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Magnetoelasticity plays a crucial role in numerous magnetic phenomena, including magnetocalorics, magnon excitation via acoustic waves, and ultrafast demagnetization/Einstein-de Haas effect. Despite a long-standing discussion on anisotropy-mediated magnetoelastic interactions of relativistic origin, including \textit{ab-initio} calculations, the exchange-mediated magnetoelastic parameters within an atomistic framework have only recently begun to be investigated. As a result, many of their behaviors and values for real materials remain poorly understood. Therefore, by using a proposed simple modification of the embedded cluster approach that reduces the computational complexity, we critically analyze the properties of exchange-mediated spin-lattice coupling parameters for elemental $3d$ ferromagnets (bcc Fe, fcc Ni, and fcc Co), comparing methods used for their extraction and relating their realistic values to symmetry considerations and orbitally-decomposed contributions. Additionally, we investigate the effects of noncollinearity (spin temperature) and applied pressure on these parameters. For Fe, we find that single-site rotations, associated with spin temperatures around $\sim100$ K, induce significant modifications, particularly in Dzyaloshinskii-Moriya-type couplings; in contrast, such interactions in Co and Ni remain almost configuration independent. Moreover, we demonstrate a notable change in the exchange-mediated magnetoelastic constants for Fe under isostatic compression. Finally, the conversion between atomistic, quantum-mechanically derived parameters and the phenomenological magnetoelastic theory is discussed, which can be an useful tool towards larger and more realistic dynamics simulations involving coupled subsystems.

We report on the stabilization of ferromagnetic skyrmions in zero external magnetic fields, in exchange-biased systems composed of ferromagnetic-antiferromagnetic (FM-AFM) bilayers. By performing atomistic spin dynamics simulations, we study cases of compensated, uncompensated, and partly uncompensated FM-AFM interfaces, and investigate the impact of important parameters such as temperature, inter-plane exchange interaction, Dzyaloshinskii-Moria interaction, and magnetic anisotropy on the skyrmions appearance and stability. The model with an uncompensated FM-AFM interface leads to the stabilization of individual skyrmions and skyrmion lattices in the FM layer, caused by the effective field from the AFM instead of an external magnetic field. Similarly, in the case of a fully compensated FM-AFM interface, we show that FM skyrmions can be stabilized. We also demonstrate that accounting for interface roughness leads to stabilization of skyrmions both in compensated and uncompensated interfaces. Moreover, in bilayers with a rough interface, skyrmions in the FM layer are observed for a wide range of exchange interaction values through the FM-AFM interface, and the chirality of the skyrmions depends critically on the exchange interaction., Comment: 8 pages, 8 figures

We study the ultrafast magnetization dynamics of bcc Fe and fcc Co using the recently suggested heat-conserving three-temperature model (HC3TM), together with atomistic spin- and lattice dynamics simulations. It is shown that this type of Langevin-based simulation is able to reproduce observed trends of the ultrafast magnetization dynamics of fcc Co and bcc Fe, in agreement with previous findings for fcc Ni. The simulations are performed by using parameters that to as large extent as possible are obtained from electronic structure theory. The one parameter that was not calculated in this way, was the damping term used for the lattice dynamics simulations, and here a range of parameters were investigated. It is found that this term has a large influence on the details of the magnetization dynamics. The dynamics of iron and cobalt is compared with previous results for nickel and similarities and differences in the materials' behavior are analysed following the absorption of a femtosecond laser pulse. Importantly, for all elements investigated so far with this model, we obtain a linear relationship between the value of the maximally demagnetized state and the fluence of the laser pulse, which is in agreement with experiments., Comment: 9 pages, 9 figures, Submitted to Physical Review B

Phase-space representations are a family of methods for dynamics of both bosonic and fermionic systems, that work by mapping the system's density matrix to a quasi-probability density and the Liouville-von Neumann equation of the Hamiltonian to a corresponding density differential equation for the probability. We investigate here the accuracy and the computational efficiency of one approximate phase-space representation, called the fermionic Truncated Wigner Approximation (fTWA), applied to the Fermi-Hubbard model. On a many-body 2D system, with hopping strength and Coulomb $U$ tuned to represent the electronic structure of graphene, the method is found to be able to capture the time evolution of first-order (site occupation) and second-order (correlation functions) moments significantly better than the mean-field, Hartree-Fock method. The fTWA was also compared to results from the exact diagonalization method for smaller systems, and in general the agreement was found to be good. The fully parallel computational requirement of fTWA scales in the same order as the Hartree-Fock method, and the largest system considered here contained 198 lattice sites.

It is demonstrated that thermally induced longitudinal spin fluctuations (LSF) play an important role in itinerant Co$_3$Mn$_2$Ge at an elevated temperature. The effect of LSF is taken into account during {\it ab initio} calculations via a simple model for the corresponding entropy contribution. We show that the magnetic entropy leads to the appearance of a medium size local moment on Co atoms. As a consequence, this leads to a renormalization of the magnetic exchange interactions with a quite substantial impact upon the calculated Curie temperature. Taking LSF into account, the calculated Curie temperature can be brought to be in good agreement with the experimental value.

