Antiphase boundaries (APBs) are ubiquitous in ordered Heusler alloys and strongly influence magnetic coercivity in Ni-Mn-Ga, yet the link between their atomic-scale exchange interactions and micrometer-scale magnetic contrast measured by magnetic force microscopy (MFM) remains unclear. We combine density functional theory (DFT) and finite-element magnetostatics to bridge these scales in Ni-Mn-Ga. DFT calculations on supercells containing planar APBs show that the lowest-energy configuration comprises a pair of parallel APBs enclosing a nanoscale region - only three Mn-Ga atomic layers thick - whose magnetization is antiparallel to the surrounding matrix due to strong antiferromagnetic exchange across each APB (in contrast to ferromagnetic coupling in bulk martensite). According to our magnetostatic finite element model, this thin region with antiparallel magnetization generates the characteristic MFM contrast extending approx. 100 nm from the APB pair. When the APBs are further apart than 50 nm, dipole-dipole penalties outweigh exchange gains, preventing formation of an extended antiparallel domain, in agreement with experimental evidence. These results identify APB pairs as the origin of the observed MFM contrast and offer an interpretation of the modest strengths of domain-wall pinning by APBs, informing the design of magnetic shape-memory alloys with tailored coercivity.

Doping is one of the most suitable methods for tuning the electronic properties of topological insulators and a promising approach for band gap opening in surface states. In this study, we developed a reliable method for preparing high-quality single crystal substrates comprising Bi2Se3 doped with VIIIB and VIB column elements. We combined experimental photoelectron spectroscopy (X-ray photoelectron spectroscopy, angle resolved photoelectron emission spectroscopy, and ultraviolet photoelectron spectroscopy) and theoretical (ab initio) methods to analyze the electronic properties and chemical states of atoms in the substitutional position and native defects in the topological insulator, which can be achieved using the free melt crystallization method for sample growth. The relationship between the position of the Dirac cone and valence band maximum was explored and discussed.

To explain the observed features of k-space photoelectron images taken on off-stoichiometric Heusler Ni49.7Mn29.1Ga21.2 single-crystals in the cubic austenitic and pseudotetragonal martensitic phases, the images were simulated theoretically. Despite the moderate structural difference of both phases, there is large difference in photoemission spectra. Analysis of the final states’ structure, matrix elements, and interface barrier scattering was performed to interpret discrepancies between the external photoemission of the austenite and martensite. The missing signal at the surface-normal emission of the martensitic phase is, ultimately, explained by repeated scatterings of escaping electrons on the interfaces between nanotwins.

We studied the doping of a Bi2Te3 single crystal using angle-resolved photoemission and ab initio electronic structure calculations. We find that at the surface, the typical bulk p-type conductivity is transformed to the n-type. The dopants from the VIII B column (Fe, Ru, and Os) give rise to the shift of the Dirac cone at the surface in the direction from the valence band maximum to the conductivity band minimum. The rearrangement of the Bi2Te3 surface electronic structure caused by doping is linked to the pinning of the Fermi level in the bulk gap, and its comparison with experimental data indicates that the dopants substitute Bi atoms rather than they occupy interstitial positions.

Atomic ordering of ferromagnetic alloys, such as Heusler compounds, vastly influences their magnetic properties and overall usability. However, in some cases x-ray diffraction cannot unambiguously determine the correct atomic structure, which hampers further research. In this paper, we analyze the atomic ordering using spectroscopic ellipsometry-a simple tabletop method that researchers can use in situ during sample deposition. The Co2Fe(Ga0.5Ge0.5) Heusler compound was chosen for the analysis, as the atomic ordering greatly influences its spin-polarizing capabilities. The ellispometric results are confronted with x-ray diffraction and with the help of ab initio calculations the qualitative changes in the optical response are linked to the changes in atomic ordering.

