  Metallic nanostructures exhibit strong nonlinear-optical response at surface
plasmon resonances, where the light-matter coupling efficiency is enhanced. An
active modulation of this response can be realized by means of an external
magnetic field. Here we utilize a nonlinear magneto-refractive effect in
spintronic multilayer antennas to achieve a resonant 20\% modulation in second
harmonic generation (SHG) in the mid-infrared. We discuss mechanisms of this
modulation and show that it cannot be explained by an unequal enhancement of
the electromagnetic field in the two spin states of the multilayer. Instead, we
propose a novel contribution to the nonlinear susceptibility, which relies on
the spin-dependent electron mean free path in metals. In contrast to
magneto-optics in ferromagnets, our approach results in no shift of the
resonance and thus ensures that the largest SHG and its strongest modulation
are simultaneously observed.
