Feedback Assisted Spin Dynamics in an Inhomogeneous Bias Magnetic Field

We study dynamics of spins in the presence of a feedback magnetic field. The inhomogeneity of the bias magnetic field results in that of the Larmor frequencies of the spins. We find that the system exhibits rich nonlinear dynamics: beyond limit cycles which have been the focus of previous studies, quasi-periodic orbits and chaos emerge in a wide parameter space. The stable regions of each phases are determined analytically or numerically. We establish the relation between the synchronization frequency of limit cycles and the field inhomogeneity. Our results have important implications to precision measurement.