AD-01 Non-Hermitian dynamics on the Bloch sphere

A system of spins under spin-polarized currents is described using a complex functional, or a non-Hermitian (NH) Hamiltonian. A single spin under a magnetic field already presents non-trivial dynamics including periodic motion [1]. We will focus on the dynamics of two exchange-coupled spins m1, m2 on the Bloch sphere [2]. For uniaxial anisotropy, there are four fixed points for the dynamics. In the case of currents leading to Parity-Time (PT) symmetry, the nonlinear system is bistable for small currents and it exhibits stable oscillating motion. This is akin to synchronized spin-torque oscillators. Simple precessional (periodic) motion can be observed while a perturbation of this gives an additional frequency of oscillation as shown in the figure. An exceptional point that survives also in the nonlinear system is identified analytically. For the full nonlinear system, two conserved quantities are derived that furnish a geometric description of the spin trajectories in phase space, indicate stability of the oscillating motion, and make contact with the conservative (Hamiltonian) system. The progress in analytical results promise to support further work on the dynamics of NH systems that are defined on the Bloch sphere not only in magnetics but also in effective spin systems arising, e.g., in polariton Bose-Einstein condensates.References: [1] A. Galda, V.M. Vinokur, Phys. Rev. B 94, 020408(R) (2016); A. Galda, V.M. Vinokur, Sci. Rep. 9, 17484 (2019). [2] S. Komineas, Phys. Rev. B 107, 094435 (2023).