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Rhombohedral ␣-Fe 2 O 3 has been studied by using density-functional theory ͑DFT͒ and the generalized gradient approximation ͑GGA͒. For the chosen supercell all possible magnetic configurations have been taken into account. We find an antiferromagnetic ground state at the experimental volume. This state is 388 meV/͑Fe atom͒ below the ferromagnetic solution. For the magnetic moments of the iron atoms we obtain 3.4 B , which is about 1.5 B below the experimentally observed value. The insulating nature of ␣-Fe 2 O 3 is reproduced, with a band gap of 0.32 eV, compared to an experimental value of about 2.0 eV. Analysis of the density of states confirms the strong hybridization between Fe 3d and O 2p states in ␣-Fe 2 O 3 . When we consider lower volumes, we observe a transition to a metallic, ferromagnetic low-spin phase, together with a structural transition at a pressure of 14 GPa, which is not seen in experiment. In order to take into account the strong on-site Coulomb interaction U present in Fe 2 O 3 we also performed DFTϩU calculations. We find that with increasing U the size of the band gap and the magnetic moments increase, while other quantities such as equilibrium volume and Fe-Fe distances do not show a monotonic behavior. The transition observed in the GGA calculations is shifted to higher pressures and eventually vanishes for high values of U. Best overall agreement, also with respect to experimental photoemission and inverse photoemission spectra of hematite, is achieved for Uϭ4 eV. The strength of the on-site interactions is sufficient to change the character of the gap from d-d to O-p-Fe-d.

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We have modelled the phase diagram of magnetic shape memory alloys of the Heusler type by using the phenomenological Ginzburg–Landau theory. When fixing the parameters by realistic values taken from experiment we are able to reproduce most details of, for example, the phase diagram of Ni2+xMn1−xGa in the (T, x) plane. We present the results of ab initio calculations of the electronic and phonon properties of several ferromagnetic Heusler alloys, which allow one to characterize the structural changes associated with the martensitic instability leading to the modulated and tetragonal phases. From the ab initio investigations emerges a complex pattern of the interplay of magic valence electron per atom numbers (Hume–Rothery rules for magnetic ternary alloys), Fermi surface nesting and phonon instability. As the main result, we find that the driving force for structural transformations is considerably enhanced by the extremely low lying optical modes of Ni in the Ni-based Heusler alloys, which interfere with the acoustical modes enhancing phonon softening of the TA2 mode. In contrast, the ferromagnetic Co-based Heusler alloys show no tendency for phonon softening.

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 Fe2P-type compounds.This article is part of the themed issue 'Taking the temperature of phase transitions in cool materials'.