The history of spin ice

High-resolution three-dimensional imaging of topological textures in nanoscale single-diamond networks

Topological defects-extended lattice deformations that are robust against local defects and annealing-have been exploited to engineer novel properties in both hard and soft materials. Yet, their formation kinetics and nanoscale three-dimensional structure are poorly understood, impeding their benefits for nanofabrication. We describe the fabrication of a pair of topological defects in the volume of a single-diamond network (space group Fd3 ¯ m) templated into gold from a triblock terpolymer crystal. Using X-ray nanotomography, we resolve the three-dimensional structure of nearly 70,000 individual single-diamond unit cells with a spatial resolution of 11.2 nm, allowing analysis of the long-range order of the network. The defects observed morphologically resemble the comet and trefoil patterns of equal and opposite half-integer topological charges observed in liquid crystals. Yet our analysis of strain in the network suggests typical hard matter behaviour. Our analysis approach does not require a priori knowledge of the expected positions of the nodes in three-dimensional nanostructured systems, allowing the identification of distorted morphologies and defects in large samples.

Proximity effect of emergent field from spin ice in an oxide heterostructure

Geometrical frustration endows magnets with degenerate ground states, resulting in exotic spin structures and quantum phenomena. Such magnets, called quantum magnets, can display non-coplanar spin textures and be a viable platform for the topological Hall effect driven by "emergent field." However, most quantum magnets are insulators, making it challenging to electrically detect associated fluctuations and excitations. Here, we probe magnetic transitions in the spin ice insulator Dy2Ti2O7, a prototypical quantum magnet, as emergent magnetotransport phenomena at the heterointerface with the nonmagnetic metal Bi2Rh2O7. Angle-dependent longitudinal resistivity exhibits peaks at the magnetic phase boundaries of spin ice due to domain boundary scattering. In addition, the anomalous Hall resistivity undergoes a sign change with the magnetic transition in Dy2Ti2O7, reflecting the inversion of the emergent field. These findings, on the basis of epitaxial techniques, connect the fundamental research on insulating quantum magnets to their potential electronic applications, possibly leading to transformative innovations in quantum technologies.

Stuffed Rare-Earth Garnets

We report the synthesis and magnetic characterization of stuffed rare-earth gallium garnets, RE3+xGa5-xO12 (RE = Lu, Yb, Er, Dy, Gd), for x up to 0.5. The excess rare-earth ions partly fill the octahedral sites normally fully occupied by Ga3+, forming disordered pairs of corner-shared face-sharing magnetic tetrahedra. The Curie-Weiss constants and observed effective moments per rare-earth are smaller than are seen for the unstuffed gallium garnets. No significant change in the field-dependent magnetization is observed but missing entropy is seen when integrating the heat capacity down to 0.5 K.

Deconstructing magnetization noise: Degeneracies, phases, and mobile fractionalized excitations in tetris artificial spin ice

Direct detection of spontaneous spin fluctuations, or "magnetization noise," is emerging as a powerful means of revealing and studying magnetic excitations in both natural and artificial frustrated magnets. Depending on the lattice and nature of the frustration, these excitations can often be described as fractionalized quasiparticles possessing an effective magnetic charge. Here, by combining ultrasensitive optical detection of thermodynamic magnetization noise with Monte Carlo simulations, we reveal emergent regimes of magnetic excitations in artificial "tetris ice." A marked increase of the intrinsic noise at certain applied magnetic fields heralds the spontaneous proliferation of fractionalized excitations, which can diffuse independently, without cost in energy, along specific quasi-1D spin chains in the tetris ice lattice.

