Non-coplanar helimagnetism in the layered van-der-Waals metal DyTe3.

Van-der-Waals magnetic materials can be exfoliated to realize ultrathin sheets or interfaces with highly controllable optical or spintronics responses. In majority, these are collinear ferro-, ferri-, or antiferromagnets, with a particular scarcity of lattice-incommensurate helimagnets of defined left- or right-handed rotation sense, or helicity. Here, we report polarized neutron scattering experiments on DyTe3, whose layered structure has highly metallic tellurium layers separated by double-slabs of dysprosium square nets. We reveal cycloidal (conical) magnetic textures, with coupled commensurate and incommensurate order parameters, and probe the evolution of this ground state in a magnetic field. The observations are well explained by a one-dimensional spin model, with an off-diagonal on-site term that is spatially modulated by DyTe3's unconventional charge density wave (CDW) order. The CDW-driven term couples to antiferromagnetism, or to the net magnetization in an applied magnetic field, and creates a complex magnetic phase diagram indicative of competing interactions in this easily cleavable van-der-Waals helimagnet.

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.

Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3.

The honeycomb magnet α-RuCl3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κxy of Majorana fermions is predicted to be half-quantized. Half-quantization of κxy/T (T, temperature) was recently reported, but this observation has proven difficult to reproduce. Here, we report detailed measurements of κxy on α-RuCl3 with the magnetic field B ∥ a (zigzag axis). In our experiment, κxy/T is observed to be strongly temperature dependent between 0.5 and 10 K. We show that its temperature profile matches the distinct form expected for topological bosonic modes in a Chern-insulator-like model. Our analysis yields magnon band energies in agreement with spectroscopic experiments. At high B, the spin excitations evolve into magnon-like modes with a Chern number of ~1. The bosonic character is incompatible with half-quantization of κxy/T.

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.

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.

Emergent electromagnetic induction in a helical-spin magnet.

An inductor, one of the most fundamental circuit elements in modern electronic devices, generates a voltage proportional to the time derivative of the input current1. Conventional inductors typically consist of a helical coil and induce a voltage as a counteraction to time-varying magnetic flux penetrating the coil, following Faraday's law of electromagnetic induction. The magnitude of this conventional inductance is proportional to the volume of the inductor's coil, which hinders the miniaturization of inductors2. Here, we demonstrate an inductance of quantum-mechanical origin3, generated by the emergent electric field induced by current-driven dynamics of spin helices in a magnet. In microscale rectangular magnetic devices with nanoscale spin helices, we observe a typical inductance as large as -400 nanohenry, comparable in magnitude to that of a commercial inductor, but in a volume about a million times smaller. The observed inductance is enhanced by nonlinearity in current and shows non-monotonous frequency dependence, both of which result from the current-driven dynamics of the spin-helix structures. The magnitude of the inductance rapidly increases with decreasing device cross-section, in contrast to conventional inductors. Our findings may pave the way to microscale, simple-shaped inductors based on emergent electromagnetism related to the quantum-mechanical Berry phase.

Topological Nernst Effect of the Two-Dimensional Skyrmion Lattice.

The topological Hall effect (THE) and its thermoelectric counterpart, the topological Nernst effect (TNE), are hallmarks of the skyrmion lattice phase (SkL). We observed the giant TNE of the SkL in centrosymmetric Gd_{2}PdSi_{3}, comparable in magnitude to the largest anomalous Nernst signals in ferromagnets. Significant enhancement (suppression) of the THE occurs when doping electrons (holes) to Gd_{2}PdSi_{3}. On the electron-doped side, the topological Hall conductivity approaches the characteristic threshold ∼1000 (Ω cm)^{-1} for the intrinsic regime. We use the filling-controlled samples to confirm Mott's relation between TNE and THE and discuss the importance of Gd-5d orbitals for transport in this compound.

Publisher's Note: Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys [Phys. Rev. Lett. 117, 236401 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.236401.

Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet.

