Monopolar and dipolar relaxation in spin ice Ho$_2$Ti$_2$O$_7$
Yishu Wang, T. Reeder, Y. Karaki, J. Kindervater, T. Halloran, N. Maliszewskyj, Yiming Qiu, J. A. Rodriguez, S. Gladchenko, S. M. Koohpayeh, S. Nakatsuji, C. Broholm
When degenerate states are separated by large energy barriers, the approach to thermal equilibrium can be slow enough that physical properties are defined by the thermalization process rather than the equilibrium. The exploration of thermalization pushes experimental boundaries and provides refreshing insights into atomic scale correlations and processes that impact steady state dynamics and prospects for realizing solid state quantum entanglement. We present a comprehensive study of magnetic relaxation in Ho$_2$Ti$_2$O$_7$ based on frequency-dependent susceptibility measurements and neutron diffraction studies of the real-time atomic-scale response to field quenches. Covering nearly ten decades in time scales, these experiments uncover two distinct relaxation processes that dominate in different temperature regimes. At low temperatures (0.6K<T<1K) magnetic relaxation is associated with monopole motion along the applied field direction through the spin-ice vacuum. The increase of the relaxation time upon cooling indicates reduced monopole conductivity driven by decreasing monopole concentration and mobility as in a semiconductor. At higher temperatures (1K<T<2K) magnetic relaxation is associated with the reorientation of monopolar bound states as the system approaches the single-spin tunneling regime. Spin fractionalization is thus directly exposed in the relaxation dynamics.
Ho2Ti2O7 and Dy2Ti2O7 spin ices exhibit elementary excitations akin to magnetic monopoles. Here we focus on Tb2Ti2O7 spin liquid, where correlated magnetic moments keep fluctuating down to very low temperatures. Using a monopole picture, we have re-analyzed the field-induced magnetic structure previously determined by neutron diffraction in Tb2Ti2O7. We show that under a high field applied along a [110] direction, Tb2Ti2O7 orders as a three dimensional arrangement of monopole and antimonopole double layers. In contrast, Ho2Ti2O7 spin ice in the same conditions behaves as a monopole-free state.…
Recent experiments on the spin-ice material Dy2Ti2O7 suggest that the Pauling "ice entropy", characteristic of its classical Coulombic spin-liquid state, may be lost at low temperatures [D. Pomaranski et al., Nature Phys. 9, 353 (2013)]. However, despite nearly two decades of intensive study, the nature of the equilibrium ground state of spin ice remains uncertain. Here we explore how long-range dipolar interactions D, short-range exchange interactions, and quantum fluctuations combine to determine the ground state of dipolar spin ice. We identify a new organisational principle, namely that or…
Recent experiments on Ce$_2$Zr$_2$O$_7$ suggest that this material may host a novel form of quantum spin ice, a three-dimensional quantum spin liquid with an emergent photon. The Ce$^{3+}$ local moments on the pyrochlore lattice are described by pseudospin 1/2 degrees of freedom, whose components transform as dipolar and octupolar moments under symmetry operations. In principle, there exist four possible quantum spin ice regimes, depending on whether the Ising component is in the dipolar/octupolar channel, and two possible flux configurations of the emergent gauge field. In this work, using ex…
The magnetically frustrated spin ice family of materials is host to numerous exotic phenomena such as magnetic monopole excitations and macroscopic residual entropy extending to low temperature. A finite-temperature ordering transition in the absence of applied fields has not been experimentally observed in the classical spin ice materials Dy2Ti2O7 and Ho2Ti2O7. Such a transition could be induced by the application of pressure, and in this work we consider the effects of uniaxial pressure on classical spin ice systems. Theoretically we find that the pressure induced ordering transition in Dy2T…
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 corresp…