A parameter-free electronic structure approach is applied to the study of stability and chemical order in the 15 substitutional body-centered cubic (bcc)-based alloys made of the six transition metals of groups 5 (V, Nb, Ta) and 6 (Cr, Mo, W) of the periodic table. The method is based on a Green's function description of the electronic structure of the random alloys. Configurational order is treated within the generalized perturbation method, and temperature effects are examined with a generalized mean-field approach. In contrast to the results summarized in the assessed phase diagrams, stability and ordering trends are predicted in a broad range of alloy composition for at least seven alloys, and explanation is found in their electronic structure properties. Short-range order results, thermodynamics analysis, and bcc-based phase diagrams are also presented.

Doping ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ by magnetic ions represents an interesting problem since it may break the time-reversal symmetry needed to maintain the topological insulator character. Mn dopants in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ represent one of the most studied examples here. However, there is a lot of open questions regarding their magnetic ordering. In the experimental literature different Curie temperatures or no ferromagnetic order at all are reported for comparable Mn concentrations. This suggests that magnetic ordering phenomena are complex and highly susceptible to different growth parameters, which are known to affect material defect concentrations. So far theory has focused on Mn dopants in one possible position, and neglected relaxation effects as well as native defects. We have used ab initio methods to calculate the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ electronic structure influenced by magnetic Mn dopants, and exchange interactions between them. We have considered two possible Mn positions, the substitutional and interstitial one, and also native defects. We have found a sizable relaxation of atoms around Mn, which affects significantly magnetic interactions. Surprisingly, very strong interactions correspond to a specific position of Mn atoms separated by a van der Waals gap. Based on the calculated data we performed spin dynamics simulations to examine systematically the resulting magnetic order for various defect contents. We have found under which conditions the experimentally measured Curie temperatures ${T}_{\mathrm{C}}$ can be reproduced, noticing that interstitial Mn atoms appear to be important here. Our theory predicts the change of ${T}_{\mathrm{C}}$ with a shift of Fermi level, which opens the way to tune the system magnetic properties by selective doping.

The electronic and transport properties of the ordered B2-(Fe60Al40) phase which undergoes a continuous transition into the disordered A2-(Fe60Al40) phase are studied from first principles. The disordering is characterized as a gradual interchange of atoms between Fe and Al sublattices under the condition that the total amount of Fe and Al atoms is kept unchanged. This is the simplest model of gradual disordering of the ordered phase due to the ion irradiation. The physical properties are strongly influenced by varying local environment of Fe atoms on both sublattices. This leads to the transition between a high moment at large disorder and a very low moment in the ordered phase. Similar behavior is found also for anomalous Hall conductivity and anomalous Hall angle. Unusual behavior of the longitudinal conductivity as a function of degree of disorder is due to the shift of the Fermi level of majority states from the sp-like part to the d states with increasing ordering. The disordered phase has a large anomalous Hall angle as contrasted with a negligible anomalous Hall angle for well ordered samples, which is in agreement with recent experiment.

We present an ab initio theory of the spin-wave stiffness tensor for ordered and disordered itinerant ferromagnets with pair exchange interactions derived from a method of infinitesimal spin rotations. The resulting formula bears an explicit form of a linear-response coefficient which involves one-particle Green's functions and effective velocity operators encountered in a recent theory of electron transport. Application of this approach to ideal metal crystals yields more reliable values of the spin stiffness than traditional ill-converging real-space lattice summations. The formalism can also be combined with the coherent potential approximation for an effective-medium treatment of random alloys, which leads naturally to an inclusion of disorder-induced vertex corrections to the spin stiffness. The calculated concentration dependence of the spin-wave stiffness of random fcc Ni-Fe alloys can be ascribed to a variation of the reciprocal value of alloy magnetization. Calculations for random iron-rich bcc Fe-Al alloys reveal that their spin-wave stiffness is strongly reduced owing to the atomic ordering; this effect takes place due to weakly coupled local magnetic moments of Fe atoms surrounded by a reduced number of Fe nearest neighbors.

