  Coupling different physical properties is a fascinating subject of physics.
Already well-known are the multiferroics which show properties of
ferroelectrics and magnets. But ferroelectricity by itself also entails the
bulk photovoltaic effect, a light-matter interaction which generates dc
currents. Here we propose a magnetic photogalvanic effect that couples the
magnetism to the light-matter interaction. This phenomenon emerges from the
$\mathbf{k}$ to $\mathbf{-k}$ symmetry-breaking in the band structure and does
not require a static polarization. It is distinct from other known bulk
photovoltaic mechanisms such as the shift current. We demonstrate such
phenomena in a newly discovered layered magnetic insulator CrI$_3$. A record
photoconductivity response (more than 200 $\mu A V^{-2} $) is generated under
the irradiation of a visible light in the antiferromagnetic phase. The current
can be reversed and switched by controllable magnetic phase transitions. Our
work paves a new route for photovoltaic and optoelectronic devices and provides
a sensitive probe for the magnetic transition.
