The ideal magnetocaloric material would lay at the borderline of a first-order and a second-order phase transition. Hence, it is crucial to unambiguously determine the order of phase transitions for both applied magnetocaloric research as well as the characterization of other phase change materials. Although Ehrenfest provided a conceptually simple definition of the order of a phase transition, the known techniques for its determination based on magnetic measurements either provide erroneous results for specific cases or require extensive data analysis that depends on subjective appreciations of qualitative features of the data. Here we report a quantitative fingerprint of first-order thermomagnetic phase transitions: the exponent n from field dependence of magnetic entropy change presents a maximum of n > 2 only for first-order thermomagnetic phase transitions. This model-independent parameter allows evaluating the order of phase transition without any subjective interpretations, as we show for different types of materials and for the Bean–Rodbell model.

Hysteresis is more than just an interesting oddity that occurs in materials with a first-order transition. It is a real obstacle on the path from existing laboratory-scale prototypes of magnetic refrigerators towards commercialization of this potentially disruptive cooling technology. Indeed, the reversibility of the magnetocaloric effect, being essential for magnetic heat pumps, strongly depends on the width of the thermal hysteresis and, therefore, it is necessary to understand the mechanisms causing hysteresis and to find solutions to minimize losses associated with thermal hysteresis in order to maximize the efficiency of magnetic cooling devices. In this work, we discuss the fundamental aspects that can contribute to thermal hysteresis and the strategies that we are developing to at least partially overcome the hysteresis problem in some selected classes of magnetocaloric materials with large application potential. In doing so, we refer to the most relevant classes of magnetic refrigerants La–Fe–Si-, Heusler- and Fe ₂ P-type compounds. This article is part of the themed issue ‘Taking the temperature of phase transitions in cool materials’.

The phase‐down scenario of conventional refrigerants used in gas–vapor compressors and the demand for environmentally friendly and efficient cooling make the search for alternative technologies more important than ever. Magnetic refrigeration utilizing the magnetocaloric effect of magnetic materials could be that alternative. However, there are still several challenges to be overcome before having devices that are competitive with those based on the conventional gas–vapor technology. In this paper a rigorous assessment of the most relevant examples of 14 different magnetocaloric material families is presented and those are compared in terms of their adiabatic temperature and isothermal entropy change under cycling in magnetic‐field changes of 1 and 2 T, criticality aspects, and the amount of heat that they can transfer per cycle. The work is based on magnetic, direct thermometric, and calorimetric measurements made under similar conditions and in the same devices. Such a wide‐ranging study has not been carried out before. This data sets the basis for more advanced modeling and machine learning approaches in the near future.

We have explored, computationally and experimentally, the magnetic properties of (${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$)${}_2\mathrm{B}$ alloys. Calculations provide a good agreement with experiment in terms of the saturation magnetization and the magnetocrystalline anisotropy energy with some difficulty in describing ${\mathrm{Co}}_2\mathrm{B}$, for which it is found that both full potential effects and electron correlations treated within dynamical mean field theory are of importance for a correct description. The material exhibits a uniaxial magnetic anisotropy for a range of cobalt concentrations between $x=0.1$ and $x=0.5$. A simple model for the temperature dependence of magnetic anisotropy suggests that the complicated nonmonotonic behavior is mainly due to variations in the band structure as the exchange splitting is reduced by temperature. Using density functional theory based calculations we have explored the effect of substitutionally doping the transition metal sublattice by the whole range of $5d$ transition metals and found that doping by Re or W elements should significantly enhance the magnetocrystalline anisotropy energy. Experimentally, W doping did not succeed in enhancing the magnetic anisotropy due to formation of other phases. On the other hand, doping by Ir and Re was successful and resulted in magnetic anisotropies that are in agreement with theoretical predictions. In particular, doping by 2.5 at. % of Re on the Fe/Co site shows a magnetocrystalline anisotropy energy which is increased by 50% compared to its parent (${\mathrm{Fe}}_{0.7}{\mathrm{Co}}_{0.3}$)${}_2\mathrm{B}$ compound, making this system interesting, for example, in the context of permanent magnet replacement materials or in other areas where a large magnetic anisotropy is of importance.