Orbital Dimer Model for Spin-Glass State in Y2_2Mo2_2O7_7

The formation of a spin glass usually requires both structural disorder and frustrated magnetic interactions. Consequently, the origin of spin-glass behaviour in Y$_2$Mo$_2$O$_7$ $-$ in which magnetic Mo$^{4+}$ ions occupy a frustrated pyrochlore lattice with minimal compositional disorder $-$ has been a longstanding question. Here, we use neutron and X-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously-reported PDF, EXAFS and NMR studies and provides a new and physical mechanism for spin-glass formation. We show that Mo$^{4+}$ ions displace according to a local "2-in/2-out" rule on each Mo$_4$ tetrahedron, driven by orbital dimerisation of Jahn-Teller active Mo$^{4+}$ ions. Long-range orbital order is prevented by the macroscopic degeneracy of dimer coverings permitted by the pyrochlore lattice. Cooperative O$^{2-}$ displacements yield a distribution of Mo$-$O$-$Mo angles, which in turn introduces disorder into magnetic interactions. Our study demonstrates experimentally how frustration of atomic displacements can assume the role of compositional disorder in driving a spin-glass transition.Comment: 6 pages, 3 figure

Spin correlations in Ca3Co2O6: A polarised-neutron diffraction and Monte Carlo study

We present polarised-neutron diffraction measurements of the Ising-like spin-chain compound Ca3Co2O6 above and below the magnetic ordering temperature TN. Below TN, a clear evolution from a single-phase spin-density wave (SDW) structure to a mixture of SDW and commensurate antiferromagnet (CAFM) structures is observed on cooling. For a rapidly-cooled sample, the majority phase at low temperature is the SDW, while if the cooling is performed sufficiently slowly, then the SDW and the CAFM structure coexist between 1.5 and 10 K. Above TN, we use Monte Carlo methods to analyse the magnetic diffuse scattering data. We show that both intra- and inter-chain correlations persist above TN, but are essentially decoupled. Intra-chain correlations resemble the ferromagnetic Ising model, while inter-chain correlations resemble the frustrated triangular-lattice antiferromagnet. Using previously-published bulk property measurements and our neutron diffraction data, we obtain values of the ferromagnetic and antiferromagnetic exchange interactions and the single-ion anisotropy.Comment: 10 pages, 7 figure

Discovering Classical Spin Liquids by Topological Search of High Symmetry Nets

Spin liquids are a paradigmatic example of a nontrivial state of matter. The search for new spin liquids is a key interdisciplinary challenge. Geometrical frustration─where the geometry of the net that the spins occupy precludes the generation of a simple ordered state─is a particularly fruitful way to generate these intrinsically disordered states. Prior focus has been on a handful of high symmetry nets. There are, however, many three-dimensional nets, each of which has the potential to form unique states. In this paper, we investigate the high symmetry nets─those which are both vertex- and edge-transitive─for the simplest possible interaction sets: nearest-neighbor couplings of antiferromagnetic Heisenberg and Ising spins. While the well-known crs (pyrochlore) net is the only nearest-neighbor Heisenberg antiferromagnet which does not order, we identify two new frustrated nets (lcx and thp) possessing finite temperature Heisenberg spin-liquid states with strongly suppressed magnetic ordering and noncollinear ground states. With Ising spins, we identify three new classical spin liquids that do not order down to T/J = 0.01. We highlight materials that contain these high symmetry nets, and which could, if substituted with appropriate magnetic ions, potentially host these unusual states. Our systematic survey will guide searches for novel magnetic phases

Hierarchy of exchange interactions in the triangular-lattice spin-liquid YbMgGaO4_{4}

The spin-1/2 triangular lattice antiferromagnet YbMgGaO$_{4}$ has attracted recent attention as a quantum spin-liquid candidate with the possible presence of off-diagonal anisotropic exchange interactions induced by spin-orbit coupling. Whether a quantum spin-liquid is stabilized or not depends on the interplay of various exchange interactions with chemical disorder that is inherent to the layered structure of the compound. We combine time-domain terahertz spectroscopy and inelastic neutron scattering measurements in the field polarized state of YbMgGaO$_{4}$ to obtain better microscopic insights on its exchange interactions. Terahertz spectroscopy in this fashion functions as high-field electron spin resonance and probes the spin-wave excitations at the Brillouin zone center, ideally complementing neutron scattering. A global spin-wave fit to all our spectroscopic data at fields over 4T, informed by the analysis of the terahertz spectroscopy linewidths, yields stringent constraints on $g$-factors and exchange interactions. Our results paint YbMgGaO$_{4}$ as an easy-plane XXZ antiferromagnet with the combined and necessary presence of sub-leading next-nearest neighbor and weak anisotropic off-diagonal nearest-neighbor interactions. Moreover, the obtained $g$-factors are substantially different from previous reports. This works establishes the hierarchy of exchange interactions in YbMgGaO$_{4}$ from high-field data alone and thus strongly constrains possible mechanisms responsible for the observed spin-liquid phenomenology

Multiple Incommensurate Magnetic States in the Kagome Antiferromagnet Na2Mn3Cl8

The kagome lattice can host exotic magnetic phases arising from frustrated and competing magnetic interactions. However, relatively few insulating kagome materials exhibit incommensurate magnetic ordering. Here, we present a study of the magnetic structures and interactions of antiferromagnetic Na$_2$Mn$_3$Cl$_8$ with an undistorted Mn$^{2+}$ kagome network. Using neutron-diffraction and bulk magnetic measurements, we show that Na$_2$Mn$_3$Cl$_8$ hosts two different incommensurate magnetic states, which develop at $T_{N1} = 1.6$ K and $T_{N2} = 0.6$ K. Magnetic Rietveld refinements indicate magnetic propagation vectors of the form $\mathbf{q} = (q_{x},q_{y},\frac{3}{2})$, and our neutron-diffraction data can be well described by cycloidal magnetic structures. By optimizing exchange parameters against magnetic diffuse-scattering data, we show that the spin Hamiltonian contains ferromagnetic nearest-neighbor and antiferromagnetic third-neighbor Heisenberg interactions, with a significant contribution from long-ranged dipolar coupling. This experimentally-determined interaction model is compared with density-functional-theory simulations. Using classical Monte Carlo simulations, we show that these competing interactions explain the experimental observation of multiple incommensurate magnetic phases and may stabilize multi-$\mathbf{q}$ states. Our results expand the known range of magnetic behavior on the kagome lattice.Comment: 13 pages, 8 figure