Magnetization orientation dependence of the quasiparticle spectrum and hysteresis in ferromagnetic metal nanoparticles

TL;DR

This study models ferromagnetic metal nanoparticles to understand how magnetization direction influences quasiparticle spectra and hysteresis, revealing complex behaviors and a crossover from weak to strong spin-orbit coupling regimes.

Contribution

It introduces a microscopic tight-binding model to analyze magnetocrystalline anisotropy and hysteresis in nanoparticles, highlighting the fluctuation of anisotropy with electron number and the complex spectral dependence on magnetic fields.

Findings

Magnetic anisotropy per atom fluctuates with electron number.

Quasiparticle spectra show non-monotonic dependence on magnetic field.

Evidence of a crossover from weak to strong spin-orbit coupling regimes.

Abstract

We use a microscopic Slater-Koster tight-binding model with short-range exchange and atomic spin-orbit interactions that realistically captures generic features of ferromagnetic metal nanoparticles to address the mesoscopic physics of magnetocrystalline anisotropy and hysteresis in nanoparticle quasiparticle excitation spectra. Our analysis is based on qualitative arguments supported by self-consistent Hartree-Fock calculations for nanoparticles containing up to 260 atoms. Calculations of the total energy as a function of magnetization direction demonstrate that the magnetic anisotropy per atom fluctuates by several percents when the number of electrons in the particle changes by one, even for the largest particles we consider. Contributions of individual orbitals to the magnetic anisotropy are characterized by a broad distribution with a mean more than two orders of magnitude smaller than its variance and with no detectable correlations between anisotropy contribution and quasiparticle energy. We find that the discrete quasiparticle excitation spectrum of a nanoparticle displays a complex non-monotonic dependence on an external magnetic field, with abrupt jumps when the magnetization direction is reversed by the field, explaining recent spectroscopic studies of magnetic nanoparticles. Our results suggests the existence of a broad cross-over from a weak spin-orbit coupling to a strong spin-orbit coupling regime, occurring over the range from approximately 200- to 1000-atom nanoparticles.