How disorder affects the Berry-phase anomalous Hall conductivity: the view from k space

Abstract

The anomalous Hall conductivity of "dirty" ferromagnetic metals is dominated by a Berry-phase contribution which is usually interpreted as an intrinsic property of the Bloch electrons in the pristine crystal. In this work we evaluate the geometric Hall current directly from the electronic ground state with disorder, and then recast it as an integral over the crystalline Brillouin zone. The integrand is a generalized k-space Berry curvature, obtained by unfolding the Berry curvature from the small Brillouin zone of a large supercell. Therein, disorder yields a net extrinsic Hall contribution, which we argue is related to the elusive side-jump effect. As an example, we unfold the first-principles Berry curvature of an Fe3Co ordered alloy from the original fcc-lattice Brillouin zone onto a bcc-lattice zone with four times the volume. Comparison with the virtual-crystal Berry curvature clearly reveals the symmetry-breaking effects of the substitutional Co atoms.

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• A fully relativistic description of spin-orbit torques by means of linear response theory
• Valley Hall effect in disordered monolayer MoS2 from first principles
• Quantum kinetic theory of quadratic responses
• Tunable valley Hall effect in gate-defined graphene superlattices
• Large anomalous Nernst coefficient in an oxide Skyrmion crystal Chern insulator
• Higher dimensional Wannier functions of multi-parameter Hamiltonians
• Transport properties of doped permalloy via ab-initio calculations: effect of the host disorder
• Unfolding optical transition weights of impurity materials for first-principles LCAO electronic structure calculations
• Terahertz magneto-optical response in ferromagnetic Fe-Co-Al alloys
• Intrinsic nonlinear Hall effect beyond Bloch geometry
• Berry-phase effect in single molecule magnets: analytical and numerical results