arXiv subjects

Börge Göbel

Publications and source records attributed to Börge Göbel.

35 records · Page 2Linked to original sources

arXiv2022

Biskyrmion-based artificial neuron with refractory period

Magnetic skyrmions are nanoscale magnetic whirls that are highly stable and can be moved by currents which has led to the prediction of a skyrmion-based artificial neuron device with leak-integrate-fire functionality. However, so far, these devices lack a refractory process, estimated to be crucial for neuronal dynamics. Here we demonstrate that a biskyrmion-based artificial neuron overcomes this insufficiency. When driven by spin-orbit torques, a single biskyrmion splits into two subskyrmions that move towards a designated location and can be detected electrically, resembling the excitation process of a neuron that fires ultimately. The attractive interaction of the two skyrmions leads to a unique trajectory: Once they reach the detector area, they automatically return to the center to reform the biskyrmion but on a different path. During this reset period, the neuron cannot fire again. Our suggested device resembles a biological neuron with the leak, integrate, fire and refractory characteristics better than all existing artificial devices so far.

cond-mat.dis-nn↗

arXiv2022

Direct visualization of Rashba-split bands and spin/orbital-charge interconversion at KTaO$_3$ interfaces

Rashba interfaces have emerged as promising platforms for spin-charge interconversion through the direct and inverse Edelstein effects. Notably, oxide-based two-dimensional electron gases (2DEGs) display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide 2DEGs is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO$_3$-2DEGs and evidence their Rashba-split bands using angle resolved photoemission spectroscopy. Fitting the bands with a tight-binding Hamiltonian, we extract the effective Rashba coefficient and bring insight into the complex multiorbital nature of the band structure. Our calculations reveal unconventional spin and orbital textures, showing compensation effects from quasi-degenerate band pairs which strongly depend on in-plane anisotropy. We compute the band-resolved spin and orbital Edelstein effects, and predict interconversion efficiencies exceeding those of other oxide 2DEGs. Finally, we suggest design rules for Rashba systems to optimize spin-charge interconversion performance.

cond-mat.mes-hall↗

arXiv2021

Quaternary-digital data storage based on magnetic bubbles in anisotropic materials

The topologically non-trivial nano-whirls, called magnetic skyrmions, are often considered attractive for spintronic applications like the racetrack data storage device. However, skyrmions do not move parallel to applied currents and typically do not coexist with other nano-objects, making the realization of such storage concepts difficult. Herein we consider materials with an anisotropic DMI, like tetragonal Heusler materials, and show that four distinct types of topologically trivial bubbles can coexist. We show that each of them can be written by spin torques and that they can be distinguished using a single magnetic tunneling junction. Due to their trivial topology, the four types of bubbles move parallel to applied electrical currents and remain equidistant under motion. Still, the bubbles have a small size and high stability comparable to topologically non-trivial spin textures. This allows to construct a quaternary-digit-based racetrack storage device that overcomes the two mentioned drawbacks of skyrmion-based racetracks.

cond-mat.str-el↗

arXiv2020

Skyrmion ratchet propagation: Utilizing the skyrmion Hall effect in AC racetrack storage devices

Magnetic skyrmions are whirl-like nano-objects with topological protection. When driven by direct currents (DC), skyrmions move but experience a transverse deflection. This so-called skyrmion Hall effect is often regarded a drawback for memory applications. Herein, we show that this unique effect can also be favorable for spintronic applications: We show that in a racetrack with a broken inversion symmetry, the skyrmion Hall effect allows to translate an alternating current (AC) into a directed motion along the track, like in a ratchet. We analyze several modes of the ratchet mechanism and show that it is unique for topological magnetic whirls. We elaborate on the fundamental differences compared to the motion of topologically trivial magnetic objects, as well as classical particles driven by periodic forces. Depending on the exact racetrack geometry, the ratchet mechanism can be soft or strict. In the latter case, the skyrmion propagates close to the efficiency maximum.

