Enhancement of the anomalous Hall effect by distorting the Kagome lattice in an antiferromagnetic material.

In topological magnetic materials, the topology of the electronic wave function is strongly coupled to the structure of the magnetic order. In general, ferromagnetic Weyl semimetals generate a strong anomalous Hall conductivity (AHC) due to a large Berry curvature that scales with their magnetization. In contrast, a comparatively small AHC is observed in noncollinear antiferromagnets. We investigated HoAgGe, an antiferromagnetic (AFM) Kagome spin-ice compound, which crystallizes in a hexagonal ZrNiAl-type structure in which Ho atoms are arranged in a distorted Kagome lattice, forming an intermetallic Kagome spin-ice state in the ab-plane. It exhibits a large topological Hall resistivity of ~1.6 µΩ-cm at 2.0 K in a field of ~3 T owing to the noncoplanar structure. Interestingly, a total AHC of 2,800 Ω-1 cm-1 is observed at ~45 K, i.e., 4 TN, which is quite unusual and goes beyond the normal expectation considering HoAgGe as an AFM Kagome spin-ice compound with a TN of ~11 K. We demonstrate further that the AHC below TN results from the nonvanishing Berry curvature generated by the formation of Weyl points under the influence of the external magnetic field, while the skew scattering led by Kagome spins dominates above the TN. These results offer a unique opportunity to study frustration in AFM Kagome lattice compounds.

Dichotomous dynamics of magnetic monopole fluids.

A recent advance in the study of emergent magnetic monopoles was the discovery that monopole motion is restricted to dynamical fractal trajectories [J. N. Hallén et al., Science 378, 1218 (2022)], thus explaining the characteristics of magnetic monopole noise spectra [R. Dusad et al., Nature 571, 234 (2019); A. M. Samarakoon et al., Proc. Natl. Acad. Sci. U.S.A. 119, e2117453119 (2022)]. Here, we apply this novel theory to explore the dynamics of field-driven monopole currents, finding them composed of two quite distinct transport processes: initially swift fractal rearrangements of local monopole configurations followed by conventional monopole diffusion. This theory also predicts a characteristic frequency dependence of the dissipative loss angle for AC field-driven currents. To explore these novel perspectives on monopole transport, we introduce simultaneous monopole current control and measurement techniques using SQUID-based monopole current sensors. For the canonical material Dy2Ti2O7, we measure [Formula: see text], the time dependence of magnetic flux threading the sample when a net monopole current [Formula: see text] is generated by applying an external magnetic field [Formula: see text] These experiments find a sharp dichotomy of monopole currents, separated by their distinct relaxation time constants before and after t ~[Formula: see text] from monopole current initiation. Application of sinusoidal magnetic fields [Formula: see text] generates oscillating monopole currents whose loss angle [Formula: see text] exhibits a characteristic transition at frequency [Formula: see text] over the same temperature range. Finally, the magnetic noise power is also dichotomic, diminishing sharply after t ~[Formula: see text]. This complex phenomenology represents an unprecedented form of dynamical heterogeneity generated by the interplay of fractionalization and local spin configurational symmetry.

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.

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.

Field angle dependent resonant dynamics of artificial spin ice lattices.

Artificial spin ice structures which are networks of coupled nanomagnets arranged on different lattices that exhibit a number of interesting phenomena are promising for future information processing. We report reconfigurable microwave properties in artificial spin ice structures with three different lattice symmetries namely square, kagome, and triangle. Magnetization dynamics are systematically investigated using field angle dependent ferromagnetic resonance spectroscopy. Two distinct ferromagnetic resonance modes are observed in square spin ice structures in contrast with the three well-separated modes in kagome and triangular spin ice structures that are spatially localized at the center of the individual nanomagnets. A simple rotation of the sample placed in magnetic field results in the merging and splitting of the modes due to the different orientations of the nanomagnets with respect to the applied magnetic field. Magnetostatic interactions are found to shift the mode positions after comparing the microwave responses from the array of nanomagnets with control simulations with isolated nanomagnets. Moreover, the extent of the mode splitting has been studied by varying the thickness of the lattice structures. The results have potential implications for microwave filter-type applications which can be operated for a wide range of frequencies with ease of tunability.

