The ``spin-ice'' state found in the rare-earth pyrochlore magnets Ho${}_{2}$Ti${}_{2}$O${}_{7}$ and Dy${}_{2}$Ti${}_{2}$O${}_{7}$ offers a beautiful realization of classical magnetostatics, complete with magnetic monopole excitations. It has been suggested that in ``quantum spin-ice'' materials, quantum-mechanical tunneling between different ice configurations, could convert the magnetostatics of spin ice into a quantum spin liquid that realizes a fully dynamical, lattice analogue of quantum electromagnetism. Here, we explore how such a state might manifest itself in experiment, within the minimal microscopic model of a such a quantum spin ice. We develop a lattice field theory for this model, and use this to make explicit predictions for the dynamical structure factor that would be observed in neutron scattering experiments on a quantum spin ice. We find that ``pinch points,'' which are the signal feature of a classical spin ice, fade away as a quantum ice is cooled to its zero-temperature ground state. We also make explicit predictions for the ghostly, linearly dispersing magnetic excitations which are the ``photons'' of this emergent electromagnetism. The predictions of this field theory are shown to be in quantitative agreement with quantum Monte Carlo simulations at zero temperature.

Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice

The ground-state properties of the spin-1 antiferromagnetic Heisenberg model on the corner-sharing tetrahedra, the pyrochlore lattice, are investigated. By breaking up each spin into a pair of 1/2-spins, the problem is reduced to the equivalent one of the spin-1/2 tetrahedral network in analogy with the valence bond solid state in one dimension. The twofold degeneracy of the spin singlets of a tetrahedron is lifted by a Jahn-Teller mechanism, leading to a cubic to tetragonal structural transition. It is proposed that the present mechanism is responsible for the phase transition observed in the spin-1 spinel compounds ${\mathrm{ZnV}}_{2}{\mathrm{O}}_{4}$ and ${\mathrm{MgV}}_{2}{\mathrm{O}}_{4}$.

Spin-Driven Jahn-Teller distortion in a Pyrochlore system

https://cyberleninka.org/article/n/859500.pdf

Quantum kagome frustrated antiferromagnets: One route to quantum spin liquids

The frustration of antiferromagnetic interactions on the loosely connected kagome lattice associated to the enhancement of quantum fluctuations for S=1/2 spins was acknowledged long ago as a keypoint to stabilize novel ground states of magnetic matter. Only very recently, the model compound Herbersmithite, ZnCu3(OH)6Cl2, a structurally perfect kagome antiferromagnet, could be synthesized and enables a close comparison to theories. We review and classify various experimental results obtained over the past years and underline some of the pending issues.

Quantum kagome antiferromagnet: ZnCu3(OH)6Cl2

We report thermodynamic measurements of the $S=\frac{1}{2}$ kagome lattice antiferromagnet ${\mathrm{ZnCu}}_{3}(\mathrm{OH}{)}_{6}{\mathrm{Cl}}_{2}$, a promising candidate system with a spin-liquid ground state. Using single crystal samples, the magnetic susceptibility both perpendicular and parallel to the kagome plane has been measured. A small, temperature-dependent anisotropy has been observed, where ${\ensuremath{\chi}}_{z}/{\ensuremath{\chi}}_{p}g1$ at high temperatures and ${\ensuremath{\chi}}_{z}/{\ensuremath{\chi}}_{p}l1$ at low temperatures. Fits of the high-temperature data to a Curie-Weiss model also reveal an anisotropy. By comparing with theoretical calculations, the presence of a small easy-axis exchange anisotropy can be deduced as the primary perturbation to the dominant Heisenberg nearest neighbor interaction. These results have great bearing on the interpretation of theoretical calculations based on the kagome Heisenberg antiferromagnet model to the experiments on ${\mathrm{ZnCu}}_{3}(\mathrm{OH}{)}_{6}{\mathrm{Cl}}_{2}$.

Refining the spin Hamiltonian in the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2 using single crystals.

We investigated the nature of the spin-glass like phase transition in the geometrically frustrated pyrochlore lattices ${\text{Y}}_{2}{\text{Mo}}_{2}{\text{O}}_{7}$ using the local probes nuclear and muon magnetic resonances, and the field-dependent long-range probes x-ray and neutron scatterings. The long-range probes indicated that ${\text{Y}}_{2}{\text{Mo}}_{2}{\text{O}}_{7}$ does not undergo any global symmetry changes, even in a field of 6 T. In contrast, the local signal indicates a lattice distortion close to the critical temperature. The nuclei show at least two inequivalent Y sites, and the muons show sublinear line broadening as a function of moment size, over a wide temperature range. The conclusion from all the measurements is that even in high field, the distortion of ${\text{Y}}_{2}{\text{Mo}}_{2}{\text{O}}_{7}$ takes place within the unit cell while its global cubic symmetry is preserved. Moreover, the muon result clearly indicates the presence of magnetoelastic coupling.

Origin of magnetic freezing in pyrochlore Y 2 Mo 2 O 7

We investigated the possibility of temperature-dependent lattice distortions in the pyrochlore compound Tb2Ti2O7 by measuring the internal magnetic field distribution, using muon spin resonance, and comparing it to the susceptibility. The measurements are done at temperatures as low as 70 mK and external fields up to 6 kG. We find that the evolution of the width of the field distribution can be explained by spin susceptibility only, thus ruling out a temperature-dependent hyperfine coupling. We conclude that lattice deformations are absent in Tb2Ti2O7.

https://iopscience.iop.org/article/10.1088/0953-8984/19/14/145270/pdf

Lack of static lattice distortion in Tb2Ti2O7

We report the results of high-field, low-temperature $\ensuremath{\mu}\mathrm{SR}$ measurements of the quasi-two-dimensional organic superconductors $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}\mathrm{Cu}{(\mathrm{NCS})}_{2}$, and $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}\mathrm{Cu}[\text{N}{(\mathrm{CN})}_{2}]\mathrm{Br}$. The $\ensuremath{\mu}\mathrm{SR}$ lineshapes for these compounds indicate the existence of partially ordered vortex lattice phases in the high-magnetic-field regime, up to 2.5 T for the former compound and 4 T for the latter compound. The observed sharp loss of order is found to be consistent with a vortex-lattice melting transition that is predicted by numerical simulations of weakly coupled layers of pancake vortices. It is argued that the robustness of the partially ordered vortex lattice phases could be due to strong flux-line pinning by a dilute ensemble of defects.

Partially ordered vortex lattices in the high-field low-temperature mixed state of quasi-two-dimensional organic superconductors

We present magnetization measurements on oriented powder of ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$ along and perpendicular to the orienting field. We find a dramatic difference in the magnetization between the two directions. It is biggest at low measurement fields $H$ or high temperatures. We show that the difference at high temperatures must emerge from Ising-like exchange anisotropy. This allows us to explain muon spin rotation data at $T\to 0$ in terms of an exotic ferromagnetic ground state.

Symmetry of the spin Hamiltonian for herbertsmithite: A spin- 1 2 kagome lattice

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Papers

Origin of magnetic freezing in pyrochlore Y 2 Mo 2 O 7

Lack of static lattice distortion in Tb2Ti2O7

Partially ordered vortex lattices in the high-field low-temperature mixed state of quasi-two-dimensional organic superconductors

Symmetry of the spin Hamiltonian for herbertsmithite: A spin- 1 2 kagome lattice