arXiv subjects

P. C. W. Holdsworth

Publications and source records attributed to P. C. W. Holdsworth.

At least 19 recordsLinked to original sources

arXiv2025

Ferromagnetic fragmented state in the pyrochlore Ho$_2$Ru$_2$O$_7$

The consecutive magnetic ordering of the Ho and Ru ions in the pyrochlore Ho2Ru2O7 and their interplay are investigated by neutron scattering, magnetic and specific heat measurements. The Ru moments order at 95 K into a $Γ_5$ easy-plane antiferromagnetic state. At 1.55 K the Ho moments order into an unusual $Γ_9$ ferromagnetic state with extensive ground state entropy and structured spin dynamics. It is shown how the internal fields with $Γ_5$ and $Γ_9$ geometry allow for two symmetry breaking transitions. The lower temperature ordering is driven by ruthenium mediated interactions between holmium moments as spin ice correlations develop. The unsaturated order is compatible with a fragmented ferromagnetic state equivalent to pyrochlore kagome ice.

cond-mat.str-el↗

arXiv2025

Satisfaction and Violation of the Fluctuation-Dissipation Relation in spin ice materials

We test the fluctuation-dissipation relation (FDR) in spin ice materials Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ by measuring both the magnetic noise and the out-of-phase part of the susceptibility and comparing their ratio. We show that it is satisfied at temperatures well into the non-ergodic region below 600 mK, indicating local equilibrium. In both materials, below 400 mK, low frequency violations develop, showing an excess of noise as in spin glasses, with a frequency threshold of 0.1 Hz. New relaxation pathways and aging properties are unveiled in this frequency range in the ac susceptibility. The FDR remains valid at higher frequencies down to 150 mK.

cond-mat.str-el↗

arXiv2025

Perfectly hidden order and Z2 confinement transition in a fully packed monopole liquid

We investigate a variant of spin ice whose degenerate ground states are densely packed monopole configurations. An applied field drives this model through a Z2 confinement transition. This phase change is a variant of the U(1) Kasteleyn transition, but instead of saturated order the system has fluctuations in the confined phase, and shows critical scaling on both sides of the transition. Remarkably, the magnetic response scales with the critical exponent of the specific heat in the 3D Ising universality class. We prove this universality using a Kramers--Wannier duality to map to an Ising model. The dual order parameter maps back to a non-local string order parameter in the original model, invisible to any local probe. Further, we describe the transition in terms of a bosonic field theory including a pairing term.

cond-mat.str-el↗

arXiv2025

Monopoles, Dirac strings and Magnetic Noise in Model Spin Ice

Using the Dirac string formalism for monopoles we expose an extensive analogy between magnetic monopole excitations in the dumbbell model of spin ice and those of the vacuum. In both cases the Dirac strings are defined in the space-time of monopole trajectories which are simulated in spin ice using transition graphs between initial and final configurations. The Stanford experiment for Dirac monopole detection is reconstructed in spin ice using the fragmentation procedure. The setup is then extended to simulate magnetic noise experiments using stochastic dynamics. It is shown that the noise from the monopoles and their constraining strings can be separated and that the correlated signal over long times comes largely from the constraining strings rather than from the monopoles themselves.

cond-mat.str-el↗

arXiv2023

Neutron scattering from fragmented frustrated magnets

The fragmentation description is used to analyse calculated neutron scattering intensities from kagomé ice and spin ice systems. The longitudinal, transverse and harmonic fragments produce independent contributions to the neutron scattering intensity. This framework is used to analyse the ordering due to quantum fluctuations in the topologically constrained phase of kagomé ice and the monopole crystal phase of spin ice. Here, quantum fluctuations are restricted to the transverse fragment and they drive the system into a double-$q$ structure in which longitudinal and transverse fragments have a different ordering wave vector. The intensity reduction of the Bragg peaks for the transverse fragments, compared with known classical limits can be used as a diagnostic tool for quantum fluctuations. Published quantum Monte Carlo data for spin ice in a $[111]$ field are consistent with the proposed protocol.

cond-mat.str-el↗

arXiv2022

Emergent tri-criticality in magnetic metamaterials

Metallic discs engineered on the 100 nm scale have an internal magnetic texture which varies from a fully magnetized state to a vortex state with zero moment. The interplay between this internal structure and the inter-disc interactions is studied in magnetic metamaterials made of square arrays of the magnetic discs. The texture is modeled by a mesospin of varying length with O(2) symmetry and the inter-disc interaction by a nearest neighbour coupling between mesospins. The thermodynamic properties of the model are studied numerically and an ordering transition is found which varies from Kosterlitz-Thouless to first order via an apparent tri-critical point. The effective critical exponent characterising the finite size magnetization evolves from the value for the 2D-XY model to less than half this value at the tri-critical point. The consequences for future experiments both in and out of equilibrium are discussed.

