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A scheme is presented to calculate on a first-principles level the spin-lattice coupling (SLC) parameters needed to perform combined molecular-spin dynamics (MSD) simulations. By treating changes to the spin configuration and atomic positions on the same level, closed expressions for the atomic SLC parameters could be derived in a coherent way up to any order. The properties of the SLC parameters are discussed considering separately the symmetric and antisymmetric parts of the SLC tensor. The changes due to atomic displacements of the spin-spin exchange coupling (SSC) parameters estimated using the SLC parameters are compared with the SSC parameters calculated for an embedded cluster with the central atom displaced, demonstrating good agreement of these results. Moreover, this allows to study the impact of different SLC contributions, linear and quadratic with respect to displacements, on the properties of the modified SSC parameters. In addition, we represent an approach to calculate the site-diagonal SLC parameters characterizing local magnetic anisotropy induced by a lattice distortion, which is a counterpart of the approach based on magnetic torque used for the investigations of magneto-crystalline anisotropy (MCA) as well as for calculations of the MCA constants. In particular, the dependence of the induced magnetic torque on different types of atomic displacements is analyzed., Comment: 16 pages

We explore possibilities for control of magnons in two-dimensional heterostructures by an external electric field acting across a dielectric barrier. By performing ab initio calculations for a Fe monolayer and Fe bilayer, both suspended in vacuum and deposited on Cu(001), we demonstrate that external electric field can significantly modify magnon lifetimes and that these changes can be related to field-induced changes in layer-resolved Bloch spectral functions. For systems with more magnon dispersion branches, the gap between high- and low-energy eigenmodes varies with the external field. These effects are strongly influenced by the substrate. Considerable variability in how the magnon spectra are sensitive to the external electric field can be expected, depending on the substrate and on the thickness of the magnetic layer.

Based on first principles calculations we investigate the electronic and magnetic properties of Pt layers in Pd$(001)$/Co/Pt thin film structures exposed to an external electric field. Due to the Co underlayer, the surface Pt layers have induced moments that are modified by an external electric field. The field induced changes can be explained by the modified spin-dependent orbital hybridization that varies non-linearly with the field strength. We calculate the x-ray absorption and the x-ray magnetic circular dichroism spectra for an applied external electric field and examine its impact on the spectra in the Pt layer around the L$_{2}$ and L$_{3}$ edges. We also determine the layer dependent magneto-crystalline anisotropy and show that the anisotropy can be tuned easily in the different layers by the external electric field., 9 pages, 11 figures

Ab initio calculations of the spin wave stiffness constant $D$ for elemental Fe and Ni performed by different groups in the past have led to values with a considerable spread of 50-100 %. We present results for the stiffness constant $D$ of Fe, Ni, and permalloy Fe$_{0.19}$Ni$_{0.81}$ obtained by three different approaches: (i) by finding the quadratic term coefficient of the power expansion of the spin wave energy dispersion, (ii) by a damped real-space summation of weighted exchange coupling constants, and (iii) by integrating the appropriate expression in reciprocal space. All approaches are implemented by means of the same Korringa-Kohn-Rostoker (KKR) Green function formalism. We demonstrate that if properly converged, all procedures yield comparable values, with uncertainties of 5-10 % remaining. By a careful analysis of the influence of various technical parameters we estimate the margin of errors for the stiffness constants evaluated by different approaches and suggest procedures to minimize the risk of getting incorrect results., Comment: 11 pages, 7 figures, 12 tables

We present a comprehensive study on the low-temperature orthorhombic phase of $\mathrm{Ba}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{As}}_{2}$ based on the Korringa-Kohn-Rostoker-Green function approach. Using this band-structure method in combination with the coherent potential approximation alloy theory we are able to investigate the evolution of the magnetic and electronic properties of this prototype iron pnictide for arbitrary concentrations $x$, while dealing with the chemical disorder without uncontrolled simplifications by using solely a rigid-band shift or the virtual crystal approximation. We discuss the development of the site-resolved magnetic moments for the experimentally observed stripe antiferromagnetic order together with the strong electronic anisotropy of the Fermi surface and compare it with angle-resolved photoemission spectroscopy measurements of detwinned crystals. We furthermore calculate magnetic exchange coupling parameters ${J}_{ij}$ and use them for Monte Carlo simulations on the basis of the classical Heisenberg model to get an insight on the temperature dependence of the magnetic ordering on the cobalt concentration.

