Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

摘要

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q. The system of equations defining order parameters M _Q ~z, M _Q ~σ, M _z, and M ~σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H a?- M Q and H a?￥ M _Q (H _Z H ~σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ~σ = 0, and longitudinal magnetic susceptibility χa?- is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x c and to a gapless state for x > x c. In the immediate vicinity of the critical impurity concentration (x ～ x _c), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.