In this article we employ density functional theory in the generalized gradient approximation to investigate the structural and electronic properties of the solid solution alloy $\text{Zn}\text{Se}_x\text{S}_{1-x}$ in the wurtzite structure. We analyzed the character of the bond lengths and angles at the atomic scale, using a supercell approach that does not impose any constraint on the crystal potential. We show that the bond lengths of pristine ZnS and ZnSe compounds are almost preserved between nearest neighbors, which is different from what would be anticipated if Vegard's law were valid at the atomic level. We also show that bond lengths start behaving in accordance to Vegard's law from the third shell of nearest neighbors onward, which in turn determines the average lattice parameters of the alloys determined by diffraction experiments. Fundamental building blocks around the anions are identified and are shown to be non-rigid but still volume preserving. Finally, the geometrical analysis is connected to the trend exhibited by the electronic structure, and in particular by the band gap. The latter is found to exhibit a small deviation from the linearity with respect to the Se concentration, in accordance to available experimental data. By assuming a quadratic dependence, we can extract a bowing parameter and analyze various contributions to it with various calculations under selected constraints. The structural deformation in response to the doping process is shown to be the driving force behind the deviation from linearity. The difference in stiffness between ZnS and ZnSe is showed to play a key role in the asymmetric behavior of the bowing parameter observed in the S-rich and Se-rich regions.

Ultrafast manipulation of the magnetic state of matter bears great potential for future information technologies. While demagnetisation in ferromagnets is governed by dissipation of angular momentum, materials with multiple spin sublattices, e.g. antiferromagnets, can allow direct angular momentum transfer between opposing spins, promising faster functionality. In lanthanides, 4$\it{f}$ magnetic exchange is mediated indirectly through the conduction electrons (the Ruderman-Kittel-Kasuya-Yosida interaction, RKKY), and the effect of such conditions on direct spin transfer processes is largely unexplored. Here, we investigate ultrafast magnetization dynamics in 4f antiferromagnets, and systematically vary the 4$\it{f}$ occupation, thereby altering the magnitude of RKKY. By combining time-resolved soft x-ray diffraction with ab-initio calculations, we find that the rate of direct transfer between opposing moments is directly determined by the magnitude of RKKY. Given the high sensitivity of RKKY to the conduction electrons, our results offer a novel approach for fine-tuning the speed of magnetic devices.

Stabilization of unusual spin-orbit driven magnetic orderings are achieved for chains of Mn atoms deposited on a W(110) substrate. First-principles electronic structure calculations show that the ground state spin configuration is non-collinear, forming spirals as a result of a competition between nearest and next-nearest neighbour exchange interactions. The orbital magnetic moments are also found to exhibit non-collinear ordering, that interestingly for some systems is incommensurate with the spin arrangement. We attribute such an exotic behaviour to the competition between the and spin-orbital interaction and crystal-field splitting effects. Model calculations based on this assumption reproduce the main findings observed in the first-principles calculations.

We present a general method of constructing \textit{in-situ} pseodopotentials from first principles, all-electron, full-potential electronic structure calculations of a solid. The method is applied to bcc Na, at equilibrium volume. The essential steps of the method involve (i) calculating an all-electron Kohn-Sham eigenstate. (ii) Replacing the oscillating part of the wavefunction (inside the muffin-tin spheres) of this state, with a smooth function. (iii) Representing the smooth wavefunction in a Fourier series, and (iv) inverting the Kohn-Sham equation, to extract the pseudopotential that produces the state generated in steps (i)-(iii). It is shown that an \textit{in-situ} pseudopotential can reproduce an all-electron, full-potential eigenvalue up to the sixth significant digit. A comparison of the all-electron theory, \textit{in-situ} pseudopotential theory and the standard nonlocal pseudopotential theory demonstrates good agreement, e.g., in the energy dispersion of the 3$s$ band state of bcc Na., Comment: 13 pages, 3 figures

A method with which to calculate the Gilbert damping parameter from a real-space electronic structure method is reported here. The anisotropy of the Gilbert damping with respect to the magnetic moment direction and local chemical environment is calculated for bulk and surfaces of Fe$_{50}$Co$_{50}$ alloys from first principles electronic structure in a real space formulation. The size of the damping anisotropy for Fe$_{50}$Co$_{50}$ alloys is demonstrated to be significant. Depending on details of the simulations, it reaches a maximum-minimum damping ratio as high as 200%. Several microscopic origins of the strongly enhanced Gilbert damping anisotropy have been examined, where in particular interface/surface effects stand out, as do local distortions of the crystal structure. Although theory does not reproduce the experimentally reported high ratio of 400% [Phys. Rev. Lett. 122, 117203 (2019)], it nevertheless identifies microscopic mechanisms that can lead to huge damping anisotropies.

