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A magnetic toroidal moment is a fundamental electronic degree of freedom inthe absence of both spatial inversion and time-reversal symmetries and givesrise to novel multiferroic and transport properties. We elucidate essentialmodel parameters of the nonlinear transport in the space-time ($\mathcal{PT}$)symmetric collinear antiferromagnetic metals accompanying a magnetic toroidalmoment. By analyzing the longitudinal and transverse components of thesecond-order nonlinear conductivity on a two-dimensionally stacked zigzag chainbased on the nonlinear Kubo formula, we show that an effective coupling betweenthe magnetic toroidal moment and the antisymmetric spin-orbit interaction is anessential source of the nonlinear conductivity. Moreover, we find that thenonreciprocal longitudinal current and nonlinear transverse current in amulti-band system are largely enhanced just below the transition temperature ofthe antiferromagnetic ordering. We also discuss the relevance of the nonlinearconductivity to the linear magnetoelectric coefficient and conductivity. Ourresult serves as a guide for exploring microscopic essence and clarifying theparameter dependence of the nonlinear conductive phenomena in ferrotoroidalmetals.

physical review. b./physical review. b

Analysis of model parameter dependences on the second-order nonlinear  conductivity in $\mathcal{PT}$-symmetric collinear antiferromagnetic metals  with magnetic toroidal moment on zigzag chains