arXiv subjects

Bernd Zimmermann

Publications and source records attributed to Bernd Zimmermann.

At least 19 recordsLinked to original sources

arXiv2020

Material systems for FM-/AFM-coupled skyrmions in Co/Pt-based multilayers

By means of systematic first-principles calculations based on density functional theory we search for suitable materials that can host antiferromagnetically coupled skyrmions. We concentrate on fcc-stacked (111)-oriented metallic $Z$/Co/Pt ($Z=4d$ series: Y$-$Pd, the noble metals: Cu, Ag, Au, post noble metals: Zn and Cd) magnetic multilayers of films of monatomic thickness. We present quantitative trends of magnetic properties: Magnetic moments, interlayer exchange coupling, spin-stiffness, Dzyaloshinskii-Moriya interaction, magnetic anisotropy, and the critical temperature. We show that some of the $Z$ elements (Zn, Y, Zr, Nb, Tc, Ru, Rh, and Cd) can induce antiferromagnetic interlayer coupling between the magnetic Co layers, and that they influence the easy magnetization axis. Employing a multiscale approach, we transfer the micromagnetic parameters determined from $ab$ $initio$ to a micromagnetic energy functional and search for one-dimensional spin-spiral solutions and two-dimensional skyrmions. We determine the skyrmion radius by numerically solving the equation of the skyrmion profile. We found an analytical expression for the skyrmion radius that covers our numerical results and is valid for a large regime of micromagnetic parameters. Based on this expression we have proposed a model that allows to extrapolate from the $ab$ $initio$ results of monatomic films to multilayers with Co films consisting of several atomic layers containing $10\,$nm skyrmions. We found thickness regimes where tiny changes of the film thickness may alter the skyrmion radius by orders of magnitude. We estimated the skyrmion size as function of temperature and found that the size can easily double going from cryogenic to room temperature. We suggest promising material systems for ferromagnetically and antiferromagnetically coupled spin-spiral and skyrmion systems.

cond-mat.mtrl-sci↗

arXiv2020

Electric dipole moment as descriptor for interfacial Dzyaloshinskii-Moriya interaction

Chiral magnets are of fundamental interest and have important technological ramifications. The origin of chiral magnets lies in the Dzyaloshinskii-Moriya interaction (DMI), an interaction whose experimental and theoretical determination is laborious. We derive an expression that identifies the electric dipole moment as descriptor for the systematic design of chiral magnetic multilayers. Using density functional theory calculations, we determine the DMI of (111)-oriented metallic ferromagnetic $Z$/Co/Pt multilayers of ultrathin films. The non-magnetic layer $Z$ determines the DMI at the Co-Pt interface. The results validate the electric and magnetic dipole moments as excellent descriptors. We found a linear relation between the electric dipole moment of Pt, the Allen electronegativity of $Z$, and the contribution of Pt to the total DMI.

cond-mat.mtrl-sci↗

arXiv2019

Comparison of first-principles methods to extract magnetic parameters in ultra-thin films: Co/Pt(111)

We compare three distinct computational approaches based on first-principles calculations within density functional theory to explore the magnetic exchange and the Dzyaloshinskii-Moriya interactions (DMI) of a Co monolayer on Pt(111), namely (i) the method of infinitesimal rotations of magnetic moments based on the Korringa-Kohn-Rostoker (KKR) Green function method, (ii) the generalized Bloch theorem applied to spiraling magnetic structures and (iii) supercell calculations with non-collinear magnetic moments, the latter two being based on the full-potential linearized augmented plane wave (FLAPW) method. In particular, we show that the magnetic interaction parameters entering micromagnetic models describing the long-wavelength deviations from the ferromagnetic state might be different from those calculated for fast rotating magnetic structures, as they are obtained by using (necessarily rather small) supercell or large spin-spiral wave-vectors. In the micromagnetic limit, which we motivate to use by an analysis of the Fourier components of the domain-wall profile, we obtain consistent results for the spin stiffness and DMI spiralization using methods (i) and (ii). The calculated spin stiffness and Curie temperature determined by subsequent Monte Carlo simulations are considerably higher than estimated from the bulk properties of Co, a consequence of a significantly increased nearest-neighbor exchange interaction in the Co-monolayer (+50%). The calculated results are carefully compared with the literature.