A non-trivial balance between Coulomb repulsion and kinematic effects determines the electronic structure of correlated electron materials. The use electromagnetic fields strong enough to rival these native microscopic interactions allows us to study the electronic response as well as the timescales and energies involved in using quantum effects for possible applications. We use element-specific transient x-ray absorption spectroscopy and high-harmonic generation to measure the response to ultrashort off-resonant optical fields in the prototypical correlated electron insulator NiO. Surprisingly, fields of up to 0.22 V/{\AA} leads to no detectable changes on the correlated Ni 3d-orbitals contrary to previous predictions. A transient directional charge transfer is uncovered, a behavior that is captured by first-principles theory. Our results highlight the importance of retardation effects in electronic screening, and pinpoints a key challenge in functionalizing correlated materials for ultrafast device operation., Comment: 6 pages, 3 figure, supplemental material not included in document

The coexistence of charge density wave (CDW) and superconductivity in tantalum disulfide (2H-TaS$_2$) at ambient pressure, is boosted by applying hydrostatic pressures up to 30GPa, thereby inducing a typical dome-shaped superconducting phase. The ambient pressure CDW ground state which begins at TCDW = 76 K, with critically small Fermi surfaces, was found to be fully suppressed at Pc = 8.7GPa. Around Pc, we observe a superconducting dome with a maximum superconducting transition temperature Tc = 9.1 K. First-principles calculations of the electronic structure predict that, under ambient conditions, the undistorted structure is characterized by a phonon instability at finite momentum close to the experimental CDW wave vector. Upon compression, this instability is found to disappear, indicating the suppression of CDW order. The calculations reveal an electronic topological transition (ETT), which occurs before the suppression of the phonon instability, suggesting that the ETT alone is not directly causing the structural change in the system. The temperature dependence of the first vortex penetration field has been experimentally obtained by two independent methods and the corresponding lower critical field H$_{c1}$ was deduced. While a d wave and single-gap BCS prediction cannot describe our H$_{c1}$ experiments, the temperature dependence of the H$_{c1}$ can be well described by a single-gap anisotropic s-wave order parameter., Comment: 6 Pages, 4 figures

We have derived an expression of the Dzyaloshinskii-Moriya (DM) interaction, where all the three components of the DM vector can be calculated independently, for a general, non-collinear magnetic configuration. The formalism is implemented in a real space - linear muffin-tin orbital - atomic sphere approximation (RS-LMTO-ASA) method. We have chosen the Cr triangular trimer on Au(111) and Mn triangular trimers on Ag(111) and Au(111) surfaces as numerical examples. The results show that the DM interaction (module and direction) is drastically different for collinear and non-collinear states. Based on the relation between the spin and charge currents flowing in the system and their coupling to the non-collinear magnetic configuration of the triangular trimer, we demonstrate that the DM interaction can be significant, even in the absence of spin-orbit coupling. This is shown to emanate from the non-collinear magnetic structure, that can induce significant spin and charge currents even with spin-orbit coupling is ignored.

We report on optically induced, ultrafast magnetization dynamics in the Heusler alloy $\mathrm{Co_{2}FeAl}$, probed by time-resolved magneto-optical Kerr effect. Experimental results are compared to results from electronic structure theory and atomistic spin-dynamics simulations. Experimentally, we find that the demagnetization time ($\tau_{M}$) in films of $\mathrm{Co_{2}FeAl}$ is almost independent of varying structural order, and that it is similar to that in elemental 3d ferromagnets. In contrast, the slower process of magnetization recovery, specified by $\tau_{R}$, is found to occur on picosecond time scales, and is demonstrated to correlate strongly with the Gilbert damping parameter ($\alpha$). Our results show that $\mathrm{Co_{2}FeAl}$ is unique, in that it is the first material that clearly demonstrates the importance of the damping parameter in the remagnetization process. Based on these results we argue that for $\mathrm{Co_{2}FeAl}$ the remagnetization process is dominated by magnon dynamics, something which might have general applicability.

Giant Gilbert damping anisotropy is identified as a signature of strong Rashba spin-orbit coupling in a two-dimensional antiferromagnet on a honeycomb lattice. The phenomenon originates in spin-orbit induced splitting of conduction electron subbands that strongly suppresses certain spin-flip processes. As a result, the spin-orbit interaction is shown to support an undamped non-equilibrium dynamical mode that corresponds to an ultrafast in-plane N\'eel vector precession and a constant perpendicular-to-the-plane magnetization. The phenomenon is illustrated on the basis of a two dimensional $s$-$d$ like model. Spin-orbit torques and conductivity are also computed microscopically for this model. Unlike Gilbert damping these quantities are shown to reveal only a weak anisotropy that is limited to the semiconductor regime corresponding to the Fermi energy staying in a close vicinity of antiferromagnetic gap., Comment: 12 pages, 3 figures

Crystallographic lattice defects strongly influence dynamical properties of magnetic materials at both microscopic and macroscopic length scales. A multi-scale approach to magnetisation dynamics, which is presented in this paper, accurately captures such effects. The method is illustrated using examples of systems with localized, non-trivial topological properties, e.g. in the form of skyrmions and chiral domain walls that interact with lattice dislocations. Technical aspects of the methodology involve multi-scale magnetisation dynamics that connects atomistic and continuum descriptions. The technique is capable of solving the Landau-Lifshitz-Gilbert equations efficiently in two regions of a magnetic material --- the mesoscopic and the atomistic regions, which are coupled in a seamless way. It is demonstrated that this methodology allows simulating realistically-sized magnetic skyrmions interacting with material defects and novel physical effects, uncovered using this theoretical methodology, are described., Comment: 9 pages, 7 figures and Supplementary information

