  We present a nonequilibrium steady-state implementation of the two-particle
self-consistent method. This approach respects the Mermin-Wagner theorem and
incorporates non-local spatial fluctuations through self-consistent static
vertices. The real-frequency implementation allows to compute spectral
properties without analytical continuation in both equilibrium and
nonequilibrium. As an interesting application, we investigate spin correlations
in the bilayer square lattice Hubbard model under a perpendicular static
electric field. In equilibrium, the result yields spin correlations which are
in good agreement with recent optical lattice experiments. Under a large enough
static electric field, the inter-layer spin correlations switch from
antiferromagnetic to ferromagnetic. We clarify how this phenomenon is linked to
the nonequilibrium modifications of the spin excitation spectrum.
