Simulation of quantum states in solid-state ferromagnetic nanostructures

Abstract

Purpose of the article. Identification and analysis of mathematical expressions for the energy spectrum of charge carriers in nano-sized magnetic films of nickel and Ni-Cu (substrate), as well as NiO-Ni-Cu (substrate) structures.Methods. In this work, based on basic quantum mechanical concepts and taking into account the boundary conditions for coupled quantum wells, expressions for the energy spectrum of electrons are obtained. The ferrimagnetic properties of nickel are taken into account through the effective mass value. The solution of nonlinear equations that determine discrete energy levels was achieved by numerical methods using the Mathcad mathematical package.Results. Transcendental expressions for the energies of free charge carriers in quantum wells of ferromagnetic nickel films are obtained, and the influence of the position of nickel on the copper substrate is shown. It has been shown that the use of a copper substrate leads to an increase in the density of energy levels in the nickel nanofilm. The influence of the oxide layer on single-electron states in nanofilms of nickel and its oxide is considered within the framework of the Anderson model. Based on the numerical solution of the transcendental equations obtained in the work, the influence of the ratio of the thicknesses of a ferromagnetic metal and its oxide on the energy levels of electrons localized in the oxide layer is shown.Conclusions. The formulas presented in the work for the energy spectrum take into account the energy relief of a complex quantum well, the dimensions of the film, surface oxide, and the significant effective mass in the region of the ferromagnetic film. It has been shown that an increase in the effective mass in magnetic heterostructures leads to an increase in the electron density of states. It was found that the density of electronic states in the region of surface nickel oxide is practically independent of the thickness of the nickel film. The results and conclusions of the work can be used for theoretical prediction of the physical properties of magnetic nanostructures, in particular spintronic elements.