Conducting and magnetic properties of a material often change in some confined geometries. However, a situation where a non-magnetic semiconductor becomes both metallic and magnetic at the surface is quite rare, and to the best of our knowledge has never been observed in experiment. In this work, we employ first-principles electronic structure theory to predict that such a peculiar magnetic state emerges in a family of quaternary Heusler compounds. We investigate magnetic and electronic properties of CoCrTiP, FeMnTiP and CoMnVAl. For the latter material, we also analyse the magnetic exchange interactions and use them for parametrizing an effective spin Hamiltonian. According to our results, magnetism in this material should persist at temperatures at least as high as 155 K., Comment: 5 pages, 3 figures + Supplementary material

In this work we use a multiscale approach toward a realistic design of a permanent magnet based on MnAl $\tau$-phase and elucidate how the antiphase boundary defects present in this material affect the energy product. We show how the extrinsic properties of a microstructure depend on the intrinsic properties of a structure with defects by performing micromagnetic simulations. For an accurate estimation of the energy product of a realistic permanent magnet based on the MnAl $\tau$-phase with antiphase boundaries, we quantify for the first time the exchange interaction strength across the antiphase boundary defect with a simple approach derived from the first-principles calculations. These two types of calculations performed at different scales are linked via atomistic spin dynamic simulations performed at an intermediate scale.

This paper describes the open Novamag database that has been developed for the design of novel Rare-Earth free/lean permanent magnets. The database software technologies, its friendly graphical user interface, advanced search tools and available data are explained in detail. Following the philosophy and standards of Materials Genome Initiative, it contains significant results of novel magnetic phases with high magnetocrystalline anisotropy obtained by three computational high-throughput screening approaches based on a crystal structure prediction method using an Adaptive Genetic Algorithm, tetragonally distortion of cubic phases and tuning known phases by doping. Additionally, it also includes theoretical and experimental data about fundamental magnetic material properties such as magnetic moments, magnetocrystalline anisotropy energy, exchange parameters, Curie temperature, domain wall width, exchange stiffness, coercivity and maximum energy product, that can be used in the study and design of new promising high-performance Rare-Earth free/lean permanent magnets. The results therein contained might provide some insights into the ongoing debate about the theoretical performance limits beyond Rare-Earth based magnets. Finally, some general strategies are discussed to design possible experimental routes for exploring most promising theoretical novel materials found in the database.

Tailoring transport properties of strongly correlated electron systems in a controlled fashion counts among the dreams of materials scientists. In copper oxides, varying the carrier concentration is a tool to obtain high-temperature superconducting phases. In manganites, doping results in exotic physics such as insulator-metal transitions (IMT), colossal magnetoresistance (CMR), orbital- or charge-ordered (CO) or charge-disproportionate (CD) states. In most oxides, antiferromagnetic order and charge-disproportionation are asssociated with insulating behavior. Here we report the realization of a unique physical state that can be induced by Mo doping in LaFeO$_3$: the resulting metallic state is a site-selective Mott insulator where itinerant electrons evolving in low-energy Mo states coexist with localized carriers on the Fe sites. In addition, a local breathing-type lattice distortion induces charge disproportionation on the latter, without destroying the antiferromagnetic order. A state, combining antiferromangetism, metallicity and CD phenomena is rather rare in oxides and may be of utmost significance for future antiferromagnetic memory devices., Comment: 8 pages, 4 figures

Ni$_{0.8}$Fe$_{0.2}$ (Py) and Py alloyed with Cu exhibit intriguing ultrafast demagnetization behavior, where the Ni magnetic moment shows a delayed response relative to the Fe, an effect which is strongly enhanced by Cu alloying. We have studied a broad range of Cu concentrations to elucidate the effects of Cu alloying in Py. The orbital/spin magnetic moment ratios are largely unaffected by Cu alloying, signifying that Cu-induced changes in the ultrafast demagnetization are not related to spin-orbit interactions. We show that magnon diffusion can explain the delayed Ni response, which we attribute to an enhanced magnon generation rate in the Fe sublattice relative to the Ni sublattice. Furthermore, Py exhibits prominent RKKY-like exchange interactions, which are strongly enhanced between Fe atoms and diminished between Ni atoms by Cu alloying. An increased Fe magnon scattering rate is expected to occur concurrently with this increased Fe-Fe exchange interaction, supporting the results obtained from the magnon diffusion model.

The static and dynamic properties of spin-polarons in La-doped $CaMnO_3$ are explored theoretically, by means of an effective low energy Hamiltonian. All parameters from the Hamiltoniain are evaluated from first principles theory, without adjustable parameters. %We compare different geometries, like spin-polarons in bulk, surface and as single two-dimensional layers. The Hamiltonian is used to investigate the temperature stability as well as the response to an external applied electric field, for spin-polarons in bulk, surface and as single two-dimensional layers. Technically this involves atomistic spin-dynamics simulations in combination with kinetic Monte Carlo simulations. Where a comparison can be made, our simulations exhibit an excellent agreement with available experimental data and previous theory. Remarkably, we find that excellent control of the mobility of spin-polarons in this material can be achieved, and that the critical parameters deciding this is the temperature and strength of the applied electrical field. We outline different technological implications of spin-polarons, and point to spin-polaronics as an emerging sub-field of nano-technology. In particular, we demonstrate that it is feasible to write and erase information on atomic scale, by use of spin-polarons in $CaMnO_3$., Comment: 13 pages, 8 figures

