  We predict a non-thermal magneto-optical effect for magnetic insulators
subject to intense light carrying orbital angular momentum (OAM). Using a
classical approach to second harmonic generation in non-linear media with
specific symmetry properties we predict a significant nonlinear contribution to
the local magnetic field triggered by light with OAM. The resulting magnetic
field originates from the displacement of electrons driven by the electrical
field (with amplitude $E_0$) of the spatially inhomogeneous optical pulse,
modeled here as a Laguerre-Gaussian beam carrying OAM. In particular, the
symmetry properties of the irradiated magnet allow for magnetic field responses
which are second-order ($\sim E_0^2$) and fourth-order ($\sim E_0^4$) in
electric-field strength and have opposite signs. For sufficiently high laser
intensities, terms $\sim E_0^4$ dominate and generate magnetic field strengths
which can be as large as several Tesla. Moreover, changing the OAM of the laser
beam is shown to determine the direction of the total light-induced magnetic
field, which is further utilized to study theoretically the non-thermal
magnetization dynamics.
