Spin Ice Compound Dy2Ti2O7 Research Articles

Dynamical fractal and anomalous noise in a clean magnetic crystal

Fractals-objects with noninteger dimensions-occur in manifold settings and length scales in nature. In this work, we identify an emergent dynamical fractal in a disorder-free, stoichiometric, and three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is born from constraints on the dynamics of the magnetic monopole excitations in spin ice, which restrict them to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments in the spin ice compound Dy2Ti2O7, and it resolves a long-standing puzzle about its rapidly diverging relaxation time. The capacity of spin ice to exhibit such notable phenomena suggests that there will be further unexpected discoveries in the cooperative dynamics of even simple topological many-body systems.

Anomalous magnetic noise in an imperfectly flat landscape in the topological magnet Dy2Ti2O7

Noise generated by motion of charge and spin provides a unique window into materials at the atomic scale. From temperature of resistors to electrons breaking into fractional quasiparticles, "listening" to the noise spectrum is a powerful way to decode underlying dynamics. Here, we use ultrasensitive superconducting quantum interference device (SQUIDs) to probe the puzzling noise in a frustrated magnet, the spin-ice compound Dy2Ti2O7 (DTO), revealing cooperative and memory effects. DTO is a topological magnet in three dimensions-characterized by emergent magnetostatics and telltale fractionalized magnetic monopole quasiparticles-whose real-time dynamical properties have been an enigma from the very beginning. We show that DTO exhibits highly anomalous noise spectra, differing significantly from the expected Brownian noise of monopole random walks, in three qualitatively different regimes: equilibrium spin ice, a "frozen" regime extending to ultralow temperatures, and a high-temperature "anomalous" paramagnet. We present several distinct mechanisms that give rise to varied colored noise spectra. In addition, we identify the structure of the local spin-flip dynamics as a crucial ingredient for any modeling. Thus, the dynamics of spin ice reflects the interplay of local dynamics with emergent topological degrees of freedom and a frustration-generated imperfectly flat energy landscape, and as such, it points to intriguing cooperative and memory effects for a broad class of magnetic materials.

Dy2−x Y x Ti2O7: phonon vibration and magnetization with dilution

In this paper, the dilution effects of non-magnetic Y ions on spin-ice compound Dy2Ti2O7 by infrared and Raman spectra and magnetization measurements were investigated. An anomalous phonon softening with temperature decreasing is found in both the parent and diluted compounds, and Y doping can relax the softening of phonons except that of the IR mode near 233 cm−1, indicating a strong phonon–phonon coupling in the spin-ice material. The magnetization measurements reveal that the non-magnetic impurities do not severely influence the spin-ice rules in the ground state when the level of dilution is not very high. However, a large amount of dilution enhance the disorder and break the spin-ice state because the collective spin-flip clusters are no longer available.

Thermal transport in spin ice

In order to analyse low temperature heat transport in the spin ice compound Dy2Ti2O7, we derive thermodynamic field equations that are based on the kinetic theory of phonons and their interaction with localised magnetic excitations. It is shown that the solution of the derived field equations for given boundary and initial values of heat-pulse experiments well describes all measured temperature profiles recorded in the temperature range from 0.3 to 15 K and in magnetic fields up to 1.5 T. The evaluated temperature and field dependencies of both the specific heat contributions and their corresponding relaxation times indicate that the magnetic excitations above the ground-state manifold of the spin ice compound Dy2Ti2O7 take the form of magnetic monopoles.

Observation of a novel phase transition induced by a magnetic field in the pyrochlore spinice compound

We present a novel field-induced phase transition in the spin ice compoundDy2Ti2O7 that is investigated by means of angle-resolved DC magnetization measurements. In thenear [112] field, the magnetization component perpendicular to the Kagomé plane shows afirst-order phase transition below 0.27 K. This transition is driven by a ferromagneticordering in the field-decoupled spins on the triangular lattice. Furthermore, we revealedanother first-order phase transition below 0.52 K in a magnetic field between the [110] and[111] directions. This phase transition is related to a breakdown of ferromagnetic Ising spinchains along or .

