Roderich Moessner

Magnetic Monopoles in Spin Ice

Electrically charged particles, such as the electron, are ubiquitous. In contrast, no elementary particles with a net magnetic charge have ever been observed, despite intensive and prolonged searches (see ref. 1 for example). We pursue an alternative strategy, namely that of realizing them not as elementary but rather as emergent particles—that is, as manifestations of the correlations present in a strongly interacting many-body system. The most prominent examples of emergent quasiparticles are the ones with fractional electric charge e/3 in quantum Hall physics. Here we propose that magnetic monopoles emerge in a class of exotic magnets known collectively as spin ice: the dipole moment of the underlying electronic degrees of freedom fractionalises into monopoles. This would account for a mysterious phase transition observed experimentally in spin ice in a magnetic field, which is a liquid–gas transition of the magnetic monopoles. These monopoles can also be detected by other means, for example, in an experiment modelled after the Stanford magnetic monopole search.

Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7

Magnetic Monopoles Magnets come with a north and a south pole. Despite being predicted to exist, searches in astronomy and in high-energy particle physics experiments for magnetic monopoles (either north or south on their own) have defied observation. Theoretical work in condensed-matter systems has predicted that spin-ice structures may harbor such elusive particles (see the Perspective by Gingras). Fennell et al. (p. 415, published online 3 September) and Morris et al. (p. 411, published online 3 September) used polarized neutron scattering to probe the spin structure forming in two spin-ice compounds—Ho2Ti2O7 and Dy2Ti2O7—and present results in support of the presence of magnetic monopoles in both materials. Neutron scattering measurements on two spin-ice compounds show evidence for magnetic monopoles. Sources of magnetic fields—magnetic monopoles—have so far proven elusive as elementary particles. Condensed-matter physicists have recently proposed several scenarios of emergent quasiparticles resembling monopoles. A particularly simple proposition pertains to spin ice on the highly frustrated pyrochlore lattice. The spin-ice state is argued to be well described by networks of aligned dipoles resembling solenoidal tubes—classical, and observable, versions of a Dirac string. Where these tubes end, the resulting defects look like magnetic monopoles. We demonstrated, by diffuse neutron scattering, the presence of such strings in the spin ice dysprosium titanate (Dy2Ti2O7). This is achieved by applying a symmetry-breaking magnetic field with which we can manipulate the density and orientation of the strings. In turn, heat capacity is described by a gas of magnetic monopoles interacting via a magnetic Coulomb interaction.

Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model

We study the quantum dimer model on the triangular lattice, which is expected to describe the singlet dynamics of frustrated Heisenberg models in phases where valence bond configurations dominate their physics. We find, in contrast to the square lattice, that there is a truly short ranged resonating valence bond phase with no gapless excitations and with deconfined, gapped, spinons for a finite range of parameters. We also establish the presence of crystalline dimer phases.

Exact results for interacting electrons in high Landau levels

We study a two-dimensional electron system in a magnetic field with a fermion hard-core interaction and without disorder. Projecting the Hamiltonian onto the {ital n}th Landau level, we show that the Hartree-Fock theory is exact in the limit {ital n}{r_arrow}{infinity}, for the high-temperature, uniform density phase of an infinite system; for a finite-size system, it is exact at all temperatures. In addition, we show that a charge-density wave arises below a transition temperature {ital T}{sub {ital t}}. Using Landau theory, we construct a phase diagram which contains both unidirectional and triangular charge-density wave phases. We discuss the unidirectional charge-density wave at zero temperature and argue that quantum fluctuations are unimportant in the large-{ital n} limit. Finally, we discuss the accuracy of the Hartree-Fock approximation for potentials with a nonzero range such as the Coulomb interaction. {copyright} {ital 1996 The American Physical Society.}

Properties of a Classical Spin Liquid: The Heisenberg Pyrochlore Antiferromagnet

We study the low-temperature behavior of the classical Heisenberg antiferromagnet with nearest neighbor 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 analyzing 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

Colloquium: Artificial spin ice : Designing and imaging magnetic frustration

{T}^{\ensuremath{-}1}

LOW-TEMPERATURE PROPERTIES OF CLASSICAL GEOMETRICALLY FRUSTRATED ANTIFERROMAGNETS

for small T.

Short-ranged resonating valence bond physics, quantum dimer models, and Ising gauge theories

Frustration, the presence of competing interactions, is ubiquitous in the physical sciences and is a source of degeneracy and disorder, which in turn gives rise to new and interesting physical phenomena. Perhaps nowhere does it occur more simply than in correlated spin systems, where it has been studied in the most detail. In disordered magnetic materials, frustration leads to spin-glass phenomena, with analogies to the behavior of structural glasses and neural networks. In structurally ordered magnetic materials, it has also been the topic of extensive theoretical and experimental studies over the past two decades. Such geometrical frustration has opened a window to a wide range of fundamentally new exotic behavior. This includes spin liquids in which the spins continue to fluctuate down to the lowest temperatures, and spin ice, which appears to retain macroscopic entropy even in the low-temperature limit where it enters a topological Coulomb phase. In the past seven years a new perspective has opened in the study of frustration through the creation of artificial frustrated magnetic systems. These materials consist of arrays of lithographically fabricated single-domain ferromagnetic nanostructures that behave like giant Ising spins. The nanostructures’ interactions can be controlled through appropriate choices of their geometric properties and arrangement on a (frustrated) lattice. The degrees of freedom of the material can not only be directly tuned, but also individually observed. Experimental studies have unearthed intriguing connections to the out-of-equilibrium physics of disordered systems and nonthermal “granular” materials, while revealing strong analogies to spin ice materials and their fractionalized magnetic monopole excitations, lending the enterprise a distinctly interdisciplinary flavor. The experimental results have also been closely coupled to theoretical and computational analyses, facilitated by connections to classic models of frustrated magnetism, whose hitherto unobserved aspects have here found an experimental realization. Considerable experimental and theoretical progress in this field is reviewed here, including connections to other frustrated phenomena, and future vistas for progress in this rapidly expanding field are outlined.

Artificial square ice and related dipolar nanoarrays.

We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbor antiferromagnetic interactions on a class of geometrically frustrated lattices, which includes the kagome and pyrochlore lattices. We explore the behavior of these magnets that results from their large ground-state degeneracies, emphasizing 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

Equilibrium states of generic quantum systems subject to periodic driving

\ensuremath{\Elzxh}{/k}_{B}T.