Unconventional Hall effect and magnetoresistance induced by metallic ferroaxial ordering

Transport property under metallic ferroaxial ordering in an external magnetic field is theoretically investigated. After presenting the relation between the magnetoconductivity tensor and ferroaxial moment from the symmetry viewpoint, we analyze the behavior of the unconventional Hall effect and magnetoconductivity for a general five $d$-orbital tight-binding model under the point group ${C}_{4\mathrm{h}}$, where the ferroaxial moment is activated. We show that the crystalline electric field that arises from the symmetry reduction from ${D}_{4\mathrm{h}}$ to ${C}_{4\mathrm{h}}$ is essential for the ferroaxial-related magnetotransport, while the relativistic spin--orbit coupling is not required. We also compare the unconventional Hall effect driven by the ferroaxial moment with the conventional Hall effect, the latter of which does not require the ferroaxial moment. The present results provide characteristic transport properties in the ferroaxial systems, which can be observed in various candidate materials like ${\mathrm{Ca}}₅{\mathrm{Ir}}₃{\mathrm{O}}₁₂$.