Spin Ice

Using extensive numerical simulations, we prob e the magnetization switching in a two dimensional artificial spin ice (ASI) system consisting of peanut-shaped nanomagnets. We also investigated the effect of external magnetic field on the degeneracy of the magnetic states in such a system. The switching field is found to b e one order smaller in the proposed ASI system with peanut-shaped nanomagnets as compared to the conventionally used highly-anisotropic nanoisland such as elliptically shaped nanomagnets. The metastable 2-in/2-out (Type I I) magnetic state is robust at the remanence. We are also able to access the other possible microstate corresponding to Type I I magnetic configurations by carefully varying the external magnetic field. It implies that one can control the degeneracy of the magnetic state by an application of suitable magnetic field. Interestingly, the magnetic charge neutrality at the vertex breaks due to the defects induced by removing nanomagnets. In such a case...

Dy2Ti2O7 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.

We used a local susceptibility approach in extensive polarized neutron diffraction studies of the spin liquid Tb2Ti2O7. For a magnetic field applied along the [110] and [111] directions, we found that, at high temperature, all Tb moments are collinear and parallel to the field. With decreasing temperature, the Tb moments reorient from the field direction to their local anisotropy axes. For the [110] field direction, the field induced magnetic structure at 10 K is spin ice-like, but with two types of Tb moments of very different magnitudes. For a field along [111], the magnetic structure resembles the so-called "one in-three out" found in spin ices, with the difference that all Tb moments have an additional component along the [111] direction due to the magnetic field. The temperature evolution of the local susceptibilities clearly demonstrates a progressive change from Heisenberg to Ising behavior of the Tb moments when lowering the temperature, which appears to be a crystal field effect.

We report the a.c. susceptibility study of DyxTb2-xTi2O7 with x ∈ [0, 2]. In addition to the single-ion effect at Ts (single-ion effect peak temperature) corresponding to the Dy 3+ spins as that in spin ice Dy2Ti2O7 and a possible spin freezing peak at T f (T f < 3 K), a new peak associated with Tb 3+ is observed in χac(T ) at nonzero magnetic field with a characteristic temperature T * (T f < T * < Ts). T * increases linearly with x in a wide composition range (0 < x < 1.5 at 5 kOe). Both application of a magnetic field and increasing doping with Dy 3+ enhance T * . The T * peak is found to be thermally driven with an unusually large energy barrier as indicated from its frequency dependence. These effects are closely related to the crystal field levels, and the underlying mechanism remains to be understood.

Artificial spin ices (ASIs) are magnetic metamaterials comprising geometrically tiled strongly-interacting nanomagnets. There is significant interest in these systems spanning the fundamental physics of many-body systems to potential applications in neuromorphic computation, logic, and recently reconfigurable magnonics. Magnonics focused studies on ASI have to date have focused on the in-field GHz spin-wave response, convoluting effects from applied field, nanofabrication imperfections (‘quenched disorder’) and microstate-dependent dipolar field landscapes. Here, we investigate zero-field measurements of the spin-wave response and demonstrate its ability to provide a ‘spectral fingerprint’ of the system microstate. Removing applied field allows deconvolution of distinct contributions to reversal dynamics from the spin-wave spectra, directly measuring dipolar field strength and quenched disorder as well as net magnetisation. We demonstrate the efficacy and sensitivity of this approac...

Muon spin rotation experiments are carried out on clinoatacamite, Cu 2 ClOH 3 , which is a new geometrically frustrated system featuring a three-dimensional network of corner-sharing tetrahedral 3d Cu 2 spins. A long-range antiferromagnetic order occurs below 18.1 K with a surprisingly small entropy release of about 0:05R ln2=Cu. Below 6.5 K, the static long-range order transforms abruptly into a metastable state with nearly complete depolarization of muon spins which suggests strong fluctuation. The system then enters a state in which partial long-range order and spin fluctuation coexist down to the lowest experimentally attainable temperature of 20 mK. This work presents a novel system for studying geometric frustration.

