  Nonlinear photocurrent in time-reversal invariant noncentrosymmetric systems
have attracted substantial interest. Here we propose two new types of
second-order nonlinear direct photocurrent as the counterpart of normal shift
photocurrent (NSC) and normal injection photocurrent (NIC), namely magnetic
shift photocurrent (MSC) and magnetic injection photocurrent (MIC) in
time-reversal symmetry and inversion symmetry broken system. We show that MSC
is mainly governed by shift vector and interband Berry curvature, and MIC is
dominated by absorption strength and asymmetry of the group velocity difference
at time-reversed $\pm$$\textbf{k}$ points. MSC and MIC can be induced by
circularly and linearly polarized light, respectively, in
$\mathcal{PT}$-symmetric systems with $\mathcal{P}$ and $\mathcal{T}$ being
individually broken. Taking $\mathcal{PT}$-symmetric magnetic topological
quantum material bilayer antiferromagnetic (AFM) MnBi$_2$Te$_4$ as an example,
we predict the presence of large MIC in the terahertz frequency regime which
can be magnetically switched between two AFM states with time-reversed spin
orderings. While NSC vanishes in $\mathcal{T}$-symmetric systems, external
electric field breaks $\mathcal{PT}$ symmetry and enables large NSC response
which can be electrically switched. MIC and NSC are perpendicular to each other
upon linearly $x$/$y$-polarized light, and are highly tunable under electric
field, resulting in giant nonlinear photocurrent response down to a few THz
regime. It suggests bilayer AFM MnBi$_2$Te$_4$ as a tunable platform with rich
THz and magneto-optoelectronic applications. The present work reveals that
nonlinear photocurrent provides a powerful tool for deciphering magnetic
structures and interactions, particularly fruitful for probing and
understanding magnetic topological quantum materials.
