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Recently, charge or spin nonlinear transport with nontrivial topologicalproperties in crystal materials has attracted much attention. In this paper, weperform a comprehensive symmetry analysis for all 122 magnetic point groups(MPGs) and provide a useful dictionary for charge and spin nonlinear transportfrom Berry curvature dipole, Berry connection polarization and Drude term withnontrivial topological nature. The results are obtained by making a fullsymmetry investigation on matrix representations of six nonlinear responsetensors. We further identify every MPG that can accommodate two or three of thenonlinear tensors. The present work gives a solid theoretical basis for overallunderstanding the second-order nonlinear responses in realistic materials.

Symmetry Dictionary on Charge and Spin Nonlinear Responses for All Magnetic Point Groups with Nontrivial Topological Nature