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Spinel ferrites in general show a rich interplay of structural, electronic, and magnetic properties. Here, we particularly focus on zinc ferrite (ZFO), which has been observed experimentally to crystallise in the cubic $normal$ spinel structure. However, its magnetic ground state is still under dispute. In addition, some unusual magnetic properties in ZFO thin films or nanostructures have been explained by a possible partial cation inversion and a different magnetic interaction between the two cation sublattices of the spinel structure compared to the crystalline bulk material. Here, density functional theory has been applied to investigate the influence of different inversion degrees and magnetic couplings among the cation sublattices on the structural, electronic, magnetic, and optical properties. Effects of exchange and correlation have been modelled using the generalised gradient approximation (GGA) together with the Hubbard `+$U$' parameter, and the more elaborate hybrid functional PBE0. While the GGA+$U$ calculations yield an antiferromagnetically coupled $normal$ spinel structure as the ground state, in the PBE0 calculations the ferromagnetically coupled $normal$ spinel is energetically slightly favoured, and the hybrid functional calculations perform much better with respect to structural, electronic and optical properties., Comment: 5 pages, 3 figures, 1 table

The development of new exchange-correlation functionals within density functional theory means that increasingly accurate information is accessible at moderate computational cost. Recently, a newly developed self-consistent hybrid functional has been proposed [Skone \textit{et al.} Phys. Rev. B \textbf{89}, 195112 (2014)], which allows for a reliable and accurate calculation of material properties using a fully \textit{ab initio} procedure. Here, we apply this new functional to wurtzite ZnO, rutile SnO$_2$, and rocksalt MgO. We present calculated structural, electronic, and optical properties, which we compare to results obtained with the PBE and PBE0 functionals. For all semiconductors considered here the self-consistent hybrid approach gives improved agreement with experimental structural data relative to the PBE0 hybrid functional for a moderate increase in computational cost, while avoiding the empiricism common to conventional hybrid functionals. The electronic properties are improved for ZnO and MgO, whereas for SnO$_2$ the PBE0 hybrid functional gives best agreement with experimental data., Comment: 6 pages, 5 figures, 1 table

Noncollinear magnetic interfaces introduced in superconductor (SC)/ferromagnet/SC heterostructures allow for spin-flipping processes and are able to generate equal-spin spin-triplet pairing correlations within the ferromagnetic region. This leads to the occurrence of the so-called long-range proximity effect. Particular examples of noncollinear magnetic interfaces include Bloch and N\'{e}el domain walls. Here, we present results for heterostructures containing Bloch and N\'{e}el domain walls based on self-consistent solutions of the spin-dependent Bogoliubov$-$de Gennes equations in the clean limit. In particular, we investigate the thickness dependence of Bloch and N\'{e}el domain walls on induced spin-triplet pairing correlations and compare with other experimental and theoretical results, including conical magnetic layers as noncollinear magnetic interfaces. It is shown that both, Bloch and N\'{e}el domain walls lead to the generation of unequal-spin spin-triplet pairing correlations of similar strength as for conical magnetic layers. However, for the particular heterostructure geometries investigated, only Bloch domain walls lead to the generation of equal-spin spin-triplet pairing correlations. They are stronger than those generated by an equivalent thickness of conical magnetic layers. In order for N\'{e}el domain walls to induce equal-spin spin-triplet pairing correlations, they have to be oriented such that the noncollinearity appears within the plane parallel to the interface region., Comment: 11 pages, 4 figures

Superconductor/ferromagnet/superconductor heterostructures exhibit a so-called long-range proximity effect provided some layers of conical magnet Holmium are included in the respective interface regions. The Ho layers lead to a spin-flip process at the interface generating equal-spin spin-triplet pairing correlations in the ferromagnet. These equal-spin spin-triplet pairing correlations penetrate much further into the heterostructure compared to the spin-singlet and unequal-spin spin-triplet correlations which occur in the absence of Ho. Here we present calculations of this effect based on the spin-dependent microscopic Bogoliubov-de Gennes equations solved within a tight-binding model in the clean limit. The influence of the ferromagnet and conical magnet layer thickness on the induced equal-spin spin-triplet pairing correlations is obtained and compared to available experimental data. It is shown that, in agreement with experiment, a critical minimum thickness of conical magnet layers has to be present in order to observe a sizeable amount of equal-spin spin-triplet pairing correlations., Comment: 8 pages, 6 figures

