Spirals and helices are common motifs of long-range order in magnetic solids, and they may also be organized into more complex emergent structures such as magnetic skyrmions and vortices. A new type of spiral state, the spiral spin-liquid, in which spins fluctuate collectively as spirals, has recently been predicted to exist. Here, using neutron scattering techniques, we experimentally prove the existence of a spiral spin-liquid in MnSc2S4 by directly observing the 'spiral surface' -a continuous surface of spiral propagation vectors in reciprocal space. We elucidate the multi-step ordering behavior of the spiral spin-liquid, and discover a vortex-like triple-q phase on application of a magnetic field. Our results prove the effectiveness of the J1-J2 Hamiltonian on the diamond lattice as a model for the spiral spin-liquid state in MnSc2S4, and also demonstrate a new way to realize a magnetic vortex lattice.Magnetic frustration, where magnetic moments (spins) are coupled through competing interactions that cannot be simultaneously satisfied 1 , usually leads to highly cooperative spin fluctuations 2,3 and unconventional longrange magnetic order 4,5 . An archetypal ordering in the presence of frustration is the spin spiral. Competing interactions and spiral orders give rise to many phenomena in magnetism, including the multitudinous magnetic phases of rare earth metals 6 , domains with multiferroic properties 7,8 , and topologically non-trivial structures such as the emergent skyrmion lattice 9,10 .Recently, a new spiral state -a spiral spin-liquid in which the ground states are a massively degenerate set of coplanar spin spirals -was predicted to exist in the J 1 -J 2 model on the diamond lattice (see Fig. 1a) [11][12][13] . Although the diamond lattice is bipartite, and therefore unfrustrated at the near-neighbour (J 1 ) level, the second-neighbour coupling (J 2 ) can generate strong competition. For classical spins, mean-field calculations show that when |J 2 /J 1 | > 0.125 the spiral spin-liquid appears, and that it is signified by an unusual continuous surface of propagation vectors q in reciprocal space (see Fig. 1b for the spiral surface of |J 2 /J 1 | = 0.85). At finite temperature, thermal fluctuations might select some specific q-vectors on the spiral surface 11 , resulting in an orderby-disorder transition 14,15 .Until now, several series of A-site spinels, in which the magnetic A ions form a diamond lattice, have been investigated, including: the cobaltates Co 3 O 4 and CoRh 2 O 4 16 ; the aluminates M Al 2 O 4 with M = Fe, Co, Mn 17-20 ; and the scandium thiospinels M Sc 2 S 4 with M = Fe, Mn 21 . For the spinels with Fe 2+ at the A-site, the e g orbital angular momentum of Fe 2+ is active, making the pure spin J 1 -J 2 model inadequate 22 . Among the other compounds, CoAl 2 O 4 and MnSc 2 S 4 manifest the strongest frustration. For CoAl 2 O 4 , the ratio of |J 2 /J 1 | has been identified as 0.109 19 , which is near, but still lower than, the 0.125 threshold for the spiral spin-liquid state. Many expe...

In vortex-like spin arrangements, multiple spins can combine into emergent multipole moments. Such multipole moments have broken space-inversion and time-reversal symmetries, and can therefore exhibit linear magnetoelectric (ME) activity. Three types of such multipole moments are known: toroidal; monopole; and quadrupole moments. So far, however, the ME activity of these multipole moments has only been established experimentally for the toroidal moment. Here we propose a magnetic square cupola cluster, in which four corner-sharing square-coordinated metal-ligand fragments form a noncoplanar buckled structure, as a promising structural unit that carries an ME-active multipole moment. We substantiate this idea by observing clear magnetodielectric signals associated with an antiferroic ME-active magnetic quadrupole order in the real material Ba(TiO)Cu 4 (PO 4 ) 4 . The present result serves as a useful guide for exploring and designing new ME-active materials based on vortex-like spin arrangements.

Spin waves in chiral magnetic materials are strongly influenced by the Dzyaloshinskii-Moriya interaction resulting in intriguing phenomena like non-reciprocal magnon propagation and magnetochiral dichroism. Here, we study the non-reciprocal magnon spectrum of the archetypical chiral magnet MnSi and its evolution as a function of magnetic field covering the field-polarized and conical helix phase. Using inelastic neutron scattering, the magnon energies and their spectral weights are determined quantitatively after deconvolution with the instrumental resolution. In the field-polarized phase the imaginary part of the dynamical susceptibility χ (ε, q) is shown to be asymmetric with respect to wavevectors q longitudinal to the applied magnetic field H, which is a hallmark of chiral magnetism. In the helimagnetic phase, χ (ε, q) becomes increasingly symmetric with decreasing H due to the formation of helimagnon bands and the activation of additional spinflip and nonspinflip scattering channels. The neutron spectra are in excellent quantitative agreement with the low-energy theory of cubic chiral magnets with a single fitting parameter being the damping rate of spin waves. This is a pre-print of our paper at https://link.aps.org/

