arXiv subjects

Steven T. Bramwell

Publications and source records attributed to Steven T. Bramwell.

At least 19 recordsLinked to original sources

arXiv2025

1/f^{3/2} Spectral Density at the Phonon Bottleneck

The common observation of anomalous `$1/f^α$' relaxation with $α<2$ constitutes one of the enduring mysteries of condensed matter physics. Here it is shown that a $1/f^α$ spectral density, with $α= 3/2$, can arise in the response of an ensemble of two--level systems coupled to a heat bath by means of a system of Bosonic quasiparticles. The model considered is the classic model of Faughnan and Strandberg of the phonon bottleneck, and the anomalous response is associated with an approximate non-equilibrium steady state of the phonons maintained by slow spin relaxation. The frequency dependence of the response to an applied field is calculated analytically, revealing the emergence, in the limit of a strong bottleneck, of $α=3/2$ behaviour over a diverging range of frequencies. The application of this result to experimental systems is discussed and comparisons are drawn with other systems that exhibit anomalous relaxation.

cond-mat.stat-mech↗

arXiv2025

Sample shape dependence of magnetic noise

Zero-field magnetic noise, characterised by the magnetic autocorrelation function $S_s(t)$, has been observed, perhaps surprisingly, to depend on sample shape $s$. The reasons for this are identified and general expressions are derived that relate the autocorrelation functions for systems of different shape to an underlying `intrinsic' form. Assuming the flcutuatiopn-dissipation theorem, it is shown that, for any noise that relaxes monotonically, the effect of sample shape is to reduce both the noise amplitude and mean relaxation time by a factor of $1+Nχ_i$, where $N$ is the demagnetizing factor and $χ_i$ the intrinsic susceptibility. In frequency space, where $S_s(t)$ Fourier transforms into the power spectrum $S_s(ω)$, the above two factors combine to suppress the zero frequency amplitude of $S_s(ω)$ by $(1+Nχ_i)^2$, while at high frequency, sample shape dependence becomes negligible. These results suggest simple and robust experimental tests of the fluctuation--dissipation theorem in magnetic systems that may be useful in distinguishing bulk from surface effects.

cond-mat.stat-mech↗

arXiv2023

Density-Jump Transitions in the Debye-Hückel Theory of Spin Ice and Electrolytes

Debye-Hückel theory, originally developed to describe dilute electrolyte solutions, has proved particularly successful as a description of magnetic monopoles in spin ice systems such as Dy$_{2}$Ti$_{2}$O$_{7}$. For this model, Ryzhkin et al. [JETP Lett. 95, 302-306 (2012)] predicted a phase transition in which the monopole density abruptly changes by several orders of magnitude but to date this transition has not been observed experimentally. Here we confirm that this transition is a robust prediction of Debye-Hückel theory, that does not rely on approximations made in the previous work. However, we also find that the transition occurs in a regime where the theory breaks downs as a description of a Coulomb fluid and may be plausibly interpreted as an indicator of monopole crystallisation. By extending Ryzhkin's model, we associate the density jump of Debye-Hückel theory with the monopole crystallisation observed in staggered-potential models of `magnetic moment fragmentation', as well as with crystallisation in conserved monopole-density models. The possibility of observing a true density-jump transition in real spin ice and electrolyte systems is discussed.

cond-mat.str-el↗

arXiv2022

Analytic Form of a Two-Dimensional Critical Distribution

This paper explores the possibility of establishing an analytic form of the distribution of the order parameter fluctuations in a two-dimensional critical spin wave model, or width fluctuations of a two dimensional Edwards-Wilkinson interface. It is shown that the characteristic function of the distribution can be expressed exactly as a Gamma function quotient, while a Charlier series, using the convolution of two Gumbel distributions as the kernel, converges to the exact result over a restricted domain. These results can also be extended to calculate the temperature dependence of the distribution and give an insight into the origin of Gumbel-like distributions in steady-state and equilibrium quantities that are not extreme values.

cond-mat.stat-mech↗

arXiv2021

Electric field fluctuations in the two-dimensional Coulomb fluid

The structure factor for electric field correlations in the two dimensional Coulomb fluid is simulated and compared to theories of the dielectric function. Singular changes in the structure factor occur at the BKT insulator to conductor transition, as well as at a higher temperature correlation transition between a poor electrolyte and perturbed Debye-Hückel fluid. Structure factors are found to differ in the canonical and grand canonical ensembles, with the poor electrolyte showing full ensemble inequivalence. We identify mechanisms of `underscreening' and `pinch point' scattering that are relevant to experiments on ionic liquids and artificial spin ice respectively.

