Dynamics of the spin in slowly rotating magnetic field*

We study the dynamics of a spin coupled to its environment in a slowly rotating magnetic field. We show that once rotation starts abruptly, the spin exhibits precession around rotating magnetic field. This precession is suppressed due to the decoherence of the spin induced by the environment. At longer times, the spin rotates with the magnetic field and has a component perpendicular to the plane of rotation of the field, which is proportional to the product of the Berry curvature and the angular velocity of the rotation. Finite temperature environment causes thermalization of the spin and, in particular, effectively reduces the magnitude of the spin in the direction perpendicular to the plane of rotation.