Order or disorder often exists in a uniform spin system consisting of one kind of magnetic ion. Nevertheless, they rarely coexist in normal conditions. Our thermodynamic and microscopic magnetic studies of Co 2 OH 3 Cl, a distorted tetrahedral lattice compound with uniform Co 2 spin, demonstrate that the spins located on one corner of the tetrahedron are periodically ordered, but those on the other three are disordered below a ferromagnetic transition at T C 10:5 K. The partial order resembles that of the fieldinduced ''kagome ´-ice'' state in spin ice pyrochlore compounds. Evidence suggests that a distortion in the tetrahedron is responsible for this partial ferromagnetic order in a zero field.

Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical applications in microelectronics [1], such as data storage, memory and logic [2]. However, it is difficult to achieve extensive degeneracy, especially in a two-dimensional system [3,4]. Here, we showcase in-situ controllable geometric frustration with massive degeneracy in a twodimensional flux quantum system. We create this in a superconducting thin film placed underneath a reconfigurable artificial-spin-ice structure [5]. The tunable magnetic charges in the artificial-spin-ice strongly interact with the flux quanta in the superconductor, enabling the switching between frustrated and crystallized flux quanta states. The different states have measurable effects on the superconducting critical current profile, which can be Nature Nanotechnology 13, 560 (2018)

Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical applications in microelectronics, such as data storage, memory and logic. However, it is difficult to achieve very high degeneracy, especially in a two-dimensional system. Here, we showcase in situ controllable geometric frustration with high degeneracy in a two-dimensional flux-quantum system. We create this in a superconducting thin film placed underneath a reconfigurable artificial-spin-ice structure. The tunable magnetic charges in the artificial-spin-ice strongly interact with the flux quanta in the superconductor, enabling switching between frustrated and crystallized flux quanta states. The different states have measurable effects on the superconducting critical current profile, which can be reconfigured by precise selection of the spin-ic...

Arrays of suitably patterned and arranged magnetic elements may display artificial spin-ice structures with topological defects in the magnetization, such as Dirac monopoles and Dirac strings. It is known that these defects strongly influence the quasi-static and equilibrium behavior of the spin-ice lattice. Here we study the eigenmode dynamics of such defects in a square lattice consisting of stadium-like thin film elements using micromagnetic simulations. We find that the topological defects display distinct signatures in the mode spectrum, providing a means to qualitatively and quantitatively analyze monopoles and strings which can be measured experimentally.

A new S = 1 kagom e compound based on vanadium(III) is reported. The structure was refined simultaneously against single-crystal neutron and X-ray diffraction data, as a gaudefroyite-type with a new supercell (a 0 = 2a þ b, b 0 = -a -2b, c 0 = c) driven by the ordering of columns of isolated triangular BO 3 3-ions. Low-temperature neutron powder diffraction and magnetic (dc and ac susceptibility) data rule out the presence of long-range magnetic order above at least 1.5 K, but specific heat data suggest that the ground state involves shortrange magnetic order, which is frustrated by the coexistence/ competition of FM and AFM correlations, together with the characteristic geometric frustration of the kagom e lattice. Magnetic susceptibility data rule out a spin-glass state, pointing to an exotic ground state comparable to the spin-ice or spin-liquid states. This makes YCa 3 (VO) 3 (BO 3 ) 4 one of the most highly frustrated experimental realizations of the kagom e lattice yet discovered.

