arXiv subjects

Stefan Blügel

Publications and source records attributed to Stefan Blügel.

At least 199 records · Page 11Linked to original sources

arXiv2014

Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles

An applied electric current through a space-inversion asymmetric magnet induces spin-orbit torques (SOTs) on the magnetic moments, which holds much promise for future memory devices. We discuss general Green's function expressions suitable to compute the linear-response SOT in disordered ferromagnets. The SOT can be decomposed into an even and an odd component with respect to magnetization reversal, where in the limit of vanishing disorder the even SOT is given by the constant Berry curvature of the occupied states, while the odd part exhibits a divergence with respect to disorder strength. Within this formalism, we perform first principles density-functional theory calculations of the SOT in Co/Pt(111) and Mn/W(001) magnetic bilayers. We find the even and odd torque components to be of comparable magnitude. Moreover, the odd torque depends strongly on an additional capping layer, while the even torque is less sensitive. We show that the even torque is nearly entirely mediated by spin currents in contrast to the odd torque, which can contain an important contribution not due to spin transfer. Our results are in agreement with experiments, showing that our linear response theory is well-suited for the description of SOTs in complex ferromagnets.

cond-mat.mtrl-sci↗

arXiv2014

Spin transport and spin-caloric effects in (Cr,Zn)Te half-metallic nanostructures: Effect of spin disorder at elevated temperatures from first principles

An important contribution to the thermoelectric and spin-caloric transport properties in magnetic materials at elevated temperatures is the formation of a spin-disordered state due to local moment fluctuations. This effect has not been largely investigated so far. We focus on various magnetic nanostructures of CrTe in the form of thin layers or nanowires embedded in ZnTe matrix, motivated by the miniaturization of spintronics devices and by recent suggestions that magnetic nanostructures can lead to extraordinary thermoelectric effects due to quantum confinement. The electronic structure of the studied systems is calculated within the multiple scattering screened Korringa-Kohn-Rostoker Green function (KKR-GF) framework. The Monte Carlo method is used to simulate the magnetization in the temperature induced spin disorder. The transport properties are evaluated from the transmission probability obtained using the Baranger-Stone approach within the KKR-GF framework. We find qualitative and quantitative changes in the thermoelectric and spin-caloric coefficients when spin-disorder is included in the calculation. Furthermore, we show that substitutional impurities in CrTe nanowires could considerably enhance the Seebeck coefficient and the thermoelectric figure of merit.

cond-mat.mtrl-sci↗

arXiv2014

Spin-orbit torques in L1$_0$-FePt/Pt thin films driven by electrical and thermal currents

Using the linear response formalism for the spin-orbit torque (SOT) we compute from first principles the SOT in a system of two layers of L1$_0$-FePt(001) deposited on an fcc Pt(001) substrate of varying thickness. We find that at room temperature the values of the SOTs that are even and odd with respect to magnetization generally lie in the range of values measured and computed for Co/Pt bilayers. We also observe that the even SOT is much more robust with respect to changing the number of layers in the substrate, and as a function of energy it follows the general trend of the even SOT exerted by the spin Hall current in fcc Pt. The odd torque, on the other hand, is strongly affected by modification of the electronic structure for a specific energy window in the limit of very thin films. Moreover, taking the system at hand as an example, we compute the values of the thermal spin-orbit torque (T-SOT). We predict that the gradients of temperature which can be experimentally created in this type of systems will cause a detectable torque on the magnetization. We also underline the correlation between the even T-SOT and the spin Nernst effect, thus motivating a more intensive experimental effort aimed at observation of both phenomena.

cond-mat.mtrl-sci↗

arXiv2014

First-principles analysis of a homo-chiral cycloidal magnetic structure in a monolayer Cr on W(110)