Magnetic Arctic Circle in a Square Ice Qubit Lattice

Under certain boundary conditions, the square ice model exhibits a phase separation in which the core of the system is disordered while its outer region remains ordered. This phenomenon, known as the "arctic circle," has been studied theoretically in combinatorial mathematics and statistical mechanics. Here, we realize the physics of the arctic circle experimentally for the first time, using a programmable lattice of superconducting qubits, and investigate its properties under the prism of a highly frustrated magnet. Our work reveals two unexpected properties. First, the disordered spin manifold confined within the arctic curve is a spin liquid whose average spin texture resembles that of an antivortex, i.e., it is a topologically charged Coulomb phase. Second, monopole quasiparticle excitations, which are totally absent in theoretical works, can be isolated in a phase-separated system. Remarkably, a monopole segregation mechanism is observed, in which the monopoles are sorted according to the magnetic charge and magnetic moment they carry, without the application of an external driving force.

Erbium-Excess Gallium Garnets

A series of garnets of formula Er3+xGa5-xO12 are described, for which we report the crystal structures for both polycrystalline and single-crystal samples. The x limit in the garnet phase is between 0.5 and 0.6 under our conditions, with the Er fully occupying the dodecahedral (24c) garnet site plus some of the octahedral site (16a) in place of the Ga normally present. Long-range antiferromagnetic order with spin-ice-like frustration is suggested by the transition temperature (TN ≈ 0.8 K) being lower than the Curie-Weiss theta. The magnetic ordering temperature does not depend on the Er excess, but there is increasing residual entropy as the Er excess is increased, highlighting the potential for unusual magnetic behavior in this system. The field-dependent magnetic entropy trend is consistent with the reported behavior for frustrated triangular magnetic systems: an increasing transition temperature with a broader hump as the applied field increases [Xing, J.; Phys. Rev. Mater. 2019, 3(11), 114413;Filippi, J.; Solid State Commun. 1977, 23(9), 613-616; Bloxsom, J. A. Thermal and Magnetic Studies of Spin Ice Compounds. University College London, 2016].

Kagome qubit ice

Topological phases of spin liquids with constrained disorder can host a kinetics of fractionalized excitations. However, spin-liquid phases with distinct kinetic regimes have proven difficult to observe experimentally. Here we present a realization of kagome spin ice in the superconducting qubits of a quantum annealer, and use it to demonstrate a field-induced kinetic crossover between spin-liquid phases. Employing fine control over local magnetic fields, we show evidence of both the Ice-I phase and an unconventional field-induced Ice-II phase. In the latter, a charge-ordered yet spin-disordered topological phase, the kinetics proceeds via pair creation and annihilation of strongly correlated, charge conserving, fractionalized excitations. As these kinetic regimes have resisted characterization in other artificial spin ice realizations, our results demonstrate the utility of quantum-driven kinetics in advancing the study of topological phases of spin liquids.

Machine Learning Methods for Multiscale Physics and Urban Engineering Problems

We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where "multiscale" refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations.

Defect-induced monopole injection and manipulation in artificial spin ice

Lithographically defined arrays of nanomagnets are well placed for application in areas such as probabilistic computing or reconfigurable magnonics due to their emergent collective dynamics and writable magnetic order. Among them are artificial spin ice (ASI), which are arrays of binary in-plane macrospins exhibiting geometric frustration at the vertex interfaces. Macrospin flips in the arrays create topologically protected magnetic charges, or emergent monopoles, which are bound to an antimonopole to conserve charge. In the absence of controllable pinning, it is difficult to manipulate individual monopoles in the array without also influencing other monopole excitations or the counter-monopole charge. Here, we tailor the local magnetic order of a classic ASI lattice by introducing a ferromagnetic defect with shape anisotropy into the array. This creates monopole injection sites at nucleation fields below the critical lattice switching field. Once formed, the high energy monopoles are fixed to the defect site and may controllably propagate through the lattice under stimulation. Defect programing of bound monopoles within the array allows fine control of the pathways of inverted macrospins. Such control is a necessary prerequisite for the realization of functional devices, e. g. reconfigurable waveguide in nanomagnonic applications.

Artificial spin ice systems offer a promising platform to study the motion of emergent magnetic monopoles, but controlled nucleation of monopoles is challenging. Here the authors demonstrate controlled injection and propagation of emergent monopoles in an artificial spin ice utilizing ferromagnetic defects.