The discovery of the spin-ice phase in Dy 2 Ti 2 O 7 numbers among the most significant findings in magnetic materials in over a decade . Spin ice has since been associated with the manifestation of magnetic monopoles 4,5 and may even inform our understanding of emergent quantum electrodynamics 6 . The spin-ice model is based on an elegant analogy to Pauling's model of geometrical frustration in water ice, and predicts the same residual entropy, as confirmed by numerous measurements 1,2,7-11 . Here we present results for the specific heat of Dy 2 Ti 2 O 7 , demonstrating why previous measurements were unable to correctly capture its lowtemperature behaviour. By carefully tracking the flow of heat into and out of the material, we observe a non-vanishing specific heat that has not previously been detected. This behaviour is confirmed in two samples of Dy 2 Ti 2 O 7 , in which cooling below 0.6 K reveals a deviation from Pauling's residual entropy, calling into question the true magnetic ground state of spin ice. Although the simple spin-ice model does account for most observed properties of the pyrochlore oxides Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 , unsolved puzzles remain. Simulations have demonstrated that longrange dipolar interactions should lift the degeneracy of the spin-ice manifold of states, and give rise to a unique, ordered ground state 12 . The Melko-den Hertog-Gingras (MDG) phase (Fig. ) was the first theoretical prediction of an ordered state in spin ice; discovered through a numerical loop algorithm . So far, however, experimental work has been unsuccessful in observing the MDG phase, concluding that the large energy barrier for fluctuations out of the ice-rules manifold does not allow ordering to occur . Recent low-temperature measurements have determined that the spin relaxation time markedly increases as temperature is lowered. For example, magnetization 14,15 and a.c.-susceptibility 16 measurements show that the spin relaxation time in Dy 2 Ti 2 O 7 is greater than 10 4 s below 0.45 K. Ref. 16 also reported Arrhenius behaviour with a barrier to relaxation of 9.79 K, much larger than the cost of a single spin flip of 4J eff = 4.44 K, where J eff is the nearestneighbour effective exchange energy 17 . This difference could be due to monopole effects 15 , or many-body phenomena such as screening, but remains as a major open question . Consequently, we would expect that thermal relaxation is dominated by this slow magnetic system in the spin-ice regime. These spin dynamics motivated us to re-measure the specific heat in a way that allows for extremely slow thermal equilibration.

Topological magnetic charges, arising due to the non-vanishing magnetic flux on spin ice vertices, serve as the origin of magnetic monopoles that traverse the underlying lattice effortlessly. Unlike spin ice materials of atomic origin, the dynamic state in artificial honeycomb spin ice is conventionally described in terms of finite size domain wall kinetics that require magnetic field or current application. Contrary to this common understanding, here we show that thermally tunable artificial permalloy honeycomb lattice manifests a perpetual dynamic state due to self-propelled magnetic charge defect relaxation in the absence of any external tuning agent. Quantitative investigation of magnetic charge defect dynamics using neutron spin echo spectroscopy reveals sub-ns relaxation times that are comparable to monopole's relaxation in bulk spin ices. Most importantly, the kinetic process remains unabated at low temperature where thermal fluctuation is negligible. This suggests that dynamic phenomena in honeycomb spin ice are mediated by quasi-particle type entities, also confirmed by quantum Monte-Carlo simulations that replicate the kinetic behavior. Our research unveils a new 'macroscopic' magnetic particle that shares many known traits of quantum particles, namely magnetic monopole and magnon.

Geometric frustration usually arises in systems that comprise magnetic moments (spins) which reside on the sites of a lattice made up of elementary triangular or tetrahedral units and which interact via antiferromagnetic nearest-neighbor exchange. Albeit much less common, geometric frustration can also arise in systems with strong non-collinear single-ion easy-axis (Ising-like) anisotropy and ferromagnetically coupled spins. This is what happens in some pyrochlore oxide materials where Ising-like magnetic rare earth moments (Ho^3+, Dy^3+) sit on a lattice of corner-shared tetrahedra and are coupled via effectively ferromagnetic (dipolar) interactions. These systems possess a macroscopic number of quasi-degenerate classical ground states and display an extensive low-temperature entropy closely related to the extensive proton disorder entropy in common water ice. For this reason, these magnetic systems are called spin ice. This chapter reviews the essential ingredients of spin ice phe...

Water ice and spin ice are important model systems in which theory can directly account for "zero point" entropy associated with quenched configurational disorder. Spin ice differs from water ice in the important respect that its fundamental constituents, the spins of the magnetic ions, can be removed through replacement with non-magnetic ions while keeping the lattice structure intact. In order to investigate the interplay of frustrated interactions and quenched disorder, we have performed systematic heat capacity measurements on spin ice materials which have been thus diluted up to 90%. Investigations of both Ho and Dy spin ices reveal that the zero point entropy depends non-monotonically on dilution and approaches the value of Rln2 in the limit of high dilution. The data are in good agreement with a generalization of Pauling's theory for the entropy of ice.

