Temperature Dependence of Anomalous Hall Conductivity in Rashba-type Ferromagnets

Abstract

The applicability and usefulness of Rashba model have been extended by recent observations in the field of spintronics, such as the spin-orbit torque at the junction interfaces between ferromagnetic (FM) metals and non-magnetic (NM) metals and the perpendicular anomalous magnetoresistance (AMR) in heterostructures such as FI/NM or FM/NI (I denotes an insulator). In particular, the observations of the perpendicular AMR effect stimulate further interest in the Rashba-type spin-orbit interaction (SOI) at interfaces. Thus, the Rashba model with exchange splitting (EXS) is considered not only to play as an effective model for the physical understanding but also to reflect actual bi-layer systems in current spintronics devices. In the present work, we have first investigated the temperature dependence of anomalous Hall conductivity (AHC) of Rashba-type ferromagnets considered effects of spin fluctuations within the disordered local moment (DLM) scheme. The most distinctive feature that we observed is that intrinsic AHC increases with increasing temperature. This can be understood from the aspect of spin chirality, which indicates that the AHC increases with decreasing EXS when the SOI is much smaller than the EXS. The extrinsic part of the Fermi surface term also increases with increasing temperature and has a large contribution, comparable to that of the intrinsic part. Although, such a behaviour has not yet been observed experimentally, we suggest that the physical picture found in this work might lurk in an anomalous Hall effects in Rashbe-type ferromagnets.