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The coupling of conduction electrons and magnetic textures leads to quantum transport phenomena described by the language of emergent electromagnetic fields1–3. For magnetic skyrmions, spin-swirling particle-like objects, an emergent magnetic field is produced by their topological winding4–6, resulting in the conduction electrons exhibiting the topological Hall effect (THE)7. When the skyrmion lattice (SkL) acquires a drift velocity under conduction electron flow, an emergent electric field is also generated8,9. The resulting emergent electrodynamics dictate the magnitude of the THE by the relative motion of SkL and conduction electrons. Here we report the emergent electrodynamics induced by SkL motion in Gd2PdSi3, facilitated by its giant THE10,11. With increasing current excitation, we observe the dynamic transition of the SkL motion from the pinned to creep regime and finally to the flow regime, in which the THE is totally suppressed. We argue that the Galilean relativity required for the total cancellation of the THE may be generically recovered in the flow regime, even in complex multiband systems such as the present compound. Moreover, the observed THE voltages are large enough to enable real-time measurement of the SkL velocity–current profile, which shows the inertial-like motion of the SkL in the creep regime, appearing as the current hysteresis of the skyrmion velocity.

The honeycomb magnet α-RuCl3has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κxyof 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 κxyon α-RuCl3with the magnetic field B ∥ a (zigzag axis). In our experiment, κxy/Tis 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.

Configurational entropy can impact crystallization processes, tipping the scales between structures of nearly equal internal energy. Using alloyed single crystals of Gd2PdSi3in 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 Gd2PdSi3are discussed.

In the class of materials called spin liquids1–3, a magnetically ordered state cannot be attained even at millikelvin temperatures because of conflicting constraints on each spin; for example, from geometric or exchange frustration. The resulting quantum spin-liquid state is currently of intense interest because it exhibits unusual excitations as well as wave-function entanglement. The layered insulator α-RuCl3orders as a zigzag antiferromagnet at low temperature in zero magnetic field4. The zigzag order is destroyed when a magnetic field is applied parallel to the zigzag axis. At moderate magnetic field strength, there is growing evidence that a quantum spin-liquid state exists. Here we report the observation of oscillations in its thermal conductivity in that field range. The oscillations, whose amplitude is very large within this field range and strongly suppressed on either side, are periodic. This is analogous to quantum oscillations in metals, even though α-RuCl3is an excellent insulator with a large gap. As the temperature is raised above 0.5 K, the oscillation amplitude decreases exponentially, anticorrelating with the emergence of an anomalous planar thermal Hall conductivity above approximately 2 K.

The antiferromagnetic material haematite, named for its blood-red colour, hosts swirling spin vortices termed merons. The rotation sense of such antiferromagnetic vortices has now been imaged in real space.

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.

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 GdRu2Si2without 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.

A recurring theme in topological matter is the protection of unusual electronic states by symmetry, for example, protection of the surface states in Z2topological 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.

Quantum critical points (QCPs) emerge when a second-order phase transition is suppressed to zero temperature. In metals the quantum fluctuations at such a QCP can give rise to new phases, including unconventional superconductivity. Whereas antiferromagnetic QCPs have been studied in considerable detail, ferromagnetic (FM) QCPs are much harder to access. In almost all metals FM QCPs are avoided through either a change to first-order transitions or through an intervening spin-density-wave (SDW) phase. Here, we study the prototype of the second case, NbFe2. We demonstrate that the phase diagram can be modelled using a two-order-parameter theory in which the putative FM QCP is buried within a SDW phase. We establish the presence of quantum tricritical points (QTCPs) at which both the uniform and finite wavevector susceptibility diverge. The universal nature of our model suggests that such QTCPs arise naturally from the interplay between SDW and FM order and exist generically near a buried FM QCP of this type. Our results promote NbFe2as the first example of a QTCP, which has been proposed as a key concept in a range of narrow-band metals, including the prominent heavy-fermion compound YbRh2Si2.

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 αxxof 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.

The polar magnetic semimetal NdAlSi hosts Weyl fermions that promote helical magnetism, and defines a roadmap for future work on correlated topological matter.