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In ferromagnets, an electric current generally induces a transverse Hall voltage in proportion to the internal magnetization. This effect is frequently used for the electrical readout of the spin-↑ and spin-↓ states. Although these properties are usually not expected in antiferromagnets, recent theoretical studies predicted that a non-coplanar antiferromagnetic order with finite scalar spin chirality—meaning a solid angle spanned by neighbouring spins—can induce a large spontaneous Hall effect even without a net magnetization or external magnetic field. This phenomenon—the spontaneous topological Hall effect—can potentially be used for the efficient electrical readout of antiferromagnetic states, but it has not been experimentally verified due to a lack of appropriate materials hosting such magnetism. Here we report the discovery of an all-in–all-out-type non-coplanar antiferromagnetic order in triangular lattice compounds CoTa3S6 and CoNb3S6. These compounds are reported to host unconventionally large spontaneous Hall effects despite their vanishingly small net magnetization, and our analysis reveals that it can be explained in terms of the topological Hall effect that originates from the fictitious magnetic field associated with scalar spin chirality. These results indicate that the scalar spin chirality mechanism offers a promising route to the realization of a giant spontaneous Hall response even in compensated antiferromagnets, and highlight intercalated van der Waals magnets as a promising quasi-two-dimensional material platform to enable various non-trivial ways of electrical reading and the possible writing of non-coplanar antiferromagnetic domains.The spontaneous topological Hall effect, combining non-coplanar antiferromagnetic order with finite scalar spin chirality in the absence of a magnetic field, is now experimentally demonstrated for the triangular lattice compounds CoTa3S6 and CoNb3S6.

A quantum-liquid state of spin–orbital-entangled magnetic moments is observed in the 5 d -electron honeycomb iridate H 3 LiIr 2 O 6 , evidenced by the absence of magnetic ordering down to 0.05 kelvin. Honeycomb hosts quantum spin liquid When materials with interacting spins are cooled, magnetic states with long-range ordering usually emerge. However, quantum effects have been predicted to prevent long-range ordering all the way down to temperatures close to absolute zero in materials known as quantum spin liquids, where the term 'liquid' refers to the disordered state of the spins. The realization of such a state in a material with a honeycomb lattice, such as graphene, is expected to also reveal topological excitations. Hidenori Takagi and colleagues demonstrate a quantum-spin-liquid state in the 5 d honeycomb iridate H 3 LiIrO 6 , which shows no magnetic ordering down to 0.05 kelvin. Signatures of unusual excitations suggest that this material is a topological quantum-spin-liquid candidate. The honeycomb lattice is one of the simplest lattice structures. Electrons and spins on this simple lattice, however, often form exotic phases with non-trivial excitations. Massless Dirac fermions can emerge out of itinerant electrons, as demonstrated experimentally in graphene 1 , and a topological quantum spin liquid with exotic quasiparticles can be realized in spin-1/2 magnets, as proposed theoretically in the Kitaev model 2 . The quantum spin liquid is a long-sought exotic state of matter, in which interacting spins remain quantum-disordered without spontaneous symmetry breaking 3 . The Kitaev model describes one example of a quantum spin liquid, and can be solved exactly by introducing two types of Majorana fermion 2 . Realizing a Kitaev model in the laboratory, however, remains a challenge in materials science. Mott insulators with a honeycomb lattice of spin–orbital-entangled pseudospin-1/2 moments have been proposed 4 , including the 5 d -electron systems α-Na 2 IrO 3 (ref. 5 ) and α-Li 2 IrO 3 (ref. 6 ) and the 4 d -electron system α-RuCl 3 (ref. 7 ). However, these candidates were found to magnetically order rather than form a liquid at sufficiently low temperatures 8 , 9 , 10 , owing to non-Kitaev interactions 6 , 11 , 12 , 13 . Here we report a quantum-liquid state of pseudospin-1/2 moments in the 5 d -electron honeycomb compound H 3 LiIr 2 O 6 . This iridate does not display magnetic ordering down to 0.05 kelvin, despite an interaction energy of about 100 kelvin. We observe signatures of low-energy fermionic excitations that originate from a small number of spin defects in the nuclear-magnetic-resonance relaxation and the specific heat. We therefore conclude that H 3 LiIr 2 O 6 is a quantum spin liquid. This result opens the door to finding exotic quasiparticles in a strongly spin–orbit-coupled 5 d -electron transition-metal oxide.

