Dipolar Spin Ice Model Research Articles

Effects of uniaxial pressure on the spin ice Ho2Ti2O7

The spin ice materials Ho2Ti2O7 and Dy2Ti2O7 are experimental and theoretical exemplars of highly frustrated magnetic materials. However, the effects of an applied uniaxial pressure are not well studied, and here we report magnetization measurements of Ho2Ti2O7 under uniaxial pressure applied in the [001], [111] and [110] crystalline directions. The basic features are captured by an extension of the dipolar spin ice model. We find a good match between our model and measurements with pressures applied along two of the three directions, and extend the framework to discuss the influence of crystal misalignment for the third direction. The parameters determined from the magnetization measurements reproduce neutron scattering measurements we perform under uniaxial pressure applied along the [110] crystalline direction. In the detailed analysis we include the recently verified susceptibility dependence of the demagnetizing factor. Our work demonstrates the application of a moderate applied pressure to modify the magnetic interaction parameters. The knowledge can be used to predict critical pressures needed to induce new phases and transitions in frustrated materials, and in the case of Ho2Ti2O7 we expect a transition to a ferromagnetic ground state for uniaxial pressures above 3.3 GPa.

Anomalous out-of-equilibrium dynamics in the spin-ice material Dy2Ti2O7 under moderate magnetic fields

We study experimentally and numerically the dynamics of the spin ice material Dy2Ti2O7 in the low temperature (T) and moderate magnetic field (B) regime (T ∈ [0.1, 1.7] K, B ∈ [0, 0.3] T). Our objective is to understand the main physics shaping the out-of-equilibrium magnetisation vs temperature curves in two different regimes. Very far from equilibrium, turning on the magnetic field after having cooled the system in zero field (ZFC) can increase the concentration of magnetic monopoles (localised thermal excitations present in these systems); this accelerates the dynamics. Similarly to electrolytes, this occurs through dissociation of bound monopole pairs. However, for spin ices the polarisation of the vacuum out of which the monopole pairs are created is a key factor shaping the magnetisation curves, with no analog. We observe a threshold field near 0.2 T for this fast dynamics to take place, linked to the maximum magnetic force between the attracting pairs. Surprisingly, within a regime of low temperatures and moderate fields, an extended Ohm’s law can be used to describe the ZFC magnetisation curve obtained with the dipolar spin-ice model. However, in real samples the acceleration of the dynamics appears even sharper than in simulations, possibly due to the presence of avalanches. On the other hand, the effect of the field nearer equilibrium can be just the opposite to that at very low temperatures. Single crystals, as noted before for powders, abandon equilibrium at a blocking temperature TB which increases with field. Curiously, this behaviour is present in numerical simulations even within the nearest-neighbours interactions model. Simulations and experiments show that the increasing trend in TB is stronger for B‖[100]. This suggests that the field plays a part in the dynamical arrest through monopole suppression, which is quite manifest for this field orientation.

Pauling Entropy, Metastability, and Equilibrium in Dy_{2}Ti_{2}O_{7} Spin Ice.

Determining the fate of the Pauling entropy in the classical spin ice material Dy_{2}Ti_{2}O_{7} with respect to the third law of thermodynamics has become an important test case for understanding the existence and stability of ice-rule states in general. The standard model of spin ice-the dipolar spin ice model-predicts an ordering transition at T≈0.15 K, but recent experiments by Pomaranski etal. suggest an entropy recovery over long timescales at temperatures as high as 0.5K, much too high to be compatible with the theory. Using neutron scattering and specific heat measurements at low temperatures and with long timescales (0.35 K/10^{6} s and 0.5 K/10^{5} s, respectively) on several isotopically enriched samples, we find no evidence of a reduction of ice-rule correlations or spin entropy. High-resolution simulations of the neutron structure factor show that the spin correlations remain well described by the dipolar spin ice model at all temperatures. Furthermore, by careful consideration of hyperfine contributions, we conclude that the original entropy measurements of Ramirez etal. are, after all, essentially correct: The short-time relaxation method used in that study gives a reasonably accurate estimate of the equilibrium spin ice entropy due to a cancellation of contributions.

