  We study a nonequilibrium ferromagnetic mean-field spin model exhibiting a
phase with spontaneous temporal oscillations of the magnetization, on top of
the usual paramagnetic and ferromagnetic phases. This behavior is obtained by
introducing dynamic field variables coupled to the spins through non-reciprocal
couplings. We determine a nonequilibrium generalization of the Landau free
energy in terms of the large deviation function of the magnetization and of an
appropriately defined smoothed stochastic time derivative of the magnetization.
While the transition between paramagnetic and oscillating phase is continuous,
the transition between ferromagnetic and oscillating phases is found to be
discontinuous, with a coexistence of both phases, one being stable and the
other one metastable. Depending on parameter values, the ferromagnetic points
may either be inside or outside the limit cycle, leading to different
transition scenarios. The stability of these steady states is determined from
the large deviation function. We also show that in the coexistence region, the
entropy production has a pronounced maximum as a function of system size.