cond-mat.stat-mech↗

arXiv2020

Experimental Measures of Topological Sector Fluctuations in the F-Model

The two dimensional F-model is an ice-rule obeying model, with a low temperature antiferroelectric state and high temperature critical Coulomb phase. Polarization in the system is associated with topological defects in the form of system-spanning windings which makes it an ideal system on which to observe topological sector fluctuations, as have been discussed in the context of spin ice and Berezinskii-Kosterlitz-Thouless (BKT) systems. Here we develop Lieb and Baxter's historic solutions of the F-model to exactly calculate relevant properties, several apparently for the first time. We further calculate properties not amenable to exact solution by an approximate cavity method and by referring to established scaling results. Of particular relevance to topological sector fluctuations are the exact results for the applied field polarization and the "energetic susceptibility". The latter is a both a measure of topological sector fluctuations and, surprisingly, in this case, a measure of the order parameter correlation exponent. In the high temperature phase, the temperature tunes the density of topological defects and algebraic correlations, with the energetic susceptibility undergoing a jump to zero at the antiferroelectric ordering temperature, analogous to the "universal jump" in BKT systems. We discuss how these results are relevant to experimental systems, including to spin ice thin films and three-dimensional dipolar spin ice and water ice, where we find that an analogous "universal jump" has previously been established in numerical studies. This unexpected result suggests a universal limit on the stability of perturbed Coulomb phases that is independent of dimension and of the order of the transition. Experimental results on water ice Ih are not inconsistent with this proposition. We complete the paper by relating our results to experimental studies of artificial spin ice arrays.

cond-mat.stat-mech↗

arXiv2020

LiHoF$_4$: Cuboidal Demagnetizing Factor in an Ising Ferromagnet

The demagnetizing factor has an important effect on the physics of ferromagnets. For cuboidal samples it depends on susceptibility and the historic problem of determining this function continues to generate theoretical and experimental challenges. To test a recent theory, we measure the magnetic susceptibility of the Ising dipolar ferromagnet LiHoF$_4$, using samples of varying aspect ratio, and we reconsider the demagnetizing transformation necessary to obtain the intrinsic material susceptibility. Our experimental results confirm that the microscopic details of the material significantly affect the transformation, as predicted. In particular, we find that the uniaxial Ising spins require a demagnetizing transformation that differs from the one needed for Heisenberg spins and that use of the wrong demagnetizing transformation would result in unacceptably large errors in the measured physical properties of the system. Our results further shed light on the origin of the mysterious `flat' susceptibility of ordered ferromagnets by demonstrating that the intrinsic susceptibility of the ordered ferromagnetic phase is infinite, regardless of sample shape.

cond-mat.str-el↗

arXiv2019

Screening and the Pinch Point Paradox in Spin Ice

A pinch point singularity in the structure factor characterizes an important class of condensed matter that is a counterpoint to the paradigm of broken symmetry. This class includes water ice, charge ice and spin ice. Of these, dipolar spin ice affords the the pre-eminent model system because it has a well-established Hamiltonian, is simple enough to allow analytical theory and numerical simulation, and is well represented in experiment by Dy$_{2}$Ti$_{2}$O$_{7}$ and Ho$_{2}$Ti$_{2}$O$_{7}$. Nevertheless it is a considerable challenge to resolve the pinch points in simulation or experiment as they represent a very long range correlation. Here we present very high resolution simulations of the polarized neutron scattering structure factor of dipolar spin ice and new analytical theory of the pinch point profiles. We compare these with existing theory and experiment. We find that our simulations are consistent with theories that reveal the pinch points to be infinitely sharp, as a result of unscreened dipolar fields. However, neither simulation nor these theories are consistent with experiments, which instead is quantitatively captured by a theory that allows for screening of the dipolar fields and consequent strong broadening of the pinch points. This striking paradox is not easily resolved: broadening of the pinch points by random disorder seems to have been ruled out by existing theory, while deficiencies in the Hamiltonian description are not relevant. Intriguingly, we are left to consider the role of quantum fluctuations or the possibility of a fundamental correction to either the standard method of simulating dipolar systems, or the theory of polarized neutron scattering. More generally, our results may have relevance far beyond ice systems. For example, spin ice is a model Debye-Hückel (magnetic) electrolyte, so our basic observation that the screening length may diverge while...

cond-mat.str-el↗

arXiv2019

Ammonium Fluoride as a Hydrogen-disordering Agent for Ice

The removal of residual hydrogen disorder from various phases of ice with acid or base dopants at low temperatures has been a focus of intense research for many decades. As an antipode to these efforts, we now show using neutron diffraction that ammonium fluoride (NH4F) is a hydrogen-disordering agent for the hydrogen-ordered ice VIII. Cooling its hydrogen-disordered counterpart ice VII doped with 2.5 mol% ND4F under pressure leads to a hydrogen-disordered ice VIII with ~31% residual hydrogen disorder illustrating the long-range hydrogen-disordering effect of ND4F. The doped ice VII could be supercooled by ~20 K with respect to the hydrogen-ordering temperature of pure ice VII after which the hydrogen-ordering took place slowly over a ~60 K temperature window. These findings demonstrate that ND4F-doping slows down the hydrogen-ordering kinetics quite substantially. The partial hydrogen order of the doped sample is consistent with the antiferroelectric ordering of pure ice VIII. Yet, we argue that local ferroelectric domains must exist between ionic point defects of opposite charge. In addition to the long-range effect of NH4F-doping on hydrogen-ordered water structures, the design principle of using topological charges should be applicable to a wide range of other 'ice-rule' systems including spin ices and related polar materials.

