Spin disorder control of topological spin texture.

Stabilization of topological spin textures in layered magnets has the potential to drive the development of advanced low-dimensional spintronics devices. However, achieving reliable and flexible manipulation of the topological spin textures beyond skyrmion in a two-dimensional magnet system remains challenging. Here, we demonstrate the introduction of magnetic iron atoms between the van der Waals gap of a layered magnet, Fe3GaTe2, to modify local anisotropic magnetic interactions. Consequently, we present direct observations of the order-disorder skyrmion lattices transition. In addition, non-trivial topological solitons, such as skyrmioniums and skyrmion bags, are realized at room temperature. Our work highlights the influence of random spin control of non-trivial topological spin textures.

Real-space observation of ergodicity transitions in artificial spin ice.

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.

A Molecular-Scale Understanding of Misorientation Toughening in Corals and Seashells.

Biominerals are organic-mineral composites formed by living organisms. They are the hardest and toughest tissues in those organisms, are often polycrystalline, and their mesostructure (which includes nano- and microscale crystallite size, shape, arrangement, and orientation) can vary dramatically. Marine biominerals may be aragonite, vaterite, or calcite, all calcium carbonate (CaCO3 ) polymorphs, differing in crystal structure. Unexpectedly, diverse CaCO3 biominerals such as coral skeletons and nacre share a similar characteristic: Adjacent crystals are slightly misoriented. This observation is documented quantitatively at the micro- and nanoscales, using polarization-dependent imaging contrast mapping (PIC mapping), and the slight misorientations are consistently between 1° and 40°. Nanoindentation shows that both polycrystalline biominerals and abiotic synthetic spherulites are tougher than single-crystalline geologic aragonite. Molecular dynamics (MD) simulations of bicrystals at the molecular scale reveal that aragonite, vaterite, and calcite exhibit toughness maxima when the bicrystals are misoriented by 10°, 20°, and 30°, respectively, demonstrating that slight misorientation alone can increase fracture toughness. Slight-misorientation-toughening can be harnessed for synthesis of bioinspired materials that only require one material, are not limited to specific top-down architecture, and are easily achieved by self-assembly of organic molecules (e.g., aspirin, chocolate), polymers, metals, and ceramics well beyond biominerals.

Switchable X-Ray Orbital Angular Momentum from an Artificial Spin Ice.

Artificial spin ices (ASI) have been widely investigated as magnetic metamaterials with exotic properties governed by their geometries. In parallel, interest in x-ray photon orbital angular momentum (OAM) has been rapidly growing. Here we show that a square ASI with a patterned topological defect, a double edge dislocation, imparts OAM to scattered x rays. Unlike single dislocations, a double dislocation does not introduce magnetic frustration, and the ASI equilibrates to its antiferromagnetic (AFM) ground state. The topological charge of the defect differs with respect to the structural and magnetic order; thus, x-ray diffraction from the ASI produces photons with even and odd OAM quantum numbers at the structural and AFM Bragg conditions, respectively. The magnetic transitions of the ASI allow the AFM OAM beams to be switched on and off by modest variations of temperature and applied magnetic field. These results demonstrate ASIs can serve as metasurfaces for reconfigurable x-ray optics that could enable selective probes of electronic and magnetic properties.

Meteorite evidence for partial differentiation and protracted accretion of planetesimals.

Modern meteorite classification schemes assume that no single planetary body could be source of both unmelted (chondritic) and melted (achondritic) meteorites. This dichotomy is a natural outcome of formation models assuming that planetesimal accretion occurred nearly instantaneously. However, it has recently been proposed that the accretion of many planetesimals lasted over ≳1 million years (Ma). This could have resulted in partially differentiated internal structures, with individual bodies containing iron cores, achondritic silicate mantles, and chondritic crusts. This proposal can be tested by searching for a meteorite group containing evidence for these three layers. We combine synchrotron paleomagnetic analyses with thermal, impact, and collisional evolution models to show that the parent body of the enigmatic IIE iron meteorites was such a partially differentiated planetesimal. This implies that some chondrites and achondrites simultaneously coexisted on the same planetesimal, indicating that accretion was protracted and that apparently undifferentiated asteroids may contain melted interiors.

