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We present a simple two-dimensional model in which the lattice degrees of freedom mediate the interactions between magnetic moments and electric dipoles. This model reproduces basic features, such as a sudden electric polarization switch-off when a magnetic field is applied and the ubiquitous dimerized distortion patterns and magnetic $\uparrow \uparrow \downarrow \downarrow$ ordering, observed in several multiferroic materials of different composition. The list includes E-type manganites, RMnO$_3$, nickelates such as in YNiO$_3$ and other materials under strain, such as TbMnO$_3$. In spite of its simplicity, the model presented here captures the essence of the origin of multiferroicity in a large class of type II multiferroics., Comment: 5 pages, 5 figures, Sup Info

The spin ice compound Dy$_2$Ti$_2$O$_7$ is well-known to realise a three-dimensional Coulomb spin liquid with magnetically charged monopole excitations. Its fate at low temperatures, however, remains an intriguing open question. Based on a low-temperature analysis of the magnetic noise and diffuse neutron scattering under different cooling protocols, combined with extensive numerical modelling, we argue that upon cooling, the spins freeze into what may be termed a `structural magnetic glass', without an a priori need for chemical or structural disorder. Specifically, our model indicates the presence of frustration on two levels, first producing a near-degenerate constrained manifold inside which phase ordering kinetics is in turn frustrated. Our results suggest that spin ice Dy$_2$Ti$_2$O$_7$ provides one prototype of magnetic glass formation specifically, and a setting for the study of kinetically constrained systems more generally., Comment: Paper+Sup. Info

We study single crystals of Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ under magnetic field and stress applied along their [001] direction. We find that many of the features that the emergent gauge field of spin ice confers to the macroscopic magnetic properties are preserved in spite of the finite temperature. The magnetisation vs. field shows an upward convexity within a broad range of fields, while the static and dynamic susceptibilities present a peculiar peak. Following this feature for both compounds, we determine a single experimental transition curve: that for the Kasteleyn transition in three dimensions, proposed more than a decade ago. Additionally, we observe that compression up to $-0.8\%$ along [001] does not significantly change the thermodynamics. However, the dynamical response of Ho$_2$Ti$_2$O$_7$ is quite sensitive to changes introduced in the ${\rm Ho}^{3+}$ environment. Uniaxial compression can thus open up experimental access to equilibrium properties of spin ice at low temperatures.

Ising models on a pyrochlore oxide lattice are usually associated with spin ice materials and "magnetic monopoles". Ever more often effects connecting magnetic and elastic degrees of freedom are reported on these and other related frustrated materials. Here we extend a spin-ice Hamiltonian to include coupling between spins and the O$^{-2}$ ions mediating superexchange; we call it the Magnetoelastic Spin Ice model (MeSI). There has been a long search for a model in which monopoles would spontaneously become the building blocks of new ground-states: the MeSI Hamiltonian is such a model. In spite of its simplicity and classical approach, it describes (both spin and oxygen lattice) the double-layered monopole crystal observed in Tb$_2$Ti$_2$O$_7$. Remarkably, the dipolar electric moment of single monopoles emerges as a probe for magnetism. As an example we show that, in principle, pinch points related to Coulomb phases could be detected in association with the O$^{-2}$-ion displacements.

The forging of strong correlations on decreasing temperature can take place without the arousal of conventional order. If this happens, as in some geometrically frustrated magnets, disorder can be a phenomenon more interesting than order itself. A Coulomb phase, for example, has critical-like pair-spin correlations, leading to neutron scattering \textit{pinch points} and emergent electromagnetism. Here we present a new instance of disorder in an Ising pyrochlore lattice: the \textit{Polarized Monopole Liquid} (PML), a dense monopole fluid with pinch points in the \textit{magnetic charge}-pair correlations. It is a phase of "monopole matter" never considered before which, in principle, can be stabilized in real materials using a magnetic field and uniaxial stress along the [100] direction. To explain how the monopole correlations arise, we show that the PML is a Coulomb phase in which spin fluctuations cannot be assigned either to monopoles or to internal magnetic moments, but necessarily comprehend both degrees of freedom. We develop a simple but nontrivial method to Helmholtz decompose the spin field into a divergenceless and a divergenceful part in magnetic charge disordered pyrochlores that shows the appearance of pinch points associated to the divergenceful component in places where Bragg peaks are observed for the "all-in/all-out" antiferromagnet.

