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This study applies magnetic fields in selected in-plane directions to disentangle the mechanisms underlying the anomalous Hall effect in a representative noncollinear antiferromagnet.

Transition of superfluid to insulator is observed in the layer-imbalanced regime of bilayer magnetoexcitons.

Fractional Chern insulators have been observed in moiré MoTe₂ at zero magnetic field, but the expected zero longitudinal resistance has not been demonstrated. Now it is shown that improving device quality allows this effect to appear.

The authors achieve magnetic trapping at optical frequencies and uncover photonic Hall effect forces by engineering spatially isolated magnetic fields interacting with a single Si nanoparticle at its magnetic dipole resonance.

This study uses a customized metasurface to unveil a distinct parity Hall effect in degenerate optical vectorial modes. This work realizes the advances in meta-devices and showcases new possibilities for manipulating optical fields based on parity.

Examples of materials with non-trivial band topology in the presence of strong electron correlations are rare. Now it is shown that quantum fluctuations near a quantum phase transition can promote topological phases in a heavy-fermion compound.

Recent work has expanded the concept of altermagnets to non-collinear magnetic materials. Here, Hu et al extend this further to non-collinear chiral materials, determining altermagnetic multipolar order parameters and predicting that such materials host large spin-hall and Edelstein effects.

Room-temperature nonlinear Hall effect has been observed in wafer-scale (001)-oriented SnTe thin films, enabling wireless, ultrabroadband and low-power rectification at zero electrical bias and zero magnetic field.

The dynamics of hole-conjugated fractional quantum Hall states is poorly understood due to the limitations of current experimental probes. Here the authors study the high-frequency dynamics of edge modes at filling factor 2/3, precisely identifying the tunneling charge and damping of constituent charge modes.

The complex electronic motion in the quantum Hall regime in semiconductors has so far eluded analysis of its microscopic structure. Here, the authors use scanning gate microscopy to measure the spatial structure of transport inside a metal in this regime, opening the way for localized manipulation of the electronic states.

The realization of the anomalous Hall effect in high-mobility two dimensional electron systems has so far remained elusive. Here, the authors observe its emergence in MgZnO/ZnO heterostructures and attribute it to skew scattering of electrons by localized paramagnetic centres.

Anomalous Hall effect (AHE) in antiferromagnets is intriguing and requires further understanding. Here the authors report large AHE in a chiral-lattice antiferromagnet CoNb₃S₆ of which the origin can be due to complex magnetic texture or broken time-reversal symmetry on the electronic band structure.

The anomalous Hall effect is a macroscopic manifestation of a quantum mechanical effect. Here, Uelandet al. report the observation of a high Hall conductivity in the heavy-fermion compound UCu5, a metallic system, and explain its origin in terms of geometric frustration effects.

Three-dimensional topological insulators are materials that are nonmagnetic insulators in the bulk but exhibit metallic surface states. Yoshimi et al, now identify a signature of such two-dimensional states, the quantum Hall effect, in bismuth-based chalcogenide topological insulators.

Skyrmions, when driven by any applied force, experience an addition sideways motion known as the skyrmion hall effect. Here, Brearton et al. present a reciprocal space method for determining the strength of the skyrmion hall effect, making measurement possible for skyrmion lattices.

Edge current quantization in the integer quantum Hall effect is understood to arise due to noninteracting electrons circulating an incompressible insulating bulk. Here, the authors evidence compressible metal-like bulk behaviour in GaAs/AlGaAs Hall bars consistent with electronic interactions.

The transport properties of materials with topologically non-trivial band structures may be manipulated by an applied magnetic field or by magnetic doping. Here, the authors demonstrate quantum Hall states for temperatures up to 2 K in thin film bilayers comprising pristine and Cr-doped topological insulators.

Fermionic currents of opposing chirality can be spatially filtered without the need for a magnetic field using the quantum geometry of topological bands in single-crystal PdGa.

Future information storage technology may exploit electrical currents to write the states of ferromagnetic nanoelements via spin torque effects. Here, the authors demonstrate such behaviour promoted by exchange bias from an interfaced antiferromagnet, which may help overcome practical device limitations.

Transition metal dichalcogenides exhibit diverse and tunable electronic states. Here the authors reveal a cascade of phase transitions upon increasing hydrostatic pressure in the few-layer 1T’-WS₂, including a re-entrant superconducting phase emerging from a normal state exhibiting anomalous Hall effect.

Whilst superlattices containing thin films of 5d transition metal oxides are expected to yield strong interfacial coupling, only weak effects have been observed. Here, the authors report strong coupling between 3d SrMnO₃ and 5d SrIrO₃due to the interplay of strong Coulomb and spin orbit interactions.

A study of the high-field Hall coefficient in thallium- and bismuth-based single-layer cuprates demonstrates a smooth evolution of this quantity from p to 1 + p over a wide doping range.

Nonlinear Hall effect is a potential tool for exploring correlated phase transitions in topological semimetals. Here, the authors demonstrate an enhanced nonlinear Hall effect arising from a one-dimensional charge density wave in TaIrTe₄.

A technique that allows the electrical detection of spin-polarized transport in semiconductors without disturbing the spin-polarized current or using magnetic elements has now been demonstrated. The approach could lead to the integration of spintronics elements into semiconductor microelectronic circuits.

The temperature-dependent transverse elongation of ferrimagnetic bubbles provides experimental evidence for an evanescent skyrmion Hall effect at zero spin density.