The spin Hall effect in fcc Pt-rich disordered solid solutions Pt-M (M = V, Nb, Ta) is studied by means of a relativistic ab initio Green-function theory.We find that the spin Hall angle of all three alloy systems exhibits similar sizable values, with a maximum slightly above 0.2, obtained for dopant concentrations around 12 at.%.This result is explained by a competition between opposite concentration trends of the intrinsic spin Hall conductivity and of the longitudinal residual resistivity while the strength of the impurity spin-orbit interaction plays only a minor role.This behavior agrees qualitatively with results of recent experiments on spin Hall torques in multilayered systems involving Pt-rich alloys with heavy and light impurities.

The high-entropy alloys AlxCrFeCoNi exist over a broad range of Al concentrations (0 < x < 2). With increasing Al content their structure is changed from the fcc to bcc phase. We investigate the effect of such structural changes on transport properties including the residual resistivity and the anomalous Hall resistivity. We have performed a detailed comparison of the first-principles simulations with available experimental data. We show that the calculated residual resistivities for all studied alloy compositions are in a fair agreement with available experimental data as concerns both the resistivity values and concentration trends. We emphasize that a good agreement with experiment was obtained also for the anomalous Hall resistivity. We have completed study by estimation of the anisotropic magnetoresistance, spin-disorder resistivity, and Gilbert damping. The obtained results prove that the main scattering mechanism is due to the intrinsic chemical disorder whereas the effect of spin polarization on the residual resistivity is appreciably weaker.

The electronic and thermal transport properties of the Earth's core are crucial for many geophysical models such as the geodynamo model of the Earth's magnetic field. We show by first-principles modeling and methods of statistical physics that the spin disorder, not considered in previous studies, gives an essential contribution to the electrical resistivity at the Earth's core conditions. The origin of this spin-disorder resistivity (SDR) consists in the existence of fluctuating local moments that are stabilized at high temperatures by the magnetic entropy even at pressures at which the ground state of iron is non-magnetic. It turns out that the contributions of various scattering mechanisms (alloy disorder, phonon scattering, spin disorder, and electron-electron correlations) are comparable, but not additive. Here we report results for iron and iron-rich alloys (Fe-O, Fe-Si, Fe-S) that can be present in the Earth's core. Special attention is paid to alloys with two magnetic elements (Fe-Ni).

The antiferromagnetic (AFM) CuMnAs alloy with tetragonal structure is a promising material for the AFM spintronics. The resistivity measurements indicate the presence of defects. We confirmed vacancies on Mn or Cu sublattices and Mncu and Cum antisites as most probable defects in CuMnAs by our new ab initio total energy calculations. We have estimated resistivities of possible defect types as well as resistivities of samples for which the X-ray structural analysis is available. In the latter case we have found that samples with Cu- and Mn-vacancies with low formation energies have also resistivities which agree well with the experiment. Finally, we have also calculated exchange interactions and estimated the Neel temperatures by using the Monte Carlo approach. A good agreement with experiment was obtained.

We present an extension of the relativistic electron transport theory for the standard (charge) conductivity tensor of random alloys within the tight-binding linear muffin-tin orbital method to the so-called spin-dependent conductivity tensor, which describes the Kubo linear response of spin currents to external electric fields. The approach is based on effective charge- and spin-current operators that correspond to intersite electron transport and that are nonrandom, which simplifies the configuration averaging by means of the coherent potential approximation. Special attention is paid to the Fermi sea term of the spin-dependent conductivity tensor, which contains a nonzero incoherent part, in contrast to the standard conductivity tensor. The developed formalism is applied to the spin Hall effect in binary random nonmagnetic alloys, both on a model level and for Pt-based alloys with an fcc structure. We show that the spin Hall conductivity consists of three contributions (one intrinsic and two extrinsic) which exhibit different concentration dependences in the dilute limit of an alloy. Results for selected Pt alloys (Pt-Re, Pt-Ta) lead to the spin Hall angles around 0.2; these sizable values are obtained for compositions that belong to thermodynamically equilibrium phases. These alloys can thus be considered as an alternative to other systems for efficient charge to spin conversion, which are often metastable crystalline or amorphous alloys.