cond-mat.mtrl-sci↗

arXiv2018

Emergent Electrochemistry in Spin Ice: Debye-Hückel Theory and Beyond

The low-temperature picture of dipolar spin ice in terms of the Coulomb fluid of its fractionalised magnetic monopole excitations has allowed analytic and conceptual progress far beyond its original microscopic spin description. Here we develop its thermodynamic treatment as a `magnetolyte', a fluid of singly and doubly charged monopoles, an analogue of the electrochemical system ${\rm 2 H_2O = H_3O^+ +OH^- = H_4O^{2+} + O^{2-}}$, but with perfect symmetry between oppositely charged ions. For this lattice magnetolyte, we present an analysis based on Debye-Hückel theory, which is accurate at all temperatures and incorporates `Dirac strings' imposed by the microscopic ice rule constraints at the level of Pauling's approximation. Our results are in close agreement with the specific heat from numerical simulations as well as new experimental measurements with an improved lattice correction, which we present here, on the spin ice materials $\mathrm{Ho_2Ti_2O_7}$ and $\mathrm{Dy_2Ti_2O_7}$. Our study of the magnetolyte shows how electrochemistry can emerge in non-electrical systems. We also provide new experimental tests of Debye-Hückel theory and its extensions. The application of our results also yields insights into the electrochemical behaviour of water ice and liquid water, which are closely related to the spin ice magnetolyte.

cond-mat.str-el↗

arXiv2017

Doping-induced quantum cross-over in Er$_2$Ti$_{2-x}$Sn$_x$O$_7$

We present the results of the investigation of magnetic properties of the Er$_2$Ti$_{2-x}$Sn$_x$O$_7$ series. For small doping values the ordering temperature decreases linearly with $x$ while the moment configuration remains the same as in the $x = 0$ parent compound. Around $x = 1.7$ doping level we observe a change in the behavior, where the ordering temperature starts to increase and new magnetic Bragg peaks appear. For the first time we present evidence of a long-range order (LRO) in Er$_2$Sn$_2$O$_7$ ($x = 2.0$) below $T_N = 130$ mK. It is revealed that the moment configuration corresponds to a Palmer-Chalker type with a value of the magnetic moment significantly renormalized compared to $x = 0$. We discuss our results in the framework of a possible quantum phase transition occurring close to $x = 1.7$.

cond-mat.str-el↗

arXiv2017

An electric-field representation of the harmonic XY model

The two-dimensional harmonic XY (HXY) model is a spin model in which the classical spins interact via a piecewise parabolic potential. We argue that the HXY model should be regarded as the canonical classical lattice spin model of phase fluctuations in two-dimensional condensates, as it is the simplest model that guarantees the modular symmetry of the experimental systems. Here we formulate a lattice electric-field representation of the HXY model and contrast this with an analogous representation of the Villain model and the two-dimensional Coulomb gas with a purely rotational auxiliary field. We find that the HXY model is a spin-model analogue of a lattice electric-field model of the Coulomb gas with an auxiliary field, but with a temperature-dependent vacuum (electric) permittivity that encodes the coupling of the spin vortices to their background spin-wave medium. The spin vortices map to the Coulomb charges, while the spin-wave fluctuations correspond to auxiliary-field fluctuations. The coupling explains the striking differences in the high-temperature asymptotes of the specific heats of the HXY model and the Coulomb gas with an auxiliary field. Our results elucidate the propagation of effective long-range interactions throughout the HXY model (whose interactions are purely local) by the lattice electric fields. They also imply that global spin-twist excitations (topological-sector fluctuations) generated by local spin dynamics are ergodically excluded in the low-temperature phase. We discuss the relevance of these results to condensate physics.

cond-mat.stat-mech↗

arXiv2016

Topological-sector fluctuations and ergodicity breaking at the Berezinskii-Kosterlitz-Thouless transition

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.

cond-mat.stat-mech↗

arXiv2016

From quantum to thermal topological-sector fluctuations of strongly interacting bosons in a ring lattice

