Abstract:
A comprehensive study of the total energy of manganese-rich Heusler compounds using density functional theory is presented. Starting from a large set of cubic parent systems, the response to tetragonal distortions is studied in detail. We single out the systems that remain cubic from those that most likely become tetragonal. The driving force of the tetragonal distortion and its effect on the magnetic properties, especially where they deviate from the Slater--Pauling rule, as well as the trends in the Curie temperatures, are highlighted. By means of partial densities of states, the electronic structural changes reveal the microscopic origin of the observed trends. We focus our attention on the magnetocrystalline anisotropy and find astonishingly high values for tetragonal Heusler compounds containing heavy transition metals accompanied by low magnetic moments, which indicates that these materials are promising candidates for spin-transfer torque magnetization-switching applications.

Abstract:
The topological band structures of the X2YZ Heusler compounds with the Hg2CuTi structure are investigated by using first-principles calculations within density functional theory. Our results clearly show that a large number of the Hg2CuTi type Heusler compounds naturally exhibit distinct band-inversion feature, which is mainly controlled by the Y-Z zinc blende sublattice. Similar to the half-Heusler family, the topological band order in Hg2CuTi type Heusler compounds is sensitive to the variation of lattice constant, and most of them possess a negative formation energy, which makes them more suitable in material growth and could easily achieve the topological insulating behavior by alloying or proper strain.

Abstract:
In the recent decade, the family of Heusler compounds has attracted tremendous scientific and technological interest in the field of spintronics. This is essentially due to their exceptional magnetic properties, which qualify them as promising functional materials in various data-storage devices, such as giant-magnetoresistance spin valves, magnetic tunnel junctions, and spin-transfer torque devices. In this article, we provide a comprehensive review on the applications of the Heusler family in magnetic data storage. In addition to their important roles in the performance improvement of these devices, we also try to point out the challenges as well as possible solutions, of the current Heusler-based devices. We hope that this review would spark further investigation efforts into efficient incorporation of this eminent family of materials into data storage applications by fully arousing their intrinsic potential.

Abstract:
We investigate the structural stability and magnetic properties of cubic, tetragonal and hexagonal phases of Mn3Z (Z=Ga, Sn and Ge) Heusler compounds using first-principles density-functional theory. We propose that the cubic phase plays an important role as an intermediate state in the phase transition from the hexagonal to the tetragonal phases. Consequently, Mn3Ga and Mn3Ge behave differently from Mn3Sn, because the relative energies of the cubic and hexagonal phases are different. This result agrees with experimental observations from these three compounds. The weak ferromagnetism of the hexagonal phase and the perpendicular magnetocrystalline anisotropy of the tetragonal phase obtained in our calculations are also consistent with experiment.

Abstract:
We determine the spin wave exchange stiffness $D$ and the exchange constant $A$ for the full Heusler compound \CFS using Brillouin light scattering spectroscopy. We find an extraordinarily large value of $D=715\pm20$ meV \AA$^2$ ($A=31.5\pm1.0$ pJ/m) which is, to the best of our knowledge, only surpassed by the intermetallic compound Fe$_{53}$Co$_{47}$ (J. Appl. Phys. \textbf{75}, 7021 (1994)). Furthermore, we provide a systematization of the exchange stiffnesses determined for a variety of Co$_2$-based Heusler compounds. We find that for the investigated compounds, the exchange stiffness is a function of the valence electron concentration and the crystallographic ordering. The exchange stiffness increases when the valence electron concentration and/or the amount of the L2$_1$ ordering increase. A qualitative explanation for the dependence on the valence electron concentration is provided.

Abstract:
Manganese-rich Heusler compounds are attracting much interest in the context of spin transfer torque and rare-earth free hard magnets. Here we give a comprehensive overview of the magnetic properties of non-centrosymmetric cubic Mn$_2$-based Heusler materials, which are characterized by an antiparallel coupling of magnetic moments on Mn atoms. Such a ferrimagnetic order leads to the emergence of new properties that are absent in ferromagnetic centrosymmetric Heusler structures. In terms of the band structure calculations, we explain the formation of this magnetic order and the Curie temperatures. This overview is intended to establish guidelines for a basic understanding of magnetism in Mn2 -based Heusler compounds.

Abstract:
We present a comprehensive study of plasmon dispersions in simple metals and Heusler compounds based on an accurate ab-initio evaluation of the momentum and frequency dependent dielectric function in the random-phase approximation. Using a momentum-dependent tetrahedron method for the computation of the dielectric function, we extract and analyze "full" and "intraband" plasmon dispersions: The "full" plasma dispersion is obtained by including all bands, the intraband plasma dispersion by including only intraband transitions. For the simple metals silver and alu- minum, we show that the intraband plasmon dispersion has an unexpected downward slope and is therefore markedly different from the results of an effective-mass electron-gas model and the full plasmon dispersion. For the two Heusler compounds Co2FeSi and Co2MnSi, we present spectra for the dielectric function, their loss functions and plasmon dispersions. The latter exhibit the same negative intraband plasmon dispersion as found in the simple metals. We also discuss the influence of spin-mixing on the plasmon dispersion.

Abstract:
Recently the Quantum Spin Hall effect (QSH) was theoretically predicted and experimentally realized in a quantum wells based on binary semiconductor HgTe[1-3]. QSH state and topological insulators are the new states of quantum matter interesting both for fundamental condensed matter physics and material science[1-11]. Many of Heusler compounds with C1b structure are ternary semiconductors which are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the band gap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by lattice parameter) and the magnitude of spin-orbit coupling (by the atomic charge). Based on the first-principle calculations we demonstrate that around fifty Heusler compounds show the band inversion similar to 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 (e. g. LaPtBi[12]) to magnetism (e. g. GdPtBi[13]) and heavy-fermion behavior (e. g. YbPtBi[14]). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors.

Abstract:
Based on first-principles electronic structure calculations, we analyze the chemical and magnetic mechanisms stabilizing the cubic phase in Fe$_2$-based Heusler materials, which were previously predicted to be tetragonal when being chemically ordered. In agreement with recent experimental data, we found that these compounds crystallize within the so-called "inverted" cubic Heusler structure perturbed by a certain portion of the intrinsic chemical disorder. Understanding these mechanisms is a necessary step to guide towards the successful future synthesis of the stable Fe$_2$-based tetragonal phases, which are very promising candidates for the fabrication of rare-earth-free permanent magnets.