A study of magnetism in the novel 2D spin system Ni 5 (TeO 3 ) 4 Br 2 , featuring a frustrated triangular geometry, is presented. We combine magnetization, heat capacity and high-field electron spin resonance measurements to investigate a long-range magnetic ordering below T N = 29 K. Additional peculiar behaviour, most likely related to the spin system, is observed below T = 14 K.

In a quantum spin liquid, the magnetic moments of the constituent electron spins evade classical longrange order to form an exotic state that is quantum entangled and coherent over macroscopic length scales 1-2 . Such phases offer promising perspectives for device applications in quantum information technologies, and their study can reveal fundamentally novel physics in quantum matter. Quantum spin ice is an appealing proposal of one such state, in which the fundamental ground state properties and excitations are described by an emergent U(1) lattice gauge theory 3-7 . This quantum-coherent regime has quasiparticles that are predicted to behave like magnetic and electric monopoles, along with a gauge boson playing the role of an artificial photon. However, this emergent lattice quantum electrodynamics has proved elusive in experiments. Here we report neutron scattering measurements of the rare-earth pyrochlore magnet Pr 2 Hf 2 O 7 that provide evidence for a quantum spin ice ground state. We find a quasielastic structure factor with pinch points -a signature of a classical spin ice -that are partially suppressed, as expected in the quantum-coherent regime of the lattice field theory at finite temperature. Our result allows an estimate for the speed of light associated with magnetic photon excitations. We also reveal a continuum of inelastic spin excitations, which resemble predictions for the fractionalized, topological excitations of a quantum spin ice. Taken together, these two signatures suggest that the low-energy physics of Pr 2 Hf 2 O 7 can be described by emergent quantum electrodynamics. If confirmed, the observation of a quantum spin ice ground state would constitute a concrete example of a threedimensional quantum spin liquid -a topical state of matter which has so far mostly been explored in lower dimensionalities.

Quantum spin ice is an appealing proposal of a quantum spin liquid -systems where the magnetic moments of the constituent electron spins evade classical long-range order to form an exotic state that is quantum entangled and coherent over macroscopic length scales. Such phases are at the edge of our current knowledge in condensed matter as they go beyond the established paradigm of symmetry-breaking order and associated excitations. Neutron scattering experiments on the pyrochlore material Pr2Hf2O7 reveal signatures of a quantum spin ice state that were predicted by theory.

We report the synthesis of powder and single-crystal samples of the cerium pyrohafnate and their characterization using neutron diffraction, thermogravimetry and X-ray absorption spectroscopy. We evaluate the amount of non-magnetic Ce 4+ defects and use this result to interpret the spectrum of crystal-electric field transitions observed using inelastic neutron scattering. The analysis of these single-ion transitions indicates the dipole-octupole nature of the ground state doublet and a significant degree of spin-lattice coupling. The single-ion properties calculated from the crystal-electric field parameters obtained spectroscopically are in good agreement with bulk magnetic susceptibility data down to about 1 K. Below this temperature, the behavior of the magnetic susceptibility indicates a correlated regime without showing any sign of magnetic long-range order or freezing down to 0.08 K. We conclude that Ce2Hf2O7 is another candidate to investigate exotic correlated states of quantum matter such as the octupolar quantum spin ice recently argued to exist in the isostructural compounds Ce2Sn2O7 and Ce2Zr2O7.

We report the low temperature magnetic properties of the pyrochlore Pr 2 Hf 2 O 7 . Polycrystalline and singlecrystal samples are investigated using time-of-flight neutron spectroscopy and macroscopic measurements, respectively. The crystal-field splitting produces a non-Kramers doublet ground state for Pr 3+ , with Ising-like anisotropy. Below 0.5 K ferromagnetic correlations develop, which suggests that the system enters a spin-ice-like state associated with the metamagnetic behavior observed at μ 0 H c ∼ 2.4 T. In this regime, the development of a discrete inelastic excitation in the neutron spectra indicates the appearance of spin dynamics that are likely related to cooperative quantum fluctuations.