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We have used inelastic neutron scattering to measure the magnetic excitation spectrum along the high-symmetry directions of the first Brillouin zone of the magnetic skyrmion hosting compound Cu 2 OSeO 3 . The majority of our scattering data are consistent with the expectations of a recently proposed model for the magnetic excitations in Cu 2 OSeO 3 , and we report best-fit parameters for the dominant exchange interactions. Important differences exist, however, between our experimental findings and the model expectations. These include the identification of two energy scales that likely arise due to neglected anisotropic interactions. This feature of our work suggests that anisotropy should be considered in future theoretical work aimed at the full microscopic understanding of the emergence of the skyrmion state in this material. [8], and in the polar magnetic semiconductor GaV 4 S 8 [9]. To understand the formation and the microscopic origin of these skyrmion phases, one needs a multiscale approach that covers the macroscopic domain of the skyrmion as well as the quantum scale of the local spins. This, however, breaks down in the above-mentioned metals because the low-energy delocalized electrons and magnetic degrees of freedom are mixed, intrinsically involving multiple energy and spatial scales.Among cubic helimagnets, Cu 2 OSeO 3 is the only insulator with magnetoelectric properties in the ground state [8,[10][11][12][13][14]. It offers an ideal laboratory to explore the microscopic ingredients that lead to skyrmion formation in a quantitative manner, since its Bloch-type ground-state properties and low-energy excitations are fully governed by the magnetic interactions between localized spins and are not affected by the presence of itinerant carriers. Exchange pathway considerations, susceptibility measurements, and ab initio calculations reveal that two magnetic energy scales divide the system into weakly coupled Cu 4 tetrahedra [15]. These Cu 4 "molecules," with an effective spin of S = 1, are the elementary magnetic building blocks of Cu 2 OSeO 3 instead of the single Cu ions. The effective spins of the Cu 4 tetrahedra are ferromagnetically coupled and form a trillium lattice, just as the Mn and Fe ions do in the B20 structure of the metallic skyrmion compounds MnSi and FeGe.Prior to the undertaking of the present work, previous studies of the magnetic excitation spectra of Cu 2 OSeO 3 were conducted using Raman scattering [16] and microwave resonance absorption [17], i.e., techniques that are sensitive only to excitations in the center of the Brillouin zone. In contrast, inelastic neutron scattering (INS) is able to measure at finite momentum transfer and is therefore uniquely suited to probe the magnetic excitation spectra of Cu 2 OSeO 3 throughout reciprocal space. The additional information afforded by INS therefore provides more rigorous tests of theoretical models aimed at describing the excitation spectra of Cu 2 OSeO 3 .Single crystals of Cu 2 OSeO 3 (cubic P 2 1 3 space group, a = 8.82Å) were gro...

Classical and quantum phase transitions (QPTs), with their accompanying concepts of criticality and universality, are a cornerstone of statistical thermodynamics. An exemplary controlled QPT is the field-induced magnetic ordering of a gapped quantum magnet. Although numerous "quasi-one-dimensional" coupled spin-chain and -ladder materials are known whose ordering transition is three-dimensional (3D), quasi-2D systems are special for several physical reasons. Motivated by the ancient pigment Han Purple (BaCuSi2O6), a quasi-2D material displaying anomalous critical properties, we present a complete analysis of Ba0.9Sr0.1CuSi2O6. We measure the zero-field magnetic excitations by neutron spectroscopy and deduce the magnetic Hamiltonian. We probe the field-induced transition by combining magnetization, specific-heat, torque and magnetocalorimetric measurements with low-temperature nuclear magnetic resonance studies near the QPT. By a Bayesian statistical analysis and large-scale Quantum Monte Carlo simulations, we demonstrate unambiguously that observable 3D quantum critical scaling is restored by the structural simplification arising from light Srsubstitution in Han Purple.

The antiferromagnetic compound Ba(TiO)Cu4(PO4)4 contains square cupola of corner-sharing CuO4 plaquettes, which were proposed to form effective quadrupolar order. To identify the magnetic structure, we have performed spherical neutron polarimetry measurements. Based on symmetry analysis and careful measurements we conclude that the orientation of the Cu 2+ spins form a non-collinear in-out structure with spins approximately perpendicular to the CuO4 motif. Strong Dzyaloshinskii-Moriya interaction naturally lends itself to explain this phenomenon. The identification of the ground state magnetic structure should serve well for future theoretical and experimental studies into this and closely related compounds.

We use neutron scattering to show that ferromagnetism and antiferromagnetism coexist in the low T state of the pyrochlore quantum magnet Yb2Ti2O7. While magnetic Bragg peaks evidence long-range static ferromagnetic order, inelastic scattering shows that short-range correlated antiferromagnetism is also present. Small-angle neutron scattering provides direct evidence for mesoscale magnetic structure that we associate with metastable antiferromagnetism. Classical Monte Carlo simulations based on exchange interactions inferred from ⟨111⟩-oriented high-field spin wave measurements confirm that antiferromagnetism is metastable within the otherwise ferromagnetic ground state. The apparent lack of coherent spin wave excitations and strong sensitivity to quenched disorder characterizing Yb2Ti2O7 is a consequence of this multiphase magnetism.