Superlattices, with a length scale and structure that differs from the parent lattice of the host material, are well-known to allow for remarkable new electronic and magnetic properties. Here, Xie et al. synthesize Cr_1/4TaS₂, and find that it exhibits an unusual anomalous Hall effect below the Néel temperature even in stoichiometric high-quality crystals.

Electronic systems with inverted band structures can support exotic topological insulator and exciton condensate states. Here, the authors demonstrate the formation of a helical exciton condensate in quantum Hall bilayers, and a quark-like quasiparticle confinement-deconfinement transition.

Spin–orbit torques could enable a new generation of low-power electrically controlled memory devices. Here, the authors experimentally disentangle the spin-Hall effect and inverse spin-galvanic effect contributions to the relativistic spin torques in a room temperature Fe/(Ga,Mn)As bilayer.

Electron pairing is a rare phenomenon which can result in exotic behaviour such as superconductivity. Here, the authors evidence robust electron pairing in the quantum Hall edge states of a Fabry–Perot interferometer via Aharonov–Bohm conductance oscillations and quantum shot noise measurements.

Conduction in ferroelectric domain walls is now an established phenomenon, yet fundamental aspects of transport physics remain elusive. Here, Campbellet al. report the type, density and mobility of carriers in conducting domain walls in ytterbium manganite using nanoscale Hall effect measurements.

Metamaterials enable the control and manipulation of light on subwavelength scales, allowing numerous optical device applications. Here, the authors show the selective excitation of spatially confined modes in an anisotropic hyperbolic metamaterial, based on the photonic spin Hall effect.

Monolayer graphene can support the quantum Hall effect up to room temperature. Here, the authors provide evidence that graphene encapsulated in hexagonal boron nitride realizes a novel transport regime where dissipation in the quantum Hall phase is mediated predominantly by electron-phonon scattering rather than disorder scattering.

Fractional quantum Hall states can be fragile, meaning that they are difficult to probe using electrical transport measurements. Now, thermal transport is shown to be a more sensitive technique for investigating these states.

The fractional quantum Hall effect, occurring for rational Landau-level filling factors, is commonly observed in GaAs heterostructures. Now, unusual even-denominator fractional quantum Hall states are reported for an oxide 2D electron system.

This Review describes the concepts behind generalized quantum Hall effects that can take place without a magnetic field, and summarizes recent experimental manifestations of these phenomena in twisted two-dimensional materials and few-layer graphene.

The topological Hall effect is observed at above room temperature in a bilayer heterostructure composed of thulium iron garnet and platinum, suggesting the formation of skyrmions in a magnetic insulator through the interfacial Dzyaloshinskii–Moriya interaction.

Unidirectional spin-hall magnetoresistance is a change in the conductivity of ferromagnetic/heavy metal bilayers that is sensitive to the magnetisation of the ferromagnetic layer. This sensitivity makes it a potential candidate for magnetic state readout. Here, Salikhov et al demonstrate ultrafast unidirectional spin hall magnetoresistance driven by terahertz fields

The anomalous Hall effect has been observed in high-quality epitaxial thin films of non-collinear antiferromagnet Mn₃Pt, and can be switched on and off using an electric field.

The superconducting proximity effect has not been experimentally demonstrated in a quantum anomalous Hall insulator. Now this effect is observed in the chiral edge state of a ferromagnetic topological insulator.

A martensitic alloy with a tensile strength exceeding 3 GPa and a fracture elongation of 5.13% is developed. These mechanical properties arise from interface complexes interacting with dense dislocation networks, which is a mechanism shown to be applicable to other compositions.

Tilgner et al. demonstrated the formation of the quantum spin Hall insulator bismuthene on SiC, intercalated underneath a protective graphene layer. A hydrogen-induced orbital filtering effect is the driving force behind this reversible phase transition.

The PCRCR complex of Plasmodium spp. binds basigin on the erythrocyte surface. While Rh5 of the complex is restricted to P. falciparum, PTRAMP, CSS and Ripr orthologs are present across the genus, for which the authors report common features.

Non-local transport measurements on mercury telluride quantum wells show clear signatures of the ballistic spin Hall effect. The ballistic nature of the experiment allows the observed effect to be interpreted as a direct consequence of the band structure of these semiconductor nanostructures, rather that being caused by impurity scattering.

Strongly correlated and topological phases of matter can be often described using the tools of quantum field theory. Here the authors report the thermal Hall effect in the antiferromagnetic skyrmion lattice of MnSc₂S₄, revealing transport features that can be attributed to an emergent SU(3) gauge field.

Ohmic contacts to n-type molybdenum disulfide can be created over a temperature range from millikelvins to 300 K using a window-contacted technique, which leads to evidence for fractional quantum Hall states at filling fractions of 4/5 and 2/5 in the lowest Landau levels of bilayer molybdenum disulfide devices.

Graphene on boron nitride gives rise to a moiré superlattice displaying the Hofstadter butterfly: a fractal dependence of energy bands on external magnetic fields. Now, by means of capacitance spectroscopy, further aspects of this system are revealed—most notably, suppression of quantum Hall antiferromagnetism at particular commensurate magnetic fluxes.

Moiré patterns have been experimentally observed in heterostructures comprised of topological insulator films. Here, the authors propose that topological insulator-based moiré heterostructures could be a host of isolated topologically non-trivial moiré minibands for the study of the interplay between topology and correlation.