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Quantum critical points (QCPs), zero-temperature phase transitions, are windows to fundamental quantum-mechanical phenomena associated with universal behaviour. Magnetic QCPs have been extensively investigated in the vicinity of antiferromagnetic order. However, QCPs are rare in metallic ferromagnets due to the coupling of the order parameter to electronic soft modes. Recently, antisymmetric spin-orbit coupling in noncentrosymmetric systems was suggested to protect ferromagnetic QCPs. Nonetheless, multiple centrosymmetric materials host FM QCPs, suggesting a more general mechanism behind their protection. In this context, CeSi 2- δ , a dense Kondo lattice crystallising in a centrosymmetric structure, exhibits ferromagnetic order when Si is replaced with Ag. We report that the Ag-substitution to CeSi 1.97 linearly suppresses the ferromagnetic order towards a QCP, accompanied by concurrent strange-metal behaviour. Herein, we suggest that, despite the centrosymmetric structure, spin-orbit coupling arising from the local noncentrosymmetric structure, in combination with nonsymmorphic symmetry, can protect ferromagnetic QCPs. Our findings offer a general guideline for discovering new ferromagnetic QCPs and highlight one new family of materials within which the interplay of topology and quantum phase transitions can be investigated in the context of strongly correlated systems. Quantum critical points in metallic ferromagnets are rare and their mechanism is poorly understood. Here the authors report a ferromagnetic quantum phase transition in the dense ferromagnet CeSi 2 with Ag-substitution and propose a general mechanism rooted in nonsymmorphicity in locally noncentrosymmetric systems.

When an order parameter has multiple components, fluctuations can suppress the ordering partially, leaving behind vestigial order. Here the authors show that nematic superconductivity in electron-doped Bi2Se3 gives way to a vestigial nematic phase driven by fluctuating Cooper pairs.

A state of matter with a multi-component order parameter can give rise to vestigial order. In the vestigial phase, the primary order is only partially melted, leaving a remaining symmetry breaking behind, an effect driven by strong classical or quantum fluctuations. Vestigial states due to primary spin and charge-density-wave order have been discussed in iron-based and cuprate materials. Here we present the observation of a partially melted superconductivity in which pairing fluctuations condense at a separate phase transition and form a nematic state with broken Z 3 , i.e., three-state Potts-model symmetry. Thermal expansion, specific heat and magnetization measurements of the doped topological insulators Nb x Bi 2 Se 3 and Cu x Bi 2 Se 3 reveal that this symmetry breaking occurs at T nem ≃ 3.8 K above T c ≃ 3.25 K , along with an onset of superconducting fluctuations. Thus, before Cooper pairs establish long-range coherence at T c , they fluctuate in a way that breaks the rotational invariance at T nem and induces a crystalline distortion. When an order parameter has multiple components, fluctuations can suppress the ordering partially, leaving behind vestigial order. Here the authors show that nematic superconductivity in electron-doped Bi 2 Se 3 gives way to a vestigial nematic phase driven by fluctuating Cooper pairs.

Charge density wave (CDW) orders in vanadium-based kagome metals have recently received tremendous attention, yet their origin remains a topic of debate. The discovery of ScV 6 Sn 6 , a bilayer kagome metal featuring an intriguing 3 × 3 × 3 CDW order, offers a novel platform to explore the underlying mechanism behind the unconventional CDW. Here, we combine high-resolution angle-resolved photoemission spectroscopy, Raman scattering and density functional theory to investigate the electronic structure and phonon modes of ScV 6 Sn 6 . We identify topologically nontrivial surface states and multiple van Hove singularities (VHSs) in the vicinity of the Fermi level, with one VHS aligning with the in-plane component of the CDW vector near the K ¯ point. Additionally, Raman measurements indicate a strong electron-phonon coupling, as evidenced by a two-phonon mode and new emergent modes. Our findings highlight the fundamental role of lattice degrees of freedom in promoting the CDW in ScV 6 Sn 6 . The mechanism of charge density wave order in V-based kagome metals has been debated. Here the authors use a range of experimental techniques combined with ab initio calculations to study the electronic structure and phonon modes of ScV 6 Sn 6 , revealing the dominant role of strong electron-phonon coupling.

