Understanding the influence of the first-order magnetic phase transition on the magnetocaloric effect: application to Gd5(SixGe1−x)4

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Abstract

In this article, we investigate the influence of the first-order ferromagnetic–paramagnetic phase transition, on the magnetocaloric effect, under the combined effect of external magnetic field, pressure and magnetoelastic deformation. An application is made to Gd5(SixGe1−x)4, for x=0.43 and 0.5. The obtained result leads to a good theoretical adjustment of the experimental data for isothermal magnetic entropy change.

Introduction

The magnetocaloric effect is the ability of some magnetic materials to heat up when they are magnetized, and cool down when removed from the magnetic field in an adiabatic process. The investigations on the magnetocaloric effect present a significant increase due to the theoretical, experimental and technological interest. Recently new magnetic materials, Gd5(Si2Ge2) and MnFeP0.45As0.55 were reported [1], [2] with giant magnetocaloric effect around room temperature. The two thermodynamic quantities that characterize the magnetic cooling potential, and required for magnetic refrigeration design, are: ΔSmag (the isothermal magnetic entropy change) and ΔTad (the adiabatic temperature change) which are observed upon changes in the external magnetic field. The concept of these two quantities connected with refrigerant capacity, efficiency of refrigeration in Ericsson and Carnot cycles was recently reported in RNi2 (R=rare earth) series [3].

Successful theoretical microscopic models have been applied to understand and simulate new magnetocaloric materials. The influence of crystalline electric field and exchange interaction was fully studied in RAl2 intermetallic compounds [4], [5], pseudobinary system [6] (Dy1−xErx)Al2 and also giant quadrupolar interaction in the YbAs system [7]. In the paramagnetic PrNi5 compound, theoretical prediction pointed out to an anomalous magnetocaloric effect, attributed to quantum crossing effect [8]. This material cools upon magnetization and warm upon demagnetization. In RCo2 compounds, where the magnetic state equations are more complex due to the contribution of both localized and itinerant magnetism [9], good theoretical and experimental agreements were obtained. Nevertheless, as far as we know, there is no a satisfactory theoretical description of the influence of first-order magnetic phase transition on magnetocaloric materials.

The highest molar magnetocaloric effect reported to date, in the large temperature range from ∼20 to 290 K, appears in the Gd5(SixGe1−x)4 alloys [1] with x⩽0.5. A full crystallograph and magnetic phase diagram was investigated showing rich behaviors [10] formed by orthorhombic and monoclinic crystallographic phase structures which depend on the Si–Ge concentration. The lattice parameters and the γ-monoclinic angle were tabulated [11]. The investigation performed by Morellon et al. in Gd5(Si0.45Ge0.55)4 leads to the conclusion that a first-order ferromagnetic–paramagnetic (F–P) phase transition occurs coupled to orthorhombic-monoclinic crystallographic phase transformation [12]. This magnetostructural transition can be reversibly induced by magnetic field and occurs with strong magnetoelastic effect ωV/V=0.4%, indicating that the contribution from the elastic energy term may be important mechanism for the first-order transition.

In this work we study the influence of first-order magnetic phase transition on magnetocaloric materials, based on the mean field model described in Ref. [13]. An application of the model is made to the materials Gd5(SixGe1−x)4 (for concentration of x=0.43 and 0.5) and the model parameters are determined using the experimental data.

Section snippets

Theory

This study is based on the assumption of phenomenological dependence of the critical Curie temperature on the deformation of the unit cell volume [13].TC=T0(1+βω).Here ω=(VV0)/V0 is the volume change (cell deformation), β=d(TC/T0)/d(V/V0) measures the slope of the critical temperature curve on the volume change and T0 is the order temperature in the absence of the lattice deformation.

The Gibbs free energy of a simple ferromagnetic lattice described by exchange, Zeeman, distortion and pressure

Results and discussions

First we consider a magnetic system, formed by Gd ions g=2 and J=72, exhibiting a second-order magnetic phase transition around TC=180 K. Since this compound presents second-order P–F phase transition, a proper choice of η is η=0 (or equivalently β=0 see relation (6)) so TC=T0. Fig. 1 shows the normalized temperature, T/T0, dependence of the magnetization per Bohr magneton considering η=0 and 1.2 (without pressure and external magnetic field). It is worth noticing that without pressure, the

Final comments

Using a simple and easily handled phenomenological model it was possible to highlight the influence of the external-controlled parameters, magnetic field and pressure, as well as the volume deformation, on the magnetocaloric effect. Some important systematic behavior, that correlates the decreases of the area under ΔSmag vs. temperature curves with the increases in ΔSmagMAX was discussed. Pressure variation can lead the magnetic system to change the order of magnetic phase transition, and in

Acknowledgements

The authors acknowledge financial support from Conselho Nacional de Desenvolvimento Cientı́fico e Tecnológico—Brazil and from FAPESP—Fundação de Amparo à Pesquisa do Estado de São Paulo.

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