The Mean-Field Theory in the Study of Ferromagnets and the Magnetocaloric Effect

Abstract

Will-be-set-by-IN-TECHPioneered by the ground-breaking work of G. V. Brown in the 1970's, the concept of room-temperature magnetic cooling has recently gathered strong interest by both the scientific and technological communities (Brück, 2005;de Oliveira & von Ranke, 2010;Gschneidner Jr. & Pecharsky, 2008;Gschneidner Jr. et al., 2005;Tishin & Spichin, 2003). The discovery of the giant MCE (Pecharsky & Gschneidner, 1997) resulted in this renewed interest in magnetic refrigeration, which, together with recent developments in rare-earth permanent magnets, opened the way to a new, efficient and environmentally-friendly refrigeration technology. The development and optimization of magnetic refrigerator devices depends on a solid thermodynamic description of the magnetic material, and its properties throughout the steps of the cooling cycles. This work will present, in detail, the use of the molecular mean-field theory in the study of ferro-paramagnetic phase transitions, and the MCE. The dependence of magnetization on external field and temperature can be described, in a wide validity range. This description is also valid for both second and first-order phase transitions, which will become particularly useful in describing the magnetic and magnetocaloric properties of the so-called "giant" and "colossal" magnetocaloric materials. An overview of the Weiss molecular mean-field model, and the inclusion of magneto-volume effects (Bean & Rodbell, 1962) is presented, providing the theoretical background for simulating the magnetic and magnetocaloric properties of second and first-order ferromagnetic phase transition systems. The numerical methods employed to solve the transcendental equation to determine the M(H, T) (where M is magnetization, H applied magnetic field and T Temperature) dependence of a ferromagnetic material with a second-order phase transition are described. In the case of first-order phase transitions, the use of the Maxwell construction is shown in order to estimate the equilibrium solution from the two distinct metastable solutions and the single unstable solution of the state equation. The generalized formulation of the molecular mean-field interaction leads to a novel mean-field scaling method (Amaral et al., 2007), that allows a direct estimation of the mean-field exchange parameters from experimental data. The application of this scaling method is explicitly shown in the case of simulated data, to exemplify its application and to highlight its robustness and general approach. Experimental magnetization data of second (La-Sr-Mn-O based) and first-order (La-Ca-Mn-O based) ferromagnetic manganites is then analyzed under this framework. We show how the Bean-Rodbell mean-field model can adequately simulate the magnetic properties of these complex magnetic systems, candidates for application for room-temperature magnetic refrigerant materials (Amaral et al., 2005;Gschneidner & Pecharsky, 2000;Phan & Yu, 2007). An overview of the MCE is presented, focusing on the use of the Maxwell relations to estimate th...

Thermodynamics of a model solid with magnetoelastic coupling

“…A separate, important field of study is the magnetocaloric effect [33][34][35] in systems with magnetoelastic coupling [36][37][38][39][40][41][42][43][44][45][46][47][48]. The description of the caloric effects for the case of many interacting subsystems constitutes an interesting problem in thermodynamics and is crucial for the correct modeling of real materials.…”

Reversibility of the Magnetocaloric Effect in the Bean-Rodbell Model

“…In the framework of the Bean-Rodbell model, the quantification of the hysteresis and the reversible response is possible. This is determined from the single-valued solution of T as function of M and H in Equation ( 4) [31]. For η > 1, metastable and instable regions appear in the solution.…”