By using a multiscale approach based on first-principles density functional theory combined with atomistic spin dynamics, we investigate the electronic structure and magnetization dynamics of an inverse Heusler and a Heusler compound and their alloys, i. e. Mn$_{2-x}Z_x$CoAl and Mn$_{2-x}Z_x$VAl, where $Z$ = Mo, W, Os and Ru, respectively. A signature of the ferrimagnetic ordering of Mn$_{2}$CoAl and Mn$_{2}$VAl Heusler alloys is reflected in the calculated Heisenberg exchange constants. They decay very rapidly with the interatomic distance and have short range, which is a consequence of the existence of the finite gap in the minority spin band. The calculated Gilbert damping parameter of both Mn$_2$CoAl and Mn$_2$VAl is high compared to other half-metals, but interestingly in the particular case of the inverse Mn$_{2}$CoAl alloys and due to the spin-gapless semiconducting property, the damping parameters decrease with the doping concentration in clear contradiction to the general trend. Atomistic spin dynamics simulations predict ultrafast magnetisation switching in Mn$_{2}$CoAl and Mn$_{2}$VAl under the influence of an external magnetic field, starting from a threshold field of $2\text{T}$. Our overall finding extends with Heusler and inverse Heusler alloys, the class of materials that exhibits laser induced magnetic switching.

We present a comprehensive study of the magnetic properties of Sr$_{3-x}$Y$_{x}$(Fe$_{1.25}$Ni$_{0.75}$)O$_{7-\delta}$ ($0 \leq x \leq 0.75$). Experimentally, the magnetic properties are investigated using superconducting quantum interference device (SQUID) magnetometry and neutron powder diffraction (NPD). This is complemented by the theoretical study based on density functional theory as well as the Heisenberg exchange parameters. Experimental results show an increase in the N\'eel temperature ($T_N$) with the increase of Y concentrations and O occupancy. The NPD data reveals all samples are antiferromagnetically ordered at low temperatures, which has been confirmed by our theoretical simulations for the selected samples. Our first-principles calculations suggest that the 3D magnetic order is stabilized due to finite inter-layer exchange couplings. The latter give rise to a finite inter-layer spin correlations which disappear above the $T_N$.

We propose a new efficient permanent magnet, SmCoNiFe3, that is a breakthrough development of the well-known SmCo5 prototype. More modern neodymium magnets of the Nd-Fe-B type have an advantage over SmCo5 because of their greater maximum energy products due to their iron-rich stoichiometry. Our new magnet, however, removes most of this disadvantage of SmCo5 while preserving its superior high-temperature efficiency over the neodymium magnets.

Multipolaron solutions were studied in the framework of the Holstein one-dimensional molecular crystal model. The study was performed in the continuous limit where the crystal model maps into the nonlinear Schr\"odinger equation for which a new periodic dnoidal solution was found for the multipolaron system. In addition, the stability of the multi-polaron solutions was examined, and it was found that cnoidal and dnoidal solutions stabilize in different ranges of the parameter space. Moreover, the model was studied under the influence of nonlocal effects and the polaronic dynamics was described in terms of internal solitonic modes., Comment: 5 pages, 2 figures and Supplementary information

We show for a simple non-collinear configuration of the atomistic spins (in particular, where one spin is rotated by a finite angle in a ferromagnetic background) that the pairwise energy variation computed in terms of multiple scattering formalism cannot be fully mapped onto a bilinear Heisen- berg spin model even in the lack of spin-orbit coupling. The non-Heisenberg terms induced by the spin-polarized host appear in leading orders in the expansion of the infinitesimal angle variations. However, an Eg-T2g symmetry analysis based on the orbital decomposition of the exchange param- eters in bcc Fe leads to the conclusion that the nearest neighbor exchange parameters related to the T2g orbitals are essentially Heisenberg-like: they do not depend on the spin configuration, and can in this case be mapped onto a Heisenberg spin model even in extreme non-collinear cases.

$La_xCa_{1-x}MnO_3$ (LCMO) has been studied in the framework of density functional theory (DFT) using Hubbard-U correction. We show that the formation of spin-polarons of different configurations is possible in the G-type antiferromagentic phase. We also show that the spin-polaron (SP) solutions are stabilized due to an interplay of magnetic and lattice effects at lower La concentrations and mostly due to the lattice contribution at larger concentrations. Our results indicate that the development of SPs is unfavorable in the C- and A-type antiferromagnetic phases. The theoretically obtained magnetic state diagram is in good agreement with previously reported experimental results, Comment: 6 pages, 4 figures

Using local density approximation plus dynamical mean-field theory (LDA+DMFT), we have computed the valence band photoelectron spectra of highly popular multiferroic BiFeO$_{3}$. Within DMFT, the local impurity problem is tackled by exact diagonalization (ED) solver. For comparison, we also present result from LDA+U approach, which is commonly used to compute physical properties of this compound. Our LDA+DMFT derived spectra match adequately with the experimental hard X-ray photoelectron spectroscopy (HAXPES) and resonant photoelectron spectroscopy (RPES) for Fe 3$d$ states, whereas the other theoretical method that we employed failed to capture the features of the measured spectra. Thus, our investigation shows the importance of accurately incorporating the dynamical aspects of electron-electron interaction among the Fe 3$d$ orbitals in calculations to produce the experimental excitation spectra, which establishes BiFeO$_{3}$ as a strongly correlated electron system. The LDA+DMFT derived density of states (DOSs) exhibit significant amount of Fe 3$d$ states at the energy of Bi lone-pairs, implying that the latter is not as alone as previously thought in the spectral scenario. Our study also demonstrates that the combination of orbital cross-sections for the constituent elements and broadening schemes for the calculated spectral function are pivotal to explain the detailed structures of the experimental spectra.