Magnetic frustration effects in artificial kagome arrays of nanomagnets with out-of-plane magnetization are investigated using Magnetic Force Microscopy and Monte Carlo simulations. Experimental and theoretical results are compared to those found for the artificial kagome spin ice, in which the nanomagnets have in-plane magnetization. In contrast with what has been recently reported, we demonstrate that long range (i.e. beyond nearest-neighbors) dipolar interactions between the nanomagnets cannot be neglected when describing the magnetic configurations observed after demagnetizing the arrays using a field protocol. As a consequence, there are clear limits to any universality in the behavior of these two artificial frustrated spin systems. We provide arguments to explain why these two systems show striking similarities at first sight in the development of pairwise spin correlations.

Magnetic frustration effects in artificial kagomé arrays of nanomagnets are investigated using X-PEEM microscopy and monte carlo 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 kagomé dipolar spin ice model captures the observed physics, while the short range kagomé spin ice model fails.

Cadmium cyanide, Cd(CN) 2 , is a flexible coordination polymer best studied for its strong and isotropic negative thermal expansion (NTE) effect. Here we show that this NTE is actually X-rayexposure dependent: Cd(CN) 2 contracts not only on heating but also on irradiation by X-rays. This behaviour contrasts that observed in other beam-sensitive materials, for which X-ray exposure drives lattice expansion. We call this effect 'negative X-ray expansion' (NXE) and suggest its origin involves an interaction between X-rays and cyanide 'flips'; in particular, we rule out local heating as a possible mechanism. Irradiation also affects the nature of a low-temperature phase transition. Our analysis resolves discrepancies in NTE coefficients reported previously on the basis of X-ray diffraction measurements, and we establish the 'true' NTE behaviour of Cd(CN) 2 across the temperature range 150-750 K. The interplay between irradiation and mechanical response in Cd(CN) 2 highlights the potential for exploiting X-ray exposure in the design of functional materials.

Neutron scattering is a sensitive probe of correlations in condensed matter physics, and measurements of spin correlations by diffuse neutron scattering is one of the foremost methods of constraining the Hamiltonian of spin ice materials such as Dy 2 Ti 2 O 7. Recent investigations of spin ices have highlighted the possibility of very slow equilibration at low temperature and/or structural defects in samples, effects which were not taken into account in the original parametrizations of the Hamiltonian. Hence, we have in this study performed a new set of diffuse magnetic neutron scattering experiments on an oxygen-annealed single crystal of the spin ice 162 Dy 2 Ti 2 O 7. Compensation coils and an in-situ AC-susceptometer were used to control the zero magnetic field at the sample position as well as determining the thermal equilibrium of the magnetic spins respectively. In addition, we performed large-scale Monte Carlo simulations as to make a statistical fit of the dipolar spin ice model to the measured structure factor in the temperature range [0.65, 2] K, where the spin ice physics starts to develop. This will enable a most carefully controlled determination of the Hamiltonian of Dy 2 Ti 2 O 7 .

The demagnetizing factor N is of both conceptual interest and practical importance. Considering localized magnetic moments on a lattice, we show that for non-ellipsoidal samples, N depends on the spin dimensionality (Ising, XY, or Heisenberg) and orientation, as well as the sample shape and susceptibility. The generality of this result is demonstrated by means of a recursive analytic calculation as well as detailed Monte Carlo simulations of realistic model spin Hamiltonians. As an important check and application, we also make an accurate experimental determination of N for a representative collective paramagnet (i.e. the Dy2Ti2O7 spin ice compound) and show that the temperature dependence of the experimentally determined N agrees closely with our theoretical calculations. Our conclusion is that the well established practice of approximating the true sample shape with "corresponding ellipsoids" for systems with long-range interactions will in many cases overlook important effects stemming from the microscopic aspects of the system under consideration.

The magnetic susceptibility of a spin ice material is a sensitive probe of the relevant physics in different temperature ranges. At high temperatures, where crystal field excitations dominate the susceptibility, the spin ice picture is not applicable. However, at temperatures below 10 K, the Ising anisotropy is well developed and the dipolar spin ice model (DSIM) can be employed. In this study we present experimental susceptibility data between 0.4 K and 10 K and revisit the DSIM in order to theoretically model this data. We find that the DSIM provides a good semi-quantitative description of both the temperature dependence of the uniform bulk susceptibility and the Q-dependent susceptibility measured by neutron scattering.

