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High-temperature superconductivity in the iron-based materials emerges from, or sometimes coexists with, their metallic or insulating parent compound states. This is surprising, as these undoped states exhibit dramatically different antiferromagnetic spin arrangements and Néel temperatures. Although there is a general consensus that magnetic interactions are important for superconductivity, much remains unknown concerning the microscopic origin of the magnetic states. In this review, we summarize the progress in this area, focusing on recent experimental and theoretical results, and their microscopic implications. We conclude that the parent compounds are in a state that is more complex than that implied by a simple Fermi surface nesting scenario, and a dual description including both itinerant and localized degrees of freedom is needed to properly describe these fascinating materials. The magnetic states found in iron-based superconductors are more complex than originally thought. This Review argues that the magnetism arises from both itinerant and localized electrons.

Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe, detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (±1, 0) at low energies E = 6–11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies, 3–5 meV, indicating a gapped four-fold (C4) mode. In the superconducting state, however, the strong nematic anisotropy is again reflected in the spin resonance (E = 3.6 meV) at QAF with incommensurate scattering around 5–6 meV. Our results highlight the extreme electronic anisotropy of the nematic phase of FeSe and are consistent with a highly anisotropic superconducting gap driven by spin fluctuations.Extreme electronic anisotropy is revealed in the high-temperature superconductor FeSe through tour de force experiments on detwinned crystals.

A hallmark of strongly correlated quantum materials is the rich phase diagram resulting from competing and intertwined phases with nearly degenerate ground-state energies 1 , 2 . A well-known example is the copper oxides, in which a charge density wave (CDW) is ordered well above and strongly coupled to the magnetic order to form spin-charge-separated stripes that compete with superconductivity 1 , 2 . Recently, such rich phase diagrams have also been shown in correlated topological materials. In 2D kagome lattice metals consisting of corner-sharing triangles, the geometry of the lattice can produce flat bands with localized electrons 3 , 4 , non-trivial topology 5 – 7 , chiral magnetic order 8 , 9 , superconductivity and CDW order 10 – 15 . Although CDW has been found in weakly electron-correlated non-magnetic A V 3 Sb 5 ( A  = K, Rb, Cs) 10 – 15 , it has not yet been observed in correlated magnetic-ordered kagome lattice metals 4 , 16 – 21 . Here we report the discovery of CDW in the antiferromagnetic (AFM) ordered phase of kagome lattice FeGe (refs.  16 – 19 ). The CDW in FeGe occurs at wavevectors identical to that of A V 3 Sb 5 (refs.  10 – 15 ), enhances the AFM ordered moment and induces an emergent anomalous Hall effect 22 , 23 . Our findings suggest that CDW in FeGe arises from the combination of electron-correlations-driven AFM order and van Hove singularities (vHSs)-driven instability possibly associated with a chiral flux phase 24 – 28 , in stark contrast to strongly correlated copper oxides 1 , 2 and nickelates 29 – 31 , in which the CDW precedes or accompanies the magnetic order. Analysis of the antiferromagnetic ordered phase of kagome lattice FeGe suggests that charge density wave is the result of a combination of electronic-correlations-driven antiferromagnetic order and instability driven by van Hove singularities.

Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature T c (ref.  1 ). Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin S  = 0 (ref.  2 ), although they can also form parallel spin-triplet Cooper pairs with S  = 1 and an odd parity wavefunction 3 . Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation 4 , 5 . Because spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations 3 , uranium-based materials near an FM instability are considered to be ideal candidates for realizing spin-triplet superconductivity 6 . Indeed, UTe 2 , which has a T c  ≈ 1.6 K (refs.  7 , 8 ), has been identified as a candidate for a chiral spin-triplet topological superconductor near an FM instability 7 – 14 , although it also has antiferromagnetic (AF) spin fluctuations 15 , 16 . Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe 2 is coupled to a sharp magnetic excitation, termed resonance 17 – 23 , at the Brillouin zone boundary near AF order. Because the resonance has only been found in spin-singlet unconventional superconductors near an AF instability 17 – 23 , its observation in UTe 2 suggests that AF spin fluctuations may also induce spin-triplet pairing 24 or that electron pairing in UTe 2 has a spin-singlet component. Inelastic neutron scattering measurements show that superconductivity in UTe 2 is associated with a resonance near antiferromagnetic order that suggests an unexpected spin-singlet component to the electron pairing.

Understanding the microscopic origins of electronic phases in high-transition temperature (high-Tc) superconductors is important for elucidating the mechanism of superconductivity. In the paramagnetic tetragonal phase of BaFe2–xTxAs2 (where T is Co or Ni) iron pnictides, an in-plane resistivity anisotropy has been observed. Here, we use inelastic neutron scattering to show that low-energy spin excitations in these materials change from fourfold symmetric to twofold symmetric at temperatures corresponding to the onset of the in-plane resistivity anisotropy. Because resistivity and spin excitation anisotropies both vanish near optimal superconductivity, we conclude that they are likely intimately connected.

Unconventional superconductors often feature competing orders, small superfluid density, and nodal electronic pairing. While unusual superconductivity has been proposed in the kagome metals A V 3 Sb 5 , key spectroscopic evidence has remained elusive. Here we utilize pressure-tuned and ultra-low temperature muon spin spectroscopy to uncover the unconventional nature of superconductivity in RbV 3 Sb 5 and KV 3 Sb 5 . At ambient pressure, we observed time-reversal symmetry breaking charge order below T 1 * ≃ 110 K in RbV 3 Sb 5 with an additional transition at T 2 * ≃ 50 K. Remarkably, the superconducting state displays a nodal energy gap and a reduced superfluid density, which can be attributed to the competition with the charge order. Upon applying pressure, the charge-order transitions are suppressed, the superfluid density increases, and the superconducting state progressively evolves from nodal to nodeless. Once optimal superconductivity is achieved, we find a superconducting pairing state that is not only fully gapped, but also spontaneously breaks time-reversal symmetry. Our results point to unprecedented tunable nodal kagome superconductivity competing with time-reversal symmetry-breaking charge order and offer unique insights into the nature of the pairing state. The nature of the superconductivity in the kagome metals AV 3 Sb 5 (A = K, Rb, Cs) remains under debate. Here, using muon spin spectroscopy, the authors find that the superconductivity in RbV 3 Sb 5 and KV 3 Sb 5 evolves from nodal to nodeless with increasing pressure and the superconducting state breaks time-reversal symmetry after suppression of the charge order.

