Recent experiments on the Ba$_3$XSb$_2$O$_9$ family have revealed materials that potentially realise spin- and spin-orbital liquid physics. However, the lattice structure of these materials is complicated due to the presence of charged X$^{2+}$-Sb$^{
5+}$ dumbbells, with two possible orientations. To model the lattice structure, we consider a frustrated model of charged dumbbells on the triangular lattice, with long-range Coulomb interactions. We study this model using Monte Carlo simulation, and find a freezing temperature, $T_{sf frz}$, at which the simulated structure factor matches well to low-temperature x-ray diffraction data for Ba$_3$CuSb$_2$O$_9$. At $T=T_{sf frz}$ we find a complicated ``branching structure of superexchange-linked X$^{2+}$ clusters, and show that this gives a natural explanation for the presence of orphan spins. Finally we provide a plausible mechanism by which such dumbbell disorder can promote a spin-orbital resonant state with delocalised orphan spins.
The spin-nematic state has proved elusive, due to the difficulty of observing the order parameter in experiment. In this article we develop a theory of spin excitations in a field-induced spin-nematic state, and use it to show how a spin-nematic orde
r can be indentified using inelastic neutron scattering. We concentrate on 2-dimensional frustrated ferromagnets, for which a two-sublattice, bond-centered spin-nematic state is predicted to exist over a wide range of parameters. First, to clarify the nature of spin-excitations, we introduce a soluble spin-1 model, and use this to derive a continuum field theory, applicable to any two-sublattice spin-nematic state. We then parameterise this field theory, using diagrammatic calculations for a realistic microscopic model of a spin-1/2 frustrated ferromagnet, and show how it can be used to make predictions for inelastic neutron scattering. As an example, we show quantitative predictions for inelastic scattering of neutrons from BaCdVO(PO_4)_2, a promising candidate to realise a spin-nematic state at an achievable hsim 4T. We show that in this material it is realistic to expect a ghostly Goldstone mode, signalling spin-nematic order, to be visible in experiment.
Motivated by the absence of both spin freezing and a cooperative Jahn-Teller effect at the lowest measured temperatures, we study the ground state of Ba3CuSb2O9. We solve a general spin-orbital model on both the honeycomb and the decorated honeycomb
lattice, revealing rich phase diagrams. The spin-orbital model on the honeycomb lattice contains an SU(4) point, where previous studies have shown the existence of a spin-orbital liquid with algebraically decaying correlations. For realistic parameters on the decorated honeycomb lattice, we find a phase that consists of clusters of nearest-neighbour spin singlets, which can be understood in terms of dimer coverings of an emergent square lattice. While the experimental situation is complicated by structural disorder, we show qualitative agreement between our theory and a range of experiments.
The idea that a quantum magnet could act like a liquid crystal, breaking spin-rotation symmetry without breaking time-reversal symmetry, holds an abiding fascination. However, the very fact that spin nematic states do not break time-reversal symmetry
renders them invisible to the most common probes of magnetism - they do not exhibit magnetic Bragg peaks, a static splitting of lines in NMR spectra, or oscillations in muSR. Nonetheless, as a consequence of breaking spin-rotation symmetry, spin-nematic states do possess a characteristic spectrum of dispersing excitations which could be observed in experiment. With this in mind, we develop a symmetry-based description of long-wavelength excitations in a spin-nematic state, based on an SU(3) generalisation of the quantum non-linear sigma model. We use this field theory to make explicit predictions for inelastic neutron scattering, and argue that the wave-like excitations it predicts could be used to identify the symmetries broken by the otherwise unseen spin-nematic order.
There is now strong theoretical evidence that a wide range of frustrated magnets should support quantum spin-nematic order in applied magnetic field. Nonetheless, the fact that spin-nematic order does not break time-reversal symmetry makes it very di
fficult to detect in experiment. In this article, we continue the theme begun in [Phys. Rev. B 88, 184430 (2013)], of exploring how spin-nematic order reveals itself in the spectrum of spin excitations. Building on an earlier analysis of inelastic neutron scattering [Phys. Rev. B 91, 174402 (2015)], we show how the NMR 1/T_1 relaxation rate could be used to identify a spin-nematic state. We emphasise the characteristic, universal features of 1/T_1, using a symmetry-based description of the spin-nematic order parameter and its fluctuations.Turning to the specific case of spin-1/2 frustrated ferromagnets, we show that the signal from competing spin-wave excitations can be suppressed through a judicious choice of nuclear site and field direction. As a worked example, we show how P NMR in the square-lattice frustrated ferromagnet BaCdVO(PO_4)_2 is sensitive to spin-nematic order.