Temperature-dependent magnetic experiments like pump-probe measurements generated by a pulsed laser have become a crucial technique for switching the magnetization in the picosecond time scale. Apart from having practical implications on the magnetic storage technology, the research field of ultrafast magnetization poses also fundamental physical questions. To correctly describe the time evolution of the atomic magnetic moments under the influence of a temperature-dependent laser pulse, it remains crucial to know if the magnetic material under investigation has magnetic excitation spectrum that is more or less dependent on the magnetic configuration, e.g. as reflected by the temperature dependence of the exchange interactions. In this article, we demonstrate from first-principles theory that the magnetic excitation spectra in Co with fcc, bcc and hcp structures are nearly identical in a wide range of non-collinear magnetic configurations. This is a curious result of a balance between the size of the magnetic moments and the strength of the Heisenberg exchange interactions, that in themselves vary with configuration, but put together in an effective spin Hamiltonian results in a configuration independent effective model. We have used such a Hamiltonian, together with ab-initio calculated damping parameters, to investigate the magnon dispersion relationship as well as the ultrafast magnetisation dynamics of Co and Co-rich CoMn alloys.

The lattice constant, bulk modulus and shear constant of TbN are calculated by means of density functional theory (DFT) in the local density approximation (LDA) and generalized gradient approximation (GGA), with 4f-states treated as valence electrons or core electrons. In addition, local Coulomb repulsions U are treated both statically as in the LDA+U approach and dynamically as in the dynamical mean-field theory (DMFT) in the Hubbard-I approximation. It is shown that all methods, except DFT-LDA with 4f electrons treated as either valence states, produce lattice constants and bulk moduli in good agreement with experiment. In the LDA+U approach multiple minima are found, and we focus on the competition between a state with cubic symmetry and a state obtained from atomic Hund's rules. We find the state with cubic symmetry to be 0.59 eV lower in energy than the Hund's rules state, while the opposite was obtained in previous literature. The shear constant is shown to be rather sensitive to the theoretical method used, and the Hund's rules state obtained in LDA+U is found to be unstable towards tetragonal shear. As to the magnetism, we find that the calculation based on the Hubbard-I approximation reproduces observations with the best accuracy. Finally, the spectral properties of TbN are discussed, together with the general applicability of the different methods in describing rare-earth elements and compounds.

Recent experiments on isolated Co clusters have shown huge orbital magnetic moments in comparison with their bulk and surface counterparts. These clusters hence provide the unique possibility to study the evolution of the orbital magnetic moment with respect to the cluster size and how competing interactions contribute to the quenching of orbital magnetism. We investigate here different theoretical methods to calculate the spin and orbital moments of Co clusters, and assess the performances of the methods in comparison with experiments. It is shown that density functional theory in conventional local density or generalized gradient approximations, or even with a hybrid functional, severely underestimates the orbital moment. As natural extensions/corrections we considered the orbital polarization correction, the LDA+U approximation as well as the LDA+DMFT method. Our theory shows that of the considered methods, only the LDA+DMFT method provides orbital moments in agreement with experiment, thus emphasizing the importance of dynamic correlations effects for determining fundamental magnetic properties of magnets in the nano-size regime.

The rare-earths are known to have intriguing changes of the valence, depending on chemical surrounding or geometry. Here we make predictions from theory that combines density functional theory with atomic multiplet-theory, on the transition of valence when transferring from the atomic divalent limit to the trivalent bulk, passing through different sized clusters, of selected rare-earths. We predict that Tm clusters show an abrupt change from pure divalent to pure trivalent at a size of 6 atoms, while Sm and Tb clusters are respectively pure divalent and trivalent up to 8 atoms. Larger Sm clusters are argued to likely make a transition to a mixed valent, or trivalent, configuration. The valence of all rare-earth clusters, as a function of size, is predicted from interpolation of our calculated results. We argue that the here predicted behavior is best analyzed by spectroscopic measurements, and provide theoretical spectra, based on dynamical mean field theory, in the Hubbard-I approximation, to ease experimental analysis.