We present a detailed theoretical overview of the thermodynamic properties of the dipolar spin ice model, which has been shown to be an excellent quantitative descriptor of the Ising pyrochlore materials Dy2Ti2O7 and Ho2Ti2O7. We show that the dipolar spin ice model can reproduce an effective quasi macroscopically degenerate ground state and spin-ice behavior of these materials when the long-range nature of dipole-dipole interaction is handled carefully using Ewald summation techniques. This degeneracy is, however, ultimately lifted at low temperature. The long-range ordered state is identified via mean field theory and Monte Carlo simulation techniques. Finally, we investigate the behavior of the dipolar spin ice model in an applied magnetic field, and compare our predictions with experimental results. We find that a number of different long-range ordered states are favored by the model depending on field direction.

Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the spin ice model proposed by Harris et al. Phys. Rev. Lett. 79, 2554 (1997). We discuss the dipolar energy scale present in both these materials and consider how they can display spin ice behavior despite the presence of long range interactions. Specifically, we present numerical simulations and a mean field analysis of pyrochlore Ising systems in the presence of nearest neighbor exchange and long range dipolar interactions. We find that two possible phases can occur, a long range ordered antiferromagnetic one and the other dominated by spin ice features. Our quantitative theory is in very good agreement with experimental data on both Ho2Ti2O7 and Dy2Ti2O7. We suggest that the nearest neighbor exchange in Dy2Ti2O7 is antiferromagnetic and that spin ice behavior is induced by long range dipolar interactions.

Submitted for the MAR16 Meeting of The American Physical Society Extended spin ice JEFFREY G. RAU, MICHEL J. P. GINGRAS, University of Waterloo-We introduce a new classical spin liquid on the pyrochlore lattice which we call 'extended spin ice'. The ground state manifold of this model is extensive and characterized by a set of local rules that extend the conventional 2-in/2-out spin ice condition. This includes the ice states in addition to a complex set of tree structures built from 3-in/1-out, 3-out/1-in and all-in/all-out tetrahedra. Under local dynamics this model freezes heterogeneously at low temperatures into a 'spin slush', with extremely slow relaxation for some spins while other spin clusters fluctuate quickly. In addition to this dynamical heterogeneity, distinctive spherical patterns in the spin correlations serve as a further signature. Possible applications to materials as well the effects of transverse quantum exchange will be discussed.

The internal magnetic field of a uniformly magnetized body depends in general on the shape of the object. The calculation of this field, and the associated demagnetization factors, is a classical subject in the study of magnetism. Here we revisit the relationship between the demagnetization factor obtained through fluxmetric, magnetometic and bulk susceptibility techniques. Apart from simple uniaxial systems we also consider more complicated systems, such as the dipolar spin ice model on a pyrochlore lattice, where we compare our results to experimental bulk susceptibility measurements performed on a variety of sample shapes.

Recently it has 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.

Magnetic measurements were carried out on Ho 2 Ru 2 O 7 and Dy 2 Ru 2 O 7 pyrochlores to study the possibility of spin ice type magnetism in these systems. Curie Weiss law fits to inverse susceptibility data in the temperature range 200-350 K gave p eff ¼ 9:60; y ¼ À4 K for the Ho and p eff ¼ 10:54; y ¼ À8:4 K for the Dy system. The saturation magnetization at 2 K was only half the value expected for the ground-state configurations of the rare earth ions. The effective nearest neighbor interaction was estimated to have small positive values for both the systems. This suggests that these pyrochlore systems have a magnetic behavior similar to the other spin ice systems despite the presence of the small moment bearing 4d Ru ions which themselves order into antiferromagnetic state at an elevated temperature of about 100 K:

The recent discovery of 'magnetricity' in spin ice raises the question of whether long-lived currents of magnetic 'monopoles' can be created and manipulated by applying magnetic fields. Here we show that they can. By applying a magnetic-field pulse to a Dy 2 Ti 2 O 7 spin-ice crystal at 0.36 K, we create a relaxing magnetic current that lasts for several minutes. We measure the current by means of the electromotive force it induces in a solenoid coupled to a sensitive amplifier, and quantitatively describe it using a chemical kinetic model of point-like charges obeying the Onsager-Wien mechanism of carrier dissociation and recombination. We thus derive the microscopic parameters of monopole motion in spin ice and identify the distinct roles of free and bound magnetic charges. Our results illustrate a basic capacitor effect for magnetic charge and should pave the way for the design and realization of 'magnetronic' circuitry.

