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

Abstract

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 MQ. The system of equations defining order parameters MQz, MQσ, Mz, and Mσ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ MQ and H ⊥ MQ (HZHσ = 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 TM 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 TM is analyzed for HZHσ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x xc. In the immediate vicinity of the critical impurity concentration (x ∼ xc), 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.