Spin and anomalous Hall effects emerging from topological degeneracy in the Dirac fermion system CuMnAs

Orthorhombic CuMnAs has been proposed as an antiferromagnetic semimetal hosting nodal line and Dirac points around the Fermi level. We investigate relations between the topological bands and transport phenomena, i.e., the spin Hall effect and anomalous Hall effect, in orthorhombic CuMnAs with first-principles calculations combined with a symmetry analysis of the magnetic structures and of the (spin) Berry curvature. We show the nodal line gapped with spin-orbit coupling in CuMnAs dominantly generates large spin Hall conductivity in the ground state. Although the magnetic symmetry in the ground state of CuMnAs forbids the finite anomalous Hall effect, applied magnetic fields produce a significant anomalous component of the Hall conductivity with the magnetic symmetry breaking. We identify that the dominant contribution to anomalous Hall components comes from the further lifting of band degeneracy under external magnetic fields for the Bloch states generated with the splitting of nodal lines by spin-orbit coupling near the Fermi energy.