We consider a class of d- and f-electron systems in which dipolar-octupolar Kramers doublets arise on the sites of the pyrochlore lattice. For such doublets, two components of the pseudospin transform like a magnetic dipole, while the other transforms like a component of the magnetic octupole tensor. Based on a symmetry analysis, we construct and study models of dipolar-octupolar doublets in itinerant and localized limits. In both limits, the resulting models are of surprisingly simple form. In the itinerant limit, we find topological insulating behavior. In the localized limit, the most gener…
Recently there have been a number of experiments on Ce$_2$Zr$_2$O$_7$ and Ce$_2$Sn$_2$O$_7$, suggesting that these materials host a three-dimensional quantum spin liquid with emergent photons and fractionalized spinon excitations. However, the interpretation of the data to determine the precise nature of the quantum spin liquids is still under debate. The Kramers doublet in Ce$^{3+}$ local moment offers unusual pseudo-spin degrees of freedom as the $x$ and $z$ components transform as a dipole and $y$ component as an octupole. This leads to a variety of possible quantum spin liquid (or quantum …
Observation of Dipolar Spin-ice--like Correlations in the Quantum Spin Ice Candidate Ce$_2$Sn$_2$O$_7$
McMaster University（麦克马斯特大学）；Clemson University（克莱姆森大学）；Harvard University（哈佛大学）；Max Planck Institute for Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Oak Ridge National Laboratory（橡树岭国家实验室）；Université de Montréal（蒙特利尔大学）
Influence of controlled disorder on the dipolar spin ice state of Ho-based pyrochlores
Oak Ridge National Laboratory（橡树岭国家实验室）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）；Perry College of Mathematics, Computing, and Sciences, University of West Georgia（佐治亚西部大学珀里数学、计算与科学学院）；Japan Atomic Energy Agency（日本原子能机构）；Brigham Young University（杨百翰大学）
Excitations in a spin ice behave as magnetic monopoles, and their population and mobility control the dynamics of a spin ice at low temperature. CdEr$_2$Se$_4$ is reported to have the Pauling entropy characteristic of a spin ice, but its dynamics are three-orders of magnitude faster than the canonical spin ice Dy$_2$Ti$_2$O$_7$. In this letter we use diffuse neutron scattering to show that both CdEr$_2$Se$_4$ and CdEr$_2$S$_4$ support a dipolar spin ice state -- the host phase for a Coulomb gas of emergent magnetic monopoles. These Coulomb gases have similar parameters to that in Dy$_2$Ti$_2$O…
We report here numerical results of the low-temperature behavior of a dipolar spin ice in a magnetic field along the [100] direction. Tuning the magnetic field, the system exhibit a half-magnetization plateau at low temperature. This half-polarized phase should correspond to a quantum solid phase in an effective 2D quantum boson model, and the transition from the Coulomb phase with a power-law correlation to this state can be regarded as a superfluid to a quantum solid transition. We discuss possible experimental signatures of this half-polarized state.
We present numerical studies of dipolar spin ice in the presence of a magnetic field slightly tilted away from the [111] axis. We find a first-order transition from a kagome ice to a $\mathbf{q}=$X state when the external field is tilted toward the $[11\bar{2}]$ direction. This is consistent with the anomalous critical scattering previously observed in the neutron scattering experiment on the spin ice material $\textrm{Ho}_{2}\textrm{Ti}_{2}\textrm{O}_{7}$ in a tilted field [Nat. Phys. 3, 566 (2007)]. We show that this ordering originates from the antiferromagnetic alignment of spin chains on …
Spin ice, a peculiar thermal state of a frustrated ferromagnet on the pyrochlore lattice, has a finite entropy density and excitations carrying magnetic charge. By combining analytical arguments and Monte Carlo simulations, we show that spin ice on the two-dimensional kagome lattice orders in two stages. The intermediate phase has ordered magnetic charges and is separated from the paramagnetic phase by an Ising transition. The transition to the low-temperature phase is of the three-state Potts or Kosterlitz-Thouless type, depending on the presence of defects in charge order.
