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Transport property under metallic ferroaxial ordering in an external magneticfield is theoretically investigated. After presenting the relation between themagnetoconductivity tensor and ferroaxial moment from the symmetry viewpoint,we analyze the behavior of the unconventional Hall effect andmagnetoconductivity for a general five $d$-orbital tight-binding model underthe point group $C_{\rm 4h}$, where the ferroaxial moment is activated. We showthat the crystalline electric field that arises from the symmetry reductionfrom $D_{\rm 4h}$ to $C_{\rm 4h}$ is essential for the ferroaxial-relatedmagnetotransport, while the relativistic spin-orbit coupling is not required.We also compare the unconventional Hall effect driven by the ferroaxial momentwith the conventional Hall effect, the latter of which does not require theferroaxial moment. The present results provide characteristic transportproperties in the ferroaxial systems, which can be observed in variouscandidate materials like Ca$_5$Ir$_3$O$_{12}$.

Unconventional Hall effect and magnetoresistance induced by metallic ferroaxial ordering