Peter C. W. Holdsworth

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

Magnetic fluctuations in the classical XY model: The origin of an exponential tail in a complex system

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

Melting artificial 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.

Violation of ensemble equivalence in the antiferromagnetic mean-field XY model

We study the probability density function for the fluctuations of the magnetic order parameter in the low-temperature phase of the XY model of finite size. In two dimensions, this system is critical over the whole of the low-temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent eta. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high-resolution molecular dynamics and Monte Carlo simulations. The asymptotes of the distribution are calculated and found to be of exponential and double exponential form. The calculated distribution is fitted to three standard functions: a generalization of Gumbels first asymptote distribution from the theory of extremal statistics, a generalized log-normal distribution, and a chi(2) distribution. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than 4, despite the fact that critical fluctuations are limited to D=2. These results are discussed in the light of similar behavior observed in models of interface growth and for dissipative systems driven into a nonequilibrium steady state.

Universal fluctuations of the Danube water level: A link with turbulence, criticality and company growth

Artificial spin ice arrays of micromagnetic islands are a means of engineering additional energy scales and frustration into magnetic materials. Here we demonstrate a magnetic phase transition in an artificial square spin ice and use the symmetry of the lattice to verify the presence of excitations far below the ordering temperature. We do this by measuring the temperature-dependent magnetization in different principal directions and comparing it with simulations of idealized statistical mechanical models. Our results confirm a dynamical pre-melting of the artificial spin ice structure at a temperature well below the intrinsic ordering temperature of the island material. We thus create a spin ice array that has the real thermal dynamics of artificial spins over an extended temperature range.

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

Abstract:It is well known that long-range interactions pose serious problems for the formulation of statistical mechanics. We show in this paper that ensemble equivalence is violated in a simple mean-field model of N fully coupled classical rotators with repulsive interaction (antiferromagnetic XY model). While in the canonical ensemble the rotators are randomly dispersed over all angles, in the microcanonical ensemble a bi-cluster of rotators separated by angle , forms in the low energy limit. We attribute this behavior to the extreme degeneracy of the ground state. We obtain empirically an analytical formula for the probability density function for the angle made by the rotator, which compares extremely well with numerical data and should become exact in the zero energy limit. At low energy, in the presence of the bi-cluster, an extensive amount of energy is located in the single harmonic mode, with the result that the energy temperature relation is modified. Although still linear, , it has the slope , instead of the canonical value .

From classical to quantum Kagomé antiferromagnet in a magnetic field

A global quantity, regardless of its precise nature, will often fluctuate according to a Gaussian limit distribution. However, in highly correlated systems, other limit distributions are possible. We have previously calculated one such distribution and have argued that this function should apply specifically, and in many instances, to global quantities that define a steady state. Here we demonstrate, for the first time, the relevance of this prediction to natural phenomena. The river level fluctuations of the Danube are observed to obey our prediction, which immediately establishes a generic statistical connection between turbulence, criticality and company growth statistics.

Statistics of extremal intensities for Gaussian interfaces

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.

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

We study the magnetic properties of the Kagome antiferromagnet going from the classical limit to the deep quantum regime of spin ½ systems. In all the cases there are special values for the magnetization, 1/3 in particular, in which a singular behavior is observed to occur in both the classical and quantum cases. We show clear evidence for a magnetization plateau for all S, in a wide range of XXZ anisotropies and for the occurrence of quantum order by disorder effects.

Criterion for universality-class-independent critical fluctuations: Example of the two-dimensional Ising model

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not coincide with the distribution of the integrated power spectrum (i.e., roughness of the surface), nor does it obey any of the known extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit distribution is, however, recovered in three cases: (i) in the nondispersive (white noise) limit, (ii) for high dimensions, and (iii) when only short-wavelength modes are kept. In the last two cases the limit distribution emerges in nonconventional scenarios.