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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

$μ$ $\mathrm{SR}$ study of the dipole-octupole quantum spin ice candidate $\mathrm{Ce_2Zr_2O_7}$

The Ce 3+ pseudospin-1/2 degrees of freedom in Ce 2 Zr 2 O 7 possess both dipolar and octupolar character which enables the possibility of novel quantum spin liquid ground states in this material. In this study, we report muon spin relaxation and rotation (μSR) measurements on single-crystal samples of Ce 2 Zr 2 O 7 in zero magnetic field and in magnetic fields directed along the [1, $\overline{1}$, 0] and [1, 1, 1] crystallographic directions, and for magnetic fields directed both longitudinal and transverse to the direction of muon polarization. Our zero-field results show no signs of magnetic ordering or spin freezing, consistent with earlier zero-field μSR measurements on a powder sample of Ce 2 Zr 2 O 7 , and also with the expectations for a quantum spin ice. However, we measure a more gentle relaxation rate for Ce 2 Zr 2 O 7 in zero field at low temperatures than was previously reported. This difference in relaxation rate is likely due to the low oxidation and, correspondingly, the high stoichiometry of our singlecrystal samples. Longitudinal field measurements confirm that the magnetic dipole moments in Ce 2 Zr 2 O 7 remain dynamic at T = 0.1 K on the microsecond timescale. For both [1, $\overline{1}$, 0] and [1, 1, 1] magnetic fields, our μSR Knight shift measurements show a field-induced leveling off of the magnetic susceptibility at low temperature which is qualitatively consistent with corresponding calculations using the numerical-linked-cluster method in combination with recent estimates for the nearest-neighbor exchange parameters of Ce 2 Zr 2 O 7 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Dynamic coupling and spin-wave dispersions in a magnetic hybrid system made of an artificial spin-ice structure and an extended NiFe underlayer

We present a combined experimental and numerical study of the spin-wave dispersion in a NiFe artificial spin-ice (ASI) system consisting of an array of stadium-shaped nanoislands deposited on the top of a continuous NiFe film with non-magnetic spacer layers of varying thickness. The spin-wave dispersion, measured by wavevector resolved Brillouin light scattering spectroscopy in the Damon–Eshbach configuration, consists of a rich number of modes, with either stationary or propagating character. We find that the lowest frequency mode displays a bandwidth of ~0.5 GHz, which is independent of the presence of the film underneath. On the contrary, the Brillouin light scattering intensity of some of the detected modes strongly depends on the presence of the extended thin-film underlayer. Micromagnetic simulations unveil the details of the dynamic coupling between the ASI lattice and film underlayer. Interestingly, the ASI lattice facilitates dynamics of the film either specific wavelengths or intensity modulation peculiar to the modes of the ASI elements imprinted in the film. Our results demonstrate that propagating spin waves can be modulated at the nanometer length scale by harnessing the dynamic mode coupling in the vertical, i.e., the out-of-plane direction of suitably designed magnonic structures.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Behavior of thermally quenched topological defects in quasicrystal artificial spin ices

We report that understanding the formation of topological defects in connected magnetic nanowires such as in artificial spin ices (ASIs) is critical to controlling their behavior. Moreover, emergent frustration behavior of these defects can be expected due to complex underlying lattice geometry of the ASIs. We have explored in situ thermalization and quenching of quasicrystalline ASIs, which exhibit additional frustration due to aperiodicity from near the Curie temperature, and we observe the formation of two sets of topological vortex defects: within the magnetic bars and within the vertices at which the bars meet. By varying the laser fluence, we show that the number of defects in the vertices varies as the quenching rate changes following a power law relation, which we interpret as being related to the ferromagnetic-to-paramagnetic phase transition. Conversely, the defects formed within the bars are metastable states related to the spontaneous magnetization reversal of the magnetic bars and are therefore strongly dependent on underlying lattice geometry. These results provide insight into the emergence and control of topological defects in confined frustrated magnetic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Real-space observation of ergodicity transitions in artificial spin ice