The magnetic structure of a Cr monolayer on a W(110) substrate is investigated by means of first-principles calculations based on the noncollinear spin density functional theory (DFT). As magnetic ground state we find a long-period homochiral left-rotating spin spiral on-top of an atomic-scale anti-ferromagnetic order of nearest neighbor atoms. The rotation angle of the magnetic moment changes inhomogeneously from atom to atom across the spiral. We predict a propagation direction along the crystallographic [001] direction with a period length of 14.3 nm, which is in excellent agreement with a modulation of the local anti-ferromagnetic contrast observed in spin-polarized scanning tunneling microscope experiments by Santos et al. [New J. Phys. 10, 013005 (2008)]. We identify the Dzyaloshinskii-Moriya interaction (DMI) as origin of the homochiral magnetic structure, competing with the Heisenberg-type exchange interaction and magneto-crystalline anisotropy energy. From DFT calculations we extract parameters for a micromagnetic model and thereby determine a considerable inhomogeneity of the spin spiral, increasing the period length by 6% compared to homogeneous spin spirals. The results are compared to the behavior of a Mn and Fe monolayer and Fe doublelayer on a W(110) substrate.

cond-mat.mtrl-sci↗

arXiv2014

Dzyaloshinskii-Moriya interaction and chiral magnetism in 3$d$-5$d$ zig-zag chains: Tight-binding model and ab initio calculations

We investigate the chiral magnetic order in free-standing planar 3$d$-5$d$ bi-atomic metallic chains (3$d$: Fe, Co; 5$d$: Ir, Pt, Au) using first-principles calculations based on density functional theory. We found that the antisymmetric exchange interaction, commonly known as Dzyaloshinskii-Moriya interaction (DMI), contributes significantly to the energetics of the magnetic structure. We used the full-potential linearized augmented plane wave method and performed self-consistent calculations of homogeneous spin spirals, calculating the DMI by treating the effect of spin-orbit interaction (SOI) in the basis of the spin-spiral states in first-order perturbation theory. To gain insight into the DMI results of our ab initio calculations, we develop a minimal tight-binding model of three atoms and 4 orbitals that contains all essential features: the spin-canting between the magnetic $3d$ atoms, the spin-orbit interaction at the $5d$ atoms, and the structure inversion asymmetry facilitated by the triangular geometry. We found that spin-canting can lead to spin-orbit active eigenstates that split in energy due to the spin-orbit interaction at the $5d$ atom. We show that, the sign and strength of the hybridization, the bonding or antibonding character between $d$-orbitals of the magnetic and non-magnetic sites, the bandwidth and the energy difference between states occupied and unoccupied states of different spin projection determine the sign and strength of the DMI. The key features observed in the trimer model are also found in the first-principles results.

cond-mat.mes-hall↗

arXiv2014

Spin-flip hot spots in ultrathin films of monovalent metals: Enhancement and anisotropy of the Elliott-Yafet parameter

In contrast to the long-known fact that spin-flip hot spots, i.e., special \vc{k}-points on the Fermi surface showing a high spin-mixing parameter, do not occur in the bulk of monovalent (noble and alkali) metals, we found them on the surface Brillouin-zone boundary of ultrathin films of these metals. Density-functional calculations within the Korringa-Kohn-Rostoker Green function method for ultrathin (001) oriented Cu, Ag, and Au films of 10-layer thickness show that the region around the hot spots can have a substantial contribution, e.g.\ 52\% in Au(001), to the integrated spin-mixing parameter, that could lead to a significant enhancement of the spin-relaxation rate or spin-Hall angle in thin films. Owing to the appearance of spin-flip hot-spots, a large anisotropy of the Elliott-Yafet parameter [50\% for Au(001)] is also found in these systems. The findings are important for spintronics applications in which noble-metals are frequently used and in which the dimensionality of the sample is reduced.

cond-mat.mtrl-sci↗

arXiv2014

Spin relaxation and spin Hall transport in 5d transition-metal ultrathin films

The spin relaxation induced by the Elliott-Yafet mechanism and the extrinsic spin Hall conductivity due to the skew-scattering are investigated in 5d transition-metal ultrathin films with self-adatom impurities as scatterers. The values of the Elliott-Yafet parameter and of the spin-flip relaxation rate reveal a correlation with each other that is in agreement with the Elliott approximation. At 10-layer thickness, the spin-flip relaxation time in 5d transition-metal films is quantitatively reported about few hundred nanoseconds at atomic percent which is one and two orders of magnitude shorter than that in Au and Cu thin films, respectively. The anisotropy effect of the Elliott-Yafet parameter and of the spin-flip relaxation rate with respect to the direction of the spin-quantization axis in relation to the crystallographic axes is also analyzed. We find that the anisotropy of the spin-flip relaxation rate is enhanced due to the Rashba surface states on the Fermi surface, reaching values as high as 97% in 10-layer Hf(0001) film or 71% in 10-layer W(110) film. Finally, the spin Hall conductivity as well as the spin Hall angle due to the skew-scattering off self-adatom impurities are calculated using the Boltzmann approach. Our calculations employ a relativistic version of the first-principles full-potential Korringa-Kohn-Rostoker Green function method.