We have revisited the valence band electronic structure of NiO by means of hard x-ray photoemission spectroscopy (HAXPES) together with theoretical calculations using both the GW method and the local density approximation + dynamical mean-field theory (LDA+DMFT) approaches. The effective impurity problem in DMFT is solved through the exact diagonalization (ED) method. We show that the LDA+DMFT method alone cannot explain all the observed structures in the HAXPES spectra. GW corrections are required for the O bands and Ni-s and p derived states to properly position their binding energies. Our results establish that a combination of the GW and DMFT methods is necessary for correctly describing the electronic structure of NiO in a proper ab-initio framework. We also demonstrate that the inclusion of photoionization cross section is crucial to interpret the HAXPES spectra of NiO.We argue that our conclusions are general and that the here suggested approach is appropriate for any complex transition metal oxide., Comment: 16 pages, 5 figures

In this work we examine critically the electronic structure of the rare-earth elements by use of the so-called Hubbard I approximation. From the theoretical side all measured features of both occupied and unoccupied states are reproduced, without significant deviations between observations and theory. We also examine cohesive properties like the equilibrium volume and bulk modulus, where we find, in general, a good agreement between theory and measurements. In addition we have reproduced the spin and orbital moments of these elements, as they are reflected from measurements of the saturation moment. We have also employed the Hubbard I approximation to extract the interatomic exchange parameters of an effective spin Hamiltonian for the heavy rare earths. We show that the Hubbard I approximation gives results which are consistent with calculations where $4f$ electrons are treated as core states for Gd. The latter approach was also used to address the series of the heavy/late rare-earths. Via Monte Carlo simulations we obtained ordering temperatures which reproduce measurements within about $20\%$. We have further illustrated the accuracy of these exchange parameters by comparing measured and calculated magnetic configurations for the heavy rare earths and the magnon dispersion for Gd. The Hubbard I approximation is compared to other theories of the electronic structure, and we argue that it is superior. We discuss the relevance of our results in general, and how this makes it possible to treat the electronic structure of materials containing rare-earth elements, such as permanent magnets, magnetostrictive compounds, photovoltaics, optical fibers, topological insulators, and molecular magnets., Comment: 21 pages, 14 figures, 2 tables, 4 appendices

The electronic structure and magnetic properties of a single Fe adatom on a CuN surface have been studied using density functional theory in the local spin density approximation (LSDA), the LSDA+U approach and the local density approximation plus dynamical mean-field theory (LDA+DMFT). The impurity problem in LDA+DMFT is solved through exact diagonalization and in the Hubbard-I approximation. The comparison of the one-particle spectral functions obtained from LSDA, LSDA+U and LDA+DMFT show the importance of dynamical correlations for the electronic structure of this system. Most importantly, we focused on the magnetic anisotropy and found that neither LSDA, nor LSDA+U can explain the measured, high values of the axial and transverse anisotropy parameters. Instead, the spin excitation energies obtained from our LDA+DMFT approach with exact diagonalization agree significantly better with experimental data. This affirms the importance of treating fluctuating magnetic moments through a realistic many-body treatment when describing this class of nano-magnetic systems. Moreover, it facilitates insight to the role of the hybridization with surrounding orbitals., Comment: 17 pages, 4 figures

The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Pad\'{e} approximants technique. We propose to remedy the well-known problems of the Pad\'{e} approximants by performing an average of several continuations, obtained by varying the number of fitted input points and Pad\'{e} coefficients independently. The suggested approach is then applied to several test cases, including Sm and Pr atomic self-energies, the Green's functions of the Hubbard model for a Bethe lattice and of the Haldane model for a nano-ribbon, as well as two special test functions. The sensitivity to numerical noise and the dependence on the precision of the numerical libraries are analysed in detail. The present approach is compared to a number of other techniques, i.e. the non-negative least-square method, the non-negative Tikhonov method and the maximum entropy method, and is shown to perform well for the chosen test cases. This conclusion holds even when the noise on the input data is increased to reach values typical for quantum Monte Carlo simulations. The ability of the algorithm to resolve fine structures is finally illustrated for two relevant test functions., Comment: 10 figures

By means of first principles calculations we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the $3d$ orbitals of $E_g$ and $T_{2g}$ symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly-interacting impurity levels. We demonstrate that, as a result of this, in Fe the $T_{2g}$ orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the $E_g$ states the Heisenberg picture breaks down, since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbour coupling indicates that the interactions among $E_g$ states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin., Comment: 5 pages, 4 figures

Electron localization and polaron mobility in oxygen deficient as well as Li doped monoclinic tungsten trioxide have been studied. We show that small polarons formed in the presence of oxygen vacancy prefer the bipolaronic $W^{5+}- W^{5+}$ configuration whereas the $W^{6+}- W^{4+}$ configuration is found to be metastable. Our calculations suggest that bipolarons are tightly bound by the vacancy and therefore largely immobile. On the contrary, polarons formed as a result of Li intercalation can be mobile, the activation energy for polaron jumping in this case varies between 98 and 124 meV depending on the crystallographic direction. The formation of $W^{5+}- W^{5+}$ bipolarons in $Li-WO_{3}$ is possible. When situated along $[001]$ the bipolaronic configuration is 8 meV lower in energy than two separate $W^{5+}$ polarons., Comment: 7 pages, 6 figures

Recent experiments showed that Co undergoes a phase transition from ferromagnetic hcp phase to non-magnetic fcc one around 100 GPa. Since the transition is of first order, a certain region of co-existence of the two phases is present. By means of \textit{ab initio} calculations, we found that the hcp phase itself undergoes a series of electronic topological transitions (ETTs), which affects both elastic and magnetic properties of the material. Most importantly, we propose that the sequence of ETTs lead to the stabilisation of a non-collinear spin arrangement in highly compressed hcp Co. Details of this non-collinear magnetic state and the interatomic exchange parameters that are connected to it, are presented here., Comment: 16 pages, 6 figures (including supplemental material)

