Generalized model of the magnetostructural phase transition in La(Fe,Si)$_{13}$ compounds under the simultaneous action of temperature, magnetic field and pressure

The paper presents a phenomenological generalized model of a first-order metamagnetic phase transition for the La(Fe,Si)$_{13}$ compounds in the approximation of localized moments under the simultaneous action of temperature, field and pressure. To achieve the maximum cooling power of magnetic solid-state cooling devices, the Curie temperature of the working bodies should be fine-tuned by two external generalized forces: a magnetic field and pressure. The thermodynamic phenomenological models presented in the literature are mostly focused on the description of the behavior of magnetocaloric materials in the vicinity of phase transition in the absence of external pressure. In turn, the latter provide a significant reduction in the field hysteresis effect by shifting the Curie temperature and expand the working temperature range of the refrigerant. To estimate the required pressure value, a new generalized model was developed that excludes the linear dependence of the phase transition temperature on the volume change and modernizes the form of the magnetic and phonon entropy, taking into account anharmonism. In addition, the equations of state describing the behavior of working bodies underwent a multistimuli cooling cycle were obtained. The model allows estimating the upper limit of the temperature and field hysteresis and predicting the required external pressure to reduce the field hysteresis.