Interaction of circularly polarized laser pulses with spherical nano-droplets generates nanometer-size magnets with lifetime on the order of hundreds of femtoseconds. Such magnetic dipoles are close enough in a cluster target and magnetic interaction takes place. We investigate such system of several magnetic dipoles and describe their rotation in the framework of Lagrangian formalism. The semi-analytical results are compared to particle-in-cell simulations, which confirm the theoretically obtained terrahertz frequency of the dipole oscillation.