Experimental data of the frequency-dependent ac susceptibility for the dipolar spin ice Dy2Ti2O7 has been analyzed by Monte Carlo simulations on the basis of the single-spin-flip Metropolis algorithm. We have directly evaluated the ac susceptibility by applying an ac magnetic field. We found that the simulated behaviors reproduces the experimental behavior of the ac susceptibility in the temperature range from 0.6 to 1.0 K, where dilute magnetic monopoles diffusively move. The conversion factor from simulation time to real time, i.e., the rate of hopping of monopoles to nearest-neighbor sites,…
Experimental identification of quantum spin ice (QSI), a U(1) quantum spin liquid on the pyrochlore lattice hosting emergent photons, is a major challenge in frustrated magnets. In this work, we propose ultrasound measurements as a novel tool for probing the emergent photons of various QSI phases. Our analysis includes QSI phases in non-Kramers doublet compounds such as $\rm{Pr}_2 \rm{Zr}_2 \rm{O}_7$ as well as dipolar-octupolar Kramers doublet compounds such as $\rm{Ce}_2 \rm{Zr}_2 \rm{O}_7$. The latter may host emergent photons associated with an octupolar component which renders them diffic…
We present single-crystal neutron-diffuse-scattering measurements with polarization analysis on the spin ice Ho2-xYxTi2O7 (x = 0, 0.3, and 1). At 2 K, the spin flip scattering patterns are typical of a nearest-neighbor spin ice and the effects of Y doping are seen in the width of the pinch points. At low-T, the spin flip patterns are characteristic of a dipolar spin ice and are unaffected by Y doping. In the non-spin flip channel, we observe the signature of strong antiferromagnetic correlations at the same T as the dipolar spin ice correlations appear in the spin flip channel. These experimen…
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 et al. in 2001 is reached using simple local spin flip dynamics. As the density is increased, the mono…
We study Ising pyrochlores by means of Monte Carlo simulations. We cover a set of exchange constants ranging from the frustrated ferromagnetic case (spin-ice) to the fully-ordered "all-in--all-out" antiferromagnet in the dipolar model, reinterpreting the results --as in an ionic system-- in terms of a temperature vs. magnetic charge density phase diagram. In spite of its spin nature and the presence of both double and single non-conserved magnetic charges, the dipolar model gives place to a phase diagram which is quite comparable with those previously obtained for on-lattice systems of electri…
The thermodynamic properties of dipolar spin ice on square, honeycomb and shakti lattices in the long-range and short-range dipole interaction models are studied. Exact solutions for the density of states, temperature dependencies of heat capacity, and entropy are obtained for these lattices with a finite number of point dipoles by means of complete enumeration. The magnetic susceptibility and average size of the largest low-energy cluster are calculated for square spin ice by means of Wang-Landau and Metropolis methods. We show that the long-range interaction leads to a blurring of the energy…
Insulating magnetic rare-earth pyrochlores related to spin ice host emergent bosonic monopolar spinons, which obey a magnetic analogue of quantum electrodynamics and may open a route to a magnetic analogue of electronics. However, the energy scales of the interactions among rare-earth moments are so low as 1 K that the possible quantum coherence can only be achieved at a sub-Kelvin. Here, we desgin high-temperature quantum spin ice materials from first principles. It is shown that the A-site deintercalated spinel iridate Ir2O4, which has been experimentally grown as epitaxial thin films, is a …
From a microscopic model for the pyrochlore antiferromagnet Tb2Sn2O7, including the crystal field Hamiltonian and interactions between the angular momenta, we compute an effective pseudospin-1/2 Hamiltonian Heff$ that incorporates perturbatively in the effective interactions the effect of excited crystal field levels. We obtain the semiclassical ground states of Heff and find a region of parameter space with a two-in/two-out spin ice configuration on each tetrahedron with ordering wavevector q=0 and with spins canted away from the local Ising axes as found in Tb2Sn2O7. This ground state can al…
