetic substances mass operator matrix molecular field Nauk SSSR neutron notation number of particles obtain the following occupation numbers perturbation theory Phys Phys.Rev problem quadratic form quantities quantum reciprocal lattice represents scattering second quantization solution spectral density spectrum spin operators spin system spin waves sublattices Substituting Eq system of equations Teor theory of magnetism tion transformation Turov Tyablikov unit cell variables Vonsovskii wave function wave vector zero