Dynamical instability in a Floquet-driven dissipative system

We analyse the magnon spectrum and distribution function of the antiferromagnetic phase of the Floquet-driven Hubbard model. Above a critical drive strength, we find a dynamical instability, resulting from a change in sign of the magnon damping at a non-zero wavevector. The change in sign means that infinitesimal fluctuations grow with time, corresponding to an instability of the driven state. Implications for the nonequilibrium distribution function and the strong drive nonlinear dynamics are discussed.