Resonating holes vs molecular spin-orbit coupled states in group-5 lacunar spinels.

The valence electronic structure of magnetic centers is one of the factors that determines the characteristics of a magnet. This may refer to orbital degeneracy, as for jeff = 1/2 Kitaev magnets, or near-degeneracy, e.g., involving the third and fourth shells in cuprate superconductors. Here we explore the inner structure of magnetic moments in group-5 lacunar spinels, fascinating materials featuring multisite magnetic units in the form of tetrahedral tetramers. Our quantum chemical analysis reveals a very colorful landscape, much richer than the single-electron, single-configuration description applied so far to all group-5 GaM4X8 chalcogenides, and clarifies the basic multiorbital correlations on M4 tetrahedral clusters: while for V strong correlations yield a wave-function that can be well described in terms of four V4+V3+V3+V3+ resonant valence structures, for Nb and Ta a picture of dressed molecular-orbital jeff = 3/2 entities is more appropriate. These internal degrees of freedom likely shape vibronic couplings, phase transitions, and the magneto-electric properties in each of these systems.

Mechanism of Skyrmion Attraction in Chiral Magnets near the Ordering Temperatures.

Isolated chiral skyrmions are investigated within the phenomenological Dzyaloshinskii model near the ordering temperatures of quasi-two-dimensional chiral magnets with Cnv symmetry and three-dimensional cubic helimagnets. In the former case, isolated skyrmions (IS) perfectly blend into the homogeneously magnetized state. The interaction between these particle-like states, being repulsive in a broad low-temperature (LT) range, is found to switch into attraction at high temperatures (HT). This leads to a remarkable confinement effect: near the ordering temperature, skyrmions exist only as bound states. This is a consequence of the coupling between the magnitude and the angular part of the order parameter, which becomes pronounced at HT. The nascent conical state in bulk cubic helimagnets, on the contrary, is shown to shape skyrmion internal structure and to substantiate the attraction between them. Although the attracting skyrmion interaction in this case is explained by the reduction of the total pair energy due to the overlap of skyrmion shells, which are circular domain boundaries with the positive energy density formed with respect to the surrounding host phase, additional magnetization "ripples" at the skyrmion outskirt may lead to attraction also at larger length scales. The present work provides fundamental insights into the mechanism for complex mesophase formation near the ordering temperatures and constitutes a first step to explain the phenomenon of multifarious precursor effects in that temperature region.

How Correlations and Spin-Orbit Coupling Work within Extended Orbitals of Transition-Metal Tetrahedra of 4d/5d Lacunar Spinels.

Spin-orbit quartet ground states are associated with rich phenomenology, ranging from multipolar phases in f1 rare-earth borides to magnetism emerging through covalency and vibronic couplings in d1 transition-metal compounds. The latter effect has been studied since the 1960s on t2g1 octahedral ML6 units in both molecular complexes and extended solid-state lattices. Here we analyze the Jeff = 3/2 quartet ground state of larger cubane-like M4L4 entities in lacunar spinels, composed of transition-metal (M) tetrahedra caged by chalcogenide ligands (L). These represent a unique platform where spin-orbit coupling acts on molecular-like, delocalized t2 orbitals. Using quantum chemical methods, we pin down the interplay of spin-orbit couplings in such a setting and many-body physics related to other molecular-like single-electron levels, both below and above the reference t21. We provide a different interpretation of resonant inelastic X-ray scattering data on GaTa4Se8 and, by comparing magnetic susceptibility data with calculated g factors, valuable insights into the important role of vibronic couplings.

Unveiling the three-dimensional magnetic texture of skyrmion tubes.

Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to control their motion has opened a new field of research, skyrmionics, that aims for the usage of skyrmions as information carriers. Further advances in skyrmionics call for a thorough understanding of their three-dimensional (3D) spin texture, skyrmion-skyrmion interactions and the coupling to surfaces and interfaces, which crucially affect skyrmion stability and mobility. Here, we quantitatively reconstruct the 3D magnetic texture of Bloch skyrmions with sub-10-nanometre resolution using holographic vector-field electron tomography. The reconstructed textures reveal local deviations from a homogeneous Bloch character within the skyrmion tubes, details of the collapse of the skyrmion texture at surfaces and a correlated modulation of the skyrmion tubes in FeGe along their tube axes. Additionally, we confirm the fundamental principles of skyrmion formation through an evaluation of the 3D magnetic energy density across these magnetic solitons.

Curvilinear One-Dimensional Antiferromagnets.

