Magnetic properties and metastable states in spin-crossover transition of Co-Fe Prussian blue analogues

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.