A quantum spin liquid is a state of matter where unpaired electrons’ spins, although entangled, do not show magnetic order even at the zero temperature. The realization of a quantum spin liquid is a long-sought goal in condensed-matter physics. Although neutron scattering experiments on the two-dimensional spin-1/2 kagome lattice ZnCu3(OD)6Cl2 and triangular lattice YbMgGaO4 have found evidence for the hallmark of a quantum spin liquid at very low temperature (a continuum of magnetic excitations), the presence of magnetic and non-magnetic site chemical disorder complicates the interpretation of the data. Recently, the three-dimensional Ce3+ pyrochlore lattice Ce2Sn2O7 has been suggested as a clean, effective spin-1/2 quantum spin liquid candidate, but evidence of a spin excitation continuum is still missing. Here, we use thermodynamic, muon spin relaxation and neutron scattering experiments on single crystals of Ce2Zr2O7, a compound isostructural to Ce2Sn2O7, to demonstrate the absence of magnetic ordering and the presence of a spin excitation continuum at 35 mK. With no evidence of oxygen deficiency and magnetic/non-magnetic ion disorder seen by neutron diffraction and diffuse scattering measurements, Ce2Zr2O7 may be a three-dimensional pyrochlore lattice quantum spin liquid material with minimum magnetic and non-magnetic chemical disorder.

To raise the superconducting-transition temperature (Tc) has been the driving force for the long-sustained effort in superconductivity research. Recent progress in hydrides with Tcs up to 287 K under pressure of 267 GPa has heralded a new era of room temperature superconductivity (RTS) with immense technological promise. Indeed, RTS will lift the temperature barrier for the ubiquitous application of superconductivity. Unfortunately, formidable pressure is required to attain such high Tcs. The most effective relief to this impasse is to remove the pressure needed while retaining the pressure-induced Tc without pressure. Here, we show such a possibility in the pure and doped high-temperature superconductor (HTS) FeSe by retaining, at ambient pressure via pressure quenching (PQ), its Tc up to 37 K (quadrupling that of a pristine FeSe at ambient) and other pressure-induced phases. We have also observed that some phases remain stable without pressure at up to 300 K and for at least 7 d. The observations are in qualitative agreement with our ab initio simulations using the solid-state nudged elastic band (SSNEB) method. We strongly believe that the PQ technique developed here can be adapted to the RTS hydrides and other materials of value with minimal effort.

Spin and lattice are two fundamental degrees of freedom in a solid, and their fluctuations about the equilibrium values in a magnetic ordered crystalline lattice form quasiparticles termed magnons (spin waves) and phonons (lattice waves), respectively. In most materials with strong spin-lattice coupling (SLC), the interaction of spin and lattice induces energy gaps in the spin wave dispersion at the nominal intersections of magnon and phonon modes. Here we use neutron scattering to show that in the two-dimensional (2D) van der Waals honeycomb lattice ferromagnetic CrGeTe 3 , spin waves propagating within the 2D plane exhibit an anomalous dispersion, damping, and breakdown of quasiparticle conservation, while magnons along the c axis behave as expected for a local moment ferromagnet. These results indicate the presence of dynamical SLC arising from the zero-temperature quantum fluctuations in CrGeTe 3 , suggesting that the observed in-plane spin waves are mixed spin and lattice quasiparticles fundamentally different from pure magnons and phonons. CrGeTe 3 is a van der Waals honeycomb ferromagnet, known for exhibiting strong coupling between lattice and spin degrees of freedom. Here, Chen et al perform neutron scattering on CrGeTe 3 , find a broadened spin-wave excitation resulting from zero-temperature motion of the atoms in the lattice.

The combination of a geometrically frustrated lattice, and similar energy scales between degrees of freedom endows two-dimensional Kagome metals with a rich array of quantum phases and renders them ideal for studying strong electron correlations and band topology. The Kagome metal, FeGe is a noted example of this, exhibiting A-type collinear antiferromagnetic (AFM) order at T N  ≈ 400 K, then establishes a charge density wave (CDW) phase coupled with AFM ordered moment below T CDW  ≈ 110 K, and finally forms a c -axis double cone AFM structure around T Canting  ≈ 60 K. Here we use neutron scattering to demonstrate the presence of gapless incommensurate spin excitations associated with the double cone AFM structure of FeGe at temperatures well above T Canting and T CDW that merge into gapped commensurate spin waves from the A-type AFM order. Commensurate spin waves follow the Bose factor and fit the Heisenberg Hamiltonian, while the incommensurate spin excitations, emerging below T N where AFM order is commensurate, start to deviate from the Bose factor around T CDW , and peaks at T Canting . This is consistent with a critical scattering of a second order magnetic phase transition with decreasing temperature. By comparing these results with density functional theory calculations, we conclude that the incommensurate magnetic structure arises from the nested Fermi surfaces of itinerant electrons and the formation of a spin density wave order. FeGe is a Kagome metal that exhibits a very rich array of magnetic and electronic phases. Here, using neutron scattering, Chen et al add to this zoo, by showing the emergence of a spin density wave order.