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Centrosymmetric compounds which host three-dimensional topological spin structures comprise a distinct subclass of materials in which multiple-$\mathbf{q}$ magnetic order is stabilized by anisotropy and bond frustration in contrast to the more common path of antisymmetric exchange interactions. Here we investigate static and dynamic magnetic properties of the cubic perovskite SrFeO$_3$ $\unicode{x2013}$ a rare example of a centrosymmetric material hosting two types of topological spin textures: skyrmion- and hedgehog-lattice phases. Our detailed magnetization and dilatometry measurements describe the domain selection processes and phase transitions in SrFeO$_3$. Spin excitations are investigated using inelastic neutron scattering for all three zero-field phases. In the higher-temperature ordered phases, high-energy magnons increasingly lose coherence, so that spin fluctuations are dominated by a distinct quasielastic component at low energies. We anticipate that this could be generic to symmetric helimagnets in which the chiral symmetry is spontaneously broken by the magnetic order.

Spin-nematic and spin-smectic phases have been reported in magnetic materials, which break rotational symmetry while preserving translational symmetry along certain directions. However, until now the analogy to liquid crystals remained incomplete because no magnetic analog of cholesteric order was known. Here we show that the bilayer perovskite Sr$_3$Fe$_2$O$_7$, previously believed to adopt a simple single-$\mathbf{q}$ spin-helical order, hosts two distinct types of multi-$\mathbf{q}$ spin textures and the first "spin-cholesteric". Its ground state represents a novel multi-$\mathbf{q}$ spin texture with unequally intense spin modulations at the two ordering vectors. This is followed in temperature by the new "spin-cholesteric" phase with spontaneously broken chiral symmetry, in which the translational symmetry is broken only along one of the crystal directions while the weaker orthogonal modulation melts, giving rise to intense short-range dynamical fluctuations. Shortly before the transition to the paramagnetic state, vortex-crystal order spanned by two equivalent $\mathbf{q}$ vectors emerges. The "spin-cholesteric" phase completes the spin analogy with liquid crystals and renders Sr$_3$Fe$_2$O$_7$ a touchstone for studying transitions among multiple-$\mathbf{q}$ spin textures in a centrosymmetric host.

The noncentrosymmetric superconductor Ru$_7$B$_3$ has in previous studies demonstrated remarkably unusual behaviour in its vortex lattice, where the nearest neighbour directions of the vortices dissociate from the crystal lattice and instead show a complex field-history dependence, and the vortex lattice rotates as the field is changed. In this study, we look at the vortex lattice form factor of Ru$_7$B$_3$ during this field-history dependence, to check for deviations from established models, such as the London model. We find that the data is well described by the anisotropic London model, which is in accordance with theoretical predictions that the alterations to the structure of the vortices due to broken inversion symmetry should be small. From this, we also extract values for the penetration depth and coherence length.

One of the key effects which is predicted to arise in superconductors without a centre of inversion is the mixing of singlet and triplet order parameters, which are no longer good quantum numbers on their own due to parity. We have probed the gap structure in the noncentrosymmetric superconductor Ru$_7$B$_3$, through small-angle neutron diffraction from the vortex lattice, in order to search for the proposed mixed order parameter. We find that the measured temperature dependence of the vortex-lattice form factor is well characterised by a model constructed to describe the effects of broken inversion symmetry on the superconducting state, indicating the presence of a mixed singlet-triplet gap and confirming the theoretical predictions.

The metallic compound FeP belongs to the class of materials that feature a complex noncollinear spin order driven by magnetic frustration. While its double-helix magnetic structure with a period $\lambda_{\text{s}} \approx 5c$, where $c$ is the lattice constant, was previously well determined, the relevant spin-spin interactions that lead to that ground state remain unknown. By performing extensive inelastic neutron scattering measurements, we obtained the spin-excitation spectra in a large part of the momentum-energy space. The spectra show that the magnons are gapped with a gap energy of $\sim$5 meV. Despite the 3D crystal structure, the magnon modes display strongly anisotropic dispersions, revealing a quasi-one-dimensional character of the magnetic interactions in FeP. The physics of the material, however, is not determined by the dominating exchange, which is ferromagnetic. Instead, the weaker two-dimensional antiferromagnetic interactions between the rigid ferromagnetic spin chains drive the magnetic frustration. Using linear spin-wave theory, we were able to construct an effective Heisenberg Hamiltonian with an anisotropy term capable of reproducing the observed spectra. This enabled us to quantify the exchange interactions in FeP and determine the mechanism of its magnetic frustration., Comment: 13 pages, 7 figures

