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Frank Freimuth

Publications and source records attributed to Frank Freimuth.

At least 37 records · Page 2Linked to original sources
arXiv2021

Laser-induced torques in spin spirals

We investigate laser-induced torques in magnetically non-collinear ferromagnets with a spin-spiral magnetic structure using \textit{ab-initio} calculations. Since spin-spirals may be used to approximate the magnetization gradients locally in domain walls and skyrmions, our method may be used to obtain the laser-induced torques in such objects from a multiscale approach. Employing the generalized Bloch-theorem we obtain the electronic structure computationally efficiently. We employ our method to assess the laser-induced torques in bcc Fe, hcp Co, and L$_{1}0$ FePt when a spin-spiral magnetic structure is imposed. We find that the laser-induced torques in these magnetically noncollinear systems may be orders of magnitude larger than those in the corresponding magnetically collinear systems and that they exist both for linearly and circularly polarized light. This result suggests that laser-induced torques driven by noncollinear magnetic order or by magnetic fluctuations may contribute significantly to processes in ultrafast magnetism.

cond-mat.mtrl-sci↗
arXiv2020

Dynamical and current-induced Dzyaloshinskii-Moriya interaction: Role for damping, gyromagnetism, and current-induced torques in noncollinear magnets

Both applied electric currents and magnetization dynamics modify the Dzyaloshinskii-Moriya interaction (DMI), which we call current-induced DMI (CIDMI) and dynamical DMI (DDMI), respectively. We report a theory of CIDMI and DDMI. The inverse of CIDMI consists in charge pumping by a time-dependent gradient of magnetization $\partial^2 M(r,t)/\partial r\partial t$, while the inverse of DDMI describes the torque generated by $\partial^2 M(r,t)/\partial r\partial t$. In noncollinear magnets CIDMI and DDMI depend on the local magnetization direction. The resulting spatial gradients correspond to torques that need to be included into the theories of Gilbert damping, gyromagnetism, and current-induced torques (CITs) in order to satisfy the Onsager reciprocity relations. CIDMI is related to the modification of orbital magnetism induced by magnetization dynamics, which we call dynamical orbital magnetism (DOM), and spatial gradients of DOM contribute to charge pumping. We present applications of this formalism to the CITs and to the torque-torque correlation in textured Rashba ferromagnets.

cond-mat.other↗
arXiv2020

Giant inverse Faraday effect in Dirac semimetals

We have studied helicity dependent photocurrent (HDP) in Bi-based Dirac semimetal thin films. HDP increases with film thickness before it saturates, changes its sign when the majority carrier type is changed from electrons to holes and takes a sharp peak when the Fermi level lies near the charge neutrality point. These results suggest that irradiation of circularly polarized light to Dirac semimetals induces an effective magnetic field that aligns the carrier spin along the light spin angular momentum and generates a spin current along the film normal. The effective magnetic field is estimated to be orders of magnitude larger than that caused by the inverse Faraday effect (IFE) in typical transition metals. We consider the small effective mass and the large $g$-factor, characteristics of Dirac semimetals with strong spin orbit coupling, are responsible for the giant IFE, opening pathways to develop systems with strong light-spin coupling.

cond-mat.mes-hall↗
arXiv2020

Theory of Current-Induced Angular Momentum Transfer Dynamics in Spin-Orbit Coupled Systems

Motivated by the importance of understanding competing mechanisms to current-induced spin-orbit torque in complex magnets, we develop a unified theory of current-induced spin-orbital coupled dynamics. The theory describes angular momentum transfer between different degrees of freedom in solids, e.g., the electron orbital and spin, the crystal lattice, and the magnetic order parameter. Based on the continuity equations for the spin and orbital angular momenta, we derive equations of motion that relate spin and orbital current fluxes and torques describing the transfer of angular momentum between different degrees of freedom. We then propose a classification scheme for the mechanisms of the current-induced torque in magnetic bilayers. Based on our first-principles implementation, we apply our formalism to two different magnetic bilayers, Fe/W(110) and Ni/W(110), which are chosen such that the orbital and spin Hall effects in W have opposite sign and the resulting spin- and orbital-mediated torques can compete with each other. We find that while the spin torque arising from the spin Hall effect of W is the dominant mechanism of the current-induced torque in Fe/W(110), the dominant mechanism in Ni/W(110) is the orbital torque originating in the orbital Hall effect of W. It leads to negative and positive effective spin Hall angles, respectively, which can be directly identified in experiments. This clearly demonstrates that our formalism is ideal for studying the angular momentum transfer dynamics in spin-orbit coupled systems as it goes beyond the "spin current picture" by naturally incorporating the spin and orbital degrees of freedom on an equal footing. Our calculations reveal that, in addition to the spin and orbital torque, other contributions such as the interfacial torque and self-induced anomalous torque within the ferromagnet are not negligible in both material systems.