A key feature of quantum spin liquids is the predicted formation of fractionalized excitations. They are expected to produce changes in the physical response, providing a way to observe the quantum spin liquid state 1 . In the honeycomb magnet α-RuCl 3 , a quantum spin liquid has been proposed to explain the behaviour observed on applying an in-plane magnetic field H || . Previous work reported that the thermal Hall conductivity took on a half-integer quantized value and suggested this as a signature of a fractionalized Majorana edge mode predicted to exist in Kitaev quantum spin liquids 2 . However, the temperature and magnetic-field range of the half-quantized signal 2 – 4 and its association with Majorana edge modes are still under debate 5 , 6 . Here we present a comprehensive study of the thermal Hall conductivity in α-RuCl 3 showing that approximately half-integer quantization exists in an extended region of the phase diagram, particularly across a plateau-like parameter regime for H || exceeding 10 T and temperature below 6.5 K. At lower fields, the thermal Hall conductivity exhibits correlations with complex anomalies in the longitudinal thermal conductivity and magnetization, and is suppressed by cooling to low temperatures. Our results can be explained by the existence of a topological state in magnetic fields above 10 T. Earlier measurements of quantized heat transport in the spin liquid candidate α-RuCl 3 agreed with the predictions of Majorana edge modes. Support for this interpretation now comes from the observations of quantization across a large parameter range.

The excitonic insulator is a long conjectured correlated electron phase of narrow-gap semiconductors and semimetals, driven by weakly screened electron–hole interactions. Having been proposed more than 50 years ago, conclusive experimental evidence for its existence remains elusive. Ta 2 NiSe 5 is a narrow-gap semiconductor with a small one-electron bandgap E G of <50 meV. Below T C =326 K, a putative excitonic insulator is stabilized. Here we report an optical excitation gap E op ∼0.16 eV below T C comparable to the estimated exciton binding energy E B . Specific heat measurements show the entropy associated with the transition being consistent with a primarily electronic origin. To further explore this physics, we map the T C – E G phase diagram tuning E G via chemical and physical pressure. The dome-like behaviour around E G ∼0 combined with our transport, thermodynamic and optical results are fully consistent with an excitonic insulator phase in Ta 2 NiSe 5 . The nature of an insulating phase in Ta 2 NiSe 5 is an open question. Here, Lu et al . report transport, thermodynamic and optical evidences being fully consistent with an excitonic insulator phase in this material.

The superconducting state is characterized by a pairing of electrons with a superconducting gap on the Fermi surface. In iron-based superconductors, an unconventional pairing state has been argued for theoretically. We used scanning tunneling microscopy on Fe(Se,Te) single crystals to image the quasi-particle scattering interference patterns in the superconducting state. By applying a magnetic field to break the time-reversal symmetry, the relative sign of the superconducting gap can be determined from the magnetic-field dependence of quasi-particle scattering amplitudes. Our results indicate that the sign is reversed between the hole and the electron Fermi-surface pockets (s±-wave), favoring the unconventional pairing mechanism associated with spin fluctuations.

Measurement of the quantum-mechanical phase in quantum matter provides the most direct manifestation of the underlying abstract physics. We used resonant x-ray scattering to probe the relative phases of constituent atomic orbitals in an electronic wave function, which uncovers the unconventional Mott insulating state induced by relativistic spin-orbit coupling in the layered 5d transition metal oxide Sr2IrO4. A selection rule based on intra-atomic interference effects establishes a complex spin-orbital state represented by an effective total angular momentum = 1/2 quantum number, the phase of which can lead to a quantum topological state of matter.

