Roderich Moessner

The spin ice compounds Dy₂Ti₂O₇ and Ho₂Ti₂O₇ are highly unusual magnets which epitomize a set of concepts of great interest in modern condensed matter physics: their low-energy physics exhibits an emergent gauge field and their excitations are magnetic monopoles which arise from the fractionalization of the microscopic magnetic spin degrees of freedom. In this review, we provide an elementary introduction to these concepts and we survey the thermodynamics, statics and dynamics - in and out of equilibrium - of spin ice from these vantage points. Along the way, we touch on topics such as emergent Coulomb plasmas, observable "Dirac strings", and irrational charges. We close with the outlook for these unique materials.

C. Castelnovo, R. Moessner and S. L. Sondhi, Annu. Rev. Condens. Matter Phys. 3, 35 (2012) ; arXiv.pdf

We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbour antiferromagnetic interactions on a class of geometrically frustrated lattices which includes the kagome and pyrochlore lattices. We explore the behaviour of these magnets that results from their large ground-state degeneracies, emphasising universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest ground-state degeneracies. For the pyrochlore magnets, we give an explicit construction of all ground states, and show that they are not separated by internal energy barriers. We study the precessional spin dynamics of the Heisenberg pyrochlore antiferromagnet. There is no freezing transition or selection of preferred states. Instead, the relaxation time at low temperature, T, is of order hbar/(k_B T). We argue that this behaviour can also be expected in some other systems, including the Heisenberg model for the compound SrCr₈Ga₄O₁₉.

R. Moessner and J. T. Chalker, Phys. Rev. B 58, 12049 (1998) ; arXiv.pdf

We study the low-temperature behaviour of the classical Heisenberg antiferromagnet with nearest neighbour interactions on the pyrochlore lattice. Because of geometrical frustration, the ground state of this model has an extensive number of degrees of freedom. We show, by analysing the effects of small fluctuations around the ground-state manifold, and from the results of Monte Carlo and molecular dynamics simulations, that the system is disordered at all temperatures, T, and has a finite relaxation time, which varies as 1/T for small T.

R. Moessner and J. T. Chalker, Phys. Rev. Lett. 80, 2929 (1998) ; arXiv.pdf

Topological states of matter present a wide variety of striking new phenomena. Prominent among these is the fractionalisation of electrons into unusual particles: Majorana fermions [1], Laughlin quasiparticles [2] or magnetic monopoles [3]. Their detection, however, is fundamentally complicated by the lack of any local order, such as, for example, the magnetisation in a ferromagnet. While there are now several instances of candidate topological spin liquids [4], their identification remains challenging [5]. Here, we provide a complete and exact theoretical study of the dynamical structure factor of a two-dimensional quantum spin liquid in gapless and gapped phases. We show that there are direct signatures - qualitative and quantitative - of the Majorana fermions and gauge fluxes emerging in Kitaev's honeycomb model. These include counterintuitive manifestations of quantum number fractionalisation, such as a neutron scattering response with a gap even in the presence of gapless excitations, and a sharp component despite the fractionalisation of electron spin. Our analysis identifies new varieties of the venerable X-ray edge problem and explores connections to the physics of quantum quenches.

J. Knolle, D. L. Kovrizhin, J. T. Chalker and R. Moessner; Phys. Rev. Lett. 112, 207203 (2014); arXiv.pdf

We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the square lattice predicts that the dimers are in a critical Coulomb phase with algebraic, dipolar, correlations, in excellent agreement with our large-scale Monte Carlo simulations. The non-bipartite FCC and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases. We conjecture that extended critical phases are realized only on bipartite lattices, even in higher dimensions.

D. A. Huse, W. Krauth, R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 91, 167004 (2003) ; arXiv.pdf

We show that there are two types of RVB liquid phases present in three-dimensional quantum dimer models, corresponding to the deconfining phases of U(1) and Z₂ gauge theories in d=3+1. The former is found on the bipartite cubic lattice and is the generalization of the critical point in the square lattice quantum dimer model found originally by Rokhsar and Kivelson. The latter exists on the non-bipartite face-centred cubic lattice and generalizes the RVB phase found earlier by us on the triangular lattice. We discuss the excitation spectrum and the nature of the ordering in both cases. Both phases exhibit gapped spinons. In the U(1) case we find a collective, linearly dispersing, transverse excitation, which is the photon of the low energy Maxwell Lagrangian and we identify the ordering as quantum order in Wen's sense. In the Z₂ case all collective excitations are gapped and, as in d=2, the low energy description of this topologically ordered state is the purely topological BF action. As a byproduct of this analysis, we unearth a further gapless excitation, the pi0n, in the square lattice quantum dimer model at its critical point.

R. Moessner and S. L. Sondhi, Phys. Rev. B 68, 184512 (2003) ; arXiv.pdf

We study a frustrated dipolar array recently manufactured lithographically by Wang et al. [Nature 439, 303 (2006)] in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck.

G. Moller and R. Moessner, Phys. Rev. Lett. 96, 237202 (2006); arXiv.pdf

We analyse an array of linearly extended monodomain dipoles forming square and kagome lattices. We find that its phase diagram contains two (distinct) finite-entropy kagome ice regimes - one disordered, one algebraic - as well as a low-temperature ordered phase. In the limit of the islands almost touching, we find a staircase of corresponding entropy plateaux, which is analytically captured by a theory based on magnetic charges. For the case of a modified square ice array, we show that the charges ('monopoles') are excitations experiencing two distinct Coulomb interactions: a magnetic 'three-dimensional' one as well as a logarithmic `two dimensional' one of entropic origin.

G. Moller and R. Moessner, Phys. Rev. B 80, 140409 (2009); arXiv.pdf

Motivated by recent neutron scattering experiments, we derive and study an effective "pseudo-dipolar" spin-1/2 model for the XY pyrochlore antiferromagnet Er2Ti2O7. While a bond-dependent in-plane exchange anisotropy removes any continuous symmetry, it does lead to a one-parameter `accidental' classical degeneracy. This degeneracy is lifted by quantum fluctuations in favor of the non-coplanar spin structure observed experimentally - a rare experimental instance of quantum order by disorder. A non-Goldstone low-energy mode is present in the excitation spectrum in accordance with inelastic neutron scattering data. Our theory also resolves the puzzle of the experimentally observed continuous ordering transition, absent from previous models.

M. E. Zhitomirsky, M. V. Gvozdikova, P. C. W. Holdsworth and R. Moessner, Phys. Rev. Lett. 109, 077204 (2012) ; arXiv.pdf

We study the effects of magnetoelastic couplings on pyrochlore antiferromagnets. We employ Landau theory, extending an investigation begun by Yamashita and Ueda for the case of S=1, and semiclassical analyses to argue that such couplings generate bond order via a spin-Peierls transition. This is followed by, or concurrent with, a transition into one of several possible low-temperature Neel phases, with most simply collinear, but also coplanar or mixed spin patterns. In a collinear Neel phase, a dispersionless string-like magnon mode dominates the resulting excitation spectrum, providing a distinctive signature of the parent geometrically frustrated state. We comment on the experimental situation.

O. Tchernyshyov, R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 88, 067203 (2002) ; arXiv.pdf