We herein present the spin freezing dynamics of stuffed polycrystalline compound Dy2Ti1.8Mn0.2O7. In Dy2Ti2O7, spin freezes with ice like spin relaxations at a temperature around 3 K (Ti) along with another spin freezing at a temperature around 0.7 K (T<Ti). These relaxations can be observed prominently with an application of varying DC magnetic field bias and applied AC-field. We show here that with fractional inclusion of Mn at Ti site in Dy2Ti2O7, there is a significant shift in these temperatures. In Dy2Ti1.8Mn0.2O7 the Ti shifts to a higher temperature around 5 K and freezing belonging to T<Ti shifts to 2.5 K without any application of external DC Bias and/or AC-field. The inclusion of Mn at Ti site also enhances the ferromagnetic interaction for Dy2Ti1.8Mn0.2O7 as compared to Dy2Ti2O7. Arrhenius fit of freezing temperature with frequency for Dy2Ti1.8Mn0.2O7 shows that these spin relaxations at Ti and T<Ti are thermally induced. Low-temperature structural change in lattice parameters and crystal field phonon coupling has been studied using synchrotron x-ray diffraction. Debye-Gruineisen analysis of temperaturedependent lattice volume shows the emergence of crystal field phonon coupling at a much higher temperature (70 K) in Dy2Ti1.8Mn0.2O7 in contrast to 40 K in Dy2Ti2O7. These findings make Dy2Ti1.8Mn0.2O7 a suitable system to explore the application of spin ice phenomenon at a workable temperature.

Spin ice materials provide a rare instance of emergent gauge symmetry and fractionalisation in three dimensions: the effective degrees of freedom of the system are emergent magnetic monopoles, and the extensively many 'ice rule' ground states are those devoid of monopole excitations. Two-dimensional (kagome) analogues of spin ice have also been shown to display a similarly rich behaviour. In kagome ice however the ground-state 'ice rule' condition implies the presence everywhere of magnetic charges. As temperature is lowered, an Ising transition occurs to a charge-ordered state, which can be mapped to a dimer covering of the dual honeycomb lattice. A second transition, of Kosterlitz-Thouless or three-state Potts type, occurs to a spin-ordered state at yet lower temperatures, due to small residual energy differences between charge-ordered states. Inspired by recent experimental capabilities in growing spin ice samples with selective (layered) substitution of non-magnetic ions, in this work we investigate the fate of the two ordering transitions when individual kagome layers are brought together to form a three-dimensional pyrochlore structure coupled by long range dipolar interactions. We also consider the response to substitutional disorder and applied magnetic fields.

The Ising model-in which degrees of freedom (spins) are binary valued (up/down)-is a cornerstone of statistical physics that shows rich behaviour when spins occupy a highly frustrated lattice such as kagome. Here we show that the layered Ising magnet Dy3Mg2Sb3O14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scattering and bulk thermomagnetic measurements reveal a phase transition at ∼0.3 K from a disordered spin-ice-like regime to an emergent charge ordered state, in which emergent magnetic charge degrees of freedom exhibit three-dimensional order while spins remain partially disordered. Monte Carlo simulations show that an interplay of inter-layer interactions, spin canting and chemical disorder stabilizes this state. Our results establish Dy3Mg2Sb3O14 as a tuneable system to study interacting emergent charges arising from kagome Ising frustration.

Artificial spin ice systems comprise two dimensional arrays of nanoscale single domain ferromagnets designed to have frustrated interactions among the moments. By decimating islands from the common square artificial spin ice, one can design lattices with so called 'vertex frustration'. In such lattices, the geometry prevents all vertices from occupying local ground states simultaneously. Using Photoemission Electron Microscopy (PEEM), we access the real time thermally induced dynamics of the moment behavior in those lattices. Operating at a proper temperature, the moment direction of each island fluctuates with a sufficiently slow frequency that it can be resolvable by acquiring successive PEEM images. We can extract information regarding the collective excitations of the moments and understand how they reflect the frustration of lattice.