The presence of both inversion ( P ) and time-reversal ( T ) symmetries in solids leads to a double degeneracy of the electronic bands (Kramers degeneracy). By lifting the degeneracy, spin textures manifest themselves in momentum space, as in topological insulators or in strong Rashba materials. The existence of spin textures with Kramers degeneracy, however, is difficult to observe directly. Here, we use quantum interference measurements to provide evidence for the existence of hidden entanglement between spin and momentum in the antiperovskite-type Dirac material Sr 3 SnO. We find robust weak antilocalization (WAL) independent of the position of E F . The observed WAL is fitted using a single interference channel at low doping, which implies that the different Dirac valleys are mixed by disorder. Notably, this mixing does not suppress WAL, suggesting contrasting interference physics compared to graphene. We identify scattering among axially spin-momentum locked states as a key process that leads to a spin-orbital entanglement. The spin texture in presence of both inversion and time-reversal symmetries has been difficult to observe. Here, Nakamura et al. report evidence of hidden entanglement between spin and momentum in antiperovskite Dirac material Sr 3 SnO.

The nature of the pseudogap phase of cuprates remains a major puzzle 1 , 2 . One of its signatures is a large negative thermal Hall conductivity 3 , whose origin is as yet unknown. This is observed even in the undoped Mott insulator La 2 CuO 4 , in which the charge carriers are localized and therefore cannot be responsible. Here, we show that the thermal Hall conductivity of La 2 CuO 4 is roughly isotropic; that is, for heat transport parallel and normal to the CuO 2 planes, it is nearly the same. This shows that the Hall response must come from phonons, as they are the only heat carriers that are able to move with the same ease both normal and parallel to the planes 4 . For doping levels higher than the critical doping level at which the pseudogap phase ends, both La 1.6 −x Nd 0.4 Sr x CuO 4 and La 1.8 −x Eu 0.2 Sr x CuO 4 show no thermal Hall signal for a heat current normal to the planes, which establishes that phonons have zero Hall response outside the pseudogap phase. Inside the pseudogap phase, the phonons must become chiral to generate the Hall response, but the mechanism by which this happens remains to be identified. It must be intrinsic (from a coupling of phonons to their electronic environment) rather than extrinsic (from structural defects or impurities), as these are the same on both sides of critical doping. Thermal transport measurements show that there is a thermal Hall effect in the out-of-plane direction in two cuprates in the pseudogap regime. This indicates that phonons are carrying the heat and that they have a handedness of unknown origin.

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p* —at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram 1 . However, the fundamental nature of p * remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range 2 that includes p* . As a function of doping, we find that C el / T is strongly peaked at p*  (where C el is the electronic contribution to C ) and exhibits a log(1/ T ) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point 3 – 5 , as observed in heavy-fermion 6 and iron-based 7 superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d -wave pairing and the anomalous scattering of charge carriers. Measurements of the specific heat of two cuprate materials at low temperature in magnetic fields large enough to suppress superconductivity and over a wide doping range reveal that the pseudogap phase of cuprates ends at a quantum critical point.

The nature of the pseudogap phase of the copper oxides (‘cuprates’) remains a puzzle. Although there are indications that this phase breaks various symmetries, there is no consensus on its fundamental nature 1 . Fermi-surface, transport and thermodynamic signatures of the pseudogap phase are reminiscent of a transition into a phase with antiferromagnetic order, but evidence for an associated long-range magnetic order is still lacking 2 . Here we report measurements of the thermal Hall conductivity (in the x – y plane, κ xy ) in the normal state of four different cuprates—La 1.6− x Nd 0.4 Sr x CuO 4 , La 1.8− x Eu 0.2 Sr x CuO 4 , La 2− x Sr x CuO 4 and Bi 2 Sr 2− x La x CuO 6+ δ . We show that a large negative κ xy signal is a property of the pseudogap phase, appearing at its critical hole doping, p *. It is also a property of the Mott insulator at p  ≈ 0, where κ xy has the largest reported magnitude of any insulator so far 3 . Because this negative κ xy signal grows as the system becomes increasingly insulating electrically, it cannot be attributed to conventional mobile charge carriers. Nor is it due to magnons, because it exists in the absence of magnetic order. Our observation is reminiscent of the thermal Hall conductivity of insulators with spin-liquid states 4 – 6 , pointing to neutral excitations with spin chirality 7 in the pseudogap phase of cuprates. The so-called pseudogap phase in hole-doped cuprate superconductors is associated with an unusually large thermal Hall effect that attains unprecedented levels as the parent Mott insulator is approached.