Feedback-Induced Nonlinear Spin Dynamics in an Inhomogeneous Magnetic Field

Nonlinear effects are the root of interesting phenomena such as masers and lasers, and play a significant role in science and engineering. In spin systems, nonlinear spin dynamics is crucial for the prediction of complex dynamical behavior such as self-organizing oscillation, with applications ranging from spin masers and time crystals to precision measurement. However, when a spin system operates in a static magnetic field, how the inhomogeneity of the field affects its dynamics is a primary concern. Here we study the dynamics of a collection of spins with multiple Larmor frequencies for modeling a static inhomogeneous magnetic field, and reveal that due to the nonlinearity induced by a feedback scheme, the spin system exhibits much richer stable dynamical phases, including quasi-periodic orbits and chaos besides the usual limit cycles emerged in previous works. These phases are generally applicable to coupled nonlinear spin systems, even with more than two intrinsic Larmor frequencies or in continuum cases. Furthermore, we discuss their robustness against the experimental noises and the feasibility of realization in several spin systems. Our findings contribute to future observation of nonlinear dynamical phases and prospective applications in precision measurement.