Table 1 Space-inversion and time-reversal symmetries of the multipole \({\chi }_{{ijk}}\) tensors for the case of MnPS₃, with \(L\) being the antiferromagnetic order parameter

MD

\({\chi }_{{ijk}}^{{{\rm{m}}}}\left(\propto {a}_{0}+{a}_{2}{L}^{2}\right)\)

axial, i

ED

\({\chi }_{{ijk}}^{{{\rm{e}}}}\left(\propto L\right)\)

polar, c

ΔED

\({\Delta \chi }_{{ijk}}^{{{\rm{e}}}} \left(={\chi }_{{ijkl}}^{{{\rm{e}}}}{E}_{l}\right)\)

polar, i