Antiferromagnets host exotic quasiparticles, support high frequency excitations and are key enablers of the prospective spintronic and spin-orbitronic technologies. Here, we propose a concept of a curvilinear antiferromagnetism where material responses can be tailored by a geometrical curvature without the need to adjust material parameters. We show that an intrinsically achiral one-dimensional (1D) curvilinear antiferromagnet behaves as a chiral helimagnet with geometrically tunable Dzyaloshinskii-Moriya interaction (DMI) and orientation of the Néel vector. The curvature-induced DMI results in the hybridization of spin wave modes and enables a geometrically driven local minimum of the low-frequency branch. This positions curvilinear 1D antiferromagnets as a novel platform for the realization of geometrically tunable chiral antiferromagnets for antiferromagnetic spin-orbitronics and fundamental discoveries in the formation of coherent magnon condensates in the momentum space.

Two types of magnetic shape-memory effects from twinned microstructure and magneto-structural coupling in Fe1+y Te.

A detailed experimental investigation of Fe1+y Te (y = 0.11, 0.12) using pulsed magnetic fields up to 60 T confirms remarkable magnetic shape-memory (MSM) effects. These effects result from magnetoelastic transformation processes in the low-temperature antiferromagnetic state of these materials. The observation of modulated and finely twinned microstructure at the nanoscale through scanning tunneling microscopy establishes a behavior similar to that of thermoelastic martensite. We identified the observed, elegant hierarchical twinning pattern of monoclinic crystallographic domains as an ideal realization of crossing twin bands. The antiferromagnetism of the monoclinic ground state allows for a magnetic-field-induced reorientation of these twin variants by the motion of one type of twin boundaries. At sufficiently high magnetic fields, we observed a second isothermal transformation process with large hysteresis for different directions of applied field. This gives rise to a second MSM effect caused by a phase transition back to the field-polarized tetragonal lattice state.

Multiplet of Skyrmion States on a Curvilinear Defect: Reconfigurable Skyrmion Lattices.

Typically, the chiral magnetic Skyrmion is a single-state excitation. Here we propose a system, where multiplet of Skyrmion states appears and one of these states can be the ground one. We show that the presence of a localized curvilinear defect drastically changes the magnetic properties of a thin perpendicularly magnetized ferromagnetic film. For a large enough defect amplitude a discrete set of equilibrium magnetization states appears forming a ladder of energy levels. Each equilibrium state has either a zero or a unit topological charge; i.e., topologically trivial and Skyrmion multiplets generally appear. Transitions between the levels with the same topological charge are allowed and can be utilized to encode and switch a bit of information. There is a wide range of geometrical and material parameters, where the Skyrmion level has the lowest energy. Thus, periodically arranged curvilinear defects can result in a Skyrmion lattice as the ground state.

Mesoscale Dzyaloshinskii-Moriya interaction: geometrical tailoring of the magnetochirality.

Crystals with broken inversion symmetry can host fundamentally appealing and technologically relevant periodical or localized chiral magnetic textures. The type of the texture as well as its magnetochiral properties are determined by the intrinsic Dzyaloshinskii-Moriya interaction (DMI), which is a material property and can hardly be changed. Here we put forth a method to create new artificial chiral nanoscale objects with tunable magnetochiral properties from standard magnetic materials by using geometrical manipulations. We introduce a mesoscale Dzyaloshinskii-Moriya interaction that combines the intrinsic spin-orbit and extrinsic curvature-driven DMI terms and depends both on the material and geometrical parameters. The vector of the mesoscale DMI determines magnetochiral properties of any curved magnetic system with broken inversion symmetry. The strength and orientation of this vector can be changed by properly choosing the geometry. For a specific example of nanosized magnetic helix, the same material system with different geometrical parameters can acquire one of three zero-temperature magnetic phases, namely, phase with a quasitangential magnetization state, phase with a periodical state and one intermediate phase with a periodical domain wall state. Our approach paves the way towards the realization of a new class of nanoscale spintronic and spinorbitronic devices with the geometrically tunable magnetochirality.

Magnetic antiskyrmions above room temperature in tetragonal Heusler materials.

Magnetic skyrmions are topologically stable, vortex-like objects surrounded by chiral boundaries that separate a region of reversed magnetization from the surrounding magnetized material. They are closely related to nanoscopic chiral magnetic domain walls, which could be used as memory and logic elements for conventional and neuromorphic computing applications that go beyond Moore's law. Of particular interest is 'racetrack memory', which is composed of vertical magnetic nanowires, each accommodating of the order of 100 domain walls, and that shows promise as a solid state, non-volatile memory with exceptional capacity and performance. Its performance is derived from the very high speeds (up to one kilometre per second) at which chiral domain walls can be moved with nanosecond current pulses in synthetic antiferromagnet racetracks. Because skyrmions are essentially composed of a pair of chiral domain walls closed in on themselves, but are, in principle, more stable to perturbations than the component domain walls themselves, they are attractive for use in spintronic applications, notably racetrack memory. Stabilization of skyrmions has generally been achieved in systems with broken inversion symmetry, in which the asymmetric Dzyaloshinskii-Moriya interaction modifies the uniform magnetic state to a swirling state. Depending on the crystal symmetry, two distinct types of skyrmions have been observed experimentally, namely, Bloch and Néel skyrmions. Here we present the experimental manifestation of another type of skyrmion-the magnetic antiskyrmion-in acentric tetragonal Heusler compounds with D2d crystal symmetry. Antiskyrmions are characterized by boundary walls that have alternating Bloch and Néel type as one traces around the boundary. A spiral magnetic ground-state, which propagates in the tetragonal basal plane, is transformed into an antiskyrmion lattice state under magnetic fields applied along the tetragonal axis over a wide range of temperatures. Direct imaging by Lorentz transmission electron microscopy shows field-stabilized antiskyrmion lattices and isolated antiskyrmions from 100 kelvin to well beyond room temperature, and zero-field metastable antiskyrmions at low temperatures. These results enlarge the family of magnetic skyrmions and pave the way to the engineering of complex bespoke designed skyrmionic structures.