Magnetic skyrmions are topologically stable spin swirls with a particle-like character and are potentially suitable for the design of high-density information bits. Although most known skyrmion systems arise in non-centrosymmetric systems with a Dzyaloshinskii-Moriya interaction, centrosymmetric magnets with a triangular lattice can also give rise to skyrmion formation, with a geometrically frustrated lattice being considered essential in this case. Until now, it remains an open question if skyrmions can also exist in the absence of both geometrically frustrated lattice and inversion symmetry breaking. Here we discover a square skyrmion lattice state with 1.9 nm diameter skyrmions in the centrosymmetric tetragonal magnet GdRu2Si2 without a geometrically frustrated lattice by means of resonant X-ray scattering and Lorentz transmission electron microscopy experiments. A plausible origin of the observed skyrmion formation is four-spin interactions mediated by itinerant electrons in the presence of easy-axis anisotropy. Our results suggest that rare-earth intermetallics with highly symmetric crystal lattices may ubiquitously host nanometric skyrmions of exotic origins.

Skyrmion phase and competing magnetic orders on a breathing kagomé lattice.

Magnetic skyrmion textures are realized mainly in non-centrosymmetric, e.g. chiral or polar, magnets. Extending the field to centrosymmetric bulk materials is a rewarding challenge, where the released helicity/vorticity degree of freedom and higher skyrmion density result in intriguing new properties and enhanced functionality. We report here on the experimental observation of a skyrmion lattice (SkL) phase with large topological Hall effect and an incommensurate helical pitch as small as 2.8 nm in metallic Gd3Ru4Al12, which materializes a breathing kagomé lattice of Gadolinium moments. The magnetic structure of several ordered phases, including the SkL, is determined by resonant x-ray diffraction as well as small angle neutron scattering. The SkL and helical phases are also observed directly using Lorentz-transmission electron microscopy. Among several competing phases, the SkL is promoted over a low-temperature transverse conical state by thermal fluctuations in an intermediate range of magnetic fields.

Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet.

Geometrically frustrated magnets can host complex spin textures, leading to unconventional electromagnetic responses. Magnetic frustration may also promote topologically nontrivial spin states such as magnetic skyrmions. Experimentally, however, skyrmions have largely been observed in noncentrosymmetric lattice structures or interfacial symmetry-breaking heterostructures. Here, we report the emergence of a Bloch-type skyrmion state in the frustrated centrosymmetric triangular-lattice magnet Gd2PdSi3 We observed a giant topological Hall response, indicating a field-induced skyrmion phase, which is further corroborated by the observation of in-plane spin modulation probed by resonant x-ray scattering. Our results may lead to further discoveries of emergent electrodynamics in magnetically frustrated centrosymmetric materials.

A gap-protected zero-Hall effect state in the quantum limit of the non-symmorphic metal KHgSb.

A recurring theme in topological matter is the protection of unusual electronic states by symmetry, for example, protection of the surface states in Z2 topological insulators by time-reversal symmetry1-3. Recently, interest has turned to unusual surface states in the large class of non-symmorphic materials4-12. In particular, KHgSb is predicted to exhibit double quantum spin Hall states10. Here we report measurements of the Hall conductivity in KHgSb in a strong magnetic field B. In the quantum limit, the Hall conductivity is observed to fall exponentially to zero, but the diagonal conductivity is finite. A large gap protects this unusual zero-Hall state. We theoretically propose that, in this quantum limit, the chemical potential drops into the bulk gap, intersecting equal numbers of right- and left-moving quantum spin Hall surface modes to produce the zero-Hall state. The zero-Hall state illustrates how topological protection in a non-symmorphic material with glide symmetry may lead to highly unusual transport phenomena.

Crystal growth and stoichiometry-dependent properties of the ferromagnetic Weyl semimetal ZrCo2-x Sn.

We report the growth of high quality bulk crystals, through crystallization from molten Sn flux, of the predicted ferromagnetic Weyl metal ZrCo2-x Sn with the L21 Heusler phase structure. The concentration of Co vacancies in the single crystals is found to be dependent on the initial concentration of Co in the flux. The saturation magnetization increases approximately linearly with decreasing Co deficiency and the ferromagnetic transition temperature changes significantly. p-type carrier conduction and an anomalous Hall effect are observed. The calculated electronic density of states of ZrCo2-x Sn shows a significant change in minority and majority spin state occupancies and a shift in the Fermi level with Co deficiency.

Anomalous Nernst Effect in the Dirac Semimetal Cd_{3}As_{2}.

