  We present a novel class of nonlinear dynamical systems - a hybrid of
relativistic quantum and classical systems, and demonstrate that multistability
is ubiquitous. A representative setting is coupled systems of a topological
insulator and an insulating ferromagnet, where the former possesses an
insulating bulk with topologically protected, dissipationless, and conducting
surface electronic states governed by the relativistic quantum Dirac
Hamiltonian and latter is described by the nonlinear classical evolution of its
magnetization vector. The interactions between the two are essentially the spin
transfer torque from the topological insulator to the ferromagnet and the local
proximity induced exchange coupling in the opposite direction. The hybrid
system exhibits a rich variety of nonlinear dynamical phenomena besides
multistability such as bifurcations, chaos, and phase synchronization. The
degree of multistability can be controlled by an external voltage. In the case
of two coexisting states, the system is effectively binary, opening a door to
exploitation for developing spintronic memory devices. Because of the
dissipationless and spin-momentum locking nature of the surface currents of the
topological insulator, little power is needed for generating a significant
current, making the system appealing for potential applications in next
generation of low power memory devices.