The spin-disorder resistivity (SDR) of a broad range of magneticmaterials, both ordered and disordered, is reviewed.We identify the SDR at the critical temperature with the residualresistivity of the corresponding system evaluated in the frameworkof the disordered local moment (DLM) model.The underlying electronic structure is determined in the frameworkof the tight-binding linear muffin-tin orbital method which employsthe coherent potential approximation to describe the DLM stateand chemical disorder.The DLM fixed-spin moment method is used in the case when the DLMmoment collapses.The Kubo-Greenwood approach is employed to estimate the resistivityof the DLM state.Formalism is applied to Fe and Ni and its alloys, Heusler alloys,and ordered ferromagnetic and antiferromagnetic alloys.Finally, the SDR of the Earth's core will be studied using thesame formalism.Calculations are compared with available experimental data.

In shape memory materials the fine twinned microstructure plays a fundamental role. Here we show that in the martensite phase of Ni-Mn-Ga Heusler alloy, the fine features of electronic structure are not caused by intrinsic electronic changes but mesoscopically different orientations of ferroelastic domains, i.e., twins. The cuts of Fermi surfaces of a (pseudo) tetragonally distorted Ni49.7Mn29.1Ga21.2 Heusler single crystal with a (100) surface orientation were measured using angle-resolved photoemission spectroscopy and compared with first-principles calculations. In this work we demonstrated that the measured photoelectron spectrum was a projection of three separate electronic structures originating from single a-a and two perpendicular a-c ferroelastic domains with a twinned relationship. The twinning results in pseudosplitting of the experimentally observed bands at Fermi level.

We revise critically existing approaches to evaluation of thermodynamic potentials within the Green's function calculations at finite electronic temperatures. We focus on the entropy and show that usual technical problems related to the multivalued nature of the complex logarithm can be overcome. This results in a simple expression for the electronic entropy, which does not require any contour integration in the complex energy plane. Properties of the developed formalism are discussed and its illustrating applications to selected model systems and to bcc iron with disordered local magnetic moments are presented as well.

The electronic and galvanomagnetic properties of the equiatomic quaternary Heusler alloy CoMnFeSi, which was recently synthesized and which crystallizes in the cubic LiMgPdSb structure, are studied from first principles. We concentrate on two problems: (i) the origin of the alloy disorder, which was found to exist in this alloy, and (ii) the evaluation of basic galvanomagnetic properties such as the dc conductivity a tot and the anomalous Hall conductivity(AHC) for swap defects, accompanied by a comparison of the calculated results with a recent experiment. The origin of the alloy disorder is investigated by estimating corresponding formation energies of possible swap defects which preserve the sample stoichiometry. We discuss various defects with respect to the sample half metallicity. The most favorable swap types are those for which the calculated a tot and AHC agree reasonably with the experiment. On the basis of calculated transport quantities a tot (AHC), the two most favorable swap types can be identified, namely, (i) the Co-Fe swaps, which preserve the half metallicity and have the lowest formation energy, and (ii) the Co-Mn swaps, which violate the half metallicity but have larger formation energy.

The electronic and thermal transport properties of the Earth's core are crucial for many geophysical models such as the geodynamo model of the Earth's magnetic field and of its reversals. Here we show, by considering bcc iron and an iron-rich iron-silicon alloy as a representative of the Earth's core composition and applying first-principles modeling, that the spin disorder at the Earth's core conditions not considered previously provides an essential contribution, of order 20 mu Omega cm, to the electrical resistivity. This value is comparable in magnitude with the electron-phonon and with the recently estimated electron-electron scattering contributions. The origin of the spin-disorder resistivity (SDR) consists of the existence of fluctuating local moments that are stabilized at high temperatures by the magnetic entropy even at pressures at which the ground state of iron is nonmagnetic. We find that electron-phonon and SDR contributions are not additive at high temperatures. We thus observe a large violation of the Matthiessen rule, not common in conventional metallic alloys at ambient conditions.