Heisenberg Hamiltonian description of multiple-sublattice itinerant-electron systems: General considerations and applications to NiMnSb and MnAs

We consider magnetic systems where the magnetic sublattices can be unambiguously separated into sublattices of inducing and induced moments. The concrete numerical calculations are performed for half-metallic ferromagnetic Heusler compound NiMnSb and hexagonal phase of MnAs. In both systems, Mn atoms possess a robust atomic moment that is much larger than the induced moments of other atoms. It is shown that the treatment of the induced moments as independent variables of the Heisenberg Hamiltonian leads to artificial features in the spin-wave spectrum. We show that the artificial features of the model do not have a dramatic influence on the estimated value of the Curie temperature. This is demonstrated within both mean-field approximation and random-phase approximation. It is shown that the calculational scheme where the induced moments are assumed to fully adjust their values and directions to the adiabatic magnetic configurations of the inducing moments is free from the artificial feature in the spin-wave spectra. In this scheme, the exchange interaction between the inducing and induced moments appears as renormalization of the exchange interactions between inducing moments. It is shown that the redistribution of the exchange interactions has strong influence on the estimated value of the Curie temperature because of the decreased number of the degrees of freedom in the thermodynamic model. Different schemes of the mapping of the systems on the Heisenberg Hamiltonian are examined. The similarities and differences in the properties of NiMnSb and MnAs are discussed.