A \emph{monopole liquid} is a magnetic charge-disordered spin system defined over an Ising pyrochlore lattice, with one single topological charge or \emph{monopole} in each tetrahedron. We define a simple model Hamiltonian for this system and compare its thermodynamics at zero magnetic field with that of spin ice ---a phase free of these charges. In spite of the liquid-like correlations between charges, we find that spins in the charged phase are uncorrelated at all temperatures, like in a perfect paramagnet. The addition of nearest neighbors interactions favoring neutral `2in-2out' excitations as a perturbation has a peculiar effect. While they decrease charge-charge correlations, new spin correlations resembling those in spin ice appear on increasing temperature. This helps us understand why dipolar correlations are observed in spin ices at unexpectedly high temperatures, and the major role of double excitations in erasing the Coulomb phase correlations. Ferromagnetic interactions strengthen the charges short range order and its associated spin correlations. Finally, we discuss how the monopole liquid can be related to other systems and materials where different phases of \emph{monopole matter} have been observed.

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 $[100]$, 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 $\approx 0.4 K$ for the parameters corresponding to the best known spin ice materials, $Dy_2Ti_2O_7$ and $Ho_2Ti_2O_7$. This shift implies effective dipolar fields as big as $0.05$ tesla opposing the applied field, and thus favoring 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 $[100]$ there are only three different stable phases at zero temperature., Comment: Accepted for publication in Journal of Physics: Condensed Matter

Among the frustrated magnetic materials, spin-ice stands out as a particularly interesting system. Residual entropy, freezing and glassiness, Kasteleyn transitions and fractionalisation of excitations in three dimensions all stem from a simple classical Hamiltonian. But is the usual spin-ice Hamiltonian a correct description of the experimental systems? Here we address this issue by measuring magnetic susceptibility in the two most studied spin-ice compounds, Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$, using a vector magnet. Using these results, and guided by a theoretical analysis of possible distortions to the pyrochlore lattice, we construct an effective Hamiltonian and explore it using Monte Carlo simulations. We show how this Hamiltonian reproduces the experimental results, including the formation of a phase of intermediate polarisation, and gives important information about the possible ground-state of real spin-ice systems. Our work suggests an unusual situation in which distortions might contribute to the preservation rather than relief of the effects of frustration., Comment: 27 pages, 8 figures, including supplementary information, accepted for publication in Nature Communications

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., Comment: 7 pages, 4 figures

In this article we study the classical nearest-neighbour spin-ice model (nnSI) by means of Monte Carlo simulations, using the Wang-Landau algorithm. The nnSI describes several of the salient features of the spin-ice materials. Despite its simplicity it exhibits a remarkably rich behaviour. The model has been studied using a variety of techniques, thus it serves as an ideal benchmark to test the capabilities of the Wang Landau algorithm in magnetically frustrated systems. We study in detail the residual entropy of the nnSI and, by introducing an applied magnetic field in two different crystallographic directions ([111] and [100],) we explore the physics of the kagome-ice phase, the transition to full polarisation, and the three dimensional Kasteleyn transition. In the latter case, we discuss how additional constraints can be added to the Hamiltonian, by taking into account a selective choice of states in the partition function and, then, show how this choice leads to the realization of the ideal Kasteleyn transition in the system., Comment: 9 pages, 9 figures

We study the dipolar spin-ice model at fixed density of single excitations, $\rho$, using a Monte Carlo algorithm where processes of creation and annihilation of such excitations are banned. In the limit of $\rho$ 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 et al. 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 $\rho$ 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., Comment: 5 pages, 4 figures

We report a study of the magnetoresistivity of high purity Sr$_3$Ru$_2$O$_7$, in the vicinity of its electronic nematic phase. By employing a triple-axis (9/1/1T) vector magnet, we were able to precisely tune both the magnitude and direction of the in-plane component of the magnetic field (H$_\parallel$). We report the dependence of the resistively determined anisotropy on H$_\parallel$ in the phase, as well as across the wider temperature-field region. Our measurements reveal a high-temperature anisotropy which mimics the behaviour of fluctuations from the underlying quantum critical point, and suggest the existence of a more complicated phase diagram than previously reported., Comment: 5 pages, 3 figures

We present a brief review of the physical properties of Sr3Ru2O7, in which the approach to a magnetic-field-tuned quantum critical point is cut off by the formation of a novel phase with transport characteristics consistent with those of a nematic electronic liquid crystal. Our goal is to summarize the physics that led to that conclusion being drawn, describing the key experiments and discussing the theoretical approaches that have been adopted. Throughout the review we also attempt to highlight observations that are not yet understood, and to discuss the future challenges that will need to be addressed by both experiment and theory., Comment: 14 pages, 7 Figures, minor corrections and updated references, accepted for publication in Physica C