cond-mat.mtrl-sci↗

arXiv2018

Dzyaloshinskii-Moriya interaction at disordered interfaces from ab initio theory: robustness against intermixing and tunability through dusting

The Dzyaloshinskii-Moriya interaction (DMI), which is essential for the stabilization of topologically non-trivial chiral magnetic textures such as skyrmions, is particularly strong in heterostructures of ultra-thin magnetic materials and heavy elements. We explore by density-functional theory calculations the possibility to modify the magnetic properties at Co/Pt interfaces with chemical disorder. In these systems, we find a particular robustness of the DMI against intermixing. Upon dusting the interface with a third element (all $4d$ transition metals and B, Cu, Au and Bi), a strong reduction of the DMI is predicted. This opens up possibilities to tune the DMI through the degrees of intermixing and dusting.

cond-mat.mtrl-sci↗

arXiv2018

First-principles investigation of chiral magnetic properties in multilayers: Rh/Co/Pt and Pd/Co/Pt

The magnetic properties of (111)-oriented Rh/Co/Pt and Pd/Co/Pt multilayers are investigated by first-principles calculations. We focus on the interlayer exchange coupling, and identify thicknesses and composition where a typical ferromagnet or a synthetic antiferromagnet across the spacer layer is formed. All systems under investigation show a collinear magnetic intralayer order, but the Dzyaloshinskii-Moriya interaction (DMI) is rather strong for Pd-based systems, so that single magnetic skyrmions can be expected. In general, we find a strong sensitivity of the magnetic parameters (especially the DMI) in Rh-based systems, but Pd-based multilayers are less sensitive to structural details.

cond-mat.mtrl-sci↗

arXiv2017

Antiskyrmions stabilized at interfaces by anisotropic Dzyaloshinskii-Moriya interaction

Chiral magnets are an emerging class of topological matter harbouring localized and topologically protected vortex-like magnetic textures called skyrmions, which are currently under intense scrutiny as a new entity for information storage and processing. Here, on the level of micromagnetics we rigorously show that chiral magnets cannot only host skyrmions but also antiskyrmions as least-energy configurations over all non-trivial homotopy classes. We derive practical criteria for their occurrence and coexistence with skyrmions that can be fulfilled by (110)-oriented interfaces in dependence on the electronic structure. Relating the electronic structure to an atomistic spin-lattice model by means of density-functional calculations and minimizing the energy on a mesoscopic scale applying spin-relaxation methods, we propose a double layer of Fe grown on a W(110) substrate as a practical example. We conjecture that ultrathin magnetic films grown on semiconductor or heavy metal substrates with $C_{2v}$ symmetry are prototype classes of materials hosting magnetic antiskyrmions.

cond-mat.mes-hall↗

arXiv2017

Non-local field-like spin-orbit torques in Rashba systems: an ab-initio study of Ag$_{2}$Bi/Ag/Fe film

We investigate from first principles the field-like spin-orbit torques (SOTs) in a Ag$_{2}$Bi-terminated Ag(111) film grown on ferromagnetic Fe(110). We find that a large part of the SOT arises from the spin-orbit interaction (SOI) in the Ag$_{2}$Bi layer far away from the Fe layers. These results clearly hint at a long range spin transfer in the direction perpendicular to the film that does not originate in the spin Hall effect. In order to bring evidence of the non-local character of the computed SOT, we show that the torque acting on the Fe layers can be engineered by the introduction of Bi vacancies in the Ag$_{2}$Bi layer. Overall, we find a drastic dependence of the SOT on the disorder type, which we explain by a complex interplay of different contributions to the SOT in the Brillouin zone.

cond-mat.mtrl-sci↗

arXiv2016

Influence of complex disorder on skew-scattering Hall effects in $L1_0$-ordered FePt alloy

