  We study the dynamical magnetic susceptibility of a strongly correlated
electronic system in the presence of a time-dependent hopping field, deriving a
generalized Bethe-Salpeter equation which is valid also out of equilibrium.
Focusing on the single-orbital Hubbard model within the time-dependent
Hartree-Fock approximation, we solve the equation in the non-equilibrium
adiabatic regime, obtaining a closed expression for the transverse magnetic
susceptibility. From this, we provide a rigorous definition of non-equilibrium
(time-dependent) magnon frequencies and exchange parameters, expressed in terms
of non-equilibrium single-electron Green functions and self-energies. In the
particular case of equilibrium, we recover previously known results.
