Analysis of the Magnetic Field Dependence of the Isothermal Entropy Change of Inverse Magnetocaloric Materials

Abstract

Power law to express the field dependence of the isothermal entropy change (ΔsT ∝ ΔHn) has been widely employed for obtaining information of the thermomagnetic second-order phase transitions (e.g. critical exponents [1] or Curie temperatures [2]). Recently, the analysis of this field dependence has been extended to materials undergoing thermomagnetic first-order phase transitions, the most promising magnetocaloric materials up to the moment. It has been shown that the value of the exponent n overshoots above 2 for first-order phase transitions, while it does not overshoot for the second-order case, allowing to establish a quantitative criterion for determining the order of the phase transitions [3]. This is in excellent agreement with previous phenomenological observations, supporting the validity of the proposed criterion. For direct magnetocaloric effect (MCE), the overshoot feature for fingerprinting first-order transitions can be validated in the frame of the Bean-Rodbell model [4], obtaining an excellent agreement between experiments (e.g., for La(Fe,Si)13 which undergoes a ferromagnetic (FM) to paramagnetic (PM) magnetoelastic transition [5]) and the model. However, for inverse MCE, the validity of the proposed criterion and the characteristics of the field dependence have only been studied experimentally. In this work, the magnetic field dependence of the inverse MCE is analyzed using a mean field approach for describing antiferromagnetic (AF) to FM magnetoelastic transitions. The model is able to describe both second- and first-order phase transitions through the introduction of a magnetovolume energy term according to the Callen-Callen theory [6] (having a Gibbs energy term of the form -βωM2/4 , being ω the relative volume change, M the magnetization and β an introduced magnetoelastic coupling parameter). Using this model, we are able to reproduce the experimentally observed features for the exponent n, showing the existence of the characteristic overshoot for first-order transitions (which corresponds to β>0) and its absence for second-order ones (β=0), as shown in Fig. 1. We explore the influence of different parameters of the model on exponent n, such as the transition temperature and Curie temperature separation or the exchange constant between the moments of the different sublattices. The existence of the overshoot feature is corroborated for all the different cases. This supports the extension of the quantitative criterion to AF-FM phase transitions and set the basis for the analysis of exponent n in these materials. A main difference with respect to direct MCE is that negative values of the exponent n are obtained at temperatures close to the transition. This is ascribed to the reduction of the inverse MC response due to the influence of the unavoidable FM to PM transition at higher temperatures. The obtained features for exponent n (field dependence and temperature dependence) are qualitatively compared to those of GdBaCo2O6 [7] (AF to FM magnetoelastic transition), showing a good agreement between both the experiment and the model. The obtained results are extrapolated to understand the behavior of the exponent n for a Ni49Mn36In15 sample [8] (low magnetization to high magnetization magnetostructural transition).Work supported by AEI/FEDER-UE (grant PID2019-105720RB-I00), US/JUNTA/FEDER-UE (grant US-1260179), Consejería de Economía, Conocimiento, Empresas y Universidad de la Junta de Andalucía (grant P18-RT-746), Army Research Laboratory under Cooperative Agreement Number W911NF-19-2-0212 and Sevilla University under VI PPIT-US program. **