The effect of the Dzyaloshinsky-Moriya interaction on the magnetic structure of an ordered FePt monolayer deposited on the $\mathrm{Pt}(\mathrm{111})$ surface has been investigated. In the ground state, the pronounced anisotropic geometry of the FePt layer with alternating Fe and Pt chains gives rise to a helimagnetic structure with a strong difference in the helicity period along the chains and perpendicular to them. In the presence of an external magnetic field, the region of stable Skyrmion magnetic structures in the B-T phase diagram has been demonstrated via Monte Carlo simulations using the parameters obtained within first-principles electronic structure calculations. The present study demonstrates clearly that the ratio of the exchange coupling parameters $J/D$ for a deposited magnetic film\char22{}being of central importance for the formation of Skyrmions\char22{}can be manipulated by growing an overlayer of 2-dimensional compounds with the atoms carrying spontaneous magnetic moments separated by the atoms of nonmagnetic elements.

We present a detailed theoretical investigation on the magnetic properties of small single-layered Fe, Co, and Ni clusters deposited on Ir(111), Pt(111), and Au(111). For this, a fully relativistic ab initio scheme based on density functional theory has been used. We analyze the element, size, and geometry specific variations of the atomic magnetic moments and their mutual exchange interactions as well as the magnetic anisotropy energy in these systems. Our results show that the atomic spin magnetic moments in the Fe and Co clusters decrease almost linearly with increasing coordination number on all three substrates, while the corresponding orbital magnetic moments appear to be much more sensitive to the local atomic environment. The isotropic exchange interaction among the cluster atoms is always very strong for Fe and Co exceeding the values for bulk bcc Fe and hcp Co, whereas the anisotropic Dzyaloshinski-Moriya interaction is, in general, one or two orders of magnitude smaller when compared to the isotropic one. For the magnetic properties of Ni clusters, the magnetic properties can show quite a different behavior, and we find in this case a strong tendency towards noncollinear magnetism.

The finite-temperature magnetic properties of ${\text{Fe}}_{x}{\text{Pd}}_{1\ensuremath{-}x}$ and ${\text{Co}}_{x}{\text{Pt}}_{1\ensuremath{-}x}$ alloys have been investigated. It is shown that the temperature-dependent magnetic behavior of these alloys cannot be described properly unless the coupling between the magnetic moments at the Fe and Co mediated through the interactions with the induced magnetic moments of the nonmagnetic Pd and Pt atoms is included. A scheme for the calculation of the Curie temperature $({T}_{C})$ for this type of systems is presented that is based on the extended Heisenberg Hamiltonian with the appropriate exchange parameters ${J}_{ij}$ obtained from ab initio electronic-structure calculations. Within the present study the Korringa-Kohn-Rostoker Green's-function method has been used to calculate the ${J}_{ij}$ parameters. The Curie temperatures obtained for ${\text{Fe}}_{x}{\text{Pd}}_{1\ensuremath{-}x}$ and ${\text{Co}}_{x}{\text{Pt}}_{1\ensuremath{-}x}$ alloys are compared with the corresponding experimental data. The experimental results for ${\text{Fe}}_{x}{\text{Pd}}_{1\ensuremath{-}x}$ alloys have been obtained within anomalous Hall-effect measurements. The agreement between theoretical results and all available experimental data is rather good.

The exchange stiffness constants of chemically disordered ${\text{Fe}}_{x}{\text{Pt}}_{1\ensuremath{-}x}$ films with thickness around 50 nm were determined by means of ferromagnetic resonance. It was found to increase with increasing Fe content from $6\ifmmode\pm\else\textpm\fi{}4\text{ }\text{pJ}/\text{m}$ for $x=0.27$ to $15\ifmmode\pm\else\textpm\fi{}4\text{ }\text{pJ}/\text{m}$ for $x=0.67$. Theoretical results from fully relativistic and scalar-relativistic band-structure calculations using the Korringa-Kohn-Rostoker method confirm the experimentally obtained values. In addition, determination of the magnetocrystalline anisotropy by angular-dependent measurements of the ferromagnetic resonance gave the possibility to estimate the exchange length that was found to be 40--50 nm for all compositions investigated in this work.

