Anisotropy of the spin Hall effect in a Dirac ferromagnet

Abstract

We study the intrinsic spin Hall effect of a Dirac Hamiltonian system with ferromagnetic exchange coupling, a minimal model combining relativistic spin-orbit interaction and ferromagnetism. The energy bands of the Dirac Hamiltonian are split after introducing a Stoner-type ferromagnetic ordering which breaks the spherical symmetry of pristine Dirac model. The totally antisymmetric spin Hall conductivity (SHC) tensor becomes axially anisotropic along the direction of external electric field. Interestingly, the anisotropy does not vanish in the asymptotic limit of zero magnetization. We show that the ferromagnetic ordering breaks the spin degeneracy of the eigenfunctions and modifies the selection rules of the interband transitions for the intrinsic spin Hall effect. The difference in the selection rule between the pristine and the ferromagnetic Dirac phases causes the anisotropy of the SHC, resulting in a discontinuity of the SHC as the magnetization, directed orthogonal to the electric field, is reduced to zero in the ferromagnetic Dirac phase and enters the pristine Dirac phase.

arXiv comment12 pages, 5 figure

References in corpus (28)

• Anomalous Hall effect
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Universal Intrinsic Spin-Hall Effect
• Magnetic switching by spin torque from the spin Hall effect
• Topological nodal semimetals
• Model Hamiltonian for Topological Insulators
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Study of Intrinsic Spin Hall Effect and Orbital Hall Effect in 4d- and 5d- Transition Metals
• Intrinsic spin Hall effect in platinum metal
• Quantum transport theory of anomalous electric, thermoelectric, and thermal Hall effects in ferromagnets
• Theory of the anomalous Hall effect from the Kubo formula and the Dirac equation
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Transport Properties and Diamagnetism of Dirac Electrons in Bismuth
• Intrinsic spin currents in ferromagnets
• Magnetic susceptibility in three-dimensional nodal semimetals
• Intrinsic Spin Hall Effect
• Spin-Hall Effect and Diamagnetism of Dirac Electrons
• Relativistic corrections in magnetic systems
• Magnetization direction dependent spin Hall effect in 3d ferromagnets
• Ferromagnetic state above room temperature in a proximitized topological Dirac semimetal
• Transport Properties of Dirac Ferromagnet
• Spin Hall effect driven by the spin magnetic moment current in Dirac materials
• Intrinsic and Extrinsic Spin Hall Effects of Dirac Electrons
• Non-equilibrium spin density and spin-orbit torque in three dimensional topological insulators - antiferromagnet heterostructure
• Inverse Faraday effect in massive Dirac electrons
• Gauge-invariant cutoff for Dirac electron systems with a vector potential