cond-mat.mtrl-sci↗

arXiv2014

Spin Spirals in Surface Alloys on Ru(0001): A First-principles Study

We have used ab initio density functional theory to compute the magnetic ground states of the surface alloy systems FeAu$_2$/Ru(0001) and MnAu$_2$/Ru(0001). For both systems, we find that the lowest energy magnetic configuration corresponds to a left-rotating spin spiral, in which the sense of rotation is determined by the Dzyaloshinskii-Moriya interaction. These spirals are lower in energy than the ferromagnetic configuration by 3-4 meV per nm$^2$. We also find that FeAu$_2$/Ru(0001) has a significantly high magnetic anisotropy energy, of the order 1 meV per Fe atom. By comparing with the corresponding freestanding alloy monolayers, we find that the presence of the Ru substrate plays a significant role in determining the magnetic properties of the surface alloy systems.

cond-mat.mtrl-sci↗

arXiv2014

Bulk Band Structure of Bi$_2$Te$_3$

The bulk band structure of Bi$_2$Te$_3$ has been determined by angle-resolved photoemission spectroscopy and compared to first-principles calculations. We have performed calculations using the local density approximation (LDA) of density functional theory and the one-shot $GW$ approximation within the all-electron full-potential linearized augmented-plane-wave (FLAPW) formalism, fully taking into account spin-orbit coupling. Quasiparticle effects produce significant changes in the band structure of \bite~when compared to LDA. Experimental and calculated results are compared in the spectral regions where distinct differences between the LDA and $GW$ results are present. Overall a superior agreement with $GW$ is found, highlighting the importance of many-body effects in the band structure of this family of topological insulators.

cond-mat.mtrl-sci↗

arXiv2014

Spin-caloric transport properties of cobalt nanostructures: spin disorder effects from first principles

The fundamental aspects of spin-dependent transport processes and their interplay with temperature gradients, as given by the spin Seebeck coefficient, are still largely unexplored and a multitude of contributing factors must be considered. We used density functional theory together with a Monte-Carlo-based statistical method to simulate simple nanostructures, such as Co nanowires and films embedded in a Cu host or in vacuum, and investigated the influence of spin-disorder scattering on electron transport at elevated temperatures. While we show that the spin-dependent scattering of electrons due to temperature induced disorder of the local magnetic moments contributes significantly to the resistance, thermoelectric and spin-caloric transport coefficients, we also conclude that the actual magnitude of these effects cannot be predicted, quantitatively or qualitatively, without such detailed calculations.

cond-mat.mtrl-sci↗

arXiv2013

Exchange interactions and local moment fluctuation corrections in ferromagnets at finite temperatures based on non-collinear density-functional calculations

We explore the derivation of interatomic exchange interactions in ferromagnets within density-functional theory (DFT) and the mapping of DFT results onto a spin Hamiltonian. We delve into the problem of systems comprising atoms with strong spontaneous moments together with atoms with weak induced moments. All moments are considered as degrees of freedom, with the strong moments thermally fluctuating only in angle and the weak moments thermally fluctuating in angle and magnitude. We argue that a quadratic dependence of the energy on the weak local moments magnitude, which is a good approximation in many cases, allows for an elimination of the weak-moment degrees of freedom from the thermodynamic expressions in favor of a renormalization of the Heisenberg interactions among the strong moments. We show that the renormalization is valid at all temperatures accounting for the thermal fluctuations and resulting in temperature-independent renormalized interactions. These are shown to be the ones directly derived from total-energy DFT calculations by constraining the strong-moment directions, as is done e.g. in spin-spiral methods. We furthermore prove that within this framework the thermodynamics of the weak-moment subsystem, and in particular all correlation functions, can be derived as polynomials of the correlation functions of the strong-moment subsystem with coefficients that depend on the spin susceptibility and that can be calculated within DFT. These conclusions are rigorous under certain physical assumptions on the measure in the magnetic phase space. We implement the scheme in the full-potential linearized augmented plane wave method using the concept of spin-spiral states, considering applicable symmetry relations and the use of the magnetic force theorem. Our analytical results are corroborated by numerical calculations employing DFT and a Monte Carlo method.

