  We investigate optically induced magnetization in Floquet-Weyl semimetals
generated by irradiation of a circularly-polarized continuous-wave laser from
the group II-V narrow gap semiconductor Zn$_3$As$_2$ in a theoretical manner.
Here, this trivial and nonmagnetic crystal is driven by the laser with a nearly
resonant frequency with a band gap to generate two types of Floquet-Weyl
semimetal phases composed of different spin states. These two phases host
nontrivial two-dimensional surface states pinned to the respective pairs of the
Weyl points. By numerically evaluating the laser-induced transient
carrier-dynamics, it is found that both spins are distributed in an uneven
manner on the corresponding surface states due to significantly different
excitation probabilities caused by the circularly-polarized laser with the
nearly resonant frequency. It is likely that such spin-polarized surface states
produce surface magnetization, and furthermore the inverse Faraday effect also
contributes almost as much as the spin magnetization. To be more specific,
excited carries with high density of the order of $10^{21}\: {\rm cm}^{-3}$ are
generated by the laser with electric field strength of a few MV/cm to result in
the surface magnetization that becomes asymptotically constant with respect to
time, around 1 mT. The magnitude and the direction of it depend sharply on both
of the intensity and frequency of the driving laser, which would be detected by
virtue of the magneto-optic Kerr effect.
