Table 1 Unified categorization of various Hall effects taking place in canted ferromagnets (FM) and antiferromagnets (AFM) as a function of ferromagnetic/staggered magnetization \({\hat{{\bf{n}}}}_{+/-}\) and structural chirality χ. Here, \({\alpha }_{i}^{{\rm{FM}}}\) and \({\beta }_{ij}^{{\rm{FM}}}\) are expansion coefficients, depending on whether the reference state is FM or AFM. The leading order is linear or quadratic in the Rashba spin-orbit interaction parameter αR.
From: The chiral Hall effect in canted ferromagnets and antiferromagnets
sA ↔ sB | Canted ferromagnet | Canted antiferromagnet |
|---|---|---|
Chiral Hall effect | Crystal Hall effect | |
\({\sigma }_{xy}^{{\rm{odd}}}\) | \({\alpha }_{i}^{{\rm{FM}}}({\hat{{\bf{n}}}}_{+}){\chi }_{i}\) | \({\alpha }_{ij}^{{\rm{AFM}}}({\hat{{\bf{n}}}}_{-}){\chi }_{i}{\chi }_{j}\) |
\({\sim}\) αR | \({\sim}\) αR | |
Crystal Hall effect | Chiral Hall effect | |
\({\sigma }_{xy}^{{\rm{even}}}\) | \({\beta }_{ij}^{{\rm{FM}}}({\hat{{\bf{n}}}}_{+}){\chi }_{i}{\chi }_{j}\) | \({\beta }_{i}^{{\rm{AFM}}}({\hat{{\bf{n}}}}_{-}){\chi }_{i}\) |
\(\sim {\alpha }_{{\rm{R}}}^{2}\) | \(\sim {\alpha }_{{\rm{R}}}^{2}\) |