cond-mat.mes-hall↗

arXiv2020

Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles

Magnetic skyrmions have attracted enormous research interest since their discovery a decade ago. The non-trivial real-space topology of these nano-whirls leads to fundamentally interesting and technologically relevant consequences - the skyrmion Hall effect of the texture and the topological Hall effect of the electrons. Furthermore, it grants skyrmions in a ferromagnetic surrounding great stability even at small sizes, making skyrmions aspirants to become the carriers of information in the future. Still, the utilization of skyrmions in spintronic devices has not been achieved yet, among other reasons, due to shortcomings in their current-driven motion. In this review, we present recent trends in the field of topological spin textures that go beyond skyrmions. The majority of these objects can be considered a combination of multiple subparticles, such as the bimeron, or the skyrmion analogues in different magnetic surroundings, such as antiferromagnetic skyrmions, as well as three-dimensional generalizations, such as hopfions. We classify the alternative magnetic quasiparticles - some of them observed experimentally, others theoretical predictions - and present the most relevant and auspicious advantages of this emerging field.

cond-mat.mes-hall↗

arXiv2020

Spin and orbital Edelstein effect in an oxide two-dimensional electron gas: theory and application to AlO$_x$/SrTiO$_{3}$

The Edelstein effect provides the purely electrical generation and control of a homogeneous magnetization in primarily nonmagnetic materials with broken inversion symmetry. Usually, only the spin density response to an external electric field is discussed. Here, we report on the electrically induced magnetization containing spin as well as orbital contributions in the topological oxide two-dimensional electron gas at the interface between SrTiO$_3$ and AlO. We find that in this particular system the orbital Edelstein effect exceeds the spin Edelstein effect by more than one order of magnitude. The main reason are orbital moments of different magnitude in the Rashba-like-split band pairs.

cond-mat.mes-hall↗

arXiv2020

Topological Hall signatures of magnetic hopfions

Magnetic hopfions are topologically protected three-dimensional solitons that are constituted by a tube which exhibits a topologically nontrivial spin texture in the cross-section profile and is closed to a torus. Here we show that the hopfion's locally uncompensated emergent field leads to a topological Hall signature, although the topological Hall effect vanishes on the global level. The topological Hall signature is switchable by magnetic fields or electric currents and occurs independently of the anomalous and conventional Hall effects. It can therefore be exploited to electrically detect hopfions in experiments and even to distinguish them from other textures like skyrmion tubes. Furthermore, it can potentially be utilized in spintronic devices. Exemplarily, we propose a hopfion-based racetrack data storage device and simulate the electrical detection of the hopfions as carriers of information.

cond-mat.mes-hall↗

arXiv2020

Compensated Quantum and Topological Hall Effects of Electrons in Polyatomic Stripe Lattices

The quantum Hall effect is generally understood for free electron gases, in which topologically protected edge states between Landau levels (LLs) form conducting channels at the edge of the sample. In periodic crystals, the LLs are imprinted with lattice properties; plateaus in the transverse Hall conductivity are not equidistant in energy anymore. Herein, crystals with a polyatomic basis are considered. For a stripe arrangement of different atoms, the band structure resorts nontrivially and exhibits strong oscillations that form a salient pattern with very small bandgaps. The Hall conductivity strongly decreases for energies within these bands, and only sharp peaks remain for energies in the gap. These effects are traced back to open orbits in the initial band structure; the corresponding LLs are formed from states with positive and negative effective mass. The partial cancellation of transverse charge conductivity also holds for different polyatomic stripe lattices and even when the magnetic field is replaced by a topologically nontrivial spin texture. The topological Hall effect is suppressed in the presence of magnetic skyrmions. The discussion is complemented by calculations of Hofstadter butterflies and orbital magnetization.

cond-mat.str-el↗

arXiv2019

Electrical writing, deleting, reading, and moving of magnetic skyrmioniums in a racetrack device

A magnetic skyrmionium (also called 2$π$-skyrmion) can be understood as a skyrmion - a topologically non-trivial magnetic whirl - which is situated in the center of a second skyrmion with reversed magnetization. Here, we propose a new optoelectrical writing and deleting mechanism for skyrmioniums in thin films, as well as a reading mechanism based on the topological Hall voltage. Furthermore, we point out advantages for utilizing skyrmioniums as carriers of information in comparison to skyrmions with respect to the current-driven motion. We simulate all four constituents of an operating skyrmionium-based racetrack storage device: creation, motion, detection and deletion of bits. The existence of a skyrmionium is thereby interpreted as a '1' and its absence as a '0' bit.