cond-mat.mes-hall↗
arXiv2019

Engineering the dynamics of topological spin textures by anisotropic spin-orbit torques

Integrating topologically stabilized magnetic textures such as skyrmions as nanoscale information carriers into future technologies requires the reliable control by electric currents. Here, we uncover that the relevant skyrmion Hall effect, which describes the deflection of moving skyrmions from the current flow direction, acquires important corrections owing to anisotropic spin-orbit torques that alter the dynamics of topological spin structures. Thereby, we propose a viable means for manipulating the current-induced motion of skyrmions and antiskyrmions. Based on these insights, we demonstrate by first-principles calculations and symmetry arguments that the motion of spin textures can be tailored by materials design in magnetic multilayers of Ir/Co/Pt and Au/Co/Pt. Our work advances the understanding of the current-induced dynamics of these magnetic textures, which underlies a plethora of memory and logic applications.

cond-mat.mtrl-sci↗
arXiv2019

The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the re-interpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.

cond-mat.mes-hall↗
arXiv2019

Wannier90 as a community code: new features and applications

Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronic-structure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectively-localised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with high-throughput automation frameworks), as well as the implementation of modern software engineering practices (unit testing, continuous integration, and automatic source-code documentation). These new features, capabilities, and code development model aim to further sustain and expand the community uptake and range of applicability, that nowadays spans complex and accurate dielectric, electronic, magnetic, optical, topological and transport properties of materials.

cond-mat.mtrl-sci↗
arXiv2018

Engineering Chiral and Topological Orbital Magnetism of Domain Walls and Skyrmions

Electrons which are slowly moving through chiral magnetic textures can effectively be described as if they where influenced by electromagnetic fields emerging from the real-space topology. This adiabatic viewpoint has been very successful in predicting physical properties of chiral magnets. Here, based on a rigorous quantum-mechanical approach, we unravel the emergence of chiral and topological orbital magnetism in one- and two-dimensional spin systems. We uncover that the quantized orbital magnetism in the adiabatic limit can be understood as a Landau-Peierls response to the emergent magnetic field. Our central result is that the spin-orbit interaction in interfacial skyrmions and domain walls can be used to tune the orbital magnetism over orders of magnitude by merging the real-space topology with the topology in reciprocal space. Our findings point out the route to experimental engineering of orbital properties of chiral spin systems, thereby paving the way to the field of chiral orbitronics.

cond-mat.mtrl-sci↗
arXiv2018

Helical magnetic structure and the anomalous and topological Hall effects in epitaxial B20 Fe$_{1-y}$Co$_y$Ge films

Epitaxial films of the B20-structure alloy Fe$_{1-y}$Co$_y$Ge were grown by molecular beam epitaxy on Si (111) substrates. The magnetization varied smoothly from the bulk-like values of one Bohr magneton per Fe atom for FeGe to zero for non-magnetic CoGe. The chiral lattice structure leads to a Dzyaloshinskii-Moriya interaction (DMI), and the films' helical magnetic ground state was confirmed using polarized neutron reflectometry measurements. The pitch of the spin helix, measured by this method, varies with Co content $y$ and diverges at $y \sim 0.45$. This indicates a zero-crossing of the DMI, which we reproduced in calculations using first principle methods. We also measured the longitudinal and Hall resistivity of our films as a function of magnetic field, temperature, and Co content $y$. The Hall resistivity is expected to contain contributions from the ordinary, anomalous, and topological Hall effects. Both the anomalous and topological Hall resistivities show peaks around $y \sim 0.5$. Our first principles calculations show a peak in the topological Hall constant at this value of $y$, related to the strong spin-polarisation predicted for intermediate values of $y$. Half-metallicity is predicted for $y = 0.6$, consistent with the experimentally observed linear magnetoresistance at this composition. Whilst it is possible to reconcile theory with experiment for the various Hall effects for FeGe, the large topological Hall resistivities for $y \sim 0.5$ are much larger then expected when the very small emergent fields associated with the divergence in the DMI are taken into account.

