Kagome Ice Research Articles

Direct observation of magnetic monopole defects in an artificial spin-ice system

Free monopoles have fascinated and eluded researchers since their prediction by Dirac1 in 1931. In spin ice, the bulk frustrated magnet, local ordering principles known as ice rules—two-in/two-out for four spins arranged in a tetrahedron—minimize magnetic charge. Remarkably, recent work2, 3, 4, 5 shows that mobile excitations, termed ‘monopole defects’, emerge when the ice rules break down2. Using a cobalt honeycomb nanostructure we study the two-dimensional planar analogue called kagome or artificial spin ice. Here we show direct images of kagome monopole defects and the flow of magnetic charge using magnetic force microscopy. We find the local magnetic charge distribution at each vertex of the honeycomb pins the magnetic charge carriers, and opposite charges hop in opposite directions in an applied field. The parameters that enter the problem of creating and imaging monopole defects can be mapped onto a simple model that requires only the ice-rule violation energy and distribution of switching fields of the individual bars of a cobalt honeycomb lattice. As we demonstrate, it is the exquisite interplay between these energy scales in the cobalt nanostructure that leads to our experimental observations.

Magnetic multipole analysis of kagome and artificial spin-ice dipolar arrays

We analyze an array of linearly extended monodomain dipoles forming square and kagome lattices. We find that its phase diagram contains two (distinct) finite-entropy kagome ice regimes---one disordered, one algebraic---as well as a low-temperature ordered phase. In the limit of the islands almost touching, we find a staircase of corresponding entropy plateaux, which is analytically captured by a theory based on magnetic charges. For the case of a modified square ice array, we show that the charges (``monopoles'') are excitations experiencing two distinct Coulomb interactions: a magnetic ``three-dimensional'' one as well as a logarithmic ``two-dimensional'' one of entropic origin.

Observation of Magnetic Monopoles in Spin Ice

Excitations from a strongly frustrated system, the kagome ice state of the spin ice Dy2Ti2O7 under magnetic fields along a [111] direction, have been studied. They are theoretically proposed to be regarded as magnetic monopoles. Neutron scattering measurements of spin correlations show that close to the critical point the monopoles are fluctuating between high- and low-density states, supporting that the magnetic Coulomb force acts between them. Specific heat measurements show that monopole-pair creation obeys an Arrhenius law, indicating that the density of monopoles can be controlled by temperature and magnetic field.

Creating Artificial Ice States Using Vortices in Nanostructured Superconductors

We demonstrate that it is possible to realize vortex ice states that are analogous to square and kagome ice. With numerical simulations, we show that the system can be brought into a state that obeys either global or local ice rules by applying an external current according to an annealing protocol. We explore the breakdown of the ice rules due to disorder in the nanostructure array and show that in square ice, topological defects appear along grain boundaries, while in kagome ice, individual defects appear. We argue that the vortex system offers significant advantages over other artificial ice systems.

Pinch points and Kasteleyn transitions in kagome ice

Complex disordered states—from liquids and glasses to exotic quantum matter—are ubiquitous in nature. Their key properties include finite entropy, power-law correlations and emergent organizing principles. In spin ice, spin correlations are determined by the ‘ice rules’ organizing principle that stabilizes a magnetic state with the same zero-point entropy as water ice. The entropy can be manipulated with great precision by an applied magnetic field: when directed along the three-fold crystallographic axis, the field produces a state of finite entropy, known as kagome ice. Here, we investigate the spin-ice material Ho2Ti2O7 by tilting the magnetic field slightly away from that axis. We thus realize a classic statistical system named after Kasteleyn, in which the entropy of a critical phase can be continuously tuned. Our neutron scattering experiments reveal how this process occurs at a microscopic level.

Artificial Square Ice and Related Dipolar Nanoarrays

We study a frustrated dipolar array recently manufactured lithographically by Wang in order to realize the square ice model in an artificial structure. We discuss models for thermodynamics and dynamics of this system. We show that an ice regime can be stabilized by small changes in the array geometry; a different magnetic state, kagome ice, can similarly be constructed. At low temperatures, the square ice regime is terminated by a thermodynamic ordering transition, which can be chosen to be ferro- or antiferromagnetic. We show that the arrays do not fully equilibrate experimentally, and identify a likely dynamical bottleneck.

Low Temperature Specific Heat of Dy2Ti2O7in the Kagome Ice State

We report the specific heat of single crystals of the spin ice compound Dy$_2$Ti$_2$O$_7$ at temperatures down to 100 mK in the so-called Kagome ice state. In our previous paper, we showed the anisotropic release of residual entropy in different magnetic field directions and reported new residual entropy associated with spin frustration in the Kagome slab for field in the [111] direction. In this paper, we confirm the first-order phase transition line in the field-temperature phase diagram and the presence of a critical point at (0.98 T, 400 mK), previously reported from the magnetization and specific-heat data. We newly found another peak in the specific heat at 1.25 T below 0.3 K. One possible explanation for the state between 1 T and 1.25 T is the coexistence of states with different spin configurations including the 2-in 2-out one (Kagome ice state), the 1-in 3-out state (ordered state) and paramagnetic one (free-spin state).

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.

Liquid–gas transition in the spin-ice dysprosium titanate

Abstract DC magnetization of Dy2Ti2O7 has been measured down to 30 mK . The ice-rule breaking spin flip appearing at H∼0.9 T ( || [1 1 1]) turns into a first-order transition for T K which is most probably of liquid–gas type. T-linear variation of the critical field suggests that the entropy release across the transition remains finite (∼0.5 J / K mol Dy ) down to 0.03 K , confirming the macroscopic degeneracy in the intermediate ‘kagome ice’ state.

新機能材料開発と構造科学 ２．新しい構造物性の芽 スピンアイスにおける磁場によって誘起される新しい巨視的縮退

Pyrochlore oxides have attracted much interest because their crystal structures include the corner-sharing tetrahedra. This represents an ideal system for studying the effect of geometrical frustration in the limit of low disorder. Recently, a new class of magnetic state known as“spin ice”is discovered in the pyrochlore rare-earth oxides. Recent our study reveals a new macroscopically degenerate ground state in the spin ice induced by a magnetic field. This is called“kagome ice”.

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.

Numerical evidence for two critical points in a triplet Ising model

It is shown that numerical data recently used to evaluate the residual entropy of Kagome ice can be adapted to form an expansion for the zero field free energy of a three-spin Ising model on a triangulated dice lattice. The expansion is used to test a recent conjecture of Wu (see J. Phys. C: Solid St. Phys. vol.7, p.181) that this model should exhibit two phase transitions.