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