Orbital Hall Effect Accompanying Quantum Hall Effect: Landau Levels Cause Orbital Polarized Edge Currents.

The quantum Hall effect emerges when two-dimensional samples are subjected to strong magnetic fields at low temperatures: Topologically protected edge states cause a quantized Hall conductivity in multiples of e^{2}/h. Here we show that the quantum Hall effect is accompanied by an orbital Hall effect. Our quantum mechanical calculations fit well the semiclassical interpretation in terms of "skipping orbits." The chiral edge states of a quantum Hall system are orbital polarized akin to a hypothetical orbital version of the quantum anomalous Hall effect in magnetic systems. The orbital Hall resistivity scales quadratically with the magnetic field, making it the dominant effect at high fields.

Gate-tuneable and chirality-dependent charge-to-spin conversion in tellurium nanowires.

Chiral materials are an ideal playground for exploring the relation between symmetry, relativistic effects and electronic transport. For instance, chiral organic molecules have been intensively studied to electrically generate spin-polarized currents in the last decade, but their poor electronic conductivity limits their potential for applications. Conversely, chiral inorganic materials such as tellurium have excellent electrical conductivity, but their potential for enabling the electrical control of spin polarization in devices remains unclear. Here, we demonstrate the all-electrical generation, manipulation and detection of spin polarization in chiral single-crystalline tellurium nanowires. By recording a large (up to 7%) and chirality-dependent unidirectional magnetoresistance, we show that the orientation of the electrically generated spin polarization is determined by the nanowire handedness and uniquely follows the current direction, while its magnitude can be manipulated by an electrostatic gate. Our results pave the way for the development of magnet-free chirality-based spintronic devices.

Atomic Scale Control of Spin Current Transmission at Interfaces.

Ferromagnet/heavy metal bilayers represent a central building block for spintronic devices where the magnetization of the ferromagnet can be controlled by spin currents generated in the heavy metal. The efficiency of spin current generation is paramount. Equally important is the efficient transfer of this spin current across the ferromagnet/heavy metal interface. Here, we show theoretically and experimentally that for Ta as heavy metal the interface only partially transmits the spin current while this effect is absent when Pt is used as heavy metal. This is due to magnetic moment reduction at the interface caused by 3d-5d hybridization effects. We show that this effect can be avoided by atomically thin interlayers. On the basis of our theoretical model we conclude that this is a general effect and occurs for all 5d metals with less than half-filled 5d shell.

Thermal Hall Effect of Magnons in Collinear Antiferromagnetic Insulators: Signatures of Magnetic and Topological Phase Transitions.

We demonstrate theoretically that the thermal Hall effect of magnons in collinear antiferromagnetic insulators is an indicator of magnetic and topological phase transitions in the magnon spectrum. The transversal heat current of magnons caused by a thermal gradient is calculated for an antiferromagnet on a honeycomb lattice. An applied magnetic field drives the system from the antiferromagnetic phase via a spin-flop phase into the field-polarized phase. In addition to these magnetic phase transitions, we find topological phase transitions within the spin-flop phase. Both types of transitions manifest themselves in prominent and distinguishing features in the thermal conductivity, which changes by several orders of magnitude. The variation of temperature provides a tool to discern experimentally the two types of phase transitions. We include numerical results for the van der Waals magnet MnPS_{3}.

Mapping spin-charge conversion to the band structure in a topological oxide two-dimensional electron gas.

While spintronics has traditionally relied on ferromagnetic metals as spin generators and detectors, spin-orbitronics exploits the efficient spin-charge interconversion enabled by spin-orbit coupling in non-magnetic systems. Although the Rashba picture of split parabolic bands is often used to interpret such experiments, it fails to explain the largest conversion effects and their relationship with the electronic structure. Here, we demonstrate a very large spin-to-charge conversion effect in an interface-engineered, high-carrier-density SrTiO3 two-dimensional electron gas and map its gate dependence on the band structure. We show that the conversion process is amplified by enhanced Rashba-like splitting due to orbital mixing and in the vicinity of avoided band crossings with topologically non-trivial order. Our results indicate that oxide two-dimensional electron gases are strong candidates for spin-based information readout in new memory and transistor designs. Our results also emphasize the promise of topology as a new ingredient to expand the scope of complex oxides for spintronics.