Field-angle dependence of the ice-rule breaking spin-flip transition inDy2Ti2O7

Ice-rule breaking spin flip in the pyrochlore spin-ice compoundDy2Ti2O7 has been studied in a field rotated in the plane, by means of angle-resolved magnetization measurements. The field-angle dependence of the spinflip field Hc(θ) has been obtained. Close to the [111] direction,Hc(θ) exhibits a marked deviation from a nearest-neighbour spin-ice model, suggesting theimportance of long-range dipolar interaction and a stability of the kagomé ice state.

Kagomé Ice State in the Dipolar Spin IceDy2Ti2O7

We have investigated the kagomé ice behavior of the dipolar spin-ice compound Dy2Ti2O7 in a magnetic field along a [111] direction using neutron scattering and Monte Carlo simulations. The spin correlations show that the kagomé ice behavior predicted for the nearest-neighbor interacting model, where the field induces dimensional reduction and spins are frustrated in each two-dimensional kagomé lattice, occurs in the dipole interacting system. The spins freeze at low temperatures within the macroscopically degenerate ground states of the nearest-neighbor model.

Magnetodielectric response of the spin-iceDy2Ti2O7

We report the magneto-dielectric response of single crystals of the spin-ice compound Dy2Ti2O7 down to 0.26 K. The dielectric constant under zero magnetic field exhibits a clear decrease reflecting the development of the local two-spins-in, two-spins-out structure below about 1.2 K. Both the real and imaginary parts of the dielectric constant under magnetic fields sensitively respond to various changes in the spin structures. We found that the real part can be described in terms of local spin correlations among the moments of tetrahedra, rather than among individual Dy3+ moments. Using the peaks in the imaginary part, we have constructed a precise field-temperature phase diagram in the [111] field direction. We thus demonstrate that the magneto-dielectric response can be a high-sensitivity local probe of the spin state of geometrically frustrated systems.

Far infrared optical properties of the pyrochlore spin ice compoundDy2Ti2O7

Near normal incidence far infrared reflectivity spectra of [111] dysprosium titanate(Dy2Ti2O7) single crystal have been measured at different temperatures. Seven phononmodes (eight at low temperature) are identified at frequencies below1000 cm−1. Optical conductivity spectra are obtained by fitting all the reflectivity spectra with thefactorized form of the dielectric function. Both the Born effective charges and the staticoptical permittivity are found to increase with decreasing temperature. Moreover, phononlinewidth narrowing and a phonon mode shift with decreasing temperature are alsoobserved, which may result from enhanced charge localization. The redshift of several lowfrequency modes is attributed to the spin–phonon coupling. All observed optical propertiescan be explained within the framework of the nearest neighbour ferromagnetic (FM) spinice model.

A Kagome ice state in the spin ice compoundDy2Ti2O7

We report on the specific heat and the entropy of single crystals of the spin ice compoundDy2Ti2O7 down to 100 mK under magnetic fields along the [111] direction in order to studydetailed low temperature properties of the Kagome ice state. Previously, we reportedanisotropic release of the residual entropy reflecting the Ising anisotropy. Wepointed out that the anisotropic behaviour can be viewed as the difference infrustration dimensionality. In an intermediate field, the entropy for the [111] fielddirection is different from those of the other principal directions. This is because thefrustration structure changes from that of a three-dimensional (3D) pyrochloreto that of a two-dimensional (2D) Kagome lattice with constraint from the icerule, accompanied by a different zero-point entropy value. We call this state ‘theKagome ice state’. In the Kagome ice state, the value of the residual entropy,ΔSKagome, isestimated as 0.598 J K−1/(mol Dy) by Pauling’s method.In the present experiment, we observed that the specific heat at 1 T exhibits a sharp peakat 400 mK and an anomalous upturn at lower temperature. This peak indicates theentropy release from a 1-in 3-out state with no residual entropy to a 1-in 3-freestate.