The influence of the spin-orbit coupling on the magnetic structure of deposited transition-metal nanostructures has been studied by fully relativistic electronic-structure calculations. The interplay of exchange coupling and magnetic anisotropy was monitored by studying the corresponding magnetic torque calculated within ab initio and model approaches. We find that a spin-orbit-induced Dzyaloshinski-Moriya interaction has a profound effect on the spin structure of such complex magnetic systems and that in combination with magnetic anisotropies and isotropic exchange this can result in peculiar magnetic properties.

The complex correlation of structure and magnetism in highly coercive monoatomic FePt surface alloys is studied using scanning tunneling microscopy, x-ray magnetic circular dichroism, and ab initio theory. Depending on the specific lateral atomic coordination of Fe either hard magnetic properties comparable to that of bulk FePt or complex noncollinear magnetism due to Dzyaloshinski-Moriya interactions are observed. Our calculations confirm the subtle dependence of the magnetic anisotropy and spin alignment on the local coordination and suggest that 3D stacking of Fe and Pt layers in bulk $L{1}_{0}$ magnets is not essential to achieve high-anisotropy values.

A different scheme to calculate the exchange tensor ${\underset{}{J}}_{ij}$ describing in a phenomenological way the anisotropic exchange coupling of two moments in a magnetically ordered system is presented. The ab initio approach is based on spin-polarized relativistic multiple-scattering theory within the framework of spin-density functional theory. The scheme is applied to ferromagnetic CrTe as well as the diluted magnetic semiconductor system ${\text{Ga}}_{1\ensuremath{-}x}{\text{Mn}}_{x}\text{As}$. In the latter case the results show that there is a noticeable anisotropy in the exchange coupling present, although not as pronounced as those suggested in recent theoretical investigations.

Systematic trends in the magnetism of Co-Pt solid-state systems are explored by studying the effects of composition, electron correlations, spin-orbit coupling (SOC), and long-range order. Ab initio fully relativistic calculations were performed for bulk Co, a substitutional Pt impurity in Co, ${\text{Co}}_{3}\text{Pt}$, CoPt, ${\text{CoPt}}_{3}$, and a substitutional Co impurity in Pt. Many-body effects beyond the local spin-density approximation (LSDA) were included via the dynamical mean-field theory (DMFT); a comparison with results based on the Brooks orbital-polarization (OP) scheme was also made. The disorder was treated within the coherent-potential approximation. We found that while the spin magnetic moments ${\ensuremath{\mu}}_{\text{spin}}$ at the Co atoms monotonously increase with increasing Pt concentration, the orbital magnetic moments ${\ensuremath{\mu}}_{\text{orb}}$ do not follow the trend of ${\ensuremath{\mu}}_{\text{spin}}$. Magnetic moments ${\ensuremath{\mu}}_{\text{spin}}$ and ${\ensuremath{\mu}}_{\text{orb}}$ at Pt atoms do not depend on Pt concentration monotonously. Most of these trends can be understood in terms of hybridization and site-dependent SOC. The OP scheme of Brooks corrects the deficiencies of a pure LSDA only if the Pt concentration is low. The $\text{LSDA}+\text{DMFT}$ scheme provides ${\ensuremath{\mu}}_{\text{orb}}/{\ensuremath{\mu}}_{\text{spin}}$ ratios for Co atoms which agree with experiment even for high Pt content. Introducing disorder leads to an enhancement of ${\ensuremath{\mu}}_{\text{spin}}$ at Co atoms and to a suppression of ${\ensuremath{\mu}}_{\text{spin}}$ at Pt atoms. The ${\ensuremath{\mu}}_{\text{orb}}$ at Co atoms does not exhibit any systematic dependence on the degree of order, while ${\ensuremath{\mu}}_{\text{orb}}$ at Pt atoms decreases with increasing disorder for all Pt concentrations.