We investigate the non-equilibrium behavior of the spin-ice material Dy$_2$Ti$_2$O$_7$ by studying its magnetization as a function of the rate at which an external field is swept. At temperatures below the enigmatic "freezing" temperature $T_{\rm equil}\approx600$ mK, we find that even the slowest sweeps fail to yield the equilibrium magnetization curve and instead give a smooth, initially much flatter curve. For higher sweep rates, the magnetization develops sharp steps accompanied by similarly sharp peaks in the temperature of the sample. We ascribe the former behavior to the energy barriers encountered in the magnetization process, which proceeds via flipping of spins on filaments traced out by the field-driven motion of the gapped, long-range interacting magnetic monopole excitations. In contrast, the peaks in temperature result from the released Zeeman energy not being carried away efficiently into the bath, with the resulting heating triggering a chain reaction., Comment: 4 pages, 3 figures

We report detailed investigation of quantum oscillations in Sr3Ru2O7, observed inductively (the de Haas-van Alphen effect) and thermally (the magnetocaloric effect). Working at fields from 3 T to 18 T allowed us to straddle the metamagnetic transition region and probe the low- and high-field Fermi liquids. The observed frequencies are strongly field-dependent in the vicinity of the metamagnetic transition, and there is evidence for magnetic breakdown. We also present the results of a comprehensive rotation study. The most surprising result concerns the field dependence of the measured quasiparticle masses. Contrary to conclusions previously drawn by some of us as a result of a study performed with a much poorer signal to noise ratio, none of the five Fermi surface branches for which we have good field-dependent data gives evidence for a strong field dependence of the mass. The implications of these experimental findings are discussed., Comment: 12 pages, 12 figures, submitted to PRB

We report measurements of quantum oscillations detected in the putative nematic phase of Sr3Ru2O7. Significant improvements in sample purity enabled the resolution of small amplitude dHvA oscillations between two first order metamagnetic transitions delimiting the phase. Two distinct frequencies were observed, and their amplitudes follow the normal Lifshitz-Kosevich profile. The Fermi surface sheets seem to correspond to a subset of those detected outside the phase. Variations of the dHvA frequencies are explained in terms of a chemical potential shift produced by reaching a peak in the density of states, and an anomalous field dependence of the oscillatory amplitude provides information on domains., Comment: 4 pages, 4 figures

In an externally applied magnetic field, ultra-pure crystals of the bilayer compound Sr$_3$Ru$_2$O$_7$ undergo a metamagnetic transition below a critical temperature, $T^*$, which varies as a function of the angle between the magnetic field $H$ and the Ru-O planes. Moreover, $T^*$ approaches zero when $H$ is perpendicular to the planes. This putative "metamagnetic quantum critical point", however, is preempted by a nematic fluid phase with order one resistive anisotropy in the {\it ab} plane. In a "realistic" bilayer model with moderate strength local Coulomb interactions, the existence of a sharp divergence of the electronic density of states near a van Hove singularity of the quasi-one-dimensional bands, and the spin-orbit couplings permitted by the presence of multiple orbitals result in a mean-field phase diagram which accounts for many of these experimentally observed phenomena. Although the spin-orbit coupling is not overly strong, it destroys the otherwise near perfect Fermi surface nesting and hence suppresses spin-density-wave (SDW) ordering., Comment: Typos fixed, References added

De Haas-van Alphen oscillations were measured in lanthanum tritelluride (LaTe_3) to probe the partially gapped Fermi surface resulting from charge density wave (CDW) formation. Three distinct frequencies were observed, one of which can be correlated with a FS sheet that is unaltered by CDW formation. The other two frequencies arise from FS sheets that have been reconstructed in the CDW state., Comment: 8 pages

