It has long been known that disorder, perturbing the energy landscape of magnetic systems, can introduce glassy dynamics. However, the controlled role of increasing disorder in driving glass formation remains difficult to isolate in naturally occurring materials. Artificial spin ice offers a unique model platform in which geometry, interactions, and disorder can be engineered at the nanoscale. Here, we investigate the impact of controlled disorder introduced through random decimation in artificial square spin ice. By systematically removing nanomagnets from random sites, we modify the vertex topology and progressively increase frustration in the spin network. Synchrotron-based photoemission electron microscopy reveals that decimation enhances the population of higher energy vertices and increases the configurational entropy of the system. Time-resolved temperature-dependent imaging further shows the emergence of slow cooperative dynamics at higher decimation, characterized by aging, a finite Edwards–Anderson order parameter, and enhanced dynamical heterogeneity quantified by the four-point susceptibility. The relaxation dynamics transition from thermally activated behavior at low decimation to Vogel–Fulcher–type freezing at higher decimation. These results demonstrate that random decimation drives artificial spin ice from long-range order to a glass-like magnetic state, establishing artificial spin systems as a tunable platform for studying glassy dynamics in frustrated matter.

Chemical disorder in compositionally complex perovskite oxides generates a broad distribution of exchange pathways and spin states, but the microscopic origin and spatial homogeneity of the resulting magnetic phases remain debated. Here, we tune the Mn fraction (x = 0.2-0.6) in epitaxial La(Cr, Mn, Fe, Co, Ni)O-3 thin films and resolve the coupled evolution of valence, spin state, and magnetism using element-specific x-ray absorption spectroscopy and x-ray magnetic circular dichroism (XMCD). Mn enrichment drives an internal redistribution of charge, in which Mn evolves toward a Mn3+-rich mixed valence, while Co converts from predominantly Co3+ to high-spin Co2+. This valence/spin-state coupling amplifies the Mn- and Co-derived ferromagnetic response by nearly an order of magnitude while increasing the magnetic onset temperature to at least 250 K, whereas Fe and Cr remain essentially trivalent with weak dichroism. Depth-resolved low-energy muon spin spectroscopy (LE-mu SR) shows magnetic homogeneity through the film thickness, with a secondary relaxation maximum near 25 K indicating a low-temperature dynamical crossover consistent with frustrated magnetism in a strongly disordered spin lattice.

High-entropy perovskite oxides offer a promising platform for tailoring magnetic functionality through compositional complexity; however, it remains unclear how targeted substitution of 4d transition metals modifies oxygen-mediated electronic structure and element-specific magnetic interactions. To address this question, we investigate the effect of Mo and Ru substitution on the electronic structure and magnetism of high-entropy perovskite oxide thin films using O K-edge and transition-metal L-edge X-ray absorption spectroscopy, X-ray magnetic circular dichroism (XMCD), and X-ray linear dichroism. O K-edge spectra reveal that Ru enhances O 2p-metal d hybridization, whereas Mo modifies charge distribution and local exchange pathways within the transition-metal sublattice. Multiplet analysis shows that Mn and Ni retain stable Mn4+ and Ni2+ states, while Co acts as the primary charge-compensation reservoir through changes in the Co2+/Co3+ ratio. Temperature-dependent XMCD demonstrates that these substitutions selectively reshape the magnetic exchange network, redistributing spin polarization among the constituent elements. Quantitative XMCD sum-rule analysis reveals that Mo substitution produces the highest reconstructed total magnetic moment across the measured temperature range, reaching values at low temperature that are nearly an order of magnitude larger than those observed in the Ru-containing compositions. These results establish a composition-driven strategy for tuning covalency, charge redistribution, and the balance between localized and itinerant magnetism in high-entropy oxide thin films, providing a pathway toward the design of tunable spintronic and multifunctional oxide materials.

We introduce the Cyrrhus spin ice geometry, a variant of decimated square ice patterns that exhibits a form of magnetic frustration known as vertex frustration. Using synchrotron-based photoemission electron microscopy, we present a temperature-dependent study of magnetic moment fluctuations in this dipolar Cyrrhus lattice. The results confirm key signatures of vertex frustration marked by an elevated presence of energetically unfavorable moment configurations and a strong adherence to an emergent ice rule. Analyzing the observed dynamics within the framework of the Thirumalai-Mountain stress metric reveals near-zero values for the relaxation exponent, suggesting ergodicity-breaking dynamics.

