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Violation of parity symmetry gives rise to various physical phenomena such asnonlinear transport and cross-correlated responses. In particular, thenonlinear conductivity has been attracting a lot of attentions in spin-orbitcoupled semiconductors, superconductors, topological materials, and so on. Inthis paper we present theoretical study of the nonlinear conductivity inodd-parity magnetic multipole ordered systems whose $\mathcal{PT}$-symmetry isessentially distinct from the previously studied acentric systems. Combiningmicroscopic formulation and symmetry analysis, we classify the nonlinearresponses in the $\mathcal{PT}$-symmetric systems as well as$\mathcal{T}$-symmetric (non-magnetic) systems, and uncover nonlinearconductivity unique to the odd-parity magnetic multipole systems. A giantnonlinear Hall effect, nematicity-assisted dichroism and magnetically-inducedBerry curvature dipole effect are proposed and demonstrated in a model forMn-based magnets.

Nonlinear electric transport in odd-parity magnetic multipole systems: Application to Mn-based compounds