Spontaneous symmetry breaking-the phenomenon where an infinitesimal perturbation can cause the system to break the underlying symmetry-is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. In the paramagnetic state at 460K, we confirm that the crystal structure is indeed hexagonal kagome lattice. On cooling to TN, the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of 10^(-4) and the associated splitting of the double degenerate phonon mode of the pristine kagome lattice. Upon further cooling to TCDW, the kagome lattice shows a small negative thermal expansion, and the crystal structure becomes more symmetric gradually upon further cooling. Increasing the crystalline symmetry upon cooling is unusual, it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter, hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system and sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant.

Magnetic order in most materials occurs when magnetic ions with finite moments arrange in a particular pattern below the ordering temperature. Intriguingly, if the crystal electric field (CEF) effect results in a spin-singlet ground state, a magnetic order can still occur due to the exchange interactions between neighboring ions admixing the excited CEF levels. The magnetic excitations in such a state are spin excitons generally dispersionless in reciprocal space. Here we use neutron scattering to study stoichiometric Ni2Mo3O8, where Ni2+ ions form a bipartite honeycomb lattice comprised of two triangular lattices, with ions subject to the tetrahedral and octahedral crystalline environment, respectively. We find that in both types of ions, the CEF excitations have nonmagnetic singlet ground states, yet the material has magnetic order. Furthermore, CEF spin excitons from the tetrahedral sites form a dispersive diffusive pattern around the Brillouin zone boundary, likely due to spin entanglement and geometric frustrations.

Quantum spin liquid (QSL) is a disordered state of quantum-mechanically entangled spins commonly arising from frustrated magnetic dipolar interactions. However, QSL in some pyrochlore magnets can also come from frustrated magnetic octupolar interactions. Although the key signature for both dipolar and octupolar interaction-driven QSL is the presence of a spin excitation continuum (spinons) arising from the spin quantum number fractionalization, an external magnetic field-induced ferromagnetic order will transform the spinons into conventional spin waves in a dipolar QSL. By contrast, in an octupole QSL, the spin waves carry octupole moments that do not couple, in the leading order, to the external magnetic field or to neutron moments but will contribute to the field dependence of the heat capacity. Here we use neutron scattering to show that the application of a large external magnetic field to Ce2Zr2O7, an octupolar QSL candidate, induces an Anderson-Higgs transition by condensing the spinons into a static ferromagnetic ordered state with octupolar spin waves invisible to neutrons but contributing to the heat capacity. Our theoretical calculations also provide a microscopic, qualitative understanding for the presence of octupole scattering at large wavevectors in Ce2Sn2O7 pyrochlore, and its absence in Ce2Zr2O7. Therefore, our results identify Ce2Zr2O7 as a strong candidate for an octupolar U (1) QSL, establishing that frustrated magnetic octupolar interactions are responsible for QSL properties in Ce-based pyrochlore magnets.

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.

Triangular lattice of rare-earth ions with interacting effective spin-1/2 local moments is an ideal platform to explore the physics of quantum spin liquids (QSLs) in the presence of strong spin-orbit coupling, crystal electric fields, and geometrical frustration. The Yb delafossites, NaYbCh(2) (Ch = O, S, Se) with Yb ions forming a perfect triangular lattice, have been suggested to be candidates for QSLs. Previous thermodynamics, nuclear magnetic resonance, and powder-sample neutron scattering measurements on NaYbCh(2) have supported the suggestion of the QSL ground states. The key signature of a QSL, the spin excitation continuum, arising from the spin quantum number fractionalization, has not been observed. Here we perform both elastic and inelastic neutron scattering measurements as well as detailed thermodynamic measurements on high-quality single-crystal NaYbSe2 samples to confirm the absence of long-range magnetic order down to 40 mK, and further reveal a clear signature of magnetic excitation continuum extending from 0.1 to 2.5 meV. The comparison between the structure of the magnetic excitation spectra and the theoretical expectation from the spinon continuum suggests that the ground state of NaYbSe2 is a QSL with a spinon Fermi surface.