Using Monte Carlo simulations we study jamming and percolation processes upon the random sequential adsorption of dimers on binary alloys with different degrees of structural order. We obtain the equimolar mixtures used as substrates by applying the isomorphism between an alloy and the Ising model (conserved order parameter). The annealing temperature $T$ of the mixture then is a continuous parameter that characterizes the different sets of substrates, shaping the deposition process. As the alloy undergoes an order-disorder phase transition at the Onsager critical temperature ($T_{c}$), the jamming and percolating properties of the dimers deposited over the substrate are subjected to non-trivial changes. These are reflected in a density-temperature phase diagram with three well-defined regions. We find that for $T < T^* = 1.22 T_{c}$ the occurrence of jamming prevents the onset of percolating clusters, while percolation is possible for $T > T^{*}$. Particular attention is focused close to $T^{*}$, where the interplay between jamming and percolation restricts fluctuations, forcing exponents seemingly different from the standard percolation universality class. By analogy with a thermal transition, we study the onset of percolation by using the {\it temperature} (in this case, the substrate annealing temperature) as a control parameter. By proposing thermal scaling Ansatzes we analyze the behavior of the percolation threshold and its thermally induced fluctuations. Also, the fractal dimension of the percolating cluster is determined. Based on these measurements and the excellent data collapsing, we conclude that the universality class of standard percolation is preserved for all temperatures., Comment: 20 pages, 10 figures

In principle, a complex assembly of strongly interacting electrons can self-organise into a wide variety of collective states, but relatively few such states have been identified in practice. We report that, in the close vicinity of a metamagnetic quantum critical point, high purity Sr3Ru2O7 possesses a large magnetoresistive anisotropy, consistent with the existence of an electronic nematic fluid. We discuss a striking phenomenological similarity between our observations and those made in high purity two-dimensional electron fluids in GaAs devices., Comment: 14 pages, 3 figures, 11 extra pages of supplementary information

The bilayer ruthenate Sr_3Ru_2O_7 has been cited as a textbook example of itinerant metamagnetic quantum criticality. However, recent studies of the ultra-pure system have revealed striking anomalies in magnetism and transport in the vicinity of the quantum critical point. Drawing on new experimental data, we propose that the anomalous phase behavior can be accommodated by a mechanism which relies on the effects of strong magnetoelastic coupling. We argue that the phenomenological theory identified here is more generic and raises the possibility of quantum tricritical behaviour., Comment: 5pages, 4 figures. Text revised for clarity and some more experimental data included

We report a study of the de Haas-van Alphen (dHvA) effect on the itinerant metamagnet Sr$_3$Ru$_2$O$_7$. Extremely high sample purity allows the observation of dHvA oscillations both above and below the metamagnetic transition field of 7.9 T. The quasiparticle masses are fairly large away from the transition, and are enhanced by up to an extra factor of three as the transition is approached, but the Fermi surface topography change is quite small. The results are qualitatively consistent with a field-induced Stoner transition in which the mass enhancement is the result of critical fluctuations., Comment: 4 pages, 3 figures

We report a systematic study of electron doping of Sr2RuO4 by non-isovalent substitution of La^(3+) for Sr^(2+). Using a combination of de Haas-van Alphen oscillations, specific heat, and resistivity measurements, we show that electron doping leads to a rigid-band shift of the Fermi level corresponding to one doped electron per La ion, with constant many-body quasiparticle mass enhancement over the band mass. The susceptibility spectrum is substantially altered and enhanced by the doping but this has surprisingly little effect on the strength of the unconventional superconducting pairing., Comment: 4 pages, 3 figures

We present measurements on ultra clean single crystals of the bilayered ruthenate metal Sr3Ru2O7, which has a magnetic-field-tuned quantum critical point. Quantum oscillations of differing frequencies can be seen in the resistivity both below and above its metamagnetic transition. This frequency shift corresponds to a small change in the Fermi surface volume that is qualitatively consistent with the small moment change in the magnetisation across the metamagnetic transition. Very near the metamagnetic field, unusual behaviour is seen. There is a strong enhancement of the resistivity in a narrow field window, with a minimum in the resistivity as a function of temperature below 1 K that becomes more pronounced as the disorder level decreases. The region of anomalous behaviour is bounded at low temperatures by two first-order phase transitions. The implications of the results are discussed. PACS: 68.35.Rh, 71.27.+a, 72.15.-v, 74.70.Pq, Comment: 12 pages 4 figures, submitted

We report the results of a study of the di erential magnetic susceptibility of Sr3Ru2O7 as a function of temperature and magnetic elds applied at a series of angles to the ab plane. By analysing the real and imaginary parts of the susceptibility, we conclude that the eld angle acts as a continuous tuning parameter for the critical end-point to a line of rst order metamagnetic phase transitions. The end-point sits at approximately 1.25K for elds applied in the ab plane, and is depressed to below 50 mK when the eld is aligned within 10 of the c axis., Comment: 9 pages 6 figs