Abstract Ever since its introduction by Ludwig Boltzmann, the ergodic hypothesis became a cornerstone analytical concept of equilibrium thermodynamics and complex dynamic processes. Examples of its relevance range from modeling decision-making processes in brain science to economic predictions. In condensed matter physics, ergodicity remains a concept largely investigated via theoretical and computational models. Here, we demonstrate the direct real-space observation of ergodicity transitions in a vertex-frustrated artificial spin ice. Using synchrotron-based photoemission electron microscopy we record thermally-driven moment fluctuations as a function of temperature, allowing us to directly observe transitions between ergodicity-breaking dynamics to system freezing, standing in contrast to simple trends observed for the temperature-dependent vertex populations, all while the entropy features arise as a function of temperature. These results highlight how a geometrically frustrated system, with thermodynamics strictly adhering to local ice-rule constraints, runs back-and-forth through periods of ergodicity-breaking dynamics. Ergodicity breaking and the emergence of memory is important for emergent computation, particularly in physical reservoir computing. Our work serves as further evidence of how fundamental laws of thermodynamics can be experimentally explored via real-space imaging.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A Brillouin light scattering study of the spin-wave magnetic field dependence in a magnetic hybrid system made of an artificial spin-ice structure and a film underlayer

We present a combined Brillouin light scattering (BLS) and micromagnetic simulation investigation of the magnetic-field-dependent spin-wave spectra in a hybrid structure made of permalloy (NiFe) artificial spin-ice (ASI) systems, composed of stadium-shaped nanoislands, deposited on the top of an unpatterned permalloy film with a nonmagnetic spacer layer. The thermal spin-wave spectra were recorded by BLS as a function of the magnetic field applied along the symmetry direction of the ASI sample. Magneto-optic Kerr effect magnetometry was used to measure the hysteresis loops in the same orientation as the BLS measurements. Here, the frequency and the intensity of several spin-wave modes detected by BLS were measured as a function of the applied magnetic field. Micromagnetic simulations enabled us to identify the modes in terms of their frequency and spatial symmetry and to extract information about the existence and strength of the dynamic coupling, relevant only to a few modes of a given hybrid system. Using this approach, we suggest a way to understand if the dynamic coupling between ASI and film modes is present or not, with interesting implications for the development of future three-dimensional magnonic applications and devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Nonlinear multi-magnon scattering in artificial spin ice

Abstract Magnons, the quantum-mechanical fundamental excitations of magnetic solids, are bosons whose number does not need to be conserved in scattering processes. Microwave-induced parametric magnon processes, often called Suhl instabilities, have been believed to occur in magnetic thin films only, where quasi-continuous magnon bands exist. Here, we reveal the existence of such nonlinear magnon-magnon scattering processes and their coherence in ensembles of magnetic nanostructures known as artificial spin ice. We find that these systems exhibit effective scattering processes akin to those observed in continuous magnetic thin films. We utilize a combined microwave and microfocused Brillouin light scattering measurement approach to investigate the evolution of their modes. Scattering events occur between resonance frequencies that are determined by each nanomagnet’s mode volume and profile. Comparison with numerical simulations reveals that frequency doubling is enabled by exciting a subset of nanomagnets that, in turn, act as nanosized antennas, an effect that is akin to scattering in continuous films. Moreover, our results suggest that tunable directional scattering is possible in these structures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Machine Learning assisted optimization and parameter space exploration dataset of spin ice Hamiltonian

This repository contains both simulated and experimental structure factor data for the data challenge involving the inverse scattering problem. The simulated data were generated during a machine-learning-assisted optimization routine described in ref[1]. The experimental structure factor was measured on a rare-earth oxide, Dy2Ti2O7 using diffuse neutron scattering from time-of-flight techniques on the CORELLI instrument at the Spallation Neutron Source, Oak Ridge National Laboratory. A Metropolis Monte Carlo code implemented to run in a High-performance computing setting was used to calculated simulated structure factors for the spin-ice Hamiltonian at 680 mK, which is the same temperature as for the experimental data. The total size of all the files in this repository is 5.12 GB. A detailed description of the files is given below. ExperimentalData_630mK.dat – A linearized version of 3-dimensional experimental data of size 61×81×21. This data was processed to remove an estimation of non-magnetic background, including nuclear scattering signal and instrumentation background. Parameters.dat – 6700 samples were evaluated over the 4-dimensional parameter space (J_1, J_2, J_3 and J_(3^' )). There is an additional parameter, D in the spin Hamiltonian to mimic the dipolar interaction between magnetic ions. However, this parameter, D was fixed to a value determined by prior work. This file contains five columns for the parameters J_1, J_2, J_3, J_(3^' ) and D respectively. 3D_Simulation_Data.dat – The simulated structure factor, S(Q) data are included in this file. Each raw contains a linearized array of 3D volumes of S(Q) calculated for the parameter set given in the corresponding row of the file Parameters.dat. The size of the volume data was matched to the experimental data. Qx(h,-h,0).dat, Qy(k,k,-2k).dat, Qz(l,l,l).dat – These files contain the h, k, and l values along with the reciprocal vectors [h,-h,0], [k,k,-2k] and [l,l,l] respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Crystal-field states and defect levels in candidate quantum spin ice Ce 2 Hf 2 O 7

Here, we report the synthesis of powder and single-crystal samples of cerium pyrohafnate and their characterization using neutron diffraction, thermogravimetry and x-ray absorption spectroscopy. We evaluate the amount of nonmagnetic 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 Ce 2 Hf 2 O 7 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 Ce 2 Sn 2 O 7 and Ce 2 Zr 2 O 7 .

