Ferromagnetism by p−d exchange spin-orbit coupling in n -type ferromagnetic semiconductors

Abstract

The exchange interaction between carrier and localized spin in magnets generates intrinsic spin-orbit coupling induced by the magnetism. Recent studies for the exchange spin-orbit coupling (ESOC) in ferromagnets and antiferromagnets suggest the ESOC and the transport phenomena for spintronics. However, the study on the effects of ESOC on the magnetic phase transition has been still lacking especially for ferromagnets even though the ESOC should be one of the fundamental interactions to stabilize the magnetic phase. In this paper, we study the role of the ferromagnetic properties of the ESOC induced by the $p\text{\ensuremath{-}}d$ exchange interaction of the valence band in $n$-type ferromagnetic semiconductors. Based on the mean-field and $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ methods, our theory explains the spin polarization of localized and carrier spin, and the Curie temperature ${T}_{c}$ for the iron concentration, electron density, and host semiconductor dependence. The theoretical ${T}_{c}$ fits experimental values well in low iron concentration and intermediate electron density regions, and the $p\text{\ensuremath{-}}d$ exchange interaction is essential for ${T}_{c}$. Furthermore, the ${T}_{c}$ is higher for narrower gap host semiconductors to provide insights into higher ${T}_{c}$. The theoretical framework of this paper is not limited to the specific materials and will find potential materials for spintronics and the fundamental aspects.