  We show that an isotropic dipolar particle in the vicinity of a substrate
made of nonreciprocal plasmonic materials can experience a lateral Casimir
force and torque when the particle's temperature differs from that of the slab
and the environment. We connect the existence of the lateral force to the
asymmetric dispersion of nonreciprocal surface polaritons and the existence of
the lateral torque to the spin-momentum locking of such surface waves. Using
the formalism of fluctuational electrodynamics, we show that the features of
lateral force and torque should be experimentally observable using a substrate
of doped Indium Antimonide (InSb) placed in an external magnetic field, and for
a variety of dielectric particles. Interestingly, we also find that the
directions of the lateral force and the torque depend on the constituent
materials of the particles, which suggests a sorting mechanism based on lateral
nonequilibrium Casimir physics.