Orbital Magnetic Moment of Magnons.

In experiments and their interpretation usually the spin magnetic moment of magnons is considered. In this Letter, we identify a complementing orbital magnetic moment of magnons brought about by spin-orbit coupling. Our microscopic theory uncovers that spin magnetization M^{S} and orbital magnetization M^{O} are independent quantities; they are not necessarily collinear. Even when the total spin moment is compensated due to antiferromagnetism, M^{O} may be nonzero. This scenario of orbital weak ferromagnetism is realized in paradigmatic kagome antiferromagnets with Dzyaloshinskii-Moriya interaction. We demonstrate that magnets exhibiting a magnonic orbital moment are omnipresent and propose transport experiments for probing it.

Stabilizing the magnetic moment of single holmium atoms by symmetry.

Single magnetic atoms, and assemblies of such atoms, on non-magnetic surfaces have recently attracted attention owing to their potential use in high-density magnetic data storage and as a platform for quantum computing. A fundamental problem resulting from their quantum mechanical nature is that the localized magnetic moments of these atoms are easily destabilized by interactions with electrons, nuclear spins and lattice vibrations of the substrate. Even when large magnetic fields are applied to stabilize the magnetic moment, the observed lifetimes remain rather short (less than a microsecond). Several routes for stabilizing the magnetic moment against fluctuations have been suggested, such as using thin insulating layers between the magnetic atom and the substrate to suppress the interactions with the substrate's conduction electrons, or coupling several magnetic moments together to reduce their quantum mechanical fluctuations. Here we show that the magnetic moments of single holmium atoms on a highly conductive metallic substrate can reach lifetimes of the order of minutes. The necessary decoupling from the thermal bath of electrons, nuclear spins and lattice vibrations is achieved by a remarkable combination of several symmetries intrinsic to the system: time reversal symmetry, the internal symmetries of the total angular momentum and the point symmetry of the local environment of the magnetic atom.

Tunable Magnon Weyl Points in Ferromagnetic Pyrochlores.

The dispersion relations of magnons in ferromagnetic pyrochlores with Dzyaloshinskii-Moriya interaction are shown to possess Weyl points, i. e., pairs of topologically nontrivial crossings of two magnon branches with opposite topological charge. As a consequence of their topological nature, their projections onto a surface are connected by magnon arcs, thereby resembling closely Fermi arcs of electronic Weyl semimetals. On top of this, the positions of the Weyl points in reciprocal space can be tuned widely by an external magnetic field: rotated within the surface plane, the Weyl points and magnon arcs are rotated as well; tilting the magnetic field out of plane shifts the Weyl points toward the center Γ[over ¯] of the surface Brillouin zone. The theory is valid for the class of ferromagnetic pyrochlores, i. e., three-dimensional extensions of topological magnon insulators on kagome lattices. In this Letter, we focus on the (111) surface, identify candidates of established ferromagnetic pyrochlores which apply to the considered spin model, and suggest experiments for the detection of the topological features.

Erratum: Spin Chirality Tuning and Topological Semimetals in Strained HgTe_{x}S_{1-x} [Phys. Rev. Lett. 114, 236805 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.114.236805.

Spin Chirality Tuning and Topological Semimetals in Strained HgTe(x)S(1-x).

By means of detailed electronic structure calculations, we show that strained HgTe(x)S(1-x) alloys show a surprisingly rich topological phase diagram. In the strong topological insulator phase, the spin chirality of the topological nontrivial surface states can be reversed by adjusting the alloy concentration x and the strain. On top of this, we predict two semimetallic topological phases, namely, a Dirac semimetal and a Weyl semimetal. The topological phases are characterized by their Z2 invariants and their mirror Chern numbers.

Two-dimensional electron gas and its electric control at the interface between ferroelectric and antiferromagnetic insulator studied from first principles.

