The "spin ice" state found in the rare earth pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 offers a beautiful realisation of classical magnetostatics, complete with magnetic monopole excitations. It has been suggested that in "quantum spin ice" materials, quantum-mechanical tunnelling between different ice configurations could convert the magnetostatics of spin ice into a quantum spin liquid which realises a fully dynamical, latticeanalogue 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 which 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.

No abstract

Spin liquid states are often described as the antithesis of magnetic order. Recently, however, it has been proposed that in certain frustrated magnets the magnetic degrees of freedom may "fragment" in such a way as to give rise to a coexistence of spin liquid and ordered phases. Recent neutron scattering results [S. Petit et al., Nature Phys., Advance online publication, (2016)] suggest that this scenario may be realized in the pyrochlore magnet Nd2Zr2O7. These observations show the characeristic pinch point features of a Coulombic spin liquid occurring alongside the Bragg peaks of an "all-in-all-out" ordered state. Here we explain the quantum origins of this apparent magnetic moment fragmentation, within the framework of a quantum model of nearest neighbour exchange, appropriate to Nd2Zr2O7. This model is able to capture both the ground state order and the pinch points observed at finite energy. The observed fragmentation arises due to the combination of the unusual symmetry properties of the Nd 3+ ionic wavefunctions and the structure of equations of motion of the magnetic degrees of freedom. The results of our analysis suggest that Nd2Zr2O7 is proximate to a U (1) spin liquid phase and is a promising candidate for the observation of a Higgs transition in a magnetic system.

If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is perhaps no less fascinating, providing an avenue for the exploration and discovery of unconventional behaviors. Here we study a realistic minimal model where a number of such mechanisms converge and which, incidentally, pertain to the perplexing quantum spin ice candidate Yb2Ti2O7. Specifically, we explain how thermal and quantum fluctuations, optimized by order-bydisorder selection, conspire to expand the stability region of a degenerate continuous U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb2Sn2O7. The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb2Ti2O7 [Lhotel et al., Phys. Rev. B 89 224419 (2014)]. By combining a gamut of numerical techniques, we obtain compelling evidence that such multiphase competition is a natural engine for the substantial sample-to-sample variability observed in Yb2Ti2O7 and is the missing key to ultimately understand the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.The vast interest in magnetic frustration largely stems from the diversity of unconventional phenomena it begets, ranging from anomalous Hall effect [1] to multiferroicity [2], to name only a few. The reason for this diversity is the indecisiveness of frustrated magnets towards ordering which opens an avenue for exotic mechanisms to control their low-temperature properties.This diversity of ordering processes is vividly illustrated within the family of rare-earth pyrochlore compounds [3][4][5][6][7]. In Er 2 Ti 2 O 7 [8-12], soft modes of excitations are claimed to lift a ground-state degeneracy whose symmetry is U(1), i.e. generated by a continuous rotation of all spins. This order-by-disorder (ObD) mechanism [13] selects the so-called ψ 2 over the ψ 3 configurations depicted in Fig. 1(b-c) Under such circumstances, we believe that in order to make progress in understanding Yb 2 Ti 2 O 7 , it is necessary to search for unifying patterns. Recent bulk measurements [18] are particularly enlightening in that respect, as they provide compelling evidence for multi-step ordering in putative disorder-free Yb 2 Ti 2 O 7 , common to both powder and single crystals. Our motivation here is twofold. Firstly, we present a thorough analysis of multiphase competition for a range of parameters near those found to describe Yb 2 Ti 2 O 7 [14]. We show how both thermal and quantum fluctuations enhance the stability of the degenerate U(1) manifold previously observed in Er 2 Ti 2 O 7 , to the detriment of a splayed ferromagnetic (SFM) phase displayed in Fig. 1(d). Then, we apply our theory to Yb 2 Ti 2 O 7 , successfully accounting for the unusual multi-step ordering process and fie...