Calculation of spin-wave energy and the mean value of Hamiltonian in a noncollinear magnetic sublattice structure by the method of Green's functions

The contribution of this work is the extension of Green's function formalism to the case of noncollinear, canted, 6-sublattice magnetic structure. The external magnetic field was considered. The selfconsistent procedure for calculation of renormalized spin-wave energies and the mean value of the Hamiltonian was discussed on the basis of both Tyablikov's and Callen's decoupling approximations and it was shown that the use of Callen's decoupling requires a preliminary solution of the problem on the basis of simpler decoupling. The equations are analogous to the Callen's equation but the temperature dependent factor has a more general form and instead of an explicit equation for energy there is an implicit equation.