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Recently, nonlinear responses have been actively studied in both experiments and theory. Particularly interesting are inversion-symmetry broken systems, where an even-order nonlinear electrical conductivity can be nonzero, resulting in nonreciprocity. Second-order nonlinear conductivities attract much attention because of their sensitivity to detect inversion-symmetry breaking in materials and their functionalities. However, while the nonlinear response has been actively studied in noninteracting systems for a long time, the nonlinear response in strongly correlated materials is still poorly understood. This paper analyzes the nonlinear conductivity in a correlated noncentrosymmetric system, namely a Kondo lattice system with Rashba type spin-orbit coupling. We mainly focus on the ferromagnetic phase, in which the second-order nonlinear conductivity becomes finite. Remarkably, we find that the second-order conductivity becomes only finite perpendicular to the ferromagnetic magnetization and has a strong spin dependence; due to a gap at the Fermi energy for one spin direction, the linear and nonlinear conductivity is only finite for the ungapped spin direction. Finally, we analyze sign changes in the nonlinear conductivity, which can be explained by a combination of correlation effects and the energetic shift due to the occurring ferromagnetism.

Magnetization can be induced by an electric field in systems without inversion symmetry P and time-reversal symmetry T . This phenomenon is called the magnetoelectric (ME) effect. The spin ME effect has been actively studied in multiferroics. The orbital ME effect also exists and has been mainly discussed in topological insulators at zero temperature. In this paper, we study the intrinsic orbital ME response in metals at finite temperature using the Kubo formula. The intrinsic response originates from the Fermi sea and does not depend on the dissipation. Especially in systems with PT -symmetry, the extrinsic orbital ME effect becomes zero, and the intrinsic ME effect is dominant. We apply the response tensor obtained in this work to a PT -symmetric model Hamiltonian with antiferromagnetic loop current order demonstrating that the intrinsic ME effect is enhanced around the Dirac points.

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