We present a comprehensive experimental and theoretical study of the pyrochlore Tb$_2$Ge$_2$O$_7$, an exemplary realization of a material whose properties are dominated by competition between magnetic dipolar and electric quadrupolar correlations. The dipolar and quadrupolar correlations evolve over three distinct regimes that we characterize via heat capacity, elastic and inelastic neutron scattering. In the first regime, above $T^*=1.1$ K, significant quadrupolar correlations lead to an intense inelastic mode that cannot be accounted for within a scenario with solely magnetic dipole-dipole c…
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 …
Complex magnetic orders in frustrated magnets may exhibit rich melting processes when the magnet is heated toward the paramagnetic phase. We show that one may tune such melting processes by quantum fluctuations. We consider a kagome lattice dipolar Ising model subject to transverse field and focus on the thermal transitions out of its magnetic ground state, which features a $\sqrt{3}\times\sqrt{3}$ magnetic unit cell. Our quantum Monte Carlo (QMC) simulations suggest that, at weak transverse field, the $\sqrt{3}\times\sqrt{3}$ phase melts by way of an intermediate magnetic charge ordered phase…
A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod kagome lattice material Ho${_3}$Mg${_2}$Sb${_3}$O${_{14}}$ unites an ice-like magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho$^{3+}$ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodyna…
The origin of the lowest-temperature anomaly reported several years ago using a polycrystalline sample of the spin ice compound Dy2Ti2O7 had remained unresolved. Here we finally clarify its origin by susceptibility measurements down to 65 mK using single crystals under accurate control of the magnetic fields in two independent directions. We demonstrate that the transition is induced under a subtle field combination that precisely cancel the nearest-neighbor spin interactions acting on the spins on the triangular lattice within the pyrochlore structure. Contrary to the other two fieldinduced t…
We study the effects of lattice deformations on the Kagome spin ice, with Ising spins coupled by nearest neighbor exchange and long range dipolar interactions, in the presence of in-plane magnetic fields. We describe the lattice energy according to the Einstein model, where each site distortion is treated independently. Upon integration of lattice degrees of freedom, effective quadratic spin interactions arise. Classical MonteCarlo simulations are performed on the resulting model, retaining up to third neighbor interactions, under different directions of the magnetic field. We find that, as th…
We study near-neighbour and dipolar Ising models on a lattice of corner-sharing octahedra. In an extended parameter range of both models, frustration between antiferromagnetism and a spin-ice-like three-in-three-out rule stabilises a Coulomb phase with correlated dipolar and quadrupolar spin textures, both yielding distinctive neutron-scattering signatures. Strong further-neighbour perturbations cause the two components to order independently, resulting in unusual multi-$k$ orders. We propose experimental realisations of our model in rare-earth antiperovskites.
Recent experiments on the dipolar-octupolar pyrochlore compound Ce$_2$Zr$_2$O$_7$ indicate that it may realize a three-dimensional quantum spin liquid (QSL). In particular, the analyses of available data suggest that the system is in a region of parameter space, where the so-called $π$-flux $U(1)$ octupolar quantum spin ice (QSI) with an emergent photon could be realized. On the other hand, because the system is far from the perturbative classical spin ice regime, it is unclear whether the quantum ground state is primarily a coherent superposition of 2-in-2-out configurations as in the canonic…
