In course of carrier motion between the sites which host random hyperfine fields, its spin experiences random precessions. Normally, this leads to the exponential decay of average spin, , with a rate proportional to the square of the magnitude of the field. We demonstrate that in low dimensions, d = 1, 2, this orthodox scenario is violated: the decay does not follow the simple-exponent behavior 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, becomes sensitive to a weak magnetic field directed along z-axis. Remarkably, for random fields located in the (x, y) - plane, the decay of in d = 1 is accompanied by the reversal. We develop an approximate analytical description of the behavior. This description is in a very good agreement with numerical simulations.
* In collaboration with Yue Zhang, Robert Roundy, and Vagharsh Mkhitaryan