cond-mat.mtrl-sci↗
arXiv2018

Spin-orbit torques and tunable Dzyaloshinskii-Moriya interaction in Co/Cu/Co trilayers

We study the spin-orbit torques (SOTs) in Co/Cu/Co magnetic trilayers based on first-principles density-functional theory calculations in the case where the applied electric field lies in-plane, i.e., parallel to the interfaces. We assume that the bottom Co layer has a fixed in-plane magnetization, while the top Co layer can be switched. We find that the SOT on the top ferromagnet can be controlled by the bottom ferromagnet because of the nonlocal character of the SOT in this system. As a consequence the SOT is anisotropic, i.e., its magnitude varies with the direction of the applied electric field. We show that the Dzyaloshinskii-Moriya interaction (DMI) in the top layer is anisotropic as well, i.e., the spin-spiral wavelength of spin-spirals in the top layer depends on their in-plane propagation direction. This effect suggests that DMI can be tuned easily in magnetic trilayers via the magnetization direction of the bottom layer. In order to understand the influence of the bottom ferromagnet on the SOTs and the DMI of the top ferromagnet we study these effects in Co/Cu magnetic bilayers for comparison. We find the SOTs and the DMI to be surprisingly large despite the small spin-orbit interaction of Cu.

cond-mat.mes-hall↗
arXiv2017

Higher-dimensional Wannier interpolation for the modern theory of the Dzyaloshinskii-Moriya interaction: Application to Co-based trilayers

We present an advanced first-principles formalism to evaluate the Dzyaloshinskii-Moriya interaction (DMI) in its modern theory as well as Berry curvatures in complex spaces based on a higher-dimensional Wannier interpolation. Our method is applied to the Co-based trilayer systems Ir$_δ$Pt$_{1-δ}$/Co/Pt and Au$_γ$Pt$_{1-γ}$/Co/Pt, where we gain insights into the correlations between the electronic structure and the DMI, and we uncover prominent sign changes of the chiral interaction with the overlayer composition. Beyond the discussed phenomena, the scope of applications of our Wannier-based scheme is particularly broad as it is ideally suited to study efficiently the Hamiltonian evolution under the slow variation of very general parameters.

cond-mat.mtrl-sci↗
arXiv2017

Chiral damping, chiral gyromagnetism and current-induced torques in textured one-dimensional Rashba ferromagnets

We investigate Gilbert damping, spectroscopic gyromagnetic ratio and current-induced torques in the one-dimensional Rashba model with an additional noncollinear magnetic exchange field. We find that the Gilbert damping differs between left-handed and right-handed Néel-type magnetic domain walls due to the combination of spatial inversion asymmetry and spin-orbit interaction (SOI), consistent with recent experimental observations of chiral damping. Additionally, we find that also the spectroscopic $g$ factor differs between left-handed and right-handed Néel-type domain walls, which we call chiral gyromagnetism. We also investigate the gyromagnetic ratio in the Rashba model with collinear magnetization, where we find that scattering corrections to the $g$ factor vanish for zero SOI, become important for finite spin-orbit coupling, and tend to stabilize the gyromagnetic ratio close to its nonrelativistic value.

cond-mat.mes-hall↗
arXiv2017

The relation of the Dzyaloshinskii-Moriya interaction to spin currents and to the spin-orbit field

