Ferromagnetic system with the first order transition and applicability of the Maxwell relation to its magnetocaloric effect

Abstract

Applicability of the Maxwell relation (MR) to the magnetocaloric effect (MCE) of ferromagnets with the first order transition (FOT) is studied by comparing the MCEs obtained without and with the aid of the MR. For this purpose, we first introduce a phenomenological free energy which gives the FOT of the ferromagnetic system, on the basis of which temperature T- and magnetic field H-dependences of the magnetization, and the magnetic phase diagram in the T-H plane are described. This free energy is also used to derive the entropy change induced by H,ΔS(H), without the aid of the MR. This entropy change ΔS(H) judges those obtained with the aid of the MR in the subsequent calculations. The a priori application of the MR to the MCE of ferromagnets with the FOT, where the MR is treated as done on ferromagnets with the second order transition, is simulated by substituting the calculated magnetization into the MR. The MCE obtained by this a priori application of the MR is shown to exhibit its insufficient agreement with the MCE without the aid of the MR. Especially, the steeple-like shape of the T-dependence of the entropy change and its maximum value going to 0 at H→0 are ascribed to the a priori application of the MR. On the other hand, the straight application of the MR is confirmed to successfully produce ΔS(H) without the aid of the MR also in the case of the FOT ferromagnet. The MR is extensively applied to analyses of the MCEs of ferromagnets which exhibit hysteretic phenomena around the FOT. Even in the presence of the hysteresis in a narrow region around the FOT, the analyses by use of the MR are shown to produce the maximum value of the entropy change and the adiabatic transition temperature change which are close to those in the absence of the hysteresis. Finally, careful numerical calculations in using the MR are also described.