Table 1 Classification of different types of Hall effects
From: Room temperature observation of the anomalous in-plane Hall effect in a Weyl ferromagnet
Property | OHE | AHE | PHE | STR | IPHE |
|---|---|---|---|---|---|
Direction of B or M | Out-of-plane | Out-of-plane | In-plane | In-plane | In-plane |
Symmetry under B or M reversal | σxy(Bz) = −σxy(−Bz) | σxy(Mz) = −σxy(−Mz) | σxy(B∥) = σxy(−B∥) | σxy(Mx) = σxy(−Mx) | σxy(B∥) = −σxy(−B∥) |
Conductivity tensor | \(\left(\begin{array}{ll}0&{\sigma }_{xy}\\ -{\sigma }_{xy}&0\end{array}\right)\) | \(\left(\begin{array}{ll}0&{\sigma }_{xy}\\ -{\sigma }_{xy}&0\end{array}\right)\) | \(\left(\begin{array}{ll}0&{\sigma }_{xy}\\ {\sigma }_{xy}&0\end{array}\right)\) | \(\left(\begin{array}{ll}0&{\sigma }_{xy}\\ {\sigma }_{xy}&0\end{array}\right)\) | \(\left(\begin{array}{ll}0&{\sigma }_{xy}\\ -{\sigma }_{xy}&0\end{array}\right)\) |
True Hall signal | Yes | Yes | No | No | Yes |
Physical origin in our measurements | Field misalignment Bz | Out-of-plane canting Mz | Magnetic field-induced AMR | Magnetization-induced AMR | Intrinsic Zeeman coupling |
Magnetic field dependence in our measurements | B-antisymmetric | B-symmetric | B-symmetric | B-symmetric | B-antisymmetric |
Dependence on ϕB and ϕE in our measurements | angle independent or \(\sin ({\phi }_{{{\rm{B}}}})\) | independent | \(\sin (2{\phi }_{{{\rm{B}}}}-2{\phi }_{{{\rm{E}}}})\) | \(\sin (2{\phi }_{{{\rm{E}}}})\) | \(\cos ({\phi }_{{{\rm{B}}}})\) |