Motivated by the recent discovery of superconductivity in infinite-layer nickelate thin films, we report on a synthesis and magnetization study on bulk samples of the parent compounds RNiO2 (R = La, Pr, Nd). The frequency-dependent peaks of the alternating current magnetic susceptibility, along with remarkable memory effects, characterize spin-glass states. Furthermore, various phenomenological parameters via different spin glass models show strong similarity within these three compounds as well as with other rare-earth metal nickelates. The universal spin-glass behaviour distinguishes the nickelates from the parent compound CaCuO2 of cuprate superconductors, which has the same crystal structure and d9 electronic configuration but undergoes a long-range antiferromagnetic order. Our investigations may indicate a distinctly different nature of magnetism and superconductivity in the bulk nickelates than in the cuprates.

Magnetic skyrmions, topological vortex-like spin textures, garner significant interest due to their unique properties and potential applications in nanotechnology. While they typically form a hexagonal crystal with distinct internal magnetisation textures known as Bloch- or Néel-type, recent theories suggest the possibility for direct transitions between skyrmion crystals of different lattice structures and internal textures. To date however, experimental evidence for these potentially useful phenomena have remained scarce. Here, we discover the polar tetragonal magnet EuNiGe 3 to host two hybrid skyrmion phases, each with distinct internal textures characterised by anisotropic combinations of Bloch- and Néel-type windings. Variation of the magnetic field drives a direct transition between the two phases, with the modification of the hybrid texture concomitant with a hexagonal-to-square skyrmion crystal transformation. We explain these observations with a theory that includes the key ingredients of momentum-resolved Ruderman–Kittel–Kasuya–Yosida and Dzyaloshinskii-Moriya interactions that compete at the observed low symmetry magnetic skyrmion crystal wavevectors. Our findings underscore the potential of polar magnets with rich interaction schemes as promising for discovering new topological magnetic phases. Magnetic skyrmions typically form hexagonal crystals with either uniquely Bloch or Néel-type textures. Here, a polar magnet EuNiGe 3 is shown to host two skyrmion crystal phases with hexagonal and square structures, and hybrid Bloch-Néel textures.

SignificanceUnderstanding the relationship between entangled degrees of freedom (DOF) is a central problem in correlated materials and the possibility to influence their balance is promising toward realizing novel functionalities. In Sr2IrO4, the interaction between spin–orbit coupling and electron correlations induces an exotic ground state with magnetotransport properties promising for antiferromagnetic spintronics applications. Moreover, the coupling between orbital and spin DOF renders the magnetic structure sensitive to the Ir–O bond environment. To date, a detailed understanding of the microscopic spin-lattice and electron–phonon interactions is still lacking. Here, we use strain engineering to perturb the local lattice environment and, by tracking the response of the low-energy elementary excitations, we unveil the response of the microscopic spin and charge interactions. In the high spin–orbit-coupled Sr2IrO4, the high sensitivity of the ground state to the details of the local lattice structure shows a large potential for the manipulation of the functional properties by inducing local lattice distortions. We use epitaxial strain to modify the Ir–O bond geometry in Sr2IrO4 and perform momentum-dependent resonant inelastic X-ray scattering (RIXS) at the metal and at the ligand sites to unveil the response of the low-energy elementary excitations. We observe that the pseudospin-wave dispersion for tensile-strained Sr2IrO4 films displays large softening along the [h,0] direction, while along the [h,h] direction it shows hardening. This evolution reveals a renormalization of the magnetic interactions caused by a strain-driven cross-over from anisotropic to isotropic interactions between the magnetic moments. Moreover, we detect dispersive electron–hole pair excitations which shift to lower (higher) energies upon compressive (tensile) strain, manifesting a reduction (increase) in the size of the charge gap. This behavior shows an intimate coupling between charge excitations and lattice distortions in Sr2IrO4, originating from the modified hopping elements between the t2g orbitals. Our work highlights the central role played by the lattice degrees of freedom in determining both the pseudospin and charge excitations of Sr2IrO4 and provides valuable information toward the control of the ground state of complex oxides in the presence of high spin–orbit coupling.

