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

Temperature- dependence of anomalous Hall conductivity in Rashba-type ferromagnets