Influence of composition, many-body effects, spin-orbit coupling, and disorder on magnetism of Co-Pt solid-state systems

Abstract

Systematic trends in the magnetism of Co-Pt solid-state systems are explored by studying the effects of composition, electron correlations, spin-orbit coupling (SOC), and long-range order. Ab initio fully relativistic calculations were performed for bulk Co, a substitutional Pt impurity in Co, ${\text{Co}}_{3}\text{Pt}$, CoPt, ${\text{CoPt}}_{3}$, and a substitutional Co impurity in Pt. Many-body effects beyond the local spin-density approximation (LSDA) were included via the dynamical mean-field theory (DMFT); a comparison with results based on the Brooks orbital-polarization (OP) scheme was also made. The disorder was treated within the coherent-potential approximation. We found that while the spin magnetic moments ${\ensuremath{\mu}}_{\text{spin}}$ at the Co atoms monotonously increase with increasing Pt concentration, the orbital magnetic moments ${\ensuremath{\mu}}_{\text{orb}}$ do not follow the trend of ${\ensuremath{\mu}}_{\text{spin}}$. Magnetic moments ${\ensuremath{\mu}}_{\text{spin}}$ and ${\ensuremath{\mu}}_{\text{orb}}$ at Pt atoms do not depend on Pt concentration monotonously. Most of these trends can be understood in terms of hybridization and site-dependent SOC. The OP scheme of Brooks corrects the deficiencies of a pure LSDA only if the Pt concentration is low. The $\text{LSDA}+\text{DMFT}$ scheme provides ${\ensuremath{\mu}}_{\text{orb}}/{\ensuremath{\mu}}_{\text{spin}}$ ratios for Co atoms which agree with experiment even for high Pt content. Introducing disorder leads to an enhancement of ${\ensuremath{\mu}}_{\text{spin}}$ at Co atoms and to a suppression of ${\ensuremath{\mu}}_{\text{spin}}$ at Pt atoms. The ${\ensuremath{\mu}}_{\text{orb}}$ at Co atoms does not exhibit any systematic dependence on the degree of order, while ${\ensuremath{\mu}}_{\text{orb}}$ at Pt atoms decreases with increasing disorder for all Pt concentrations.