Thermodynamic determination of the equilibrium first-order phase-transition line hidden by hysteresis in a phase diagram

In some materials exhibiting field-induced first-order transitions (FOTs), the equilibrium phase-transition line is hidden by the hysteresis region associated with the FOT. In general, phase diagrams form the basis for the study of material science, and the profiles of phase-transition lines separating different thermodynamic phases include comprehensive information about thermodynamic quantities, such as latent heat. However, in a field-induced FOT, the equilibrium phase-transition line cannot be precisely determined from measurements of resistivity, magnetization, etc, especially when the transition is accompanied by large hysteresis. Here, we demonstrate a thermodynamics-based method for determining the hidden equilibrium FOT line in a material exhibiting a field-induced FOT. This method is verified for the field-induced FOT between antiferromagnetic and ferrimagnetic states in magneto-electric compounds ( Fe_0.95Zn_0.05)_2Mo_3O_8 . The equilibrium FOT line determined based on the Clausius–Clapeyron equation exhibits a reasonable profile in terms of the third law of thermodynamics, and it shows marked differences from the midpoints of the hysteresis region. Our findings highlight that for a field-induced FOT exhibiting large hysteresis, care should be taken for referring to the hysteresis midpoint line when discussing field-induced latent heat or magnetocaloric effects.