A multiferroic interface between the antiferromagnetic Slater insulator SrTcO3 and ferroelectric BaTiO3 (BTO) is studied from first principles. Although the interfacial magnetoelectric coupling of SrTcO3(001) is relatively small, we found that a two-dimensional electron gas (2DEG) appears for both BaO/TcO2 and TiO2/SrO terminations. The charge character of the carriers, induced in the band gap due to polar BTO, can be switched from electrons to holes by the reversal of the electric polarization in BTO. The 2DEG is robust and stable against the degree of electronic correlations, whereas the paraelectric state of BTO suppresses the 2DEG. The origin of the 2DEG at the BTO/SrTcO3 interface and its key factors are discussed.

Dual topological character of chalcogenides: theory for Bi2Te3.

A topological insulator is realized via band inversions driven by the spin-orbit interaction. In the case of Z2 topological phases, the number of band inversions is odd and time-reversal invariance is a further unalterable ingredient. For topological crystalline insulators, the number of band inversions may be even but mirror symmetry is required. Here, we prove that the chalcogenide Bi2Te3 is a dual topological insulator: it is simultaneously in a Z2 topological phase with Z2 invariants (ν0;ν1ν2ν3) = (1;0 0 0) and in a topological crystalline phase with mirror Chern number -1. In our theoretical investigation we show in addition that the Z2 phase can be broken by magnetism while keeping the topological crystalline phase. As a consequence, the Dirac state at the (111) surface is shifted off the time-reversal invariant momentum Γ; being protected by mirror symmetry, there is no band gap opening. Our observations provide theoretical groundwork for opening the research on magnetic control of topological phases in quantum devices.

Impact of electron-impurity scattering on the spin relaxation time in graphene: a first-principles study.

The effect of electron-impurity scattering on momentum and spin relaxation times in graphene is studied by means of relativistic ab initio calculations. Assuming carbon and silicon adatoms as natural impurities in graphene, we are able to simulate fast spin relaxation observed experimentally. We investigate the dependence of the relaxation times on the impurity position and demonstrate that C or Si adatoms act as real-space spin hot spots inducing spin-flip rates about 5 orders of magnitude larger than those of in-plane impurities. This fact confirms the hypothesis that the adatom-induced spin-orbit coupling leads to fast spin relaxation in graphene.

Ultrafast spin dynamics: complementing theoretical analyses by quantum state measures.

In theoretical analyses of ultrafast spin dynamics simulated phenomena are commonly discussed in terms of observables. In this paper we report on possible benefits of complementing such studies by quantum state (QS) measures. These measures quantify specific properties of QSs, e.g. distance in Hilbert space and mixing. For Co/Cu heterostructures illuminated by femtosecond laser pulses, we discuss the general behavior of selected measures, but address in particular the degree of perturbation by a laser pulse. It turns out that the measures are especially sensitive to variations of the polarization of a laser pulse and the sample composition. Moreover, they are closely linked to magnetization and number of photo-excited electrons.

Generation of out-of-plane polarized spin current by spin swapping.

The generation of spin currents and their application to the manipulation of magnetic states is fundamental to spintronics. Of particular interest are chiral antiferromagnets that exhibit properties typical of ferromagnetic materials even though they have negligible magnetization. Here, we report the generation of a robust spin current with both in-plane and out-of-plane spin polarization in epitaxial thin films of the chiral antiferromagnet Mn3Sn in proximity to permalloy thin layers. By employing temperature-dependent spin-torque ferromagnetic resonance, we find that the chiral antiferromagnetic structure of Mn3Sn is responsible for an in-plane polarized spin current that is generated from the interior of the Mn3Sn layer and whose temperature dependence follows that of this layer's antiferromagnetic order. On the other hand, the out-of-plane polarized spin current is unrelated to the chiral antiferromagnetic structure and is instead the result of scattering from the Mn3Sn/permalloy interface. We substantiate the later conclusion by performing studies with several other non-magnetic metals all of which are found to exhibit out-of-plane polarized spin currents arising from the spin swapping effect.

Atomic Displacements Enabling the Observation of the Anomalous Hall Effect in a Non-Collinear Antiferromagnet.