Starting from the general Berry phase theory of the Dzyaloshinskii-Moriya interaction (DMI) we derive an expression for the linear contribution of the spin-orbit interaction (SOI). Thereby, we show analytically that at the first order in SOI DMI is given by the ground-state spin current. We verify this finding numerically by ab-initio calculations in Mn/W(001) and Co/Pt(111) magnetic bilayers. We show that despite the strong SOI from the 5$d$ heavy metals DMI is well-approximated by the first order in SOI, while the ground-state spin current is not. We decompose the SOI-linear contribution to DMI into two parts. One part has a simple interpretation in terms of the Zeeman interaction between the spin-orbit field and the spin misalignment that electrons acquire in magnetically noncollinear textures. This interpretation provides also an intuitive understanding of the symmetry of DMI on the basis of the spin-orbit field and it explains in a simple way why DMI and ground-state spin currents are related. Moreover, we show that energy currents driven by magnetization dynamics and associated to DMI can be explained by counter-propagating spin currents that carry energy due to their Zeeman interaction with the spin-orbit field. Finally, we discuss options to modify DMI by nonequilibrium spin currents excited by electric fields or light.

cond-mat.mtrl-sci↗
arXiv2017

Chiral and Topological Orbital Magnetism of Spin Textures

Using a semiclassical Green's function formalism, we discover the emergence of chiral and topological orbital magnetism in two-dimensional chiral spin textures by explicitly finding the corrections to the orbital magnetization, proportional to the powers of the gradients of the texture. We show that in the absence of spin-orbit coupling, the resulting orbital moment can be understood as the electronic response to the emergent magnetic field associated with the real-space Berry curvature. By referring to the Rashba model, we demonstrate that by tuning the parameters of surface systems the engineering of emergent orbital magnetism in spin textures can pave the way to novel concepts in orbitronics.

cond-mat.mtrl-sci↗
arXiv2017

Mixed Weyl semimetals and dissipationless magnetization control in insulators by spin-orbit torques

Reliable and energy efficient magnetization switching by electrically-induced spin-orbit torques is of crucial technological relevance for spintronic devices implementing memory and logic functionality. Here we predict that the strength of spin-orbit torques and the related Dzyaloshinskii-Moriya interaction in topologically non-trivial magnetic insulators can exceed by far that of conventional metallic magnets. In analogy to the quantum anomalous Hall effect, we explain this extraordinary response in absence of longitudinal currents as a hallmark of magnetic monopoles in the electronic structure of systems that are interpreted most naturally within the framework of mixed Weyl semimetals. We thereby launch the effect of spin-orbit torque into the field of topology and reveal its crucial role in mediating the topological phase transitions arising due to the complex interplay between magnetization direction and momentum-space topology. The concepts presented here may be exploited to understand and utilize magneto-electric coupling phenomena in insulating ferromagnets and antiferromagnets.

cond-mat.mtrl-sci↗
arXiv2017

Geometrical contributions to the exchange constants: Free electrons with spin-orbit interaction

Using thermal quantum field theory we derive an expression for the exchange constant that resembles Fukuyama's formula for the orbital magnetic susceptibility (OMS). Guided by this formal analogy between the exchange constant and OMS we identify a contribution to the exchange constant that arises from the geometrical properties of the band structure in mixed phase space. We compute the exchange constants for free electrons and show that the geometrical contribution is generally important. Our formalism allows us to study the exchange constants in the presence of spin-orbit interaction (SOI). Thereby, we find sizable differences between the exchange constants of helical and cycloidal spin spirals. Furthermore, we discuss how to calculate the exchange constants based on a gauge-field approach in the case of the Rashba model with an additional exchange splitting and show that the exchange constants obtained from this gauge-field approach are in perfect agreement with those obtained from the quantum field theoretical method.

cond-mat.mes-hall↗
arXiv2017

Charge pumping driven by the laser-induced dynamics of the exchange splitting

We show that electric currents are induced in inversion asymmetric ferromagnets if the exchange splitting varies in time after excitation by laser pulses. We interpret this phenomenon as the magnetic variant of the inverse Edelstein effect. Based on \textit{ab initio} calculations we determine the size of this effect in Co/Pt(111) and Mn/W(001) magnetic bilayer systems and investigate its dependence on the magnetization direction. The comparison of our theoretical results to experiments measuring the THz signal emitted after laser excitation suggests that ultrafast demagnetization in 3$d$ transition metal ferromagnets is dominated by transverse spin fluctuations rather than by a reduction of the exchange splitting.

cond-mat.mtrl-sci↗