Inspired by recent experiments on Bose-Einstein condensates in ring traps, we investigate the topological properties of the phase of a one-dimensional Bose field in the presence of both thermal and quantum fluctuations -- the latter ones being tuned by the depth of an optical lattice applied along the ring. In the regime of large filling of the lattice, quantum Monte Carlo simulations give direct access to the full statistics of fluctuations of the Bose-field phase, and of its winding number $W$ along the ring. At zero temperature the winding-number (or topological-sector) fluctuations are driven by quantum phase slips localized around a Josephson link between two lattice wells, and their { susceptibility} is found to jump at the superfluid-Mott insulator transition. At finite (but low) temperature, on the other hand, the winding number fluctuations are driven by thermal activation of nearly uniform phase twists, whose activation rate is governed by the superfluid fraction. A quantum-to-thermal crossover in winding number fluctuations is therefore exhibited by the system, and it is characterized by a conformational change in the topologically non-trivial configurations, from localized to uniform phase twists, which can be experimentally observed in ultracold Bose gases via matter-wave interference.

cond-mat.quant-gas↗

arXiv2015

Phase order in superfluid helium films

Classic experimental data on helium films are transformed to estimate a finite-size phase order parameter that measures the thermal degradation of the condensate fraction in the two-dimensional superfluid. The order parameter is found to evolve thermally with the exponent $β= 3 π^2/128$, a characteristic, in analogous magnetic systems, of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Universal scaling near the BKT fixed point generates a collapse of experimental data on helium and ferromagnetic films, and implies new experiments and theoretical protocols to explore the phase order. These results give a striking example of experimental finite-size scaling in a critical system that is broadly relevant to two-dimensional Bose fluids.

cond-mat.stat-mech↗

arXiv2014

AC Wien effect in spin ice, manifest in non-linear non-equilibrium susceptibility

We predict the non-linear non-equilibrium response of a "magnetolyte", the Coulomb fluid of magnetic monopoles in spin ice. This involves an increase of the monopole density due to the second Wien effect---a universal and robust enhancement for Coulomb systems in an external field---which in turn speeds up the magnetization dynamics, manifest in a non-linear susceptibility. Along the way, we gain new insights into the AC version of the classic Wien effect. One striking discovery is that of a frequency window where the Wien effect for magnetolyte and electrolyte are indistinguishable, with the former exhibiting perfect symmetry between the charges. In addition, we find a new low-frequency regime where the growing magnetization counteracts the Wien effect. We discuss for what parameters best to observe the AC Wien effect in Dy$_2$Ti$_2$O$_7$.

cond-mat.stat-mech↗

arXiv2013

Onsager's Wien Effect on a Lattice

The Second Wien Effect describes the non-linear, non-equilibrium response of a weak electrolyte in moderate to high electric fields. Onsager's 1934 electrodiffusion theory along with various extensions has been invoked for systems and phenomena as diverse as solar cells, surfactant solutions, water splitting reactions, dielectric liquids, electrohydrodynamic flow, water and ice physics, electrical double layers, non-Ohmic conduction in semiconductors and oxide glasses, biochemical nerve response and magnetic monopoles in spin ice. In view of this technological importance and the experimental ubiquity of such phenomena, it is surprising that Onsager's Wien effect has never been studied by numerical simulation. Here we present simulations of a lattice Coulomb gas, treating the widely applicable case of a double equilibrium for free charge generation. We obtain detailed characterisation of the Wien effect and confirm the accuracy of the analytical theories as regards the field evolution of the free charge density and correlations. We also demonstrate that simulations can uncover further corrections, such as how the field-dependent conductivity may be influenced by details of microscopic dynamics. We conclude that lattice simulation offers a powerful means by which to investigate system-specific corrections to the Onsager theory, and thus constitutes a valuable tool for detailed theoretical studies of the numerous practical applications of the Second Wien Effect.

cond-mat.mtrl-sci↗

arXiv2012

Generalised Longitudinal Susceptibility for Magnetic Monopoles in Spin Ice

The generalised longitudinal susceptibility $χ({\bf q}, ω)$ affords a sensitive measure of the spatial and temporal correlations of magnetic monopoles in spin ice. Starting with the monopole model, a mean field expression for $χ({\bf q}, ω)$ is derived as well as expressions for the mean square longitudinal field and induction at a point. Monopole motion is shown to be strongly correlated, and both spatial and temporal correlations are controlled by the dimensionless monopole density $x$ which defines the ratio of the magnetization relaxation rate and the monopole hop rate. Thermal effects and spin lattice relaxation are also considered. The derived equations are applicable in the temperature range where the Wien effect for magnetic monopoles is negligible. They are discussed in the context of existing theories of spin ice and the following experimental techniques: dc and ac-magnetization, neutron scattering, neutron spin echo, and longitudinal and transverse field $μ$SR. The monopole theory is found to unify diverse experimental results, but several discrepancies between theory and experiment are identified. One of these, concerning the neutron scattering line shape, is explained by means of a phenomenological modification to the theory.

cond-mat.str-el↗