Antiferromagnets with non-collinear spin structures display various properties that make them attractive for spintronic devices. Some of the most interesting examples are an anomalous Hall effect despite negligible magnetization and a spin Hall effect with unusual spin polarization directions. However, these effects can only be observed when the sample is set predominantly into a single antiferromagnetic domain state. This can only be achieved when the compensated spin structure is perturbed and displays weak moments due to spin canting that allows for external domain control. In thin films of cubic non-collinear antiferromagnets, this imbalance is previously assumed to require tetragonal distortions induced by substrate strain. Here, it is shown that in Mn3 SnN and Mn3 GaN, spin canting is due to structural symmetry lowering induced by large displacements of the magnetic manganese atoms away from high-symmetry positions. These displacements remain hidden in X-ray diffraction when only probing the lattice metric and require measurement of a large set of scattering vectors to resolve the local atomic positions. In Mn3 SnN, the induced net moments enable the observation of the anomalous Hall effect with an unusual temperature dependence, which is conjectured to result from a bulk-like temperature-dependent coherent spin rotation within the kagome plane.

Controlled Electronic and Magnetic Landscape in Self-Assembled Complex Oxide Heterostructures.

Complex oxide heterointerfaces contain a rich playground of novel physical properties and functionalities, which give rise to emerging technologies. Among designing and controlling the functional properties of complex oxide film heterostructures, vertically aligned nanostructure (VAN) films using a self-assembling bottom-up deposition method presents great promise in terms of structural flexibility and property tunability. Here, the bottom-up self-assembly is extended to a new approach using a mixture containing a 2Dlayer-by-layer film growth, followed by a 3D VAN film growth. In this work, the two-phase nanocomposite thin films are based on LaAlO3 :LaBO3 , grown on a lattice-mismatched SrTiO3001 (001) single crystal. The 2D-to-3D transient structural assembly is primarily controlled by the composition ratio, leading to the coexistence of multiple interfacial properties, 2D electron gas, and magnetic anisotropy. This approach provides multidimensional film heterostructures which enrich the emergent phenomena for multifunctional applications.

Extrinsic spin Nernst effect from first principles.

We present an ab initio description of the thermal transport phenomenon called the spin Nernst effect. It refers to generation of a spin accumulation or a pure spin current transverse to an applied temperature gradient. This is similar to the intensively studied spin Hall effect described by intrinsic and extrinsic mechanisms due to an applied electric field. Analogously, several contributions are present for the spin Nernst effect. Here we investigate the extrinsic skew scattering mechanism which is dominant in the limit of dilute alloys. Our calculations are based on a fully relativistic Korringa-Kohn-Rostoker method and a solution of the linearized Boltzmann equation. As a first application, we consider a Cu host with Au, Ti, and Bi impurities.

Setting of the magnetic structure of chiral kagome antiferromagnets by a seeded spin-orbit torque.

The current-induced spin-orbit torque switching of ferromagnets has had huge impact in spintronics. However, short spin-diffusion lengths limit the thickness of switchable ferromagnetic layers, thereby limiting their thermal stability. Here, we report a previously unobserved seeded spin-orbit torque (SSOT) by which current can set the magnetic states of even thick layers of the chiral kagome antiferromagnet Mn3Sn. The mechanism involves setting the orientation of the antiferromagnetic domains in a thin region at the interface with spin currents arising from an adjacent heavy metal while also heating the layer above its magnetic ordering temperature. This interface region seeds the resulting spin texture of the entire layer as it cools down and, thereby, overcomes the thickness limitation of conventional spin-orbit torques. SSOT switching in Mn3Sn can be extended beyond chiral antiferromagnets to diverse magnetic systems and provides a path toward the development of highly efficient, high-speed, and thermally stable spintronic devices.

Direct visualization of Rashba-split bands and spin/orbital-charge interconversion at KTaO3 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 display a large and gate-tunable conversion efficiency, as determined by transport measurements. However, a direct visualization of the Rashba-split bands in oxide two-dimensional electron gases is lacking, which hampers an advanced understanding of their rich spin-orbit physics. Here, we investigate KTaO3 two-dimensional electron gases 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 two-dimensional electron gases. Finally, we suggest design rules for Rashba systems to optimize spin-charge interconversion performance.