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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