Proposal for the detection of magnetic monopoles in spin ice via nanoscale magnetometry

We present a proposal for applying nanoscale magnetometry to the search for magnetic monopoles in the spin ice materials holmium and dysprosium titanate. Employing Monte Carlo simulations of the dipolar spin ice model, we find that when cooled to below $1.5\,$K these materials exhibit a sufficiently low monopole density to enable the direct observation of magnetic fields from individual monopoles. At these temperatures we demonstrate that noise spectroscopy can capture the intrinsic fluctuations associated with monopole dynamics, allowing one to isolate the qualitative effects associated with both the Coulomb interaction between monopoles and the topological constraints implied by Dirac strings. We describe in detail three different nanoscale magnetometry platforms (muon spin rotation, nitrogen vacancy defects, and nanoSQUID arrays) that can be used to detect monopoles in these experiments, and analyze the advantages of each.

The 3D Kasteleyn transition in dipolar spin ice: a numerical study with the conserved monopoles algorithm

We study the three-dimensional Kasteleyn transition in both nearest neighbours and dipolar spin ice models using an algorithm that conserves the number of excitations. We first limit the interactions range to nearest neighbours to test the method in the presence of a field applied along , and then focus on the dipolar spin ice model. The effect of dipolar interactions, which is known to be greatly self screened at zero field, is particularly strong near full polarization. It shifts the Kasteleyn transition to lower temperatures, which decreases ≈0.4 K for the parameters corresponding to the best known spin ice materials, and . This shift implies effective dipolar fields as big as 0.05 T opposing the applied field, and thus favouring the creation of ‘strings’ of reversed spins. We compare the reduction in the transition temperature with results in previous experiments, and study the phenomenon quantitatively using a simple molecular field approach. Finally, we relate the presence of the effective residual field to the appearance of string-ordered phases at low fields and temperatures, and we check numerically that for fields applied along there are only three different stable phases at zero temperature.

An intermediate state between the kagome-ice and the fully polarized state in Dy$_2$Ti$_2$O$_7$

Dy$_2$Ti$_2$O$_7$ is at present the cleanest example of a spin-ice material. Previous theoretical and experimental work on the first-order transition between the kagome-ice and the fully polarized state has been taken as a validation for the dipolar spin-ice model. Here we investigate in further depth this phase transition using ac-susceptibility and dc-magnetization, and compare this results with Monte-Carlo simulations and previous magnetization and specific heat measurements. We find signatures of an intermediate state between the kagome-ice and full polarization. This signatures are absent in current theoretical models used to describe spin-ice materials.Received: 17 May 2015, Accepted: 12 June 2015; Edited by: A. Vindigni; Reviewed by: M. Perfetti, Dipartimento di Chimica, Universitá di Firenze, Italy; DOI: http://dx.doi.org/10.4279/PIP.070009Cite as: S A Grigera, R A Borzi, D G Slobinsky, A S Gibbs, R Higashinaka, Y Maeno, T S Grigera, Papers in Physics 7, 070009 (2015)This paper, by S A Grigera, R A Borzi, D G Slobinsky, A S Gibbs, R Higashinaka, Y Maeno, T S Grigera, is licensed under the Creative Commons Attribution License 3.0.

Coulombic charge ice

We consider a classical model of charges $\pm q$ on a pyrochlore lattice in the presence of long range Coulomb interactions. This model first appeared in the early literature on charge order in magnetite. In the limit where the interactions become short-ranged, the model has a ground state with an extensive entropy and dipolar charge-charge correlations. When long range interactions are introduced, the exact degeneracy is broken. We study the thermodynamics of the model and show the presence of a correlated charge liquid within a temperature window in which the physics is well described as a liquid of screened charged defects. The structure factor in this phase, which has smeared pinch points at the reciprocal lattice points, may be used to detect charge ice experimentally. In addition, the model exhibits fractionally charged excitations $\pm q/2$ which are shown to interact via a $1/r$ potential. At lower temperatures, the model exhibits a transition to a long-range ordered phase. We are able to treat the Coulombic charge ice model and the dipolar spin ice model on an equal footing by mapping both to a constrained charge model on the diamond lattice. We find that states of the two ice models are related by a staggering field which is reflected in the energetics of these two models. From this perspective we can understand the origin of the spin ice and charge ice ground states as coming from a dipolar model on a diamond lattice. We study the properties of charge ice in an external electric field finding that the correlated liquid is robust to the presence of a field in contrast to the case of spin ice in a magnetic field. Finally, we comment on the transport properties of Coulombic charge ice in the correlated liquid phase.

