Recently the quantum spin Hall effect was theoretically predicted and experimentally realized in quantum wells based on the binary semiconductor HgTe (refs 1-3). The quantum spin Hall state and topological insulators are new states of quantum matter interesting for both fundamental condensed-matter physics and material science. Many Heusler compounds with C1(b) structure are ternary semiconductors that are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the bandgap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by the lattice parameter) and magnitude of spin-orbit coupling (by the atomic charge). Based on first-principle calculations we demonstrate that around 50 Heusler compounds show band inversion similar to that of HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantum-well structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare-earth element Ln, which can realize additional properties ranging from superconductivity (for example LaPtBi; ref. 12) to magnetism (for example GdPtBi; ref. 13) and heavy fermion behaviour (for example YbPtBi; ref. 14). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors.

Spintronics is a multidisciplinary field involving physics, chemistry, and engineering, and is a new research area for solid-state scientists. A variety of new materials must be found to satisfy different demands. The search for ferromagnetic semiconductors and stable half-metallic ferromagnets with Curie temperatures higher than room temperature remains a priority for solid-state chemistry. A general understanding of structure-property relationships is a necessary prerequisite for the design of new materials. In this Review, the most important developments in the field of spintronics are described from the point of view of materials science.

In this work, results of ab-initio band structure calculations for A 2 BC Heusler compounds that have A and B sites occupied by transition metals and C by a main group element are presented.This class of materials includes some interesting half-metallic and ferromagnetic properties. The calculations have been performed in order to understand the properties of the minority band gap and the peculiar magnetic behavior found in these materials. Among the interesting aspects of the electronic structure of the materials are the contributions from both A and B atoms to states near the Fermi energy and to the total magnetic moment. The magnitude of the total magnetic moment, which depends as well on the kind of C atoms, shows a trend consistent with the Slater-Pauling type behavior in several classes of these compounds. The localized moment in these magnetic compounds resides at the B site. Other than in the classical Cu 2 -based Heusler compounds, the A atoms in Co 2 , Fe 2 , and Mn 2 based compounds may contribute pronounced to the total magnetic moment.

In this work a simple concept was used for a systematic search for new materials with high spin polarization. It is based on two semi-empirical models. Firstly, the Slater-Pauling rule was used for estimation of the magnetic moment. This model is well supported by electronic structure calculations. The second model was found particularly for Co2 based Heusler compounds when comparing their magnetic properties. It turned out that these compounds exhibit seemingly a linear dependence of the Curie temperature as function of the magnetic moment.Stimulated by these models, Co2FeSi was revisited. The compound was investigated in detail concerning its geometrical and magnetic structure by means of X-ray diffraction, X-ray absorption and Mößbauer spectroscopies as well as high and low temperature magnetometry. The measurements revealed that it is, currently, the material with the highest magnetic moment (6µB ) and Curietemperature (1100K) in the classes of Heusler compounds as well as half-metallic ferromagnets. The experimental findings are supported by detailed electronic structure calculations.

This work reports about the electronic, magnetic, and structural properties of the binary compound Mn3Ga. The tetragonal DO22 phase of Mn3Ga was successfully synthesized and investigated. It has been found that the material is hard magnetic with an energy product of Hc×Br=52.5kJm−3 and an average saturation magnetization of about 0.25μB∕at. at 5K. The saturation magnetization indicates a ferrimagnetic order with partially compensating moments at the Mn atoms on crystallographically different sites. The Curie temperature is above 730K where the onset of decomposition is observed. The electronic structure calculations indicate a nearly half-metallic ferrimagnetic order with 88% spin polarization at the Fermi energy.