cond-mat.mes-hall↗

arXiv2021

Fragmentation in Frustrated Magnets -- A review

Spin liquids are exotic phases of matter that often support emergent gauge fields and quasi-particle excitations. While spin liquids are commonly known for remaining disordered, their definition has been extended to include phases with broken symmetry corresponding to (partial) long-range order, such as chiral and nematic spin liquids for example. For Coulomb spin liquids, this ordering can be quantitatively understood via a Helmholtz decomposition between divergence-free and divergence-full terms. This phenomenon has been coined fragmentation, where spin degrees of freedom fragment into two components; the fluctuating disordered part and the ordered one. In this review, we will cover the theoretical and experimental aspects of this growing field, in particular its relation to magnetic monopoles in spin ice, its phase diagram and the possibility to observe it in solid-state crystal and artificial networks.

cond-mat.str-el↗

arXiv2021

Tunable critical correlations in kagome ice

We present a comprehensive experimental and theoretical study of the kagome ice Coulomb phase, that explores the fine tuning of critical correlations by applied field, temperature and crystal orientation. The continuous modification of algebraic correlations is observed by polarised neutron scattering experiments and is found to be well described by numerical simulations of an idealised model. We further clarify the thermodynamics of field tuned Kasteleyn transitions and demonstrate some dramatic finite size scaling properties that depend on how topological string defects wind around the system boundaries. We conclude that kagome ice is a remarkable example of a critical and topological state in a real system that may be subject to fine experimental control.

cond-mat.stat-mech↗

arXiv2020

Fragmented monopole crystal, dimer entropy and Coulomb interactions in Dy$_2$Ir$_2$O$_7$

Neutron scattering, specific heat and magnetisation measurements on both powders and single crystals reveal that Dy$_2$Ir$_2$O$_7$ realizes the fragmented monopole crystal state in which antiferromagnetic order and a Coulomb phase spin liquid co-inhabit. The measured residual entropy is that of a hard core dimer liquid, as predicted. Inclusion of Coulomb interactions allows for a quantitative description of both the thermodynamic data and the magnetisation dynamics, with the energy scale given by deconfined defects in the emergent ionic crystal. Our data reveal low energy excitations, as well as a large distribution of energy barriers down to low temperatures, while the magnetic response to an applied field suggests that domain wall pinning is important; results that call for further theoretical modelling.

cond-mat.str-el↗

arXiv2019

The multiple symmetry sustaining phase transitions of spin ice

We present the full phase diagram of the dumbbell model of spin ice as a function of temperature, chemical potential and staggered chemical potential which breaks the translational lattice symmetry in favour of charge crystal ordering. We observe a double winged structure with five possible phases, monopole fluid (spin ice), fragmented single monopole crystal phases and double monopole crystal, the zinc blend structure. Our model provides a skeleton for liquid-liquid phase transitions and for the winged structures observed for itinerant magnets under pressure and external field. We relate our results to recent experiments on Ho$_2$Ir$_2$O$_7$ and propose a wide ranging set of new experiments that exploit the phase diagram, including high pressure protocols, dynamical scaling of Kibble-Zurek form and universal violations of the fluctuation-dissipation theorem.

cond-mat.str-el↗

arXiv2016

Spin Ice Thin Film: Surface Ordering, Partial Magnetic Wetting and Emergent Square Ice

Motivated by recent realizations of Dy$_{2}$Ti$_{2}$O$_{7}$ and Ho$_{2}$Ti$_{2}$O$_{7}$ spin ice thin films, and more generally by the physics of confined gauge fields, we study a model of spin ice thin film with surfaces perpendicular to the $[001]$ cubic axis. The resulting open boundaries make half of the bonds on the interfaces inequivalent. By tuning the strength of these inequivalent "orphan" bonds, dipolar interactions induce a surface ordering equivalent to a two-dimensional crystallization of magnetic surface charges. This surface ordering can also be expected on the surfaces of bulk crystals. In analogy with partial wetting in soft matter, spins just below the surface are more correlated than in the bulk, but \emph{not} ordered. For ultrathin films made of one cubic unit cell, once the surfaces are ordered, a square ice phase is stabilized over a finite temperature window, as confirmed by its entropy and the presence of pinch points in the structure factor. Ultimately, the square ice degeneracy is lifted at lower temperature and the system orders in analogy with the well-known $F$-transition of the $6$-vertex model.

cond-mat.stat-mech↗

arXiv2014

Nature of finite-temperature transition in anisotropic pyrochlore Er2Ti2O7

We study the finite-temperature transition in a model XY antiferromagnet on a pyrochlore lattice, which describes the pyrochlore material Er2Ti2O7. The ordered magnetic structure selected by thermal fluctuations is six-fold degenerate. Nevertheless, our classical Monte Carlo simulations show that the critical behavior corresponds to the three-dimensional XY universality class. We determine an additional critical exponent nu_6=0.75>nu characteristic of a dangerously irrelevant scaling variable. Persistent thermal fluctuations in the ordered phase are revealed in Monte Carlo simulations by the peculiar coexistence of Bragg peaks and diffuse magnetic scattering, the feature also observed in neutron diffraction experiments.

