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.

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}.

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.

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 NSk = ±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.

Nonlocal electron correlations in an itinerant ferromagnet.

Our understanding of the properties of ferromagnetic materials, widely used in spintronic devices, is fundamentally based on their electronic band structure. However, even for the most simple elemental ferromagnets, electron correlations are prevalent, requiring descriptions of their electronic structure beyond the simple picture of independent quasi-particles. Here, we give evidence that in itinerant ferromagnets like cobalt these electron correlations are of nonlocal origin, manifested in a complex self-energy Σσ(E,k) that disperses as function of spin σ, energy E, and momentum vector k. Together with one-step photoemission calculations, our experiments allow us to quantify the dispersive behaviour of the complex self-energy over the whole Brillouin zone. At the same time we observe regions of anomalously large "waterfall"-like band renormalization, previously only attributed to strong electron correlations in high-TC superconductors, making itinerant ferromagnets a paradigmatic test case for the interplay between band structure, magnetism, and many-body correlations.

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.

Impact of the Topological Surface State on the Thermoelectric Transport in Sb2Te3 Thin Films.

Ab initio electronic structure calculations based on density functional theory and tight-binding methods for the thermoelectric properties of p-type Sb2Te3 films are presented. The thickness-dependent electrical conductivity and the thermopower are computed in the diffusive limit of transport based on the Boltzmann equation. Contributions of the bulk and the surface to the transport coefficients are separated, which enables to identify a clear impact of the topological surface state on the thermoelectric properties. When the charge carrier concentration is tuned, a crossover between a surface-state-dominant and a Fuchs-Sondheimer transport regime is achieved. The calculations are corroborated by thermoelectric transport measurements on Sb2Te3 films grown by atomic layer deposition.

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.

Direct observation of interband spin-orbit coupling in a two-dimensional electron system.

We report the direct observation of interband spin-orbit (SO) coupling in a two-dimensional (2D) surface electron system, in addition to the anticipated Rashba spin splitting. Using angle-resolved photoemission experiments and first-principles calculations on Bi-Ag-Au heterostructures, we show that the effect strongly modifies the dispersion as well as the orbital and spin character of the 2D electronic states, thus giving rise to considerable deviations from the Rashba model. The strength of the interband SO coupling is tuned by the thickness of the thin film structures.

Atom-specific spin mapping and buried topological states in a homologous series of topological insulators.

A topological insulator is a state of quantum matter that, while being an insulator in the bulk, hosts topologically protected electronic states at the surface. These states open the opportunity to realize a number of new applications in spintronics and quantum computing. To take advantage of their peculiar properties, topological insulators should be tuned in such a way that ideal and isolated Dirac cones are located within the topological transport regime without any scattering channels. Here we report ab-initio calculations, spin-resolved photoemission and scanning tunnelling microscopy experiments that demonstrate that the conducting states can effectively tuned within the concept of a homologous series that is formed by the binary chalcogenides (Bi(2)Te(3), Bi(2)Se(3) and Sb(2)Te(3)), with the addition of a third element of the group IV.

Interference of spin states in photoemission from Sb/Ag(111) surface alloys.

Using a three-dimensional spin polarimeter we have gathered evidence for the interference of spin states in photoemission from the surface alloy Sb/Ag(111). This system features a small Rashba-type spin splitting of a size comparable to the momentum broadening of the quasiparticles, thus causing an intrinsic overlap between states with orthogonal spinors. Besides a small spin polarization caused by the spin splitting, we observe a large spin polarization component in the plane normal to the quantization axis of the Rashba effect. Strongly suggestive of coherent spin rotation, this effect is largely independent of the photon energy and photon polarization.

Tunable spin gaps in a quantum-confined geometry.

We have studied the interplay of a giant spin-orbit splitting and of quantum confinement in artificial Bi-Ag-Si trilayer structures. Angle-resolved photoelectron spectroscopy reveals the formation of a complex spin-dependent gap structure, which can be tuned by varying the thickness of the Ag buffer layer. This provides a means to tailor the electronic structure at the Fermi energy, with potential applications for silicon-compatible spintronic devices.

Giant spin splitting through surface alloying.

The long-range ordered surface alloy Bi/Ag(111) is found to exhibit a giant spin splitting of its surface electronic structure due to spin-orbit coupling, as is determined by angle-resolved photoelectron spectroscopy. First-principles electronic structure calculations fully confirm the experimental findings. The effect is brought about by a strong in-plane gradient of the crystal potential in the surface layer, in interplay with the structural asymmetry due to the surface-potential barrier. As a result, the spin polarization of the surface states is considerably rotated out of the surface plane.