Structure and Magnetic Properties of Melilite-Type Compounds RE2Be2GeO7 (RE = Pr, Nd, Gd-Yb) with Rare-Earth Ions on Shastry-Sutherland Lattice

Rare-earth (RE)-based frustrated magnets, such as typical systems of combining strong spin-orbit coupling (SOC), geometric frustration, and anisotropic exchange interaction, can give rise to diverse exotic magnetic ground states such as quantum spin liquid. The discovery of new RE-based frustrated materials is crucial for exploring the exotic magnetic phases. Herein, we report the synthesis, structure, and magnetic properties of a family of melilite-type RE₂Be₂GeO₇ (RE = Pr, Nd, and Gd-Yb) compounds crystallized in a tetragonal P4̅2₁m structure, where magnetic RE³⁺ ions lay out on the Shastry-Sutherland lattice (SSL) within the ab plane and are well separated by nonmagnetic [GeBe₂O₇]^6- polyhedrons along the c-axis. Temperature (T)-dependent susceptibilities χ(T) and isothermal magnetization M(H) measurements reveal that most RE₂Be₂GeO₇ compounds except RE = Tb show no magnetic ordering down to 2 K despite the dominant antiferromagnetic (AFM) interactions, where Tb₂Be₂GeO₇ undergoes AFM transition with Néel temperature T_N ∼ 2.5 K and field-induced spin flop behaviors (T < T_N). In addition, the calculated magnetic entropy change ΔS_m from the isothermal M(H) curves reveals viable magnetocaloric effect for RE₂Be₂GeO₇ (RE = Gd and Dy) in liquid helium temperature regimes; Gd₂Be₂GeO₇ shows the maximum ΔS_m up to 54.8 J K^-1 kg^-1 at ΔH = 7 T and Dy₂Be₂GeO₇ has the largest value ΔS_m = 16.1 J K^-1 kg^-1 at ΔH = 2 T in this family. More excitingly, the rich diversity of RE ions in this family enables an archetype for exploring exotic quantum magnetic phenomena with large variability of spin located on the SSL lattice.

Robust spin-ice freezing in magnetically frustrated Ho2GexTi2-xO7pyrochlore

Structural analysis of spin frustrated Ho2GexTi2-xO7(x= 0, 0.1, 0.15 & 0.25) pyrochlore oxides has been performed using high resolution x-ray diffraction pattern and low temperature synchrotron x-ray diffraction pattern. The effect of positive chemical pressure on the spin dynamics of Ho2GexTi2-xO7has been analysed through the study of static (M-TandM-H; magnetisation against temperature & magnetisation against magnetic field) and dynamical (ac susceptibility) magnetic measurements. In lower temperature regime (∼2 K), such systems are predominantly governed by competing exchange (Jnn) and dipolar (Dnn) magnetic interactions. Magnetic measurements indicate that the application of increased chemical pressure in Ho2Ti2O7matrix propels the system towards diminished ferromagnetic interaction. Dipolar coupling constant remains almost unchanged but Curie-Weiss temperature (θcw) reduces to -0.04 K from 0.33 K (for an applied magnetic field;H= 100 Oe) with increasingxin Ho2GexTi2-xO7. Positive chemical pressure establishes the dominance of Ho-Ho antiferromagnetic interactionJnnover dipolar interactionDnn. Spin relaxation feature corresponding to thermally activated single ion freezing (Ts∼15 K) is shifted towards lower temperature. This chemical pressure-drivenTsshift is ascribed to the alteration in crystal field effect, which reduces the activation energy for singe ion spin freezing. The reduction in the activation energy indicates crystal field-phonon coupling in Ho2GexTi2-xO7system. The robustness in spin ice freezing (second spin relaxation feature in ac susceptibility curve) remains unaffected with increasingly chemical pressure. This spin freezing ('2 in-2 out' spin arrangement in tetrahedra) is related to quantum tunnelling phenomenon, atTice∼ 2 K. It indicates that majority of spins still follows the 'ice rule' in Ho2GexTi2-xO7even after the application of chemical pressure.