Toward a geometric theory of magnetization dynamics : electronic contribution in the semiclassical approach
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This dissertation presents theoretical studies of the magnetization dynamics in ferromagnetic materials. To give a general description of the influences of electric fields or currents on magnetization dynamics, we developed a semiclassical theory for the magnetization implicitly coupled to electronic degrees of freedom. In the absence of electric fields, the Bloch electron Hamiltonian changes the Berry curvature, the effective H fields and the damping in the dynamical equation of the magnetization, which we classify into intrinsic and extrinsic effects. Static electric field modifies these as first-order perturbations, with which we are able to give a physically clear interpretation of the current-induced spin-orbit torques. In analogy of the electromagnetic fields, the Berry curvature is the magnetic field and the gradient of energy is the static electric field in the magnetization space. If the system is driven by external forces, an additional Faraday H field appears. The Faraday H field can be provided by electron motion, e.g. in the presence of electric fields, giving the intrinsic spin-orbital torque. We use a toy model mimicking a ferromagnet-topological-insulator interface to illustrate the various effects, and we predict an anisotropic gyromagnetic ratio and the dynamical stability for an in-plane magnetization. In the presence of inhomogeneity, the Faraday H field can be provided by electron velocity, giving rise to the intrinsic spin-transfer torque. In the semiclassical framework, the electronic spin dipole is found to influence the magnetization dynamics in terms of Dzyaloshinskii-Mariya interaction. We obtain both the equilibrium spin dipole and the field-induced spin dipole, for the equilibrium and non-equilibrium Dzyaloshinskii-Mariya interaction, respectively. In addition, the induced effective H field has a geometric contribution in the second Chern form, extending the first Chern form in uniform systems. Our results provide methods for the electric field control of magnetic structures.