Geometrical Frustration and Planar Triangular Antiferromagnetism in Quasi-Three-Dimensional Artificial Spin Architecture.

We present a realization of highly frustrated planar triangular antiferromagnetism achieved in a quasi-three-dimensional artificial spin system consisting of monodomain Ising-type nanomagnets lithographically arranged onto a deep-etched silicon substrate. We demonstrate how the three-dimensional spin architecture results in the first direct observation of long-range ordered planar triangular antiferromagnetism, in addition to a highly disordered phase with short-range correlations, once competing interactions are perfectly tuned. Our work demonstrates how escaping two-dimensional restrictions can lead to new types of magnetically frustrated metamaterials.

Emergent magnetic monopole dynamics in macroscopically degenerate artificial spin ice.

Magnetic monopoles, proposed as elementary particles that act as isolated magnetic south and north poles, have long attracted research interest as magnetic analogs to electric charge. In solid-state physics, a classical analog to these elusive particles has emerged as topological excitations within pyrochlore spin ice systems. We present the first real-time imaging of emergent magnetic monopole motion in a macroscopically degenerate artificial spin ice system consisting of thermally activated Ising-type nanomagnets lithographically arranged onto a pre-etched silicon substrate. A real-space characterization of emergent magnetic monopoles within the framework of Debye-Hückel theory is performed, providing visual evidence that these topological defects act like a plasma of Coulomb-type magnetic charges. In contrast to vertex defects in a purely two-dimensional artificial square ice, magnetic monopoles are free to evolve within a divergence-free vacuum, a magnetic Coulomb phase, for which features in the form of pinch-point singularities in magnetic structure factors are observed.

Complex strain evolution of polar and magnetic order in multiferroic BiFeO3 thin films.

Electric-field control of magnetism requires deterministic control of the magnetic order and understanding of the magnetoelectric coupling in multiferroics like BiFeO3 and EuTiO3. Despite this critical need, there are few studies on the strain evolution of magnetic order in BiFeO3 films. Here, in (110)-oriented BiFeO3 films, we reveal that while the polarization structure remains relatively unaffected, strain can continuously tune the orientation of the antiferromagnetic-spin axis across a wide angular space, resulting in an unexpected deviation of the classical perpendicular relationship between the antiferromagnetic axis and the polarization. Calculations suggest that this evolution arises from a competition between the Dzyaloshinskii-Moriya interaction and single-ion anisotropy wherein the former dominates at small strains and the two are comparable at large strains. Finally, strong coupling between the BiFeO3 and the ferromagnet Co0.9Fe0.1 exists such that the magnetic anisotropy of the ferromagnet can be effectively controlled by engineering the orientation of the antiferromagnetic-spin axis.

Spatial and Temporal Correlations of XY Macro Spins.

We use nano disk arrays with square and honeycomb symmetry to investigate magnetic phases and spin correlations of XY dipolar systems at the micro scale. Utilizing magnetization sensitive X-ray photoemission electron microscopy, we probe magnetic ground states and the "order-by-disorder" phenomenon predicted 30 years ago. We observe the antiferromagnetic striped ground state in square lattices, and 6-fold symmetric structures, including trigonal vortex lattices and disordered floating vortices, in the honeycomb lattice. The spin frustration in the honeycomb lattice causes a phase transition from a long-range ordered locked phase over a floating phase with quasi long-range order and indications of a Berezinskii-Thouless-Kosterlitz-like character, to the thermally excited paramagnetic state. Absent spatial correlation and quasi periodic switching of isolated vortices in the quasi long-range ordered phase suggest a degeneracy of the vortex circulation.

Patterning-Induced Ferromagnetism of Fe3GeTe2 van der Waals Materials beyond Room Temperature.

Magnