Topological Nernst Effect of the Two-Dimensional Skyrmion Lattice

Measurement setup for Nernst and Seebeck effect at high temperatures and magnetic fields tested on elemental bismuth and full-Heusler compounds

In this work, a measurement setup to study the Seebeck and Nernst effect at high temperatures and high magnetic fields is introduced and discussed. The measurement system allows for simultaneous measurements of both thermoelectric effects up to 700 K and magnetic fields up to 12 T. Based on theoretical concepts, measurement equations are derived that counteract constant spurious offset voltages and, therefore, inhibit systematic errors in the measurement setup. The functionality is demonstrated on polycrystalline samples of elemental bismuth as well as various full-Heusler materials, exhibiting an anomalous Nernst effect. In all samples, the measured Seebeck and Nernst coefficients align excellently with the reported values. This allows future research to substantially extend the measured temperature and field intervals, commonly limited to temperatures below room temperature. For the first time, the thermoelectric and thermomagnetic properties of these materials are reported up to temperatures of 560 K.

Crystal Thermal Transport in Altermagnetic RuO_{2}

We demonstrate the emergence of a pronounced thermal transport in the recently discovered class of magnetic materials-altermagnets. From symmetry arguments and first-principles calculations performed for the showcase altermagnet, RuO_{2}, we uncover that crystal Nernst and crystal thermal Hall effects in this material are very large and strongly anisotropic with respect to the Néel vector. We find the large crystal thermal transport to originate from three sources of Berry's curvature in momentum space: the Weyl fermions due to crossings between well-separated bands, the strong spin-flip pseudonodal surfaces, and the weak spin-flip ladder transitions, defined by transitions among very weakly spin-split states of similar dispersion crossing the Fermi surface. Moreover, we reveal that the anomalous thermal and electrical transport coefficients in RuO_{2} are linked by an extended Wiedemann-Franz law in a temperature range much wider than expected for conventional magnets. Our results suggest that altermagnets may assume a leading role in realizing concepts in spin caloritronics not achievable with ferromagnets or antiferromagnets.

Spontaneous Vortex-Antivortex Pairs and Their Topological Transitions in a Chiral-Lattice Magnet

The spontaneous formation and topological transitions of vortex-antivortex pairs have implications for a broad range of emergent phenomena, for example, from superconductivity to quantum computing. Unlike magnets exhibiting collinear spin textures, helimagnets with noncollinear spin textures provide unique opportunities to manipulate topological forms such as (anti)merons and (anti)skyrmions. However, it is challenging to achieve multiple topological states and their interconversion in a single helimagnet due to the topological protection for each state. Here, the on-demand creation of multiple topological states in a helimagnet Fe0.5 Co0.5 Ge, including a spontaneous vortex pair of meron with topological charge N = -1/2 and antimeron with N = 1/2, and a vortex-antivortex bundle, that is, a bimeron (meron pair) with N = -1 is reported. The mutual transformation between skyrmions and bimerons with respect to the competitive effects of magnetic field and magnetic shape anisotropy is demonstrated. It is shown that electric currents drive the individual bimerons to form their connecting assembly and then into a skyrmion lattice. These findings signify the feasibility of designing topological states and offer new insights into the manipulation of noncollinear spin textures for potential applications in various fields.

Topological magneto-optical effect from skyrmion lattice

The magnetic skyrmion is a spin-swirling topological object characterized by its nontrivial winding number, holding potential for next-generation spintronic devices. While optical readout has become increasingly important towards the high integration and ultrafast operation of those devices, the optical response of skyrmions has remained elusive. Here, we show the magneto-optical Kerr effect (MOKE) induced by the skyrmion formation, i.e., topological MOKE, in Gd2PdSi3. The significantly enhanced optical rotation found in the skyrmion phase demonstrates the emergence of topological MOKE, exemplifying the light-skyrmion interaction arising from the emergent gauge field. This gauge field in momentum space causes a dramatic reconstruction of the electronic band structure, giving rise to magneto-optical activity ranging up to the sub-eV region. The present findings pave a way for photonic technology based on skyrmionics.

Kagome Lattice Promotes Chiral Spin Fluctuations

Dynamical spin fluctuations in magnets can be endowed with a slight bent toward left- or right-handed chirality by Dzyaloshinskii-Moriya interactions. However, little is known about the crucial role of lattice geometry on these chiral spin fluctuations and on fluctuation-related transport anomalies driven by the quantum-mechanical (Berry) phase of conduction electrons. Via thermoelectric Nernst effect and electric Hall effect experiments, we detect chiral spin fluctuations in the paramagnetic regime of a kagome lattice magnet; these signals are largely absent in a comparable triangular lattice magnet. Supported by Monte Carlo calculations, we identify lattices with at least two dissimilar plaquettes as most promising for Berry phase phenomena driven by thermal fluctuations in paramagnets.

Real-Space Observations of Three-Dimensional Antiskyrmions and Skyrmion Strings

Nanometric topological spin textures, such as skyrmions (Sks) and antiskyrmions (antiSks), have attracted much attention recently. However, most studies have focused on two-dimensional spin textures in films with inherent or synthetic antisymmetric spin-exchange interaction, termed Dzyaloshinskii-Moriya interaction, although three-dimensional (3D) topological spin textures, such as antiSks composed of alternating Bloch- and Néel-type spin spirals, chiral bobbers carrying emergent magnetic monopoles, and deformed Sk strings, are ubiquitous. To elucidate these textures, we have developed a 3D nanometric magnetic imaging technique, tomographic Lorentz transmission electron microscopy (TEM). The approach enables the visualization of the 3D shape of magnetic objects and their 3D vector field mapping. Here we report 3D vector field maps of deformed Sk-strings and antiSk using the technique. This research approach will lead to discoveries and understanding of fertile 3D magnetic structures in a broad class of magnets, providing insight into 3D topological magnetism.

Entropy-Assisted, Long-Period Stacking of Honeycomb Layers in an AlB2-Type Silicide

Configurational entropy can impact crystallization processes, tipping the scales between structures of nearly equal internal energy. Using alloyed single crystals of Gd₂PdSi₃ in the AlB₂-type structure, we explore the formation of complex layer sequences made from alternating, two-dimensional triangular and honeycomb slabs. A four-period and an eight-period stacking sequence are found to be very close in internal energy, the latter being favored by entropy associated with covering the full configuration space of interlayer bonds. Possible consequences of polytype formation on magnetism in Gd₂PdSi₃ are discussed.

Low-Energy Excitations of Skyrmion Crystals in a Centrosymmetric Kondo-Lattice Magnet: Decoupled Spin-Charge Excitations and Nonreciprocity

We theoretically study spin and charge excitations of skyrmion crystals stabilized by conduction-electron-mediated magnetic interactions via spin-charge coupling in a centrosymmetric Kondo-lattice model by large-scale spin-dynamics simulations combined with the kernel polynomial method. We reveal clear segregation of spin and charge excitation channels and nonreciprocal nature of the spin excitations governed by the Fermi-surface geometry, which are unique to the skyrmion crystals in centrosymmetric itinerant hosts and can be a source of novel physical phenomena.

Fermi-Surface Origin of Skyrmion Lattices in Centrosymmetric Rare-Earth Intermetallics

We show from first principles that barrel-shaped structures within the Fermi surface of the centrosymmetric intermetallic compounds GdRu_{2}Si_{2} and Gd_{2}PdSi_{3} give rise to Fermi surface nesting, which determines the strength and sign of quasi-two-dimensional Ruderman-Kittel-Kasuya-Yosida pairwise exchange interactions between the Gd moments. This is the principal mechanism leading to their helical single-q spin-spiral ground states, providing transition temperatures and magnetic periods in good agreement with experiment. Using atomistic spin-dynamic simulations, we draw a direct line between the subtleties of the three-dimensional Fermi surface topology and the stabilization of a square skyrmion lattice in GdRu_{2}Si_{2} at applied magnetic fields as observed in experiment.

Magneto-optical spectroscopy on Weyl nodes for anomalous and topological Hall effects in chiral MnGe

Physics of Weyl electrons has been attracting considerable interests and further accelerated by recent discoveries of giant anomalous Hall effect (AHE) and topological Hall effect (THE) in several magnetic systems including non-coplanar magnets with spin chirality or small-size skyrmions. These AHEs/THEs are often attributed to the intense Berry curvature generated around the Weyl nodes accompanied by band anti-crossings, yet the direct experimental evidence still remains elusive. Here, we demonstrate an essential role of the band anti-crossing for the giant AHE and THE in MnGe thin film by using the terahertz magneto-optical spectroscopy. The low-energy resonance structures around ~ 1.2 meV in the optical Hall conductivity show the enhanced AHE and THE, indicating the emergence of at least two distinct anti-crossings near the Fermi level. The theoretical analysis demonstrates that the competition of these resonances with opposite signs is a cause of the strong temperature and magnetic-field dependences of observed DC Hall conductivity. These results lead to the comprehensive understanding of the interplay among the transport phenomena, optical responses and electronic/spin structures.

Previous work has proposed that the anomalous and topological Hall effects, associated with Weyl nodes, should have a signature in optical conductivity. Here, using THz optical spectroscopy, the authors assign these two effects to optical conductivity resonances, arising near band anti-crossings, in thin films of MnGe.

Topological spin crystals by itinerant frustration

Spin textures with nontrivial topology, such as vortices and skyrmions, have attracted attention as a source of unconventional magnetic, transport, and optical phenomena. Recently, a new generation of topological spin textures has been extensively studied in itinerant magnets; in contrast to the conventional ones induced, e.g., by the Dzyaloshinskii-Moriya interaction in noncentrosymmetric systems, they are characterized by extremely short magnetic periods and stable even in centrosymmetric systems. Here we review such new types of topological spin textures with particular emphasis on their stabilization mechanism. Focusing on the interplay between charge and spin degrees of freedom in itinerant electron systems, we show that itinerant frustration, which is the competition among electron-mediated interactions, plays a central role in stabilizing a variety of topological spin crystals including a skyrmion crystal with unconventional high skyrmion number, meron crystals, and hedgehog crystals. We also show that the essential ingredients in the itinerant frustration are represented by bilinear and biquadratic spin interactions in momentum space. This perspective not only provides a unified understanding of the unconventional topological spin crystals but also stimulates further exploration of exotic topological phenomena in itinerant magnets.

Large Hall and Nernst responses from thermally induced spin chirality in a spin-trimer ferromagnet

The long-range order of noncoplanar magnetic textures with scalar spin chirality (SSC) can couple to conduction electrons to produce an additional (termed geometrical or topological) Hall effect. One such example is the Hall effect in the skyrmion lattice state with quantized SSC. An alternative route to attain a finite SSC is via the spin canting caused by thermal fluctuations in the vicinity of the ferromagnetic ordering transition. Here, we report that for a highly conducting ferromagnet with a two-dimensional array of spin trimers, the thermally generated SSC can give rise to a gigantic geometrical Hall conductivity even larger than the intrinsic anomalous Hall conductivity of the ground state. We also demonstrate that the SSC induced by thermal fluctuations leads to a strong response in the Nernst effect. A comparison of the sign and magnitude of fluctuation-Nernst and Hall responses in fundamental units indicates the need for a momentum-space picture to model these thermally induced signals.

Unconventional Transverse Transport above and below the Magnetic Transition Temperature in Weyl Semimetal EuCd_{2}As_{2}

As exemplified by the growing interest in the quantum anomalous Hall effect, the research on topology as an organizing principle of quantum matter is greatly enriched from the interplay with magnetism. In this vein, we present a combined electrical and thermoelectrical transport study on the magnetic Weyl semimetal EuCd_{2}As_{2}. Unconventional contribution to the anomalous Hall and anomalous Nernst effects were observed both above and below the magnetic transition temperature of EuCd_{2}As_{2}, indicating the existence of significant Berry curvature. EuCd_{2}As_{2} represents a rare case in which this unconventional transverse transport emerges both above and below the magnetic transition temperature in the same material. The transport properties evolve with temperature and field in the antiferromagnetic phase in a different manner than in the paramagnetic phase, suggesting different mechanisms to their origin. Our results indicate EuCd_{2}As_{2} is a fertile playground for investigating the interplay between magnetism and topology, and potentially a plethora of topologically nontrivial phases rooted in this interplay.

Formation Mechanism of the Helical Q Structure in Gd-Based Skyrmion Materials

Using the ab initio local force method, we investigate the formation mechanism of the helical spin structure in GdRu_{2}Si_{2} and Gd_{2}PdSi_{3}. We calculate the paramagnetic spin susceptibility and find that the Fermi surface nesting is not the origin of the incommensurate modulation, in contrast to the naive scenario based on the Ruderman-Kittel-Kasuya-Yosida mechanism. We then decompose the exchange interactions between the Gd spins into each orbital component, and show that spin-density-wave type interaction between the Gd-5d orbitals is ferromagnetic, but the interaction between the Gd-4f orbitals is antiferromagnetic. We conclude that the competition of these two interactions, namely, the interorbital frustration, stabilizes the finite-Q structure.