Ludovic D. C. Jaubert

Signature of magnetic monopole and Dirac string dynamics in spin ice

Magnetic monopoles have eluded experimental detection since their prediction nearly a century ago by Dirac. Recently it has been shown that classical analogues of these enigmatic particles occur as excitations out of the topological ground state of a model magnetic system, dipolar spin ice. These quasi-particle excitations do not lead to a modification of Maxwells equations, but they do interact via Coulombs law and they are of magnetic origin. In this paper we present an experimentally measurable signature of monopole dynamics and show that magnetic relaxation measurements in spin ice materials can be interpreted entirely in terms of their diffusive motion on a diamond lattice in the grand canonical ensemble. The monopole trajectories are constrained to lie on a network of Dirac strings filling the quasi-particle vacuum. We find quantitative agreement between the time scales for relaxation in the Dirac string network and the magnetic relaxation data for the spin ice material

Three-dimensional Kasteleyn transition: spin ice in a [100] field.

Dy_{2}Ti_{2}O_{7}

Topological-Sector Fluctuations and Curie-Law Crossover in Spin Ice

. In the presence of a magnetic field the topology of the network prevents charge flow in the steady state, but transient monopole currents do occur, as well as monopole density gradients near the surface of an open system.

Semiclassical propagation of wavepackets with complex and real trajectories

We examine the statistical mechanics of spin-ice materials with a [100] magnetic field. We show that the approach to saturated magnetization is, in the low-temperature limit, an example of a 3D Kasteleyn transition, which is topological in the sense that magnetization is changed only by excitations that span the entire system. We study the transition analytically and using a Monte Carlo cluster algorithm, and compare our results with recent data from experiments on Dy2Ti2O7.

Are Multiphase Competition and Order by Disorder the Keys to Understanding Yb(2)Ti(2)O(7)

At low temperatures, a spin ice enters a Coulomb phase—a state with algebraic correlations and topologically constrained spin configurations. We show how analytical and numerical approaches for model spin-ice systems reveal a crossover between two Curie laws. One of these laws characterizes the high-temperature paramagnetic regime, while the other, which we call the “spin-liquid Curie law,” characterizes the low-temperature Coulomb-phase regime, which provides implicit evidence that the topological sector fluctuates. We compare our theory with experiment for Ho2Ti2O7, where this process leads to a nonstandard temperature evolution of the bulk susceptibility and the wave-vector-dependent magnetic susceptibility, as measured by neutron scattering. Theory and experiment agree for bulk quantities and at large scattering wave vectors, but differences at small wave vectors indicate that the classical spin-ice states are not equally populated at low temperatures. More generally, the crossover appears to be a generic property of the emergent gauge field for a classical spin liquid, and it sheds light on the experimental difficulty of measuring a precise Curie-Weiss temperature in frustrated materials. The susceptibility at finite wave vectors is shown to be a local probe of fluctuations among topological sectors on varying length scales.

Magnetic-Moment Fragmentation and Monopole Crystallization

We consider a semiclassical approximation, first derived by Heller and coworkers, for the time evolution of an originally Gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield three different semiclassical formulae involving different real trajectories. One of these formulae is Heller’s thawed Gaussian approximation. The other approximations are nonGaussian and may involve several trajectories determined by mixed initial–final conditions. These different formulae are tested for the cases of scattering by a hard wall, scattering by an attractive Gaussian potential and bound motion in a quartic oscillator. The formula with complex trajectories gives good results in all cases. The non-Gaussian approximations with real trajectories work well in some cases, whereas the thawed Gaussian works only in very simple situations.

Theory of multiple-phase competition in pyrochlore magnets with anisotropic exchange with application to Yb2Ti2O7, Er2Ti2O7, and Er2Sn2O7

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, which, incidentally, pertain to the perplexing quantum spin ice candidate Yb(2)Ti(2)O(7). Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder 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 Yb(2)Ti(2)O(7). The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb(2)Ti(2)O(7) [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 Yb(2)Ti(2)O(7) 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.

Spin ice under pressure: symmetry enhancement and infinite order multicriticality

The Coulomb phase, with its dipolar correlations and pinch-point–scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets. The emergent Coulomb phase of lattice-based systems has been associated with divergence-free fields and the absence of long-range order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can emerge naturally as a persistent fluctuating background in an otherwise ordered system. To explain this behavior, we introduce the concept of the fragmentation of the field of magnetic moments into two parts, one giving rise to a magnetic monopole crystal, the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Our theory is backed up by numerical simulations, and we discuss its importance with regard to the interpretation of a number of experimental results.

Crystal shape-dependent magnetic susceptibility and Curie law crossover in the spin ices Dy2Ti2O7 and Ho2Ti2O7

The family of magnetic rare-earth pyrochlore oxides R2M2O7 plays host to a diverse array of exotic phenomena, driven by the interplay between geometrical frustration and spin-orbit interaction, which leads to anisotropy in both magnetic moments and their interactions. In this article we establish a general, symmetry-based theory of pyrochlore magnets with anisotropic exchange interactions. Starting from a very general model of nearest-neighbor exchange between Kramers ions, we find four distinct classical ordered states, all with q=0, competing with a variety of spin liquids and unconventional forms of magnetic order. The finite-temperature phase diagram of this model is determined by Monte Carlo simulation, supported by classical spin-wave calculations. We pay particular attention to the region of parameter space relevant to the widely studied materials Er2Ti2O7, Yb2Ti2O7, and Er2Sn2O7. We find that many of the most interesting properties of these materials can be traced back to the “accidental” degeneracies where phases with different symmetries meet. These include the ordered ground-state selection by fluctuations in Er2Ti2O7, the dimensional reduction observed in Yb2Ti2O7, and the lack of reported magnetic order in Er2Sn2O7. We also discuss the application of this theory to other pyrochlore oxides.Han Yan, 2 Owen Benton, 3 Ludovic Jaubert, 4 and Nic Shannon 2, 3 Okinawa Institute of Science and Technology, Onna-son, Okinawa 904-0412, Japan Clarendon Laboratory, University of Oxford, Parks Rd., Oxford OX1 3PU, UK H. H. Wills Physics Laboratory, University of Bristol, Tyndall Av, Bristol BS8–1TL, UK Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1–6 Keeble Rd, Oxford OX1 3NP, UK (Dated: November 15, 2013)

A kagome map of spin liquids from XXZ to Dzyaloshinskii–Moriya ferromagnet

We study the low-temperature behavior of spin ice when uniaxial pressure induces a tetragonal distortion. There is a phase transition between a Coulomb liquid and a fully magnetized phase. Unusually, it combines features of discontinuous and continuous transitions: the order parameter exhibits a jump, but this is accompanied by a divergent susceptibility and vanishing domain wall tension. All these aspects can be understood as a consequence of an emergent SU(2) symmetry at the critical point. We map out a possible experimental realization.