Anisotropic low-temperature properties of the cubic spinel helimagnet ZnCr2Se4 in the single-domain spin-spiral state are investigated by a combination of neutron scattering, thermal conductivity, ultrasound velocity, and dilatometry measurements. In an applied magnetic field, neutron spectroscopy shows a complex and nonmonotonic evolution of the spin-wave spectrum across the quantum-critical point that separates the spin-spiral phase from the field-polarized ferromagnetic phase at high fields. A tiny spin gap of the pseudo-Goldstone magnon mode, observed at wave vectors that are structurally equivalent but orthogonal to the propagation vector of the spin helix, vanishes at this quantum critical point, restoring the cubic symmetry in the magnetic subsystem. The anisotropy imposed by the spin helix has only a minor influence on the lattice structure and sound velocity but has a much stronger effect on the heat conductivities measured parallel and perpendicular to the magnetic propagation vector. The thermal transport is anisotropic at T < 2 K, highly sensitive to an external magnetic field, and likely results directly from magnonic heat conduction. We also report long-time thermal relaxation phenomena, revealed by capacitive dilatometry, which are due to magnetic domain motion related to the destruction of the single-domain magnetic state, initially stabilized in the sample by the application and removal of magnetic field. Our results can be generalized to a broad class of helimagnetic materials in which a discrete lattice symmetry is spontaneously broken by the magnetic order., Comment: 13 pages, 8 figures + Supplemental Material

We present a comprehensive investigation of lattice dynamics in the double-helix antiferromagnet FeP by means of high-resolution time-of-flight neutron spectroscopy and ab-initio calculations. Phonons can hybridize with the magnetic excitations in noncollinear magnets to significantly influence their properties. We observed a rich spectrum of phonon excitations, which extends up to $\sim$50 meV. We performed detailed analysis of the observed and calculated spectra for all high-symmetry points and high-symmetry directions of the Brillouin zone. We show that the DFT calculations quantitatively capture the essential features of the observed phonons, including both dispersions and scattering intensities. By making use of the detailed intensity comparison between the theory and the data, we were able to identify displacement vectors for the majority of the observed modes. The overall excellent agreement between the DFT predictions and the experimental results breaks down for the lowest mode at the $Y$-point, whose energy is lower than calculated by $\sim$13%. The present study provides vital information on the lattice dynamics in FeP and demonstrates applicability of the DFT to novel pressure-induced phenomena in related materials, such as MnP and CrAs., Comment: 12 pages, 10 figures

The multiferroic ferrimagnet Cu$_2$OSeO$_3$ with a chiral crystal structure attracted a lot of recent attention due to the emergence of magnetic skyrmion order in this material. Here, the topological properties of its magnon excitations are systematically investigated by linear spin-wave theory and inelastic neutron scattering. When considering Heisenberg exchange interactions only, two degenerate Weyl magnon nodes with topological charges $\pm$2 are observed at high-symmetry points. Each Weyl point splits into two as the symmetry of the system is further reduced by including into consideration the nearest-neighbor Dzyaloshinsky-Moriya interaction, crucial for obtaining an accurate fit to the experimental spin-wave spectrum. The predicted topological properties are verified by surface state and Chern number analysis. Additionally, we predict that a measurable thermal Hall conductivity can be associated with the emergence of the Weyl points, the position of which can be tuned by changing the crystal symmetry of the material.

We observe a hysteretic reorientation of the magnetic vortex lattice in the noncentrosymmetric superconductor Ru7B3, with the change in orientation driven by altering magnetic field below Tc. Normally a vortex lattice chooses either a single or degenerate set of orientations with respect to a crystal lattice at any given field or temperature, a behavior well described by prevailing phenomenological and microscopic theories. Here, in the absence of any typical VL structural transition, we observe a continuous rotation of the vortex lattice which exhibits a pronounced hysteresis and is driven by a change in magnetic field. We propose that this rotation is related to the spontaneous magnetic fields present in the superconducting phase, which are evidenced by the observation of time-reversal symmetry breaking, and the physics of broken inversion symmetry. Finally, we develop a model from the Ginzburg-Landau approach which shows that the coupling of these to the vortex lattice orientation can result in the rotation we observe.

Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. Here we employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet ZnCr2Se4 with a cubic spinel structure, in which spin-3/2 magnetic Cr3+ ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional Goldstone mode emanating from the (0 0 q) ordering vector, low-energy magnetic excitations in the single-domain proper-screw spiral phase show soft helimagnon modes with a small energy gap of ~0.17 meV, emerging from two orthogonal wave vectors (q 0 0) and (0 q 0) where no magnetic Bragg peaks are present. We term them pseudo-Goldstone magnons, as they appear gapless within linear spin-wave theory and only acquire a finite gap due to higher-order quantum-fluctuation corrections. Our results are likely universal for a broad class of symmetric helimagnets, opening up a new way of studying weak magnon-magnon interactions with accessible spectroscopic methods., Comment: V3: Final version to be published in Phys. Rev. X

We performed small-angle neutron scattering (SANS) measurements on the helimagnetic spinel compound ZnCr2Se4. The ground state of this material is a multi-domain spin-spiral phase, which undergoes domain selection in a magnetic field and reportedly exhibits a transition to a proposed spin-nematic phase at higher fields. We observed a continuous change in the magnetic structure as a function of field and temperature, as well as a weak discontinuous jump in the spiral pitch across the domain-selection transition upon increasing field. From our SANS results we have established the absence of any long-range magnetic order in the high-field (spin-nematic) phase. We also found that all the observed phase transitions are surprisingly isotropic with respect to the field direction.