We report experimental signatures of topological transitions among the Weyl semimetal states of pyrochlore Pr2Ir2O7, where the Kondo coupling between the Ir topological electrons and the spin-ice like orders of Pr moments plays a decisive role. The magnetic-field dependence of resistivity and the Hall conductivity exhibits a plateau and a sharp jump associated with a magnetic-field hysteresis, similar to a liquid-gas-like transition in dipolar spin ice system. Furthermore, the Kondo coupling is controlled by the hydrostatic pressure, revealing that the field-induced displacement of Weyl points…
We combine two aspects of magnetic frustration, multiferroicity and emergent quasi-particles in spin liquids, by studying magneto-electric monopoles. Spin ice offers to couple these emergent topological defects to external fields, and to each other, in unusual ways, making possible to lift the degeneracy underpinning the spin liquid and to potentially stabilize novel forms of charge crystals, opening the path to a "magnetic crystallography". In developing the general phase diagram including nearest-neighbour coupling, Zeeman energy, electric and magnetic dipolar interactions, we uncover the em…
Classical symmetry enriched topological orders and distinct monopole charges for dipole-octupole spin ices
International Center for Quantum Materials, Peking University（北京大学量子材料中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；The University of Hong Kong, Shenzhen Institute of Research and Innovation（香港大学深圳研究院）；Beijing Key Laboratory of Quantum Devices, Peking University（北京大学量子器件北京市重点实验室）
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 …
Recent work has highlighted remarkable effects of classical thermal fluctuations in the dipolar spin ice compounds, such as "artificial magnetostatics", manifesting as Coulombic power-law spin correlations and particles behaving as diffusive "magnetic monopoles". In this paper, we address quantum spin ice, giving a unifying framework for the study of magnetism of a large class of magnetic compounds with the pyrochlore structure, and in particular discuss Yb2Ti2O7 and extract its full set of Hamiltonian parameters from high field inelastic neutron scattering experiments. We show that fluctuatio…
We study spin correlations for the highly frustrated classical pyrochlore lattice antiferromagnets with O(N) symmetry in the limit T->0. We conjecture that a local constraint obeyed by the extensively degenerate ground states dictates a dipolar form for the asymptotic spin correlations, at all N $\ne$ 2 for which the system is paramagnetic down to T=0. We verify this conjecture in the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion about the solvable N=infinity limit. Remarkably, the N=infinity formulae are an excellent fit, at all distances, to the correlators at N=3 a…
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 $T\approx 0.15$ K, but recent experiments by Pomaranski $et\ al.$ suggest an entropy recovery over long time scales at temperatures as high as $0.5$ K, much too high to be compatible with theory. Using neutron scattering and specific heat measurem…
We report that the lattice constant of Dy$_2$Ge$_{2-x}$Si$_x$O$_7$ ($x=0, 0.02, 0.08, 0.125$) can be systematically reduced by substituting the non-magnetic germanium ion in the cubic pyrochlore oxide with silicon. A multi-anvil high-pressure synthesis was performed up to 16 GPa and 1100 $^\circ$C to obtain polycrystalline samples in a solid-state reaction. Measurements of magnetization, ac susceptibility, and heat capacity reveal the typical signatures of a spin-ice phase. From the temperature shift of the peaks, observed in the temperature-dependent heat capacity, we deduce an increase of th…
We report the low-temperature magnetothermal properties and spin dynamics of a mixed pyrochlore, Dy2GaSbO7 through the coordination of measurements of dc magnetization, ac susceptibility, and heat capacity, and CF computation. In Dy2GaSbO7, the spins freeze at temperature Tice = 3.1 K, corresponding to dynamical spin-freezing into a disordered state in compliance with the spin-ice rules, but with enhanced zero-point entropy, unlike cannonical dipolar spin-ice materials, Dy2Ti2O7 and Ho2Ti2O7, due to random disorder and varied chemical pressure of B-site (GaSb tetrahedra) ions.