cond-mat.mtrl-sci↗

arXiv2013

Ab-initio calculation of the effective on-site Coulomb interaction parameters for half-metallic magnets

Correlation effects play an important role in the electronic structure of half-metallic (HM) magnets. In particular, they give rise to non-quasiparticle states above (or below) the Fermi energy at finite temperatures that reduce the spin polarization and, as a consequence, the efficiency of spintronics devices. Employing the constrained random-phase approximation (cRPA) within the full-potential linearized augmented-plane-wave (FLAPW) method using maximally localized Wannier functions, we calculate the strength of the effective on-site Coulomb interaction (Hubbard $U$ and Hund exchange $J$) between localized electrons in different classes of HM magnets considering: (i) \emph{sp}-electron ferromagnets in rock-salt structure, (ii) zincblende 3\emph{d} binary ferromagnets, as well as (iii) ferromagnetic and ferrimagnetic semi- and full-Heusler compounds.

cond-mat.str-el↗

arXiv2013

Anomalous Hall effect in ferromagnets with Gaussian disorder

Using the Kubo formalism we derived expressions and implemented the method for calculating the anomalous Hall conductivity (AHC) in ferromagnets with short-range Gaussian disorder directly from first-principles electronic structure of the perfect crystal. We used this method to calculate the AHC in bcc Fe, fcc Co, L1o-FePd, L1o-FePt as well as thin bcc Fe(001) films. Within our approach we can transparently decompose the conductivity into intrinsic (IC), side jump (SJ) and intrinsic skew-scattering (ISK) contributions. The existence of ISK, which originates from asymmetric Mott scattering but is clearly distinguishable from conventional skew-scattering in that it converges to a finite value in clean limit, was pointed out by Sinitsyn et al. [Phys. Rev. B 75, 045315 (2007)]. Here, we collect all contributions to the AHC in ferromagnets which result in "scattering-independent" AHE in clean limit, and analyze their relative magnitude from first principles calculations. By comparing our results to existing experiments we show that the Gaussian disorder is well suited to model various types of disorder present in real materials, to some extent including the effect of temperature. In particular, we show that in addition to intrinsic and side-jump AHE, the intrinsic skew-scattering can be a major player in determining the magnitude of the AHE in ferromagnets.

cond-mat.mes-hall↗

arXiv2013

Magnetism- and impurity-assisted chain creation in Ir and Pt break junctions

Applying the generalization of the model for chain formation in break-junctions [JPCM 24, 135501 (2012)], we study the effect of light impurities on the energetics and elongation properties of Pt and Ir chains. Our model enables us with a tool ideal for detailed analysis of impurity assisted chain formation, where zigzag bonds play an important role. In particular we focus on H (s-like) and O (p-like) impurities and assume, for simplicity, that the presence of impurity atoms in experiments results in ..M-X-M-X-... (M: metal, X: impurity) chain structure in between the metallic leads. Feeding our model with material-specific parameters from systematic full-potential first-principles calculations, we find that the presence of such impurities strongly affects the binding properties of the chains. We find that while both types of impurities enhance the probability of chains to be elongated, the s-like impurities lower the chain's stability. We also analyze the effect of magnetism and spin-orbit interaction on the growth properties of the chains.

cond-mat.mes-hall↗

arXiv2013

Exchange parameters and adiabatic magnon energies from spin-spiral calculations

We present a method of extracting the exchange parameters of the classical Heisenberg model from first-principles calculations of spin-spiral total energies based on density functional theory. The exchange parameters of the transition-metal monoxides MnO and NiO are calculated and used to estimate magnetic properties such as transition temperatures and magnon energies. Furthermore we show how to relate the magnon energies directly to differences in spin-spiral total energies for systems containing an arbitrary number of magnetic sublattices. This provides a comparison between magnon energies using a finite number of exchange parameters and the infinite limit.