Charge Ordering in a Pure Spin Model: Dipolar Spin Ice

We study the dipolar spin-ice model at fixed density of single excitations, ρ, using a Monte Carlo algorithm where processes of creation and annihilation of such excitations are banned. In the limit of ρ going to zero, this model coincides with the usual dipolar spin-ice model at low temperatures, with the additional advantage that a negligible number of monopoles allows for equilibration even at the lowest temperatures. Thus, the transition to the ordered fundamental state found by Melko, den Hertog, and Gingras in 2001 is reached using simple local spin flip dynamics. As the density is increased, the monopolar nature of the excitations becomes apparent: the system shows a rich ρ vs T phase diagram with "charge" ordering transitions analogous to that observed for Coulomb charges in lattices. A further layer of complexity is revealed by the existence of order both within the charges and their associated vacuum, which can only be described in terms of spins--the true microscopic degrees of freedom of the system.

Magnetic monopole dynamics in spin ice

One of the most remarkable examples of emergent quasi-particles is that of the‘fractionalization’ of magnetic dipoles in the low energy configurations of materials knownas ‘spin ice’ into free and unconfined magnetic monopoles interacting via Coulomb’s1/r law (Castelnovo et al 2008 Nature 451 42–5). Recent experiments have shown that aCoulomb gas of magnetic charges really does exist at low temperature in these materialsand this discovery provides a new perspective on otherwise largely inaccessiblephenomenology. In this paper, after a review of the different spin ice models, we presentdetailed results describing the diffusive dynamics of monopole particles starting both fromthe dipolar spin ice model and directly from a Coulomb gas within the grand canonicalensemble. The diffusive quasi-particle dynamics of real spin ice materials within the‘quantum tunnelling’ regime is modelled with Metropolis dynamics, with theparticles constrained to move along an underlying network of oriented paths, whichare classical analogues of the Dirac strings connecting pairs of Dirac monopoles.

Artificial Kagome Arrays of Nanomagnets: A Frozen Dipolar Spin Ice

Magnetic frustration effects in artificial kagome arrays of nanomagnets are investigated using x-ray photoemission electron microscopy and MonteCarlo simulations. Spin configurations of demagnetized networks reveal unambiguous signatures of long range, dipolar interaction between the nanomagnets. As soon as the system enters the spin ice manifold, the kagome dipolar spin ice model captures the observed physics, while the short range kagome spin ice model fails.

The temperature evolution of the magnetic correlations in pure and diluted spin ice Ho2−xYxTi2O7

Diffuse polarized neutron scattering studies have been carried out on single crystals of pyrochlore spin ice Ho2−xYxTi2O7 (x=0, 0.3, and 1) to investigate the effects of doping and anisotropy on spin correlations in the system. The crystals were aligned with the (1−10) orientation coincident with the direction of neutron polarization. For all the samples studied the spin flip (SF) diffuse scattering (i.e. the in-plane component) reveals that the spin correlations can be described using a nearest-neighbour spin ice model (NNSM) at higher temperatures (T=3.6K) and a dipolar spin ice model (DSM) as the temperature is reduced (T=30mK). In the non-spin flip (NSF) channel (i.e. the out-of-plane component), the signature of strong antiferromagnetic correlations is observed for all the samples at the same temperature as the dipolar spin ice behaviour appears in the SF channel. Our studies show that the non-magnetic dopant Y does not significantly alter SF or NSF scattering for the spin ice state, even when Y doping is as high as 50%. In this paper, we focus on the experimental results of the highly doped spin ice HoYTi2O7 and compare our results with pure spin ice Ho2Ti2O7. The crossover from a dipolar to a nearest-neighbour spin ice behaviour and the doping insensitivity in spin ices are briefly discussed.