Emergent Spin Dynamics Enabled by Lattice Interactions in a Bicomponent Artificial Spin Ice.

Artificial spin ice (ASI) networks are arrays of nanoscaled magnets that can serve both as models for frustration in atomic spin ice as well as for exploring new spin-wave-based strategies to transmit, process, and store information. Here, we exploit the intricate interplay of the magnetization dynamics of two dissimilar ferromagnetic metals arranged on complementary lattice sites in a square ASI to modulate the spin-wave properties effectively. We show that the interaction between the two sublattices results in unique spectra attributed to each sublattice, and we observe inter- and intralattice dynamics facilitated by the distinct magnetization properties of the two materials. The dynamic properties are systematically studied by angular-dependent broadband ferromagnetic resonance and confirmed by micromagnetic simulations. We show that combining materials with dissimilar magnetic properties enables the realization of a wide range of two-dimensional structures, potentially opening the door to new concepts in nanomagnonics.

Spin-Wave Dynamics and Symmetry Breaking in an Artificial Spin Ice.

Artificial spin ices are periodic arrangements of interacting nanomagnets which allow investigating emergent phenomena in the presence of geometric frustration. Recently, it has been shown that artificial spin ices can be used as building blocks for creating functional materials, such as magnonic crystals. We investigate the magnetization dynamics in a system exhibiting anisotropic magnetostatic interactions owing to locally broken structural inversion symmetry. We find a rich spin-wave spectrum and investigate its evolution in an external magnetic field. We determine the evolution of individual modes, from building blocks up to larger arrays, highlighting the role of symmetry breaking in defining the mode profiles. Moreover, we demonstrate that the mode spectra exhibit signatures of long-range interactions in the system. These results contribute to the understanding of magnetization dynamics in spin ices beyond the kagome and square ice geometries and are relevant for the realization of reconfigurable magnonic crystals based on spin ices.

Observation of Coherent Spin Waves in a Three-Dimensional Artificial Spin Ice Structure.

Harnessing high-frequency spin dynamics in three-dimensional (3D) nanostructures may lead to paradigm-shifting, next-generation devices including high density spintronics and neuromorphic systems. Despite remarkable progress in fabrication, the measurement and interpretation of spin dynamics in complex 3D structures remain exceptionally challenging. Here, we take a first step and measure coherent spin waves within a 3D artificial spin ice (ASI) structure using Brillouin light scattering. The 3D-ASI was fabricated by using a combination of two-photon lithography and thermal evaporation. Two spin-wave modes were observed in the experiment whose frequencies showed nearly monotonic variation with the applied field strength. Numerical simulations qualitatively reproduced the observed modes. The simulated mode profiles revealed the collective nature of the modes extending throughout the complex network of nanowires while showing spatial quantization with varying mode quantization numbers. The study shows a well-defined means to explore high-frequency spin dynamics in complex 3D spintronic and magnonic structures.

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.

Reconfigurable Pinwheel Artificial-Spin-Ice and Superconductor Hybrid Device.

The ability to control the potential landscape in a medium of interacting particles could lead to intriguing collective behavior and innovative functionalities. Here, we utilize spatially reconfigurable magnetic potentials of a pinwheel artificial-spin-ice (ASI) structure to tailor the motion of superconducting vortices. The reconstituted chain structures of the magnetic charges in the pinwheel ASI and the strong interaction between magnetic charges and superconducting vortices allow significant modification of the transport properties of the underlying superconducting thin film, resulting in a reprogrammable resistance state that enables a reversible and switchable vortex Hall effect. Our results highlight an effective and simple method of using ASI as an in situ reconfigurable nanoscale energy landscape to design reprogrammable superconducting electronics, which could also be applied to the in situ control of properties and functionalities in other magnetic particle systems, such as magnetic skyrmions.

Emergent Dynamics of Artificial Spin-Ice Lattice Based on an Ultrathin Ferromagnet.