We present a comprehensive study of Ho(Ni 0.2 Co 0.2 Fe 0.2 Mn 0.2 Cr 0.2 )O 3 high-entropy oxide perovskite thin films. Aside from growth, structural, chemical, and macroscopic magnetic characterization, we performed element-specific, temperature-dependent X-ray absorption spectroscopy (XAS) using X-ray magnetic circular dichroism (XMCD) and X-ray magnetic linear dichroism (XMLD) at all relevant absorption edges. The results indicate predominant ferrimagnetic order with a transition temperature below 150 K and the formation of antiferromagnetic clusters below 50 K.

The transition from planar to three-dimensional (3D) magnetic nanostructures represents a significant advancement in both fundamental research and practical applications, offering vast potential for next-generation technologies like ultrahigh-density storage, memory, logic, and neuromorphic computing. Despite being a relatively new field, the emergence of 3D nanomagnetism presents numerous opportunities for innovation, prompting the creation of a comprehensive roadmap by leading international researchers. This roadmap aims to facilitate collaboration and interdisciplinary dialogue to address challenges in materials science, physics, engineering, and computing. The roadmap comprises eighteen sections, roughly divided into three blocks. The first block explores the fundamentals of 3D nanomagnetism, focusing on recent trends in fabrication techniques and imaging methods crucial for understanding complex spin textures, curved surfaces, and small-scale interactions. Techniques such as two-photon lithography and focused electron beam-induced deposition enable the creation of intricate 3D architectures, while advanced imaging methods like electron holography and synchrotron x-ray tomography provide nanoscale spatial resolution for studying magnetization dynamics in three dimensions. Various 3D magnetic systems, including coupled multilayer systems, artificial spin-ice, magneto-plasmonic systems, topological spin textures, and molecular magnets are discussed. The second block introduces analytical and numerical methods for investigating 3D nanomagnetic structures and curvilinear systems, highlighting geometrically curved architectures, interconnected nanowire systems, and other complex geometries. Finite element methods are emphasized for capturing complex geometries, along with direct frequency domain solutions for addressing magnonic problems. The final block focuses on 3D magnonic crystals and networks, exploring their fundamental properties and potential applications in magnonic circuits, memory, and spintronics. Computational approaches using 3D nanomagnetic systems and complex topological textures in 3D spintronics are highlighted for their potential to enable faster and more energy-efficient computing.

We introduce the Aleppo spin ice geometry, another variation of decimated square ice patterns, which in contrast to similar systems previously studied, does not exhibit vertex frustration. Using synchrotron-based photoemission electron microscopy, we directly visualize low-energy states achieved after thermal annealing, in addition to temperature-dependent moment fluctuations. The results reveal the observation of ground state patterns and the absence of ergodicity-breaking dynamics. Our observations further confirm vertex frustration to be an important criterion for the emergence of ergodicity transitions.

We present a study on the structural and magnetic properties of thin films of the high entropy perovskite Dy(Fe0.2Mn0.2Co0.2Cr0.2Ni0.2)O3 (Dy5BO). An element-sensitive investigation was performed using synchrotron-based x-ray absorption spectroscopy, employing x-ray magnetic circular and linear dichroism. The results reveal that the moments residing on the 3d transition metal ions and the rare-earth Dy ions produce a saturation magnetization one order of magnitude larger than any previously studied high-entropy oxide perovskite. Employing temperature-dependent x-ray magnetic linear dichroism, we see clear features of a spin reorientation at the Mn and Fe sites, occurring around 18 K, likely driven by the interaction of the corresponding transition metal ions and Dy.

We present a study on the structural and magnetic properties of Sr(Fe0.2Mn0.2Co0.2Ti0.2V0.2)O3 (S5BO) high-entropy oxide perovskite thin films. We use synchrotron-based x-ray absorption spectroscopy employing x-ray magnetic circular dichroism (XMCD) and reveal an enhanced presence of high-spin Co2+, which appears to feature a magnetic response opposing that of the two other magnetic transition metal elements, Fe and Mn. This is marked by both opposite XMCD signals and an inverted XMCD hysteresis loop for Co, while Fe and Mn show regularly shaped hysteresis curves, as the picture of a ferrimagnetic ground state emerges for S5BO.

We introduce the stretched pentagonal spin ice and study low-energy configurations achieved after thermal annealing. Using synchrotron-based photoemission electron microscopy, we reveal highly disordered configurations dominated by short-range order. Real-space observations reveal that an adherence to local order, in the form of a strict ice-rule obedience, acts as a main factor in enforcing vertex frustration and hindering long-range order. Our results open up pathways to create forms of frustrated systems that have seemed elusive thus far.