In magnetic Weyl semimetals, where magnetism breaks time-reversal symmetry, large magnetically sensitive anomalous transport responses are anticipated that could be useful for topological spintronics. The identification of new magnetic Weyl semimetals is therefore in high demand, particularly since in these systems Weyl node configurations may be easily modified using magnetic fields. Here we explore experimentally the magnetic semimetal PrAlGe, and unveil a direct correspondence between easy-axis Pr ferromagnetism and anomalous Hall and Nernst effects. With sizes of both the anomalous Hall conductivity and Nernst effect in good quantitative agreement with first principles calculations, we identify PrAlGe as a system where magnetic fields can connect directly to Weyl nodes via the Pr magnetisation. Furthermore, we find the predominantly easy-axis ferromagnetic ground state co-exists with a low density of nanoscale textured magnetic domain walls. We describe how such nanoscale magnetic textures could serve as a local platform for tunable axial gauge fields of Weyl fermions.

In quantum magnetic materials, ordered phases induced by an applied magnetic field can be described as the Bose-Einstein condensation (BEC) of magnon excitations. In the strongly frustrated system SrCu 2 (BO 3 ) 2 , no clear magnon BEC could be observed, pointing to an alternative mechanism, but the high fields required to probe this physics have remained a barrier to detailed investigation. Here we exploit the first purpose-built high-field neutron scattering facility to measure the spin excitations of SrCu 2 (BO 3 ) 2 up to 25.9 T and use cylinder matrix-product-states (MPS) calculations to reproduce the experimental spectra with high accuracy. Multiple unconventional features point to a condensation of S  = 2 bound states into a spin-nematic phase, including the gradients of the one-magnon branches and the persistence of a one-magnon spin gap. This gap reflects a direct analogy with superconductivity, suggesting that the spin-nematic phase in SrCu 2 (BO 3 ) 2 is best understood as a condensate of bosonic Cooper pairs. SrCu 2 (BO 3 ) 2 realizes the Shastry-Sutherland model (SSM), a 2D frustrated dimer model. Here, via high-magnetic-field inelastic neutron scattering measurements and matrix-product-state calculations, Fogh et al. find evidence for Bose-Einstein condensation of S  = 2 two-triplon bound states, which is a spin-nematic phase.

The interplay between superconductivity and charge or spin order is a key focus in condensed matter physics, with kagome lattice systems providing unique insights. The kagome superconductor LaRu 3 Si 2 ( T c  ≃ 6.5 K) features a characteristic kagome band structure and a hierarchy of charge order transitions at T co,I  ≃ 400 K and T co,II  ≃ 80 K, along with an additional transition at T * ≃ 35 K associated with electronic and magnetic responses. Using magnetotransport under pressure up to 40 GPa, we find T c peaks at 9 K (2 GPa)—the highest among kagome superconductors—remains nearly constant up to 12 GPa, and then decreases to 2 K at 40 GPa, forming a dome-shaped phase diagram. Similarly, both the resistivity anomaly at T * and the magnetoresistance exhibit a dome-shaped pressure dependence. Moreover, above 12 GPa, X-ray diffraction reveals that the charge order evolves from long-range to short-range, coinciding with the suppression of T c . These observations indicate that superconductivity in LaRu 3 Si 2 is closely linked to the charge-ordered state and the electronic responses at T co,II and T *. The authors study kagome superconductor LaRu3Si2 under pressure up to 40 GPa. They find a superconducting dome as a function of pressure, with Tc reaching its maximum when the coexisting charge order remains long-range.