cond-mat.str-el↗

arXiv2019

Forming individual magnetic biskyrmions by merging two skyrmions in a centrosymmetric nanodisk

When two magnetic skyrmions - whirl-like, topologically protected quasiparticles - form a bound pair, a biskyrmion state with a topological charge of $N_\mathrm{Sk}=\pm 2$ is constituted. Recently, especially the case of two partially overlapping skyrmions has brought about great research interest. Since for its formation the individual skyrmions need to posses opposite in-plane magnetizations, such a biskyrmion cannot be stabilized by the Dzyaloshinskii-Moriya-interaction (DMI), which is the interaction that typically stabilizes skyrmions in non-centrosymmetric materials and at interfaces. Here, we show that these biskyrmions can be stabilized by the dipole-dipole interaction in centrosymmetric materials in which the DMI is forbidden. Analytical considerations indicate that the bound state of a biskyrmion is energetically preferable over two individual skyrmions. As a result, when starting from two skyrmions in a micromagnetic simulation, a biskyrmion is formed upon relaxation. We propose a scheme that allows to control this biskyrmion formation in nanodisks and analyze the individual steps.

cond-mat.str-el↗

arXiv2019

Magnetic bimerons as skyrmion analogues in in-plane magnets

A magnetic bimeron is a pair of two merons and can be understood as the in-plane magnetized version of a skyrmion. Here we theoretically predict the existence of single magnetic bimerons as well as bimeron crystals, and compare the emergent electrodynamics of bimerons with their skyrmion analogues. We show that bimeron crystals can be stabilized in frustrated magnets and analyze what crystal structure can stabilize bimerons or bimeron crystals via the Dzyaloshinskii-Moriya interaction. We point out that bimeron crystals, in contrast to skyrmion crystals, allow for the detection of a pure topological Hall effect. By means of micromagnetic simulations, we show that bimerons can be used as bits of information in in-plane magnetized racetrack devices, where they allow for current-driven motion for torque orientations that leave skyrmions in out-of-plane magnets stationary.

cond-mat.mes-hall↗

arXiv2019

Magnetoelectric effect and orbital magnetization in skyrmion crystals: Detection and characterization of skyrmions

Skyrmions are small magnetic quasiparticles, which are uniquely characterized by their topological charge and their helicity. In this Rapid Communication, we show via calculations how both properties can be determined without relying on real-space imaging. The orbital magnetization and topological Hall conductivity measure the arising magnetization due to the circulation of electrons in the bulk and the occurrence of topologically protected edge channels due to the emergent field of a skyrmion crystal. Both observables quantify the topological Hall effect and distinguish skyrmions from antiskyrmions by sign. Additionally, we predict a magnetoelectric effect in skyrmion crystals, which is the generation of a magnetization (polarization) by application of an electric (magnetic) field. This effect is quantified by spin toroidization and magnetoelectric polarizability. The dependence of the transverse magnetoelectric effect on the skyrmion helicity fits that of the classical toroidal moment of the spin texture and allows to differentiate skyrmion helicities: it is largest for Bloch skyrmions and zero for Neel skyrmions. We predict distinct features of the four observables that can be used to detect and characterize skyrmions in experiments.

cond-mat.str-el↗

arXiv2019

Overcoming the speed limit in skyrmion racetrack devices by suppressing the skyrmion Hall effect

Magnetic skyrmions are envisioned as carriers of information in racetrack storage devices. Unfavorably, the skyrmion Hall effect hinders the fast propagation of skyrmions along an applied electric current and limits the device's maximum operation speed. In this Rapid Communication, we show that the maximum skyrmion velocity increases by a factor of 10 when the skyrmion Hall effect is suppressed, since the straight-line motion of the skyrmion allows for the application of larger driving currents. We consider a ferromagnet on a heavy metal layer, which converts the applied charge current into a spin current by the spin Hall effect. The spin current drives the skyrmions in the ferromagnet via spin-orbit torque. We show by analytical considerations and simulations that the deflection angle decreases, when the spin current is polarized partially along the applied current direction and derive the condition for complete suppression of the skyrmion Hall effect.