cond-mat.str-el↗

arXiv2013

Crystal Shape-Dependent Magnetic Susceptibility and Curie Law Crossover in the Spin Ices Dy2Ti2O7 and Ho2Ti2O7

We present an experimental determination of the isothermal magnetic susceptibility of the spin ice materials Dy2Ti2O7 and Ho2Ti2O7 in the temperature range 1.8-300 K. The use of spherical crystals has allowed the accurate correction for demagnetizing fields and allowed the true bulk isothermal susceptibility X_T(T) to be estimated. This has been compared to a theoretical expression based on a Husimi tree approximation to the spin ice model. Agreement between experiment and theory is excellent at T > 10 K, but systematic deviations occur below that temperature. Our results largely resolve an apparent disagreement between neutron scattering and bulk measurements that has been previously noted. They also show that the use of non-spherical crystals in magnetization studies of spin ice may introduce very significant systematic errors, although we note some interesting - and possibly new - systematics concerning the demagnetizing factor in cuboidal samples. Finally, our results show how experimental susceptibility measurements on spin ices may be used to extract the characteristic energy scale of the system and the corresponding chemical potential for emergent magnetic monopoles.

cond-mat.str-el↗

arXiv2012

Quantum order by disorder and accidental soft mode Er2Ti2O7

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.

cond-mat.str-el↗

arXiv2009

The Kasteleyn transition in three dimensions: spin ice in a [100] field

We discuss the nearest neighbour spin ice model in the presence of a magnetic field placed along the cubic [100] direction. As recently shown in Phys. Rev. Lett. 100, 067207, 2008, the symmetry sustaining ordering transition observed at low temperature is a three dimensional Kasteleyn transition. We confirm this with numerical data using a non-local algorithm that conserves the topological constraints at low temperature and from analytic calculations from a Bethe lattice of corner sharing tetrahedra . We present a thermodynamic description of the Kasteleyn transition and discuss the relevance of our results to recent neutron scattering experiments on spin ice materials.

cond-mat.stat-mech↗

arXiv2008

Low energy theory of the t-t'-t''-U Hubbard Model at half-filling: interaction strengths in cuprate superconductors and an effective spin-only description of La_2CuO_4

Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many new types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band structure calculations and photoemission experiments on these systems, we include second and third neighbor hopping parameters, t' and t'', into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed, four hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on La2CuO4. Performing a spin wave analysis, we calculate the magnon dispersion as a function of U,t,t' and t''. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377, {2001}] for La2CuO4. The ring exchange terms are found essential, in particular to determine the relative sign of t' and t'', with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength U~8t consistent with Mott insulating behavior.

cond-mat.str-el↗

arXiv2008

Site Dilution in the Half-Filled One-Band Hubbard Model: Ring Exchange, Charge Fluctuations and Application to La2Cu_{1-x}(Mg/Zn)_xO4

We study the ground state quantum spin fluctuations around the Néel ordered state for the one-band ($t,U$) Hubbard model on a site-diluted square lattice. An effective spin Hamiltonian, $H_{\rm s}^{(4)}$, is generated using the canonical transformation method, expanding to order $t(t/U)^3$. $H_{\rm s}^{(4)}$ contains four-spin ring exchange terms as well as second and third neighbor bilinear spin-spin interactions. Transverse spin fluctuations are calculated to order $1/S$ using a numerical real space algorithm first introduced by Walker and Walsteadt. Additional quantum charge fluctuations appear to this order in $t/U$, coming from electronic hopping and virtual excitations to doubly occupied sites. The ground state staggered magnetization on the percolating cluster decreases with site dilution $x$, vanishing very close to the percolation threshold. We compare our results in the Heisenberg limit, $t/U \to 0$, with quantum Monte Carlo (QMC) results on the same model and confirm the existence of a systematic $x$-dependent difference between $1/S$ and QMC results away from $x=0$. For finite $t/U$, we show that the effects of both the ring exchange and charge fluctuations die away rapidly with increasing $t/U$. We use our finite $t/U$ results to make a comparison with results from experiments on La$_2$Cu$_{1-x}$(Mg/Zn)$_x$O$_4$.

cond-mat.stat-mech↗

arXiv2005

Neel order, ring exchange and charge fluctuations in the half-filled Hubbard model

We investigate the ground state properties of the two dimensional half-filled one band Hubbard model in the strong (large-U) to intermediate coupling limit ({\it i.e.} away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order t(t/U)^3. We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as t/U is increased from the t/U -> 0 Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an S=1/2 antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of t/U, despite the fact that the moment of the spin Hamiltonien, which depends on transverse spin fluctuations only, in an increasing function of t/U. We also comment on quantitative aspects of the t/U and 1/S expansions.

cond-mat.str-el↗