We present a simple methodology to compute the anomalous Hall conductivity (AHC) as a function of the canting angles in ferromagnets and altermagnets, starting from a nonmagnetic Hamiltonian obtained from first-principles calculations that preserves the full symmetry of the crystal structure. Magnetism is introduced by including on-site spin splitting, spin-orbit coupling, and spin-canting angles. As a representative material, we study ${\mathrm{SrRuO}}_3$, which supports spin canting and exhibits a sign change of the AHC. In the ferromagnetic phase, the low-energy AHC is found to be close to zero at the Fermi level, in agreement with experimental observations. We show that the dependence of the AHC on the relevant physical parameters is most pronounced in the central region of the electronic bandwidth. We determine the symmetry-allowed components of the AHC for different magnetic orders in the large family of transition-metal perovskite ${AB\mathrm{O}}_3$ compounds with space group 62, including the spontaneous in-plane anomalous Hall effect. Within density functional theory, we evaluate the range of spin-canting angles in ${\mathrm{SrRuO}}_3$ and demonstrate that it is suppressed as electronic correlations increase. By analyzing the AHC as a function of the canting angle, we find that the collinear magnetic configurations contribute most to the AHC, while spin canting plays a secondary role in determining its magnitude in noncollinear ferromagnets and altermagnets. However, canting can become relevant and induce a sign change of the AHC when the collinear magnetic state exhibits an AHC close to zero. Finally, we investigate the locations of Weyl points in the Brillouin zone and their evolution as a function of the canting angle.

Close

PrevNext

View figure in article

• Electronic structure
• Magnetism
• Spin-orbit coupling
• Symmetry protected topological states
• Topological phases of matter
• Topological materials
• Density functional theory
• Materials modeling
• Tight-binding model
• Wannier function methods