Dirac and Weyl semimetals display a host of novel properties. In Cd_{3}As_{2}, the Dirac nodes lead to a protection mechanism that strongly suppresses backscattering in a zero magnetic field, resulting in ultrahigh mobility (∼10^{7} cm^{2} V^{-1} s^{-1}). In an applied magnetic field, an anomalous Nernst effect is predicted to arise from the Berry curvature associated with the Weyl nodes. We report the observation of a large anomalous Nernst effect in Cd_{3}As_{2}. Both the anomalous Nernst signal and transport relaxation time τ_{tr} begin to increase rapidly at ∼50 K. This suggests a close relation between the protection mechanism and the anomalous Nernst effect. In a field, the quantum oscillations of bulk states display a beating effect, suggesting that the Dirac nodes split into Weyl states, allowing the Berry curvature to be observed as an anomalous Nernst effect.

Time-Reversal-Breaking Weyl Fermions in Magnetic Heusler Alloys.

Weyl fermions have recently been observed in several time-reversal-invariant semimetals and photonics materials with broken inversion symmetry. These systems are expected to have exotic transport properties such as the chiral anomaly. However, most discovered Weyl materials possess a substantial number of Weyl nodes close to the Fermi level that give rise to complicated transport properties. Here we predict, for the first time, a new family of Weyl systems defined by broken time-reversal symmetry, namely, Co-based magnetic Heusler materials XCo_{2}Z (X=IVB or VB; Z=IVA or IIIA). To search for Weyl fermions in the centrosymmetric magnetic systems, we recall an easy and practical inversion invariant, which has been calculated to be -1, guaranteeing the existence of an odd number of pairs of Weyl fermions. These materials exhibit, when alloyed, only two Weyl nodes at the Fermi level-the minimum number possible in a condensed matter system. The Weyl nodes are protected by the rotational symmetry along the magnetic axis and separated by a large distance (of order 2π) in the Brillouin zone. The corresponding Fermi arcs have been calculated as well. This discovery provides a realistic and promising platform for manipulating and studying the magnetic Weyl physics in experiments.

Magnetic phase diagram of underdoped YBa2Cu3O y inferred from torque magnetization and thermal conductivity.

Strong evidence for charge-density correlation in the underdoped phase of the cuprate YBa2Cu3O y was obtained by NMR and resonant X-ray scattering. The fluctuations were found to be enhanced in strong magnetic fields. Recently, 3D charge-density-wave (CDW) formation with long-range order (LRO) was observed by X-ray diffraction in [Formula: see text] 15 T. To elucidate how the CDW transition impacts the pair condensate, we have used torque magnetization to 45 T and thermal conductivity [Formula: see text] to construct the magnetic phase diagram in untwinned crystals with hole density p = 0.11. We show that the 3D CDW transitions appear as sharp features in the susceptibility and [Formula: see text] at the fields [Formula: see text] and [Formula: see text], which define phase boundaries in agreement with spectroscopic techniques. From measurements of the melting field [Formula: see text] of the vortex solid, we obtain evidence for two vortex solid states below 8 K. At 0.5 K, the pair condensate appears to adjust to the 3D CDW by a sharp transition at 24 T between two vortex solids with very different shear moduli. At even higher H (41 T), the second vortex solid melts to a vortex liquid which survives to fields well above 41 T. de Haas-van Alphen oscillations appear at fields 24-28 T, below the lower bound for the upper critical field [Formula: see text].

The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi.

The Dirac and Weyl semimetals are unusual materials in which the nodes of the bulk states are protected against gap formation by crystalline symmetry. The chiral anomaly, predicted to occur in both systems, was recently observed as a negative longitudinal magnetoresistance (LMR) in Na3Bi (ref. ) and in TaAs (ref. ). An important issue is whether Weyl physics appears in a broader class of materials. We report evidence for the chiral anomaly in the half-Heusler GdPtBi. In zero field, GdPtBi is a zero-gap semiconductor with quadratic bands. In a magnetic field, the Zeeman energy leads to Weyl nodes. We have observed a large negative LMR with the field-steering properties specific to the chiral anomaly. The chiral anomaly also induces strong suppression of the thermopower. We report a detailed study of the thermoelectric response function αxx of Weyl fermions. The scheme of creating Weyl nodes from quadratic bands suggests that the chiral anomaly may be observable in a broad class of semimetals.