Gravitomagnetic resonance in the field of a gravitational wave

Using the construction of the Fermi frame, the field of a gravitational wave can be described in terms of gravitoelectromagnetic fields that are transverse to the propagation direction and orthogonal to each other. In particular, the gravitomagnetic field acts on spinning particles and we show that, due to the action of the gravitational-wave field, a new phenomenon - which we call gravitomagnetic 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 gravitomagnetic effects of a gravitational wave.