Unconventional magnetism via optical pumping of interacting spin systems.

We consider strongly interacting systems of effective spins, subject to dissipative spin-flip processes associated with optical pumping. We predict the existence of novel magnetic phases in the steady state of this system, which emerge due to the competition between coherent and dissipative processes. Specifically, for strongly anisotropic spin-spin interactions, we find ferromagnetic, antiferromagnetic, spin-density-wave, and staggered-XY steady states, which are separated by nonequilibrium phase transitions meeting at a Lifshitz point. These transitions are accompanied by quantum correlations, resulting in spin squeezing. Experimental implementations in ultracold atoms and trapped ions are discussed.