The presence of a spin-flip potential at the interface between a superconductor and a ferromagnetic metal allows for the generation of equal-spin spin-triplet Cooper pairs. These Cooper pairs are compatible with the exchange interaction within the ferromagnetic region and hence allow for the long-range proximity effect through a ferromagnet or half-metal. One suitable spin-flip potential is provided by incorporating the conical magnet Holmium (Ho) into the interface. The conical magnetic structure is characterised by an opening angle $\alpha$ with respect to the crystal $c$-axis and a turning (or pitch) angle $\beta$ measuring the rotation of magnetisation with respect to the adjacent layers. Here, we present results showing the influence of conical magnet interface layers with varying $\alpha$ and $\beta$ on the efficiency of the generation of equal-spin spin-triplet pairing. The results are obtained by self-consistent solutions of the microscopic Bogoliubov$-$de Gennes equations in the clean limit within a tight-binding model of the heterostructure. In particular, the dependence of unequal-spin and equal-spin spin-triplet pairing correlations on the conical magnetic angles $\alpha$ and $\beta$ are discussed in detail., Comment: 12 pages, 6 figures

At the interface between a superconductor and a ferromagnetic metal spin-singlet Cooper pairs can penetrate into the ferromagnetic part of the heterostructure with an oscillating and decaying spin-singlet Cooper pair density. However, if the interface allows for a spin-mixing effect, equal-spin spin-triplet Cooper pairs can be generated that can penetrate much further into the ferromagnetic part of the heterostructure, known as the long-range proximity effect. Here, we present results of spin-mixing based on self-consistent solutions of the microscopic Bogoliubov-de Gennes equations incorporating a tight-binding model. In particular, we include a conical magnet into our model heterostructure to generate the spin-triplet Cooper pairs and analyse the influence of conical and ferromagnetic layer thickness on the unequal-spin and equal-spin spin-triplet pairing correlations. It will be show that, in agreement with experimental observations, a minimum thickness of the conical magnet is necessary to generate a sufficient amount of equal-spin spin-triplet Cooper pairs allowing for the long-range proximity effect., Comment: 14 pages, 7 figures, 1 table

We assess the potential of the ferrimagnetic spinel ferrites CoFe2O4 and NiFe2O4 to act as spin filtering barriers in magnetic tunnel junctions. Our study is based on the electronic structure calculated by means of first-principles density functional theory within different approximations for the exchange correlation energy. We show that, in agreement with previous calculations, the densities of states suggest a lower tunneling barrier for minority spin electrons, and thus a negative spin-filter effect. However, a more detailed analysis based on the complex band-structure reveals that both signs for the spin-filtering efficiency are possible, depending on the band alignment between the electrode and the barrier materials and depending on the specific wave-function symmetry of the relevant bands within the electrode., Comment: 8 pages, 5 Figures, 1 Table

We present calculations of magnetostriction constants for the spinel ferrites CoFe2O4 and NiFe2O4 using density functional theory within the GGA+U approach. Special emphasis is devoted to the influence of different possible cation distributions on the B site sublattice of the inverse spinel structure on the calculated elastic and magnetoelastic constants. We show that the resulting symmetry-lowering has only a negligible effect on the elastic constants of both systems as well as on the magnetoelastic response of NiFe2O4, whereas the magnetoelastic response of CoFe2O4 depends more strongly on the specific cation arrangement. In all cases our calculated magnetostriction constants are in good agreement with available experimental data. Our work thus paves the way for more detailed first-principles studies regarding the effect of stoichiometry and cation inversion on the magnetostrictive properties of spinel ferrites., Comment: 11 pages, 6 figures

The effect of epitaxial strain on the cation distribution in spinel ferrites CoFe2O4 and NiFe2O4 is investigated by GGA+U total energy calculations. We obtain a very strong (moderate) tendency for cation inversion in NiFe2O4 (CoFe2O4), in agreement with experimental bulk studies. This preference for the inverse spinel structure is reduced by tensile epitaxial strain, which can lead to strong sensitivity of the cation distribution on specific growth conditions in thin films. Furthermore, we obtain significant energy differences between different cation arrangements with the same degree of inversion, providing further evidence for recently proposed short range B site order in NiFe2O4., Comment: 9 pages, 2 figures, revised version