Superconducting gap structure of FeSe.

The microscopic mechanism governing the zero-resistance flow of current in some iron-based, high-temperature superconducting materials is not well understood up to now. A central issue concerning the investigation of these materials is their superconducting gap symmetry and structure. Here we present a combined study of low-temperature specific heat and scanning tunnelling microscopy measurements on single crystalline FeSe. The results reveal the existence of at least two superconducting gaps which can be represented by a phenomenological two-band model. The analysis of the specific heat suggests significant anisotropy in the gap magnitude with deep gap minima. The tunneling spectra display an overall "U"-shaped gap close to the Fermi level away as well as on top of twin boundaries. These results are compatible with the anisotropic nodeless models describing superconductivity in FeSe.

Strongly frustrated triangular spin lattice emerging from triplet dimer formation in honeycomb Li2IrO3.

Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir(4+) in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir-Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.

Synthesis and Characterization of Ba[CoSO]: Magnetic Complexity in the Presence of Chalcogen Ordering.

Barium thio-oxocobaltate(II), Ba[CoS2/2 O2/2 ], was synthesized by the reaction of equimolar amounts of BaO, Co, and S in closed silica ampoules. The title compound (Cmcm, a=3.98808(3), b=12.75518(9), c=6.10697(4) Å) is isostructural to Ba[ZnSO]. The use of soft X-ray absorption spectroscopy confirmed that cobalt is in the oxidation state +2 and tetrahedrally coordinated. Its coordination consists of two sulfur and two oxygen atoms in an ordered fashion. High-temperature magnetic susceptibility data indicate strong low-dimensional spin-spin interactions, which are suggested to be closely related to the layer-type crystal structure and perhaps the ordered distribution of sulfur and oxygen. Antiferromagnetic ordering below TN =222 K is observed as an anomaly in the specific heat, coinciding with a significant lowering of the magnetic susceptibility. Density functional theory calculations within a generalized-gradient approximation (GGA)+U approach identify an antiferromagnetic ground state within the square-like two-dimensional layers of Co, and antiferromagnetic correlations for nearest and next nearest neighbors along bonds mediated by oxygen or sulfur. However, this magnetic state is subject to frustration by relatively strong interlayer couplings.

Manipulating topological states by imprinting non-collinear spin textures.

Topological magnetic states, such as chiral skyrmions, are of great scientific interest and show huge potential for novel spintronics applications, provided their topological charges can be fully controlled. So far skyrmionic textures have been observed in noncentrosymmetric crystalline materials with low symmetry and at low temperatures. We propose theoretically and demonstrate experimentally the design of spin textures with topological charge densities that can be tailored at ambient temperatures. Tuning the interlayer coupling in vertically stacked nanopatterned magnetic heterostructures, such as a model system of a Co/Pd multilayer coupled to Permalloy, the in-plane non-collinear spin texture of one layer can be imprinted into the out-of-plane magnetised material. We observe distinct spin textures, e.g. vortices, magnetic swirls with tunable opening angle, donut states and skyrmion core configurations. We show that applying a small magnetic field, a reliable switching between topologically distinct textures can be achieved at remanence.

The quantum nature of skyrmions and half-skyrmions in Cu2OSeO3.

The Skyrme-particle, the skyrmion, was introduced over half a century ago in the context of dense nuclear matter. But with skyrmions being mathematical objects--special types of topological solitons--they can emerge in much broader contexts. Recently skyrmions were observed in helimagnets, forming nanoscale spin-textures. Extending over length scales much larger than the interatomic spacing, they behave as large, classical objects, yet deep inside they are of quantum nature. Penetrating into their microscopic roots requires a multi-scale approach, spanning the full quantum to classical domain. Here, we achieve this for the first time in the skyrmionic Mott insulator Cu2OSeO3. We show that its magnetic building blocks are strongly fluctuating Cu4 tetrahedra, spawning a continuum theory that culminates in 51 nm large skyrmions, in striking agreement with experiment. One of the further predictions that ensues is the temperature-dependent decay of skyrmions into half-skyrmions.