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Through analysis of variable temperature neutron powder diffraction data, we present solutions for the magnetic structures of SrMn$_7$O$_{12}$, CdMn$_7$O$_{12}$, and PbMn$_7$O$_{12}$ in all long-range ordered phases. The three compounds were found to have magnetic structures analogous to that reported for CaMn$_7$O$_{12}$. They all feature a higher temperature lock-in phase with \emph{commensurate} magneto-orbital coupling, and a delocked, multi-\textbf{k} magnetic ground state where \emph{incommensurate} magneto-orbital coupling gives rise to a constant-moment magnetic helix with modulated spin helicity. CdMn$_7$O$_{12}$ represents a special case in which the orbital modulation is commensurate with the crystal lattice and involves stacking of fully and partially polarized orbital states. Our results provide a robust confirmation of the phenomenological model for magneto-orbital coupling previously presented for CaMn$_7$O$_{12}$. Furthermore, we show that the model is universal to the $A^{2+}$ quadruple perovskite manganites synthesised to date, and that it is tunable by selection of the $A$-site ionic radius.

Magneto-electric coupling in pyroelectric CaBaCo$_4$O$_7$ is investigated using ab-intio calculations and Landau theory. The former shows that exchange-striction is strong enough to produce a giant change in electric polarization upon ferrimagnetic ordering, comparable to the experimentally determined value of ~17 mC/m$^2$ . Furthermore, Landau theory demonstrates that magneto-elastic coupling in CaBaCo$_4$O$_7$ is responsible for the strong magneto-electric coupling appearing close to the magnetic phase transition.

Orbitally ordered states evolving coincidentally with structural distortions and magnetic ordering provide a novel route to controlling electronic and magnetic properties of materials through external fields. We report an unprecedented magneto-orbital helix in CaMn7O12, found to give rise to the largest magnetically induced ferroelectric polarisation measured to date. Characterisation of the structural modulation using x-ray diffraction, and analysis of magnetic exchange shows that orbital order is crucial in stabilising a chiral magnetic structure, thus allowing for electric polarisation. Additionally, the presence of a global structural rotation enables the coupling between this polarisation and magnetic helicity required for multiferrocitiy. These novel principles open up the possibility of discovering new high-temperature multiferroics., Submitted to Nature Communications

We report inelastic neutron scattering measurements on Na2IrO3, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zig-zag magnetic order. The onset of long-range magnetic order below 15.3 K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90 deg Ir-O-Ir bonds required for dominant Kitaev exchange., Comment: 12 pages; fixed typos

We have studied the frustrated system YBaCo4O7 generally described as an alternating stacking of Kagome and triangular layers of magnetic ions on a trigonal lattice, by single crystal neutron diffraction experiments above the Neel ordering transition. Experimental data reveals pronounced magnetic diffuse scattering, which is successfully modeled by direct Monte-Carlo simulations. Long-range magnetic correlations are found along the c-axis, due to the presence of corner-sharing bipyramids, creating quasi one-dimensional order at finite temperature. In contrast, in the Kagome layers ab-plane, the spin-spin correlation function -displaying a short-range 120 degrees configuration- decays rapidly as typically found in spin-liquids. YBaCo4O7 experimentally realizes a new class of two-dimensional frustrated systems where the strong out-of-plane coupling does not lift the in-plane degeneracy, but instead act as an external "field".

The S=2 anisotropic triangular lattice alpha-NaMnO2 is studied by neutron inelastic scattering. Antiferromagnetic order occurs at T ~ 45 K with opening of a spin gap. The spectral weight of the magnetic dynamics above the gap (Delta ~ 7.5 meV) has been analysed by the single-mode approximation. Excellent agreement with the experiment is achieved when a dominant exchange interaction (|J|/k_B ~ 73 K), along the monoclinic b-axis and a sizeable easy-axis magnetic anisotropy (|D|/k_B ~ 3 K) are considered. Despite earlier suggestions for two-dimensional spin interactions, the dynamics illustrate strongly coupled antiferromagnetic S=2 chains and cancellation of the interchain exchange due to the lattice topology. alpha-NaMnO2 therefore represents a model system where the geometric frustration is resolved through the lowering of the dimensionality of the spin interactions., 4 pages, 4 figures, to be published in Physical Review Letters

We have studied the crystal and magnetic structures of the magnetoelectric materials RMn2O5 (R = Tb, Ho, Dy) using neutron diffraction as a function of temperature. All three materials display incommensurate antiferromagnetic ordering below 40 K, becoming commensurate on further cooling. For R = Tb, Ho, a commensurate-incommensurate transition takes place at low temperatures. The commensurate magnetic structures have been solved and are discussed in terms of competing exchange interactions. The spin configuration within the ab plane is essentially the same for each system, and the radius of R determines the sign of the magnetic exchange between adjacent planes. The inherent magnetic frustration in these materials is lifted by a small lattice distortion, primarily involving shifts of the Mn3+ cations and giving rise to a canted antiferroelectric phase., Comment: 23 pages