Reducing the dimensionality of a physical system can have a profound e ect on its properties, as in the ordering of low-dimensional magnetic materials 1 , phonon dispersion in mercury chain salts 2 , sliding phases 3 , and the electronic states of graphene 4. Here we explore the emergence of quasi-one-dimensional behaviour in two-dimensional artificial spin ice, a class of lithographically fabricated nanomagnet arrays used to study geometrical frustration 5-7. We extend the implementation of artificial spin ice by fabricating a new array geometry, the so-called tetris lattice 8. We demonstrate that the ground state of the tetris lattice consists of alternating ordered and disordered bands of nanomagnetic moments. The disordered bands can be mapped onto an emergent thermal one-dimensional Ising model. Furthermore, we show that the level of degeneracy associated with these bands dictates the susceptibility of island moments to thermally induced reversals, thus establishing that vertex frustration can reduce the relevant dimensionality of physical behaviour in a magnetic system. Arrays of interacting, single-domain nanomagnets known as artificial spin ice have proved to be useful model systems with which to experimentally explore the microscopic nature of geometrical frustration 6-8. Simple square and kagome artificial spin ice lattices have been subject to intense study because they provide unique insight into the consequences of frustrated magnetism, such as residual entropy 9,10 and magnetic charge excitations 11-14. In the past few years, improved thermalization methods have provided access to the low-energy phases of artificial spin ice structures 10,15,16 and even their dynamics 17-19. There is now growing awareness that one could even employ these artificial systems to design desired emergent behaviours and exotic states 20. To this end, a number of new lattice geometries have been proposed to produce novel emergent phenomena through 'vertex frustration' , where the lattice geometry forces groups of neighbouring island moments, called vertices, into higher-energy configurations that would not otherwise be observed in the ground state 8,21. Here we combine these theoretical and experimental advances to study thermal fluctuations about the ground state of the tetris lattice 8 , a regular two-dimensional lattice with reduced symmetry that is designed to exhibit vertex frustration. By analysis of the thermalized ground state, we demonstrate that the lattice decomposes into alternating stripes of two kinds, one of which exhibits the expected disordered state for a ferromagnetic one-dimensional Ising model.

Return point memory, in which the spins of a magnet return to their original configuration after the magnet is driven through a hysteresis loop, has been studied extensively with theory, simulations, and bulk experimental probes. However, due to the difficulties associated with directly imaging single spins, microscopic experimental examination of return point memory has proven to be elusive. Here we describe a study of return point memory in arrays of single-domain nanomagnets known as artificial spin ice. In this system, the individual moments can be experimentally resolved by magnetic force microscopy (MFM), so we can both verify the existence of return point memory and explore the mechanism by which it develops. We find that, in artificial spin ice, magnetic monopole excitations drive the development of return point memory through a ratchet-like interaction with the local field produced by the surrounding nanoislands. The number of hysteresis loops required to produce return point memory can be adjusted by tuning the applied magnetic field and array geometry.

We have studied frustrated kagome arrays and unfrustrated honeycomb arrays of magnetostatically-interacting single-domain ferromagnetic islands with magnetization normal to the plane. The measured pairwise spin correlations of both lattices can be reproduced by models based solely on nearest-neighbor correlations. The kagome array has qualitatively different magnetostatics but identical lattice topology to previously-studied 'artificial spin ice' systems composed of in-plane moments. The two systems show striking similarities in the development of moment pair correlations, demonstrating a universality in artificial spin ice behavior independent of specific realization in a particular material system.

We report a magneto-optical Kerr effect study of the collective magnetic response of artificial square spin ice, a lithographically-defined array of single-domain ferromagnetic islands. We find that the anisotropic inter-island interactions lead to a non-monotonic angular dependence of the array coercive field. Comparisons with micromagnetic simulations indicate that the two perpendicular sublattices exhibit distinct responses to island edge roughness, which clearly influence the magnetization reversal process. Furthermore, such comparisons demonstrate that disorder associated with roughness in the island edges plays a hitherto unrecognized but essential role in the collective behavior of these systems.