36 MATERIALS SCIENCE↗
DOE OSTI2025

Quantum Spin Ice in Three-Dimensional Rydberg Atom Arrays

Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of Z 2 topological order [G. Semeghini , ], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a U(1) quantum spin liquid in three spatial dimensions, described by the deconfined phase of U(1) gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of “magnetic” monopoles and the Higgs transition driven by a proliferation of “electric” charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator. Published by the American Physical Society 2025

Shah, Jeet (ORCID:0000000158738129)↗
DOE OSTI2021

Low-temperature high-frequency dynamic magnetic susceptibility of classical spin-ice Dy 2 Ti 2 O 7

In this study, radio-frequency (14.6 MHz) AC magnetic susceptibility, , of Dy 2 Ti 2 O 7 was measured using self-oscillating tunnel-diode resonator. Measurements were made with the excitation AC field parallel to the superimposed DC magnetic field up to 5 T in a wide temperature range from 50 mK to 100 K. At 14.6 MHz, a known broad peak of from kHz—range audio-frequency measurements around 15 K for both [111] and [110] directions shifts to 45 K, continuing the Arrhenius activated behavior with the same activation energy barrier of E a ≈ 230 K. Magnetic field dependence of along [111] reproduces previously reported low-temperature two-in-two-out to three-in-one-out spin configuration transition at about 1 T, and an intermediate phase between 1 and 1.5 T. The boundaries of the intermediate phase show reasonable overlap with the literature data and connect at a critical endpoint of the first order transition line, suggesting that these features are frequency independent. An unusual upturn of the magnetic susceptibility at T → 0 was observed in magnetic fields between 1.5 T and 2 T for both magnetic field directions, before fully polarized configuration sets in above 2 T.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Integration of machine learning with neutron scattering for the Hamiltonian tuning of spin ice under pressure

Quantum materials research requires co-design of theory with experiments and involves demanding simulations and the analysis of vast quantities of data, usually including pattern recognition and clustering. Artificial intelligence is a natural route to optimise these processes and bring theory and experiments together. Here, we propose a scheme that integrates machine learning with high-performance simulations and scattering measurements, covering the pipeline of typical neutron experiments. Our approach uses nonlinear autoencoders trained on realistic simulations along with a fast surrogate for the calculation of scattering in the form of a generative model. We demonstrate this approach in a highly frustrated magnet, Dy 2 Ti 2 O 7 , using machine learning predictions to guide the neutron scattering experiment under hydrostatic pressure, extract material parameters and construct a phase diagram. Our scheme provides a comprehensive set of capabilities that allows direct integration of theory along with automated data processing and provides on a rapid timescale direct insight into a challenging condensed matter system.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Reconfigurable training and reservoir computing in an artificial spin-vortex ice via spin-wave fingerprinting

Strongly interacting artificial spin systems are moving beyond mimicking naturally occurring materials to emerge as versatile functional platforms, from reconfigurable magnonics to neuromorphic computing. Typically, artificial spin systems comprise nanomagnets with a single magnetization texture: collinear macrospins or chiral vortices. Here, by tuning nanoarray dimensions we have achieved macrospin–vortex bistability and demonstrated a four-state metamaterial spin system, the ‘artificial spin-vortex ice’ (ASVI). ASVI can host Ising-like macrospins with strong ice-like vertex interactions and weakly coupled vortices with low stray dipolar field. Vortices and macrospins exhibit starkly differing spin-wave spectra with analogue mode amplitude control and mode frequency shifts of Δf = 3.8 GHz. The enhanced bitextural microstate space gives rise to emergent physical memory phenomena, with ratchet-like vortex injection and history-dependent non-linear fading memory when driven through global magnetic field cycles. We employed spin-wave microstate fingerprinting for rapid, scalable readout of vortex and macrospin populations, and leveraged this for spin-wave reservoir computation. ASVI performs non-linear mapping transformations of diverse input and target signals in addition to chaotic time-series forecasting.

97 MATHEMATICS AND COMPUTING↗