Thermodynamical properties of a Heisenberg model with Dzyaloshinski–Moriya interactions

Abstract

Within the framework of a new correlated effective-field theory (CEF) the effects of the Dzyaloshinski–Moriya (DM) interactions on magnetic properties of the spin-1/2 anisotropic Heisenberg model are discussed. The CEF theory is based on a generalized but approximate Callen–Suzuki spin relation for cluster with two spins, and makes use of the Honmura–Kaneyoshi exponential operator technique. The phase diagram and the thermal behavior of magnetization are analyzed for the simple cubic lattice, and compared with the corresponding two-spin cluster mean-field (MFA) predictions. It is shown that for the easy direction (D=Dz; where D is the DM vector coupling), the model exhibit a tricritical point (TCP), at which the phase transition changes from second to first order. The TCP is explicitly obtained, and the tricritical temperature, Tt, is independent of the exchange anisotropy parameter Δ (Δ=0 and Δ=1, correspond the isotropic Heisenberg and Ising models, respectively), while the tricritical parameter, Dt, has dependence on Δ. In spite of its simplicity, the present CEF formalism yields results, which represent a remarkable improvement on the usual MFA treatment.