We present high-frequency dynamics of magnetic nanostructure lattices, fabricated in the form of "artificial spin-ice", that possess magnetically frustrated states. Dynamics of such structures feature multiple resonance excitation that reveals rich and intriguing microwave characteristics, which are highly dependent on field-cycle history. Geometrical parameters such as dimensions and ferromagnetic layer thickness, which control the interplay of different demagnetizing factors, are found to play a pivotal role in governing the dynamics. Our findings are highlighted by the evolution of unique excitations pertaining to magnetic frustration, which are well supported by static magnetometry studies and micromagnetic simulations.

Modal Frustration and Periodicity Breaking in Artificial Spin Ice.

Here, an artificial spin ice lattice is introduced that exhibits unique Ising and non-Ising behavior under specific field switching protocols because of the inclusion of coupled nanomagnets into the unit cell. In the Ising regime, a magnetic switching mechanism that generates a uni- or bimodal distribution of states dependent on the alignment of the field is demonstrated with respect to the lattice unit cell. In addition, a method for generating a plethora of randomly distributed energy states across the lattice, consisting of Ising and Landau states, is investigated through magnetic force microscopy and micromagnetic modeling. It is demonstrated that the dispersed energy distribution across the lattice is a result of the intrinsic design and can be finely tuned through control of the incident angle of a critical field. The present manuscript explores a complex frustrated environment beyond the 16-vertex Ising model for the development of novel logic-based technologies.

Spin Ice-like Magnetic Relaxation of a Two-dimensional Network based on Manganese(III) Salen-type Single-Molecule Magnets.

Spin ice is an exotic type of magnetism displayed by bulk rare-earth pyrochlore oxides. We discovered a spin ice-like magnetic relaxation of [{Mn(saltmen)}4 {Mn(CN)6 }](ClO4 )⋅13 H2 O (saltmen2- =N,N'-(1,1,2,2-tetramethylethylene)bis(salicylideneiminate)). This magnetic system can be considered as a two-dimensional network of MnIII salen-type single-molecule magnets (SMMs) in which each SMM unit (ST =4) has two orthogonally oriented axial anisotropies and is connected ferromagnetically through the [Mn(CN)6 ]3- unit (S=1). This work illustrates that a two-dimensional SMM network with competition between the ferromagnetic interaction and local noncollinear magnetic anisotropies on SMMs is a new type of magnetic system exhibiting slow relaxation of magnetization with a Davidson-Cole-type broad distribution of the relaxation time.

Muon spin relaxation and emergence of disorder-induced unconventional dynamic magnetic fluctuations in Dy2Zr2O7.

The disordered pyrochlore oxide Dy2Zr2O7shows the signatures of field-induced spin freezing with remnant zero-point spin-ice entropy at 5 kOe magnetic field. We have performed zero-field and longitudinal field Muon spin relaxation (µSR) studies on Dy2Zr2O7. Our zero field studies reveal the absence of both long-range ordering and spin freezing down to 62 mK. TheµSR relaxation rate exhibits a temperature-independent plateau below 4 K, indicating a dynamic ground state of fluctuating spins similar to the well-known spin ice system Dy2Ti2O7. The low-temperature spin fluctuations persist in the longitudinal field of 20 kOe as well and show unusual field dependence of the relaxation rate, which is uncommon for a spin-liquid system. Our results, combined with the previous studies do not show any evidence of spin ice or spin glass ground state, rather point to a disorder-induced dynamic magnetic ground state in the Dy2Zr2O7material.

Modelling nanomagnet vertex dynamics through Coulomb charges.

We investigate the magnetization dynamics in nanomagnet vertices often found in artificial spin ices. Our analysis involves creating a simplified model that depicts edge magnetization using magnetic charges. We utilize the model to explore the energy landscape, its associated curvatures, and the fundamental modes. Our study uncovers specific magnonic regimes and transitions between magnetization states, marked by zero-modes, which can be understood within the framework of Landau theory. To verify our model, we compare it with micromagnetic simulations, demonstrating a noteworthy agreement.

Tailoring magnon modes by extending square, kagome, and trigonal spin ice lattices vertically via interlayer coupling of trilayer nanomagnets.

