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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.

The spin waves in single crystals of the layered van der Waals antiferromagnet CoPS 3 have been measured using inelastic neutron scattering. The data show four distinct spin wave branches with large ( 14 meV) energy gaps at the Brillouin zone center indicating significant anisotropy. The data were modeled using linear spin wave theory derived from a Heisenberg Hamiltonian. Exchange interactions up to the third nearest-neighbor in the layered planes were required to fit the data with ferromagnetic J 1 = −1.37 meV between first neighbors, antiferromagnetic J 3 = 3.0 meV between third neighbors, and a very small J 2 = 0.09 meV between second neighbors. A biaxial single-ion anisotropy was required, with a collinear term D x = −0.77 meV for the axis parallel to the aligned moment direction and a coplanar term D z = 6.07 meV for an axis approximately normal to the layered crystal planes.

Quantum magnets display a wide variety of collective excitations, including spin waves (magnons), coherent singlet-triplet excitations (triplons), and pairs of fractional spins (spinons). These modes differ radically in nature and properties, and in all conventional analyses any given material is interpreted in terms of only one type. We report inelastic neutron scattering measurements on the spin-1/2 antiferromagnet SeCuO 3 , which demonstrate that this compound exhibits all three primary types of spin excitation. Cu 1 sites form strongly bound dimers while Cu 2 sites form a network of spin chains, whose weak three-dimensional (3D) coupling induces antiferromagnetic order. We perform quantitative modeling to extract all of the relevant magnetic interactions and show that magnons of the Cu 2 system give a lower bound to the spinon continua, while the Cu 1 system hosts a band of high-energy triplons at the same time as frustrating the 3D network.

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We report high-resolution single-crystal inelastic neutron scattering measurements on the spin-1/2 antiferromagnet Ba(TiO)Cu 4 (PO 4 ) 4 . This material is formed from layers of four-site "cupola" structures, oriented alternately upwards and downwards, which constitute a rather special realization of two-dimensional (2D) square-lattice magnetism. The strong Dzyaloshinskii-Moriya (DM) interaction within each cupola, or plaquette, unit has a geometry largely unexplored among the numerous studies of magnetic properties in 2D Heisenberg models with spin and spatial anisotropies. We have measured the magnetic excitations at zero field and in fields up to 5 T, finding a complex mode structure with multiple characteristic features that allow us to extract all the relevant magnetic interactions by modeling within the linear spin-wave approximation. We demonstrate that Ba(TiO)Cu 4 (PO 4 ) 4 is a checkerboard system with almost equal intra-and interplaquette couplings, in which the intraplaquette DM interaction is instrumental both in enforcing robust magnetic order and in opening a large gap at the Brillouin-zone center. We place our observations in the perspective of generalized phase diagrams for spin-1/2 square-lattice models and materials, where exploring anisotropies and frustration as routes to quantum disorder remains a frontier research problem.

We report neutron diffraction studies of the magnetic structure in BaTiOCu4(PO4)4 , which is a newly discovered magnetic insulator crystallizing in a tetragonal chiral crystal structure with P4212 space group [1]. The crystal structure is characterized by an antiferro-rotative arrangement of Cu4O12 square cupola clusters formed by four corner sharing CuO4 plaquettes. Below 9.5 K these magnetic clusters order in a complex noncollinear magnetic structure which can be described by an antiferroic order of magnetic quadrupole moments on Cu4O12 square cupolas. The magnetic transition is accompanied by a magnetic-field-induced peak in dielectric constant divergent toward T = 9.5 K, indicative of an onset of field-induced antiferroelectric order [2]. To the best of our knowledge, this is the first experimental observation of the magnetoelectric-activity due to magnetic quadrupole moments [3], which opens the arena for further studies of this and related compounds. In this presentation, we shall focus on the determination of the magnetic structure exploiting a combination of powder neutron diffraction and so-called spherical neutron polarimetry. The powder diffraction measurement was able to identify two possible models for the magnetic structure, as depicted in the figure. Both structures are noncollinear, but differ by having the moments either in or out of the CuO4 planes. Powder diffraction could only provide limited discrimination between the two models. Spherical neutron polarimetry is a convenient, albeit rarely used tool for understanding complex magnetic structures which often can provide unambiguous solutions to withstanding problems. In this case spherical neutron polarimetry unambiguously identifies structure (b) with the moments pointing out of the CuO4 planes.

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