Scaling of the anomalous Hall effect in the insulating regime

Abstract

We develop the theory of the scaling of the anomalous Hall effect (AHE) in the insulating regime, which is observed in experiments to relate the anomalous Hall and diagonal conductivities by σ AH xy ∝ σ 1.40∼1.75 xx for a large range of materials. This scaling is qualitatively different from the ones observed in metals. Basing our theory on the phonon-assisted hopping mechanism and percolation theory in random networks, we derive a general formula for the anomalous Hall conductivity (AHC), in which the percolation theory averaging of the random linked triad clusters is a key aspect that captures the correct observed physics. We show that it scales with the longitudinal conductivity as σ AH xy ∼ σ γ xx with γ predicted to be 1.33 ≤ γ ≤ 1.76, quantitatively in agreement with the experimental observations. Our theory predicts that this scaling remains similar regardless of whether the hopping process is long range type (variable range hopping) or short range type (activation hopping), or is influenced by interactions, i.e. Efros-Shklovskii (E-S) regime. Our theory completes the understanding of the AHE phase diagram in the insulating regime.

Unified theory of spin dynamics in a two-dimensional electron gas with arbitrary spin-orbit coupling strength at finite temperature

“…The width of the quantum well is normally around 11nm. Besides reproducing all known limits and previously derived results at zero temperature, 9,10,12,15,18 it succeeds dramatically in describing quantitatively the non-monotonic behavior of the spin lifetime of the SHE mode as shown in Fig. 1 in a wide temperature range.…”

Itinerant ferromagnetism and intrinsic anomalous Hall effect in amorphous iron-germanium

“…2 emphasizes that this intrinsic contribution to the arXiv:1908.06055v2 [cond-mat.mes-hall] 30 Oct 2019 AHC depends only on the topology of the band structure and not on the details of scattering in the material. 8,9 The relative importance of these three mechanisms has long been disputed, but some clarity has come from a unified theory, originally proposed by Onoda 10 and elaborated upon by Liu,11 which separates systems into three regimes based on longitudinal conductivity σ xx = ρ −1 xx : a high conductivity "clean" limit where σ xx 10 6 (Ωcm) −1 and σ AH xy ∝ σ xx , indicating that the AHC is dominated by skew-scattering; an intermediate "good metal" regime where 10 4 σ xx 10 6 (Ω cm) −1 and σ AH xy is independent of σ xx , indicating that the intrinsic mechanism dominates the AHC; and a low conductivity regime where σ xx 10 4 (Ω cm) −1 , which was less well understood. At the time of Onoda's work, this last regime was described empirically as having σ AH xy ∼ σ γ xx , with γ ranging between 1.6−1.8; Onoda recovered the scaling γ = 1.6 in the hopping regime, and Liu found 1.33 ≤ γ ≤ 1.76 by studying multiple hopping processes which typically occur deep in the low conductivity regime (σ xx 10 2 (Ω cm) −1 ), demonstrating that the microscopic origin of the AHE determines its scaling in this insulating regime.…”

Magnetotransport Anomaly in Room‐Temperature Ferrimagnetic NiCo2O4 Thin Films

“…However, given the limited σ xx variation in this regime, we cannot rule out the possibility that the weak σ xx ‐dependence is a transition behavior, or the enhanced electron correlation modifies the Berry curvature of the band. For the 5 uc film, on the other hand, σ xy slightly decreases with temperature, which may be due to phonon‐assisted hopping or enhanced disorder correlation as the film approaches the electric dead layer thickness . For both types of behaviors, future experiments at temperatures below 2 K and additional theoretical insights on the effect of electron correlation are required to fully understand the AHE at the low‐temperature regime.…”