Based on numerically accurate density functional theory (DFT) calculations, we systematically investigate the ground-state structure and the spin and orbital magnetism including the magnetic anisotropy energy (MAE) of 3d- and 4d-transition-metal dimer benzene complexes (TM2Bz, TM = Fe, Co, Ni, Ru, Rh, Pd; Bz = C6H6). These systems are chosen to model TM-dimer adsorption on graphene or on graphite. We find that Fe2, Co2, Ni2, and Ru2 prefer the upright adsorption mode above the center of the benzene molecule, while Rh2 and Pd2 are adsorbed parallel to the benzene plane. The ground state of Co2Bz (with a dimer adsorption energy of about 1 eV) is well separated from other possible structures and spin states. In conjunction with similar results obtained by ab initio quantum chemical calculations, this implies that a stable Co2Bz complex with C6v symmetry is likely to exist. Chemical bonding to the carbon ring does not destroy the magnetic state and the characteristic level scheme of the cobalt dimer. Calculations including spin- orbit coupling show that the huge MAE of the free Co dimer is preserved in the Co2Bz structure. The MAE predicted for this structure is much larger than the MAE of other magnetic molecules known hitherto, making it an interesting candidate for high-density magnetic recording. Among all the other investigated complexes, only Ru2Bz shows a potential for strong-MAE applications, but it is not as stable as Co2Bz. The electronic structure of the complexes is analyzed and the magnitude of their MAE is explained by perturbation theory., Comment: 35 pages, 7 figures

The inverse spinels CoFe2O4 and NiFe2O4, which have been of particular interest over the past few years as building blocks of artificial multiferroic heterostructures and as possible spin-filter materials, are investigated by means of density functional theory calculations. We address the effect of epitaxial strain on the magneto-crystalline anisotropy and show that, in agreement with experimental observations, tensile strain favors perpendicular anisotropy, whereas compressive strain favors in-plane orientation of the magnetization. Our calculated magnetostriction constants $\lambda_{100}$ of about -220 ppm for CoFe2O4 and -45 ppm for NiFe2O4 agree well with available experimental data. We analyze the effect of different cation arrangements used to represent the inverse spinel structure and show that both LSDA+U and GGA+U allow for a good quantitative description of these materials. Our results open the way for further computational investigations of spinel ferrites.

Theoretical studies on M$_{13}$ (M = Fe, Co, Ni) and M$_{13}$Pt$_n$ (for $n$ = 3, 4, 5, 20) clusters including the spin-orbit coupling are done using density functional theory. The magnetic anisotropy energy (MAE) along with the spin and orbital moments are calculated for M$_{13}$ icosahedral clusters. The angle-dependent energy differences are modelled using an extended classical Heisenberg model with local anisotropies. From our studies, the MAE for Jahn-Teller distorted Fe$_{13}$, Mackay distorted Fe$_{13}$ and nearly undistorted Co$_{13}$ clusters are found to be 322, 60 and 5 $\mu$eV/atom, respectively, and are large relative to the corresponding bulk values, (which are 1.4 and 1.3 $\mu$eV/atom for bcc Fe and fcc Co, respectively.) However, for Ni$_{13}$ (which practically does not show relaxation tendencies), the calculated value of MAE is found to be 0.64 $\mu$eV/atom, which is approximately four times smaller compared to the bulk fcc Ni (2.7 $\mu$eV/atom). In addition, MAE of the capped cluster (Fe$_{13}$Pt$_4$) is enhanced compared to the uncapped Jahn-Teller distorted Fe$_{13}$ cluster.

It is demonstrated by means of density functional and ab-initio quantum chemical calculations, that transition metal - carbon systems have the potential to enhance the presently achievable area density of magnetic recording by three orders of magnitude. As a model system, Co_2-benzene with a diameter of 0.5 nm is investigated. It shows a magnetic anisotropy in the order of 0.1 eV per molecule, large enough to store permanently one bit of information at temperatures considerably larger than 4 K. A similar performance can be expected, if cobalt dimers are deposited on graphene or on graphite. It is suggested that the subnanometer bits can be written by simultaneous application of a moderate magnetic and a strong electric field., Comment: 13 pages, 4 figures

Dimers are the smallest chemical objects that show magnetic anisotropy. We focus on 3$d$ and 4$d$ transition metal dimers that have magnetic ground states in most cases. Some of these magnetic dimers have a considerable barrier against re-orientation of their magnetization, the so-called magnetic anisotropy energy, MAE. The height of this barrier is important for technological applications, as it determines, e.g., the stability of information stored in magnetic memory devices. It can be estimated by means of relativistic density functional calculations. Our approach is based on a full-potential local-orbital method (FPLO) in a four-component Dirac-Kohn-Sham implementation. Orbital polarization corrections to the local density approximation are employed. They are discussed in the broader context of orbital dependent density functionals. Ground state properties (spin multiplicity, bond length, harmonic vibrational frequency, spin- and orbital magnetic moment, and MAE) of the 3$d$ and 4$d$ transition metal dimers are evaluated and compared with available experimental and theoretical data. We find exceptionally high values of MAE, close to 0.2 eV, for four particular dimers: Fe$_2$, Co$_2$, Ni$_2$, and Rh$_2$., Comment: 15 pages, 3 figures, J. Comput. Chemistry (accepted)