Geometric frustration in the kagome lattice makes it a great host for the flat electronic band, nontrivial topological properties, and novel magnetism. Here, we use magnetotransport measurements to map out the field-temperature phase diagram of the centrosymmetric YMn6Sn6 with a Mn kagome lattice and show that the system exhibits the topological Hall effect (THE) with an in-plane applied magnetic field around 240 K. In addition, our neutron diffraction results demonstrate that the observed THE cannot arise from a magnetic skyrmion lattice, but instead from an in-plane field-induced double-fan spin structure with c-axis components. This paper provides a platform to understand the influence of a field-induced novel magnetic structure on magnetoelectric response in topological kagome metals.

We use neutron scattering to show that ferromagnetic (FM) phase transition in the two-dimensional (2D) honeycomb lattice ${\mathrm{CrI}}_{3}$ is a weakly first order transition and controlled by spin-orbit coupling (SOC) induced magnetic anisotropy, instead of magnetic exchange coupling as in a conventional ferromagnet. With increasing temperature, the magnitude of magnetic anisotropy, seen as a spin gap at the Brillouin zone center, decreases in a power law fashion and vanishes at ${T}_{C}$, while the in-plane and $c$-axis spin-wave stiffnesses associated with magnetic exchange couplings remain robust at ${T}_{C}$. We also compare parameter regimes where spin waves in ${\mathrm{CrI}}_{3}$ can be described by a Heisenberg Hamiltonian with Dzyaloshinskii-Moriya interaction or a Heisenberg-Kitaev Hamiltonian. These results suggest that the SOC induced magnetic anisotropy plays a dominant role in stabilizing the FM order in single layer 2D van der Waals ferromagnets.

The geometrical frustration nature of the kagome lattice makes it a great host to flat electronic band, non-trivial topological properties, and novel magnetisms. Metallic kagome antiferromagnet YMn_6Sn_6 exhibits the topological Hall effect (THE) when an in-plane magnetic field is applied. THE is typically associated with the nanometer-sized non-coplanar spin structure of skyrmions in non-centrosymmetric magnets with large Dzyaloshinskii-Moriya interaction. Here we use single crystal neutron diffraction to determine the field/temperature dependence of the magnetic structure in YMn_6Sn_6. We find that the observed THE cannot arise from a magnetic skyrmion lattice, but instead from an in-plane field-induced double fan spin structure with c-axis components (DFC). Our work provides the experimental basis from which a microscopic theory can be established to understand the observed THE.

Lebing Chen ,1 Jae-Ho Chung,2,* Tong Chen,1 Chunruo Duan,1 Astrid Schneidewind ,3 Igor Radelytskyi,3 David J. Voneshen,4 Russell A. Ewings ,4 Matthew B. Stone ,5 Alexander I. Kolesnikov ,5 Barry Winn,5 Songxue Chi,5 R. A. Mole,6 D. H. Yu,6 Bin Gao ,1 and Pengcheng Dai 1,† 1Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA 2Department of Physics, Korea University, Seoul 02841, Korea 3Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science (JCNS) at Heinz Maier-Leibnitz Zentrum (MLZ), Lichtenbergstrasse 1, 85748 Garching, Germany 4ISIS Pulsed Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxon, OX11 0QX, United Kingdom 5Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 6Australian Nuclear Science and Technology Organisation, Locked bag 2001, Kirrawee DC, New South Wales 2232, Australia

The composition dependence of the structural transition between the monoclinic 1T' and orthorhombic T-d phases in the Mo1-xWxTe2 Weyl semimetal was investigated by elastic neutron scattering on single crystals up to x approximate to 0.54. First observed in MoTe2, the transition from T-d to 1T' is accompanied by an intermediate pseudo-orthorhombic phase, T-d*. Upon doping with W, the T-d* phase vanishes by x 0.34. Above this concentration, a phase coexistence behavior with both T-d and 1T' is observed instead. The interlayer in-plane positioning parameter delta, which relates to the 1T' beta angle, decreases with temperature as well as with W substitution, likely due to strong anharmonicity in the interlayer interactions. The temperature width of the phase coexistence remains almost constant up to x approximate to 0.54, in contrast to the broadening reported under pressure.

