  It is known that intrinsic currents in magnetic metals often appear in the
direction perpendicular to the external field for linear and nonlinear
responses. Distinct from three kinds of known nonlinear currents, namely, the
Drude contribution, the Berry curvature dipole induced current and the Berry
connection polarization induced current, here we report a intrinsic nonlinear
current with breaking time-reversal symmetry. This new kind of intrinsic
nonlinear current from the nontrivial Berry connection polarizability may
emerge in the longitudinal or transverse direction, and both are dissipative
Ohmic currents. We unveil 66 magnetic point group symmetries that can
accommodate such nonlinear current, and possible candidate materials are
proposed. This theory is also applied to observe the nonlinear current we
proposed in one- and two-dimensional Dirac systems as examples.