Dynamic Spin Ice:Pr2Sn2O7

In this Letter, we report a new spin ice--Pr2Sn2O7--which appears to have enhanced residual entropy due to the dynamic nature of the spins. Neutron scattering experiments show that at 200 mK, there is a significant amount of magnetic diffuse scattering which can be fit to the dipolar spin-ice model. However, these short-ranged ordered spins have a quasielastic response that is atypical of the canonical spin ices, and suggests that the ground state is dynamic (i.e., composed of locally ordered two-in-two-out spin configurations that can tunnel between energetically equivalent orientations). We report this as an example of a dynamic spin ice down to 200 mK.

Neutron scattering investigation of the spin ice state inDy2Ti2O7

Dy2Ti2O7 has been advanced as an ideal spin ice. We present a neutron scattering investigation of a sample of 162Dy2Ti2O7. The scattering intensity has been mapped in zero applied field in the hhl and hk0 planes at temperatures between 0.05 K and 20 K. The measured diffuse scattering (in the static approximation) has been compared to that predicted by the dipolar spin ice model. The comparison is good, except at the Brillouin zone boundaries where extra scattering appears in the experimental data. It is concluded that the dipolar spin ice model provides a successful basis for understanding Dy2Ti2O7, but that there are issues which remain to be clarified.

Magnetic anisotropy of the spin-ice compound Dy2Ti2O7

We report magnetization and ac susceptibility of single crystals of the spin ice compound Dy2Ti2O7. Saturated moments at 1.8 K along the charasteristic axes [100] and [110] agree with the expected values for an effective ferromagnetic nearest-neighbor Ising pyrochlore with local <111> anisotropy, where each magnetic moment is constrained to obey the `ice-rule'. At high enough magnetic fields along the [111] axis, the saturated moment exhibits a beaking of the ice-rule; it agrees with the value expected for a three-in one-out spin configuration. Assuming the realistic magnetic interaction between Dy ions given by the dipolar spin ice model, we completely reproduce the results at 2 K by Monte Carlo calculations. However, down to at least 60 mK, we have not found any experimental evidence of the long-range magnetic ordering predicted by this model to occur at around 180 mK. Instead, we confirm the spin freezing of the system below 0.5 K.

Structural and magnetic characterization of Ho3SbO7 and Dy3SbO7

We present an experimental investigation of the structural and magnetic properties of Ho3SbO7 and Dy3SbO7. These compounds adopt the Y3TaO7 structure, space group C2221. The magnetic rare-earth ions occupy an intricate lattice related to the pyrochlore lattice that occurs in Ho2Ti2O7 and Dy2Ti2O7. The crystal structure of Ho3SbO7 is determined by Rietveld refinement of the powder X-ray diffraction pattern at ambient temperature, and that of the Dy analogue is inferred to be similar. Magnetic susceptibility measurements show that Ho3SbO7 and Dy3SbO7 have negative Curie–Weiss temperatures: –8.4 K (Ho) and –9.2 K (Dy). Magnetic transitions have been detected at 2.0 K (Ho) and 3.0 K (Dy). We discuss the results in terms of the ``dipolar spin ice model'' that has been used to describe Ho2Ti2O7 and Dy2Ti2O7. PACS Nos.: 75.25+z, 75.50Ee, 61.10Nz

Long-range order at low temperatures in dipolar spin ice.

It has recently been suggested that long-range magnetic dipolar interactions are responsible for spin ice behavior in the Ising pyrochlore magnets Dy2Ti2O7 and Ho2Ti2O7. We report here numerical results on the low temperature properties of the dipolar spin ice model, obtained via a new loop algorithm which greatly improves the dynamics at low temperature. We recover the previously reported missing entropy in this model, and find a first order transition to a long-range ordered phase with zero total magnetization at very low temperature. We discuss the relevance of these results to Dy2Ti2O7 and Ho2Ti2O7.

Spin Correlations inHo2Ti2O7: A Dipolar Spin Ice System

The pyrochlore material Ho2Ti2O7 has been suggested to show "spin ice" behavior. We present neutron scattering and specific heat results that establish unambiguously that Ho2Ti2O7 exhibits spin ice correlations at low temperature. Diffuse magnetic neutron scattering is quite well described by a nearest neighbor spin ice model and very accurately described by a dipolar spin ice model. The heat capacity is well accounted for by the sum of a dipolar spin ice contribution and an expected nuclear spin contribution, known to exist in other Ho3+ salts. These results settle the question of the nature of the low temperature spin correlations in Ho2Ti2O7 for which contradictory claims have been made.