We show by first-principles calculations that the skew-scattering anomalous Hall and spin-Hall angles of L$1_0$-ordered FePt drastically depend on different types of disorder. A different sign of the AHE is obtained when slightly deviating from the stoichiometric ratio towards the Fe-rich side as compared to the Pt-rich side. For stoichiometric samples, short-range ordering of defects has a profound effect on the Hall angles and can change them by a factor of $2$ as compared to the case of uncorrelated disorder. This might explain the vast range of anomalous Hall angles measured in experiments, which undergo different preparation procedures and thus might differ in their crystallographic quality.

cond-mat.mtrl-sci↗

arXiv2016

Role of Dzyaloshinskii-Moriya interaction for magnetism in transition-metal chains at Pt step-edges

We explore the emergence of chiral magnetism in one-dimensional monatomic Mn, Fe, and Co chains deposited at the Pt(664) step-edge carrying out an ab-initio study based on density functional theory (DFT). The results are analyzed employing several models: (i) a micromagnetic model, which takes into account the Dzyaloshinskii-Moriya interaction (DMI) besides the spin stiffness and the magnetic anisotropy energy, and (ii) the Fert-Levy model of the DMI for diluted magnetic impurities in metals. Due to the step-edge geometry, the direction of the Dzyaloshinskii vector (D-vector) is not predetermined by symmetry and points in an off-symmetry direction. For the Mn chain we predict a long-period cycloidal spin-spiral ground state of unique rotational sense on top of an otherwise atomic-scale antiferromagnetic phase. The spins rotate in a plane that is tilted relative to the Pt surface by $62^\circ$ towards the upper step of the surface. The Fe and Co chains show a ferromagnetic ground state since the DMI is too weak to overcome their respective magnetic anisotropy barriers. Beyond the discussion of the monatomic chains we provide general expressions relating ab-initio results to realistic model parameters that occur in a spin-lattice or in a micromagnetic model. We prove that a planar homogeneous spiral of classical spins with a given wave vector rotating in a plane whose normal is parallel to the D-vector is an exact stationary state solution of a spin-lattice model for a periodic solid that includes Heisenberg exchange and DMI. The validity of the Fert-Levy model for the evaluation of micromagnetic DMI parameters and for the analysis of ab-initio calculations is explored for chains. The results suggest that some care has to be taken when applying the model to infinite periodic one-dimensional systems.

cond-mat.mes-hall↗

arXiv2016

Strong spin-orbit fields and Dyakonov-Perel spin dephasing in supported metallic films

Spin dephasing by the Dyakonov-Perel mechanism in metallic films deposited on insulating substrates is revealed, and quantitatively examined by means of density functional calculations combined with a kinetic equation. The surface-to-substrate asymmetry, probed by the metal wave functions in thin films, is found to produce strong spin-orbit fields and a fast Larmor precession, giving a dominant contribution to spin decay over the Elliott-Yafet spin relaxation up to a thickness of 70 nm. The spin dephasing is oscillatory in time with a rapid (sub-picosecond) initial decay. However, parts of the Fermi surface act as spin traps, causing a persistent tail signal lasting 1000 times longer than the initial decay time. It is also found that the decay depends on the direction of the initial spin polarization, resulting in a spin-dephasing anisotropy of 200% in the examined cases.

cond-mat.mes-hall↗

arXiv2016

Giant spin Nernst effect induced by resonant scattering at surfaces of metallic films

A new concept realizing giant spin Nernst effect in nonmagnetic metallic films is introduced. It is based on the idea of engineering an asymmetric energy dependence of the longitudinal and transverse electrical conductivities, as well as a pronounced energy dependence of the spin Hall angle in the vicinity of the Fermi level by the resonant impurity states at the Fermi level. We employ an analytical model and demonstrate the emergence of a giant spin Nernst effect in Ag(111) films using {\it ab-initio} calculations combined with the Boltzmann approach for transport properties arising from skew scattering off impurities.

