Quantum Model of Hysteresis in a Single-Domain Magnetically Soft Ferromagnet

A quantum model of a magnetically soft ferromagnet constructed based on a single domain of an alpha-Fe crystal magnetized to saturation and placed in an alternating magnetic field is suggested. Based on the method of an effective Hamiltonian, the model takes into account the Zeeman energy, the spin-orbital interaction, and the interaction with the crystal field. In order to take into account the magnetic anisotropy, an expansion of a trial single-electron wave function into a series in terms of a small parameter of the spin-orbital interaction is suggested. The nonlinear equations of motion for the magnetization and orbital moment of the domain have been determined within the Heisenberg representation. The parameters of the nonlinear equations have been determined by comparing with the experimental data on the magnetic anisotropy of iron. The equations were solved numerically using the Runge-Kutta method with taking into account the magnetic friction introduced phenomenologically. The dependence of the magnetization of a single domain on the strength of the applied magnetic field has been characterized by hysteresis. The main parameters of the hysteresis loop are in quantitative agreement with the experimentally measured magnetic properties of nanoparticles of iron and iron oxide. A method of simulating the magnetization dynamics of a multidomain ferromagnet in the approximation of a strong crystal field has been suggested.