In this work high-frequency magnetization dynamics and statics of artificial spin-ice lattices with different geometric nanostructure array configurations are studied where the individual nanostructures are composed of ferromagnetic/non-magnetic/ferromagnetic trilayers with different non-magnetic thicknesses. These thickness variations enable additional control over the magnetic interactions within the spin-ice lattice that directly impacts the resulting magnetization dynamics and the associated magnonic modes. Specifically the geometric arrangements studied are square, kagome and trigonal spin ice configurations, where the individual lithographically patterned nanomagnets (NMs) are trilayers, made up of two magnetic layers ofNi81Fe19of 30 nm and 70 nm thickness respectively, separated by a non-magnetic copper layer of either 2 nm or 40 nm. We show that coupling via the magnetostatic interactions between the ferromagnetic layers of the NMs within square, kagome and trigonal spin-ice lattices offers fine-control over magnetization states and magnetic resonant modes. In particular, the kagome and trigonal lattices allow tuning of an additional mode and the spacing between multiple resonance modes, increasing functionality beyond square lattices. These results demonstrate the ability to move beyond quasi-2D single magnetic layer nanomagnetics via control of the vertical interlayer interactions in spin ice arrays. This additional control enables multi-mode magnonic programmability of the resonance spectra, which has potential for magnetic metamaterials for microwave or information processing applications.

Magnetization Dynamics in Quasiperiodic Magnonic Crystals.

Quasiperiodic magnonic crystals, in contrast to their periodic counterparts, lack strict periodicity which gives rise to complex and localised spin wave spectra characterized by numerous band gaps and fractal features. Despite their intrinsic structural complexity, quasiperiodic nature of these magnonic crystals enables better tunability of spin wave spectra over their periodic counterparts and therefore holds promise for the applications in reprogrammable magnonic devices. In this article, we provide an overview of magnetization reversal and precessional magnetization dynamics studied so far in various quasiperiodic magnonic crystals, illustrating how their quasiperiodic nature gives rise to tailored band structure, enabling unparalleled control over spin waves. The review is concluded by highlighting the possible potential applications of these quasiperiodic magnonic crystals, exploring potential avenues for future exploration followed by a brief summary.

Exact diagonalization for a 16-site spin-1/2 pyrochlore cluster.

We find exact solutions to the Hamiltonian of a 16-site spin-1/2 pyrochlore cluster with nearest neighbour exchange interactions. The methods of group theory (symmetry) are used to completely block-diagonalize the Hamiltonian, yielding precise details about symmetry of the eigenstates, in particular those components which arespin icestates, in order to evaluate the spin ice density at finite temperature. At low enough temperatures, a 'perturbed' spin ice phase, where the '2-in-2-out' ice rule is largely obeyed, is clearly outlined within the four parameter space of the general model of exchange interactions. The quantum spin ice phase is expected to exist within these boundaries.

Emergence of field-induced memory effect in spin ices.

Out-of-equilibrium investigation of strongly correlated materials deciphers the hidden equilibrium properties. Herein, we have investigated the out-of-equilibrium magnetic properties of polycrystalline Dy2Ti2O7and Ho2Ti2O7spin ices. Our experimental findings reveal the emergence of magnetic field-induced anomalous hysteresis observed solely in temperature-and magnetic field-dependent AC susceptibility measurements. The observed memory effect (anomalous thermomagnetic hysteresis) exhibits a strong dependence on both thermal and non-thermal driving variables. Owing to the non-collinear spin structure, the applied DC bias magnetic field produces quenched disorder sites in the cooperative Ising spin matrix and suppresses the spin-phonon coupling. These quench disorders create a dynamic spin correlation, having slow spin relaxation and quick decay time, which additionally contribute to AC susceptibility. The initial conditions and measurement protocol decide the magnitude and sign of this dynamical term contributing to AC susceptibility. It is being suggested that such out-of-equilibrium properties arise from the combined influences of geometric frustration, disorder, and the cooperative nature of spin dynamics exhibited by these materials.

Controlling degeneracy and magnetization switching in an artificial spin ice system of peanut-shaped nanomagnets.

Using extensive numerical simulations, we probe 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 be 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 two-in/two-out (Type II) magnetic state is robust at the remanence. We are also able to access the other possible microstate corresponding to Type II 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, the system also appears to have one-out/three-in or three-out/one-in (Type III) spin state, reminiscent of magnetic monopole at the vertex. We believe that our study is highly desirable in the context of developing the next-generation spintronics-based devices for future technologies.