  Using the construction of the Fermi frame, the field of a gravitational wave
can be described in terms of gravito-electromagnetic fields that are transverse
to the propagation direction and orthogonal to each other. In particular, the
gravito-magnetic field acts on spinning particles and we show that, due to the
action of the gravitational wave field, a new phenomenon, that we call
gravito-magnetic resonance, may appear. We give both a classical and a quantum
description of this phenomenon and suggest that it can be used as the basis for
a new type of gravitational wave detectors. Our results highlight the
effectiveness of collective spin excitations, e.g. spin waves in magnetized
materials, in detecting high frequency gravitational waves. Here we suggest
that, when gravitational waves induce a precession of the electron spin, power
is released in the ferromagnetic resonant mode endowed with quadrupole symmetry
of a magnetized sphere. This offers a possible path to the detection of the
gravito-magnetic effects of a gravitational wave.