cond-mat.mes-hall↗

arXiv2016

Spin-orbit torques and spin accumulation in FePt/Pt and Co/Cu thin films from first principles: the role of impurities

Using the Boltzmann formalism based on the first principles electronic structure and scattering rates, we investigate the current-induced spin accumulation and spin-orbit torques in FePt/Pt and Co/Cu bilayers in the presence of substitutional impurities. In FePt/Pt bilayers we consider the effect of intermixing of Fe and Pt atoms in the FePt layer, and find a crucial dependence of spin accumulation and spin-orbit torques on the details of the distribution of these defects. In Co/Cu bilayers we predict that the magnitude and sign of the spin-orbit torque and spin accumulation depend very sensitively on the type of the impurities used to dope the Cu substrate. Moreover, simultaneously with impurity-driven scattering we consider the effect of an additional constant quasiparticle broadening of the states at the Fermi surface to simulate phonon scattering at room temperature, and discover that even a small broadening of the order of 25 meV can drastically influence the magnitude of the considered effects. We explain our findings based on the analysis of the complex interplay of several competing Fermi surface contributions to the spin accumulation and spin-orbit torques in these structurally and chemically non-uniform systems.

cond-mat.mtrl-sci↗

arXiv2016

Fermi surfaces, spin-mixing parameter, and colossal anisotropy of spin relaxation in transition metals from ab initio theory

The Fermi-surfaces and Elliott-Yafet spin-mixing parameter (EYP) of several elemental metals are studied by \emph{ab initio} calculations. We focus first on the anisotropy of the EYP as a function of the direction of the spin-quantization axis [Phys.~Rev.~Lett.\ \textbf{109}, 236603 (2012)]. We analyze in detail the origin of the gigantic anisotropy in $5d$ hcp metals as compared to $5d$ cubic metals by band-structure calculations and discuss the stability of our results against an applied magnetic field. We further present calculations of light (4$d$ and 3$d$) hcp crystals, where we find a huge increase of the EYP anisotropy, reaching colossal values as large as $6000\%$ in hcp Ti. We attribute these findings to the reduced strength of spin-orbit coupling, which promotes the anisotropic spin-flip hot loops at the Fermi surface. In order to conduct these investigations, we developed an adapted tetrahedron-based method for the precise calculation of Fermi surfaces of complicated shape and accurate Fermi-surface integrals within the full-potential relativistic Korringa-Kohn-Rostoker Green-function method.

cond-mat.mtrl-sci↗

arXiv2015

Skew scattering in dilute ferromagnetic alloys

The challenging problem of skew scattering for Hall effects in dilute ferromagnetic alloys, with intertwined effects of spin-orbit coupling, magnetism and impurity scattering, is studied here from first principles. Our main aim is to identify chemical trends and work out simple rules for large skew scattering in terms of the impurity and host states at the Fermi surface, with particular emphasis on the interplay of the spin and anomalous Hall effects in one and the same system. The predicted trends are benchmarked by referring to three different \emph{ab initio} methods based on different approximations with respect to the electronic structure and transport properties.

cond-mat.mtrl-sci↗

arXiv2014

Quantum well states and amplified spin-dependent Friedel oscillations in thin films

Electrons mediate many of the interactions between atoms in a solid. Their propagation in a material determines its thermal, electrical, optical, magnetic and transport properties. Therefore, the constant energy contours characterizing the electrons, in particular the Fermi surface, have a prime impact on the behavior of materials. If anisotropic, the contours induce strong directional dependence at the nanoscale in the Friedel oscillations surrounding impurities. Here we report on giant anisotropic charge density oscillations focused along specific directions with strong spin-filtering after scattering at an oxygen impurity embedded in the surface of a ferromagnetic thin film of Fe grown on W(001). Utilizing density functional theory, we demonstrate that by changing the thickness of the Fe films, we control quantum well states confined to two dimensions that manifest as multiple flat energy contours, impinging and tuning the strength of the induced charge oscillations which allow to detect the oxygen impurity at large distances ($\approx$ 50nm).

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↗