Low-temperature spin freezing in theDy2Ti2O7spin ice

We report a study of the low temperature bulk magnetic properties of the spin ice compound Dy2Ti2O7 with particular attention to the (T < 4 K) spin freezing transition. While this transition is superficially similar to that in a spin glass, there are important qualitative differences from spin glass behavior: the freezing temperature increases slightly with applied magnetic field, and the distribution of spin relaxation times remains extremely narrow down to the lowest temperatures. Furthermore, the characteristic spin relaxation time increases faster than exponentially down to the lowest temperatures studied. These results indicate that spin-freezing in spin ice materials represents a novel form of magnetic glassiness associated with the unusual nature of geometrical frustration in these materials.

Quantum-classical reentrant relaxation crossover in Dy2Ti2O7 spin ice.

We have studied spin relaxation in the spin ice compound Dy2Ti2O7 through measurements of the ac magnetic susceptibility. While the characteristic spin-relaxation time (tau) is thermally activated at high temperatures, it becomes almost temperature independent below T(cross) approximately 13 K. This behavior, combined with nonmonotonic magnetic field dependence of tau, indicates that quantum tunneling dominates the relaxational process below that temperature. As the low-entropy spin ice state develops below T(ice) approximately 4 K, tau increases sharply with decreasing temperature, suggesting the emergence of a collective degree of freedom for which thermal relaxation processes again become important as the spins become strongly correlated.

Anisotropic release of the residual zero-point entropy in the spin ice compoundDy2Ti2O7:Kagome ice behavior

We report the specific heat and entropy of single crystals of the spin ice compound Dy2Ti2O7 at temperatures down to 0.35 K. We apply magnetic fields along the four characteristic directions: [100], [110], [111] and [112]. Because of Ising anisotropy, we observe anisotropic release of the residual zero-point entropy, attributable to the difference in frustration dimensionality. In the high magnetic field along these four directions, the residual entropy is almost fully released and the activation entropy reaches Rln2. However, in the intermediate field region, the entropy in fields along the [111] direction is different from those for the other three field directions. For the [111] direction the frustration structure changes from that of three-dimensional(3D) pyrochlore to that of two-dimensional(2D) Kagome-like lattice with constraint due to the ice rule, leading to different values of zero-point entropy.

Observation of a Liquid-Gas-Type Transition in the Pyrochlore Spin Ice CompoundDy2Ti2O7in a Magnetic Field

Low temperature magnetization measurements on the pyrochlore spin ice compound Dy2Ti2O7 reveal that the ice-rule breaking spin flip, appearing at H approximately 0.9 T applied parallel to the [111] direction, turns into a novel first-order transition for T<0.36 K which is most probably of a liquid-gas type. T-linear variation of the critical field observed down to 0.03 K suggests the unusual situation that the entropy release across the transition remains finite [approximately 0.5 (J/K) x mol-Dy] as T-->0, in accordance with a breaking of the macroscopic degeneracy in the intermediate "kagomé ice" state.

Specific Heat of Kagomé Ice in the Pyrochlore Oxide Dy2Ti2O7

A novel macroscopically degenerate state called kagome ice, which was recently found in a spin ice compound Dy2Ti2O7 in a magnetic field applied along the [111] direction of the cubic unit cell, is studied by specific heat measurements. The residual entropy of the kagome ice is estimated to be 0.65 J/K mol Dy, which is nearly 40 % of that for the tetrahedral spin ice obtained in a zero field (1.68 J/K mol Dy) and is in good agreement with a theoretical prediction. It is also reported that the kagom ice state, which is stabilized at a range of magnetic field of 0.3 ~ 0.6 T, is a 'gas' phase and condenses into a 'liquid' phase with nearly zero entropy at a critical field of 1 T.

Magnetic anisotropy of the spin-ice compound Dy2Ti2O7

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