We present a study on the structural and magnetic properties of $\mathrm{Lu}({\mathrm{Fe}}_{0.2}{\mathrm{Mn}}_{0.2}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_{0.2}{\mathrm{Ni}}_{0.2}){\mathrm{O}}_{3}$ (Lu5BO) high-entropy oxide perovskite thin films. We use synchrotron-based x-ray absorption spectroscopy employing x-ray magnetic circular and linear dichroism (XMCD and XMLD) to perform an element-sensitive study on single-crystal epitaxial Lu5BO thin films. Together with XMCD magnetometry, the results reveal dominant antiferromagnetic order with a transition temperature around 100 K.

We present a study on the structural and magnetic properties of Lu(Fe0.2Mn0.2Co0.2Cr0.2Ni0.2)O-3 (Lu5BO) high-entropy oxide perovskite thin films. We use synchrotron-based x-ray absorption spectroscopy employing x-ray magnetic circular and linear dichroism (XMCD and XMLD) to perform an element-sensitive study on single-crystal epitaxial Lu5BO thin films. Together with XMCD magnetometry, the results reveal dominant antiferromagnetic order with a transition temperature around 100 K.

High-entropy oxides (HEOs) have gained significant interest in recent years due to their unique structural characteristics and potential to tailor functional properties. However, the electronic structure of the HEOs currently remains vastly unknown. In this work, combining magnetometry measurements, scanning transmission electron microscopy, and element-specific X-ray absorption spectroscopy, the electronic structure and magnetic properties of the perovskite-HEO La(Cr0.2Mn0.2Fe0.2Co0.2Ni0.2)O3 epitaxial thin films are systemically studied. It is found that enhanced magnetic frustration emerges from competing exchange interactions of the five transition-metal cations with energetically favorable half-filled/full-filled electron configurations, resulting in an unprecedented large vertical exchange bias effect in the single-crystalline films. Furthermore, our findings demonstrate that the La(Cr0.2Mn0.2Fe0.2Co0.2Ni0.2)O3 layer with a thickness down to 1 nm can be used as a pinning layer and strongly coupled with a ferromagnetic La0.7Sr0.3MnO3 layer, leading to a notable exchange bias and coercivity enhancement in a cooling field as small as 5 Oe. Our studies not only provide invaluable insight into the electronic structure of HEOs but also pave the way for a new era of large bias materials for spintronics devices.

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.

Coordinate files of every nanomagnet's position and orientation recorded at each moment in time and several temperatures.

Spin glasses, generally defined as disordered systems with randomized competing interactions1,2, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those describing brain function3,4, error-correcting codes5 or stock-market dynamics6. This wide interest in spin glasses provides strong motivation to generate an artificial spin glass within the framework of artificial spin ice systems7–9. Here we present the experimental realization of an artificial spin glass consisting of dipolar coupled single-domain Ising-type nanomagnets arranged onto an interaction network that replicates the aspects of a Hopfield neural network10. Using cryogenic X-ray photoemission electron microscopy (XPEEM), we performed temperature-dependent imaging of thermally driven moment fluctuations within these networks and observed characteristic features of a two-dimensional Ising spin glass. Specifically, the temperature dependence of the spin glass correlation function follows a power-law trend predicted from theoretical models on two-dimensional spin glasses11. Furthermore, we observe clear signatures of the hard-to-observe rugged spin glass free energy1 in the form of sub-aging, out-of-equilibrium autocorrelations12 and a transition from stable to unstable dynamics1,13. A spin glass is a disordered system with randomized competing magnetic interactions. Now, a metamaterial artificial spin glass based on nanomagnets is reported, with rudimentary features of a neural network.

We have studied the structural and magnetic properties of Tb(Fe0.2Mn0.2Co0.2Cr0.2Ni0.2)O-3 (T5BO) high-entropy oxide perovskite (HEOP) thin films. Using synchrotron-based x-ray absorption spectroscopy, employing x-ray magnetic circular dichroism, we performed an element-sensitive study of epitaxial T5BO thin films. The measurements reveal a magnetic multiphase with variable ferromagnetic ordering of all transition metal elements, providing a promising route towards designer ferroic properties in Tb-based HEOP thin films.

High-entropy oxide thin films have recently been introduced as an attractive strategy to design and enhance ferroic properties. Here, the authors perform element-sensitive x-ray absorption spectroscopy and magnetometry on high-entropy oxide perovskite thin films, shedding light on how different transition metal elements contribute to the overall magnetic response. The results demonstrate not only how disorder can lead to enhancement of magnetic properties but also provide a route towards further improvements of other desired properties in corresponding oxide thin films.