  The combination of spin transitions and magnetic ordering provides an
interesting structure of phase transitions in Prussian blue analogues (PBAs).
To understand the structure of stable and metastable states of Co-Fe PBA, it is
necessary to clarify free energy as a function of magnetization and the
fraction of the high-temperature component. Including the magnetic interaction
between high-temperature states, we study the magnetic phase transition of
Co-Fe PBA in addition to spin transitions. Here, we take into account the
degeneracy changes due to charge transfer between Co and Fe atoms accompanying
the spin transition. In this study, the charge transfer between Co and Fe atoms
is explicitly taken into account and also the ferrimagnetic structure of Co-Fe
PBAs is expressed in the proper way. First, we found systematic changes in the
structures of stable and metastable states as functions of system parameters
using mean field theory. In particular, the existence of a metastable
magnetic-ordered high-temperature state is confirmed at temperatures lower than
that of the hysteresis region of spin transitions. Second, we found that the
magnetic interaction causes complex ordering processes of a spin transition and
a magnetic phase transition. The effect of a magnetic field on the phase
structure is also investigated and we found metamagnetic magnetization
processes. Finally, the dynamical properties of this metastable state are
studied by Monte Carlo method.
