Spin relaxation of a diffusively moving carrier in a random hyperfine field

Relaxation, < S-z(t)>, of the average spin of a carrier in a course of hops over sites hosting random hyperfine fields is studied theoretically. In low dimensions, d = 1,2, the decay of average spin with time is nonexponential at all times. The origin of the effect is that for d = 1,2 a typical random-walk trajectory exhibits numerous self-intersections. Multiple visits of the carrier to the same site accelerates the relaxation since the corresponding partial rotations of spin during these visits add up. Another consequence of self-intersections of the random-walk trajectories is that, in all dimensions, the average, < S-z(t)>, becomes sensitive to a weak magnetic field directed along z. Our analytical predictions are complemented by the numerical simulations of < S-z(t)>. The scenario of acceleration of spin relaxation due to returns applies also to the non-Markovian decoherence of a qubit surrounded by multiple fluctuators.