We present the results of an ab initio study of magnetic properties of Fe, Co and Ni surfaces. In particular, we discuss their electronic structure and magnetic exchange interactions (Jij), as obtained by means of a combination of density functional theory and dynamical mean-field theory. All studied systems have a pronounced tendency to ferromagnetism both for bulk and surface atoms. The presence of narrow-band surface states is shown to enhance the magnetic moment as well as the exchange couplings. The most interesting results were obtained for the Fe surface where the atoms have a tendency to couple antiferromagnetically with each other. This interaction is relatively small, when compared to interlayer ferromagnetic interaction, and strongly depends on the lattice parameter. Local correlation effects are shown to lead to strong changes of the overall shape of the spectral functions. However, they seem to not play a decisive role on the overall picture of the magnetic couplings studied here. We have also investigated the influence of correlations on the spin and orbital moments of the bulk-like and surface atoms. We found that dynamical correlations in general lead to enhanced values of the orbital moment., Comment: 13 pages, 12 figures

In this paper we present an accurate numerical scheme for extracting inter-atomic exchange parameters ($J_{ij}$) of strongly correlated systems, based on first-principles full-potential electronic structure theory. The electronic structure is modelled with the help of a full-potential linear muffin-tin orbital method. The effects of strong electron correlations are considered within the charge self-consistent density functional theory plus dynamical mean-field theory (DFT+DMFT). The exchange parameters are then extracted using the magnetic force theorem, hence all the calculations are performed within a single computational framework. The method allows to investigate how the $J_{ij}$-parameters are affected by dynamical electron correlations. In addition to describing the formalism and details of the implementation, we also present magnetic properties of a few commonly discussed systems, characterised by different degrees of electron localisation. In bcc Fe we found a minor renormalisation of the $J_{ij}$ interactions once the dynamical correlations are introduced. However, generally, if the magnetic coupling has several competing contributions from different orbitals, the redistribution of the spectral weight and changes in the exchange splitting of these states can lead to a dramatic modification of the total interaction parameter. In NiO we found that both static and dynamical mean-field results provide an adequate description of the exchange interactions, which is somewhat surprising given the fact that these two methods result in quite different electronic structures. By employing Hubbard-I approximation for the treatment of the $4f$ states in hcp Gd we reproduce the experimentally observed multiplet structure. The calculated exchange parameters result to be rather close to the ones obtained by treating the $4f$ electrons as non-interacting core states.

We have explored, computationally and experimentally, the magnetic properties of \fecob{} alloys. Calculations provide a good agreement with experiment in terms of the saturation magnetization and the magnetocrystalline anisotropy energy with some difficulty in describing Co$_2$B, for which it is found that both full potential effects and electron correlations treated within dynamical mean field theory are of importance for a correct description. The material exhibits a uniaxial magnetic anisotropy for a range of cobalt concentrations between $x=0.1$ and $x=0.5$. A simple model for the temperature dependence of magnetic anisotropy suggests that the complicated non-monotonous temperature behaviour is mainly due to variations in the band structure as the exchange splitting is reduced by temperature. Using density functional theory based calculations we have explored the effect of substitutional doping the transition metal sublattice by the whole range of 5$d$ transition metals and found that doping by Re or W elements should significantly enhance the magnetocrystalline anisotropy energy. Experimentally, W doping did not succeed in enhancing the magnetic anisotropy due to formation of other phases. On the other hand, doping by Ir and Re was successful and resulted in magnetic anisotropies that are in agreement with theoretical predictions. In particular, doping by 2.5~at.\% of Re on the Fe/Co site shows a magnetocrystalline anisotropy energy which is increased by 50\% compared to its parent (Fe$_{0.7}$Co$_{0.3}$)$_2$B compound, making this system interesting, for example, in the context of permanent magnet replacement materials or in other areas where a large magnetic anisotropy is of importance., Comment: 15 pages 17 figures

We examine the distribution of the magnetic anisotropy (MA) experienced by a magnetic impurity embedded in a metallic nano-grain. As an example of a generic magnetic impurity with partially filled $d$-shell, we study the case of $d^{1}$ impurities imbedded into ordered and disordered Au nano-grains, described in terms of a realistic band structure. Confinement of the electrons induces a magnetic anisotropy that is large, and can be characterized by 5 real parameters, coupling to the quadrupolar moments of the spin. In ordered (spherical) nano-grains, these parameters exhibit symmetrical structures and reflect the symmetry of the underlying lattice, while for disordered grains they are randomly distributed and, - for stronger disorder, - their distribution is found to be characterized by random matrix theory. As a result, the probability of having small magnetic anisotropies $K_L$ is suppressed below a characteristic scale $\Delta_E$, which we predict to scale with the number of atoms $N$ as $\Delta_E\sim 1/N^{3/2}$. This gives rise to anomalies in the specific heat and the susceptibility at temperatures $T\sim \Delta_E$ and produces distinct structures in the magnetic excitation spectrum of the clusters, that should be possible to detect experimentally.