cond-mat.mtrl-sci↗

arXiv2013

Berry phase theory of Dzyaloshinskii-Moriya interaction and spin-orbit torques

Recent experiments on current-induced domain wall motion in chiral magnets suggest important contributions both from spin-orbit torques (SOTs) and from the Dzyaloshinskii-Moriya interaction (DMI). We derive a Berry phase expression for the DMI and show that within this Berry phase theory DMI and SOTs are intimately related, in a way formally analogous to the relation between orbital magnetization (OM) and anomalous Hall effect (AHE). We introduce the concept of the \textit{twist torque moment}, which probes the internal twist of wave packets in chiral magnets in a similar way like the orbital moment probes the wave packet's internal self rotation. We propose to interpret the Berry phase theory of DMI as a theory of \textit{spiralization} in analogy to the modern theory of OM. We show that the twist torque moment and the spiralization together give rise to a Berry phase governing the response of the SOT to thermal gradients, in analogy to the intrinsic anomalous Nernst effect. The Berry phase theory of DMI is computationally very efficient because it only needs the electronic structure of the collinear magnetic system as input. As an application of the formalism we compute the DMI in Pt/Co, Pt/Co/O and Pt/Co/Al magnetic trilayers and show that the DMI is highly anisotropic in these systems.

cond-mat.mtrl-sci↗

arXiv2013

Elimination of the linearization error and improved basis-set convergence within the FLAPW method

We analyze in detail the error that arises from the linearization in linearized augmented-plane-wave (LAPW) basis functions around predetermined energies $E_l$ and show that it can lead to undesirable dependences of the calculated results on method-inherent parameters such as energy parameters $E_l$ and muffin-tin sphere radii. To overcome these dependences, we evaluate approaches that eliminate the linearization error systematically by adding local orbitals (LOs) to the basis set. We consider two kinds of LOs: (i) constructed from solutions $u_l(r,E)$ to the scalar-relativistic approximation of the radial Dirac equation with $E>E_l$ and (ii) constructed from second energy derivatives $\partial^2 u_l(r,E) / \partial E^2$ at $E=E_l$. We find that the latter eliminates the error most efficiently and yields the density functional answer to many electronic and materials properties with very high precision. Finally, we demonstrate that the so constructed LAPW+LO basis shows a more favorable convergence behavior than the conventional LAPW basis due to a better decoupling of muffin-tin and interstitial regions, similarly to the related APW+lo approach, which requires an extra set of LOs to reach the same total energy, though.

cond-mat.mtrl-sci↗

arXiv2013

Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures

Current-induced spin torques are of great interest to manipulate the orientation of nanomagnets without applying external magnetic fields. They find direct application in non-volatile data storage and logic devices, and provide insight into fundamental processes related to the interdependence between charge and spin transport. Recent demonstrations of magnetization switching induced by in-plane current injection in ferromagnetic heterostructures have drawn attention to a class of spin torques based on orbital-to-spin momentum transfer, which is alternative to pure spin transfer torque (STT) between noncollinear magnetic layers and amenable to more diversified device functions. Due to the limited number of studies, however, there is still no consensus on the symmetry, magnitude, and origin of spin-orbit torques (SOTs). Here we report on the quantitative vector measurement of SOTs in Pt/Co/AlO trilayers using harmonic analysis of the anomalous and planar Hall effects as a function of the applied current and magnetization direction. We provide an all-purpose scheme to measure the amplitude and direction of SOTs for any arbitrary orientation of the magnetization, including corrections due to the interplay of Hall and thermoelectric effects. Based on general space and time inversion symmetry arguments, we show that asymmetric heterostructures allow for two different SOTs having odd and even behavior with respect to magnetization reversal. Our results reveal a scenario that goes beyond established models of the Rashba and spin Hall contributions to SOTs. The even SOT is STT-like but stronger than expected from the spin Hall effect in Pt. The odd SOT is composed of a constant field-like term and an additional component, which is strongly anisotropic and does not correspond to a simple Rashba field.

cond-mat.mes-hall↗