In spin ice research, small variations in structure or interactions drive a multitude of different behaviors, yet the collection of known materials relies heavily on the `227' pyrochlore structure. Here, we present thermodynamic, structural and inelastic neutron scattering data on a new spin-ice material, MgEr$_2$Se$_4$, which contributes to the relatively under-explored family of rare-earth spinel chalcogenides. X-ray and neutron diffraction confirm a normal spinel structure, and places Er$^{3+}$ moments on an ideal pyrochlore sublattice. Measurement of crystal electric field excitations with…
The spin ice materials Ho$_{2}$Ti$_{2}$O$_{7}$ and Dy$_{2}$Ti$_{2}$O$_{7}$ are by now perhaps the best-studied classical frustrated magnets. A crucial step towards the understanding of their low temperature behaviour -- both regarding their unusual dynamical properties and the possibility of observing their quantum coherent time evolution -- is a quantitative understanding of the spin-flip processes which underpin the hopping of magnetic monopoles. We attack this problem in the framework of a quantum treatment of a single-ion subject to the crystal, exchange and dipolar fields from neighbourin…
The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength ($J_{eff}$) determines the relative energies of the different spin-ice states. With this work, we display the capability of capacitive torque magnetometry in characterizing the magneto-chemical potential associated with monopole formation. We build a magnetic phase diagram of Ho$_2$Ti$_2$O$_7$, and show that the magneto-chemical potential depends on the spin-sublattice ($α$ or $β$), i.e.,…
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…
The recent discovery of Spin-ice is a spectacular example of non-coplanar spin arrangements that can arise in the pyrochlore A2B2O7 structure. We present magnetic and thermodynamic studies on the metallic-ferromagnet pyrochlore Sm2Mo2O7. Our studies, carried out on oriented crystals, suggest that the Sm spins have an ordered spin-ice ground state below about T* = 15 K. The temperature- and field-evolution of the ordered spin-ice state are governed by an antiferromagnetic coupling between the Sm and Mo spins. We propose that as a consequence of a robust feature of this coupling, the tetrahedra …
We present a numerical study of magnetic ordering in spin ice on kagome, a two-dimensional lattice of corner-sharing triangles. The magnet has six ground states and the ordering occurs in two stages, as one might expect for a six-state clock model. In spin ice with short-range interactions up to second neighbors, there is an intermediate critical phase separated from the paramagnetic and ordered phases by Kosterlitz-Thouless transitions. In dipolar spin ice, the intermediate phase has long-range order of staggered magnetic charges. The high and low-temperature phase transitions are of the Isin…
Spin ices, frustrated magnetic materials analogous to common water ice, are exemplars of high frustration in three dimensions. Recent experimental studies of the low-temperature properties of the paradigmatic Dy$_2$Ti$_2$O$_7$ spin ice material, in particular whether the predicted transition to long-range order occurs, raise questions as per the currently accepted microscopic model of this system. In this work, we combine Monte Carlo simulations and mean-field theory calculations to analyze data from magnetization, elastic neutron scattering and specific heat measurements on Dy$_2$Ti$_2$O$_7$.…
We investigate the transport properties of itinerant electrons interacting with a background of localized spins in a correlated paramagnetic phase of the pyrochlore lattice. We find a residual resistivity at zero temperature due to the scattering of electrons by the static dipolar spin-spin correlation that characterizes the metallic Coulomb phase. As temperature increases, thermally excited topological defects, also known as magnetic monopoles, reduce the spin correlation, hence suppressing electron scattering. Combined with the usual scattering processes in metals at higher temperatures, thi…
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 betwe…
Thermodynamic properties of a spin ice model on a Kagomé lattice are obtained from dynamic simulations and compared with properties in square lattice spin ice. The model assumes three-component Heisenberg-like dipoles of an array of planar magnetic islands situated on a Kagomé lattice. Ising variables are avoided. The island dipoles interact via long-range dipolar interactions and are restricted in their motion due to local shape anisotropies. We define various order parameters and obtain them and thermodynamic properties from the dynamics of the system via a Langevin equation, solved by the H…
Magnetic monopoles can appear as emergent structures in a wide range of physical settings, ranging from spin ice to Weyl points in semimetals. Here, a distribution of synthetic (Berry) monopoles in parameter space of a slowly changing external magnetic field is demonstrated in a system of interacting spin-$\frac{1}{2}$ particles with broken spherical symmetry. These monopoles can be found at points where the external field is nonzero. The spin-spin interaction provides a mechanism for splitting the synthetic local magnetic charges until their magnitude reach the smallest allowed value $\frac{1…
We study the two-dimensional kagome-ice model derived from a pyrochlore lattice with second- and third-neighbor interactions. The canted moments align along the local $\langle 111 \rangle$ axes of the pyrochlore and respond to both in-plane and out-of-plane external fields. We find that the combination of further-neighbor interactions together with the external fields introduces a rich phase diagram with different spin textures. Close to the phase boundaries, metastable $\textit{"snake"}$ domains emerge with extremely long relaxation time. Our kinetic Monte Carlo analysis of the magnetic-field…
