Abstract:The anomalous Hall effect (AHE) in strongly disordered magnetic systems has been buried in persistent confusion despite its long history. We report the AHE in perpendicularly magnetized L10-MnAl epitaxial films with variable orbital two-channel Kondo (2CK) effect arising from the strong coupling of conduction electrons and the structural disorders of two-level systems. The AHE is observed to excellently scale with ρAH/f=a0ρxx0+bρxx 2 at high temperatures where phonon scattering prevails. In contrast, significant deviation occurs at low temperatures where the orbital 2CK effect becomes important, suggesting a negative AHE contribution. The deviation of the scaling agrees with the orbital 2CK effect in the breakdown temperatures and deviation magnitudes. The scaling between longitudinal resistivity (ρxx) and anomalous Hall resistivity (ρAH) can provide access to the detailed mechanisms of the AHE. Present theories predict a scaling of ρAH~ρxx n , with n = 2 for side jump and intrinsic contribution [4,5], and n = 1 for skew scattering [6]. The intrinsic contribution is related to the topological Berry curvature of band structure [4], while the extrinsic side jump and skew scattering result from spin-orbit interaction-induced asymmetric impurity scattering of conduction electrons [5,6]. Notably, in contrast to the conventional picture that ρAH scales with the total resistivity irrespective of its sources [3], recent experimental studies have revealed that both ρAH and the scaling relation are qualitatively different for various types of electron scattering. Phonon scattering was found to have no distinguishable contribution to extrinsic part of ρAH in ferromagnetic Fe, Co, Ni, L10-Mn1.5Ga films, Co/Pt multilayers, and paramagnetic Ni34Cu66 films [7][8][9][10][11][12]. When ρxx is dominated by phonon and static defect scattering, the AHE has a scaling of ρAH = a0 ρxx0+bρxx 2 , where ρxx0 is the residual resistivity, a0ρxx0 is the extrinsic contribution from both side jump and skew scattering, and b is the intrinsic anomalous Hall conductivity (AHC). In magnetic materials with relatively low Curie temperature, the temperature (T) induced variation of the magnetization must be taken into account [13]. For the simplest case that ρAH scales proportionally with magnetization (M) which is not the fact in some magnetic systems [14,15], the AHE scaling can be modified into a more general expression explicitly as ρAH/f = a0 ρxx0+bρxx 2 . Here, f = M / M0, where M0 is magnetization at 0 K; the Tindependence of a0 and b is not considered. In the presence of strong disorder effects (dirty metal [1]), the AHE scaling is more complex. In the hopping conduction regime, the AHE was reported to scale as ρAH~ρxx 0.4 [19][20][21]. Therefore, further experimental and theoretical attempts are crucial for better understanding of the AHE, especially in disordered magnetic systems.
Key words:AnomalousThe Kondo effect is a striking consequence of conduction electrons coupling with localized spin or "pseudospin" impurities. The on...