cond-mat.str-el↗

arXiv2018

The family of topological Hall effects for electrons in skyrmion crystals

Hall effects of electrons can be produced by an external magnetic field, spin orbit-coupling or a topologically non-trivial spin texture. The topological Hall effect (THE) - caused by the latter - is commonly observed in magnetic skyrmion crystals. Here, we show analogies of the THE to the conventional Hall effect (HE), the anomalous Hall effect (AHE), and the spin Hall effect (SHE). In the limit of strong coupling between conduction electron spins and the local magnetic texture the THE can be described by means of a fictitious, 'emergent' magnetic field. In this sense the THE can be mapped onto the HE caused by an external magnetic field. Due to complete alignment of electron spin and magnetic texture, the transverse charge conductivity is linked to a transverse spin conductivity. They are disconnected for weak coupling of electron spin and magnetic texture; the THE is then related to the AHE. The topological equivalent to the SHE can be found in antiferromagnetic skyrmion crystals. We substantiate our claims by calculations of the edge states for a finite sample. These states reveal in which situation the topological analogue to a quantized HE, quantized AHE, and quantized SHE can be found.

cond-mat.str-el↗

arXiv2017

Signatures of lattice geometry in quantum and topological Hall effect

The topological Hall effect (THE) of electrons in skyrmion crystals is strongly related to the quantum Hall effect (QHE) on lattices. This relation suggests to revisit the QHE because its Hall conductivity can be unconventionally quantized. It exhibits a jump and changes sign abruptly if the Fermi level crosses a van Hove singularity. In this Paper, we investigate the unconventional QHE features by discussing band structures, Hall conductivities, and topological edge states for square and triangular lattices; their origin are Chern numbers of bands in the skyrmion crystal (THE) or of the corresponding Landau levels (QHE). Striking features in the energy dependence of the Hall conductivities are traced back to the band structure without magnetic field whose properties are dictated by the lattice geometry. Based on these findings, we derive an approximation that allows us to determine the energy dependence of the topological Hall conductivity on any twodimensional lattice. The validity of this approximation is proven for the honeycomb lattice. We conclude that skyrmion crystals lend themselves for experiments to validate our findings for the THE and - indirectly - the QHE.

cond-mat.str-el↗

arXiv2017

Antiferromagnetic skyrmion crystals: generation, topological Hall and topological spin Hall effect

Skyrmions are topologically nontrivial, magnetic quasi-particles, that are characterized by a topological charge. A regular array of skyrmions - a skyrmion crystal (SkX) - features the topological Hall effect (THE) of electrons, that, in turn, gives rise to the Hall effect of the skyrmions themselves. It is commonly believed that antiferromagnetic skyrmion crystals (AFM-SkXs) lack both effects. In this Rapid Communication, we present a generally applicable method to create stable AFM-SkXs by growing a two sublattice SkX onto a collinear antiferromagnet. As an example we show that both types of skyrmion crystals - conventional and antiferromagnetic - exist in honeycomb lattices. While AFM-SkXs with equivalent lattice sites do not show a THE, they exhibit a topological spin Hall effect. On top of this, AFM-SkXs on inequivalent sublattices exhibit a nonzero THE, which may be utilized in spintronics devices. Our theoretical findings call for experimental realization.

cond-mat.str-el↗

arXiv2017

Unconventional Topological Hall Effect in Skyrmion Crystals Caused by the Topology of the Lattice

The hallmark of a skyrmion crystal (SkX) is the topological Hall effect (THE). In this Article, we predict and explain an unconventional behavior of the topological Hall conductivity in SkXs. In simple terms, the spin texture of the skyrmions causes an inhomogeneous emergent magnetic field whose associated Lorentz force acts on the electrons. By making the emergent field homogeneous, the THE is mapped onto the quantum Hall effect (QHE). Consequently, each electronic band of the SkX is assigned to a Landau level. This correspondence of THE and QHE allows to explain the unconventional behavior of the THE of electrons in SkXs. For example, a skyrmion crystal on a triangular lattice exhibits a quantized topological Hall conductivity with steps of $2 \cdot e^2/h$ below and with steps of $1 \cdot e^2/h$ above the van Hove singularity. On top of this, the conductivity shows a prominent sign change at the van Hove singularity. These unconventional features are deeply connected to the topology of the structural lattice.

cond-mat.str-el↗