Spin-triplet superconductors are of extensive current interest because they can host topological state and Majorana ferimons important for quantum computation. The uranium based heavyfermion superconductor UTe$_2$ has been argued as a spin-triplet superconductor similar to UGe$_2$, URhGe, and UCoGe, where the superconducting phase is near (or coexists with) a ferromagnetic (FM) instability and spin-triplet electron pairing is driven by FM spin fluctuations. Here we use neutron scattering to show that although UTe$_2$ exhibits no static magnetic order down to 0.3 K, its magnetism is dominated by incommensurate spin fluctuations near antiferromagnetic (AF) ordering wave vector and extends to at least 2.6 meV. We are able to understand the dominant incommensurate spin fluctuations of UTe$_2$ in terms of its electronic structure calculated using a combined density functional and dynamic mean field theory.

Electronic tunability in crystals with weakly-bound layers can be achieved through layer stacking order. One such example is MoTe_2, where the low-temperature orthorhombic T_d phase is topological and host to Weyl quasiparticles. The transition mechanism to the non-trivial topology is elucidated by single crystal neutron diffraction. Upon cooling from the monoclinic 1T' to the T_d phase, diffuse scattering accompanies the transition, arising from random, in-plane layer displacements, and dissipates upon entering the T_d phase. Diffuse scattering is observed only in the H0L plane due to irreversible layer shifts along the c-axis that break the centrosymmetry of the monoclinic lattice.

Using elastic neutron scattering on single crystals of MoTe$_{2}$ and Mo$_{1-x}$W$_{x}$Te$_{2}$ ($x \lesssim 0.01$), the temperature dependence of the recently discovered T$_{d}^{*}$ phase, present between the low temperature orthorhombic T$_{d}$ phase and high temperature monoclinic 1T$^{\prime}$ phase, is explored. The T$_{d}^{*}$ phase appears only on warming from T$_{d}$ and is observed in the hysteresis region prior to the 1T$^{\prime}$ transition. This phase consists of four layers in its unit cell, and is constructed by an AABB sequence of layer stacking operations rather than the AB and AA sequences of the 1T$^{\prime}$ and T$_{d}$ phases, respectively. Though the T$_{d}^{*}$ phase emerges without disorder on warming from T$_{d}$, on cooling from 1T$^{\prime}$ diffuse scattering is observed that suggests a frustrated tendency toward the AABB stacking.

Td phase across the Td–1T ′ phase boundary in Weyl semimetal MoTe2 Yu Tao, John A. Schneeloch, Chunruo Duan, Masaaki Matsuda, Sachith E. Dissanayake, ∗ Adam A. Aczel, 3 Jaime A. Fernandez-Baca, Feng Ye, and Despina Louca † Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA

Using elastic neutron scattering on single crystals of MoTe_2 and Mo_1-xW_xTe_2 (x ≲ 0.01), the temperature dependence of the recently discovered T_d^* phase, present between the low temperature orthorhombic T_d phase and high temperature monoclinic 1T^' phase, is explored. The T_d^* phase appears only on warming from T_d and is observed in the hysteresis region prior to the 1T^' transition. This phase consists of four layers in its unit cell, and is constructed by an "AABB" sequence of layer stacking operations rather than the "AB" and "AA" sequences of the 1T^' and T_d phases, respectively. Though the T_d^* phase emerges without disorder on warming from T_d, on cooling from 1T^' diffuse scattering is observed that suggests a frustrated tendency toward the "AABB" stacking.

Using elastic neutron scattering on single crystals of MoTe2 and Mo1-xWxTe2 (x less than or similar to 0.01), the temperature dependence of the recently discovered T-d* phase, present between the low-temperature orthorhombic T-d phase and high-temperature monoclinic 1T' phase, is explored. The T-d* phase appears only on warming from T-d and is observed in the hysteresis region prior to the 1T' transition. This phase consists of four layers in its unit cell, and is constructed by an "AABB" sequence of layer stacking operations rather than the "AB" and "AA" sequences of the 1T' and T-d phases, respectively. Though the T-d* phase emerges without disorder on warming from T-d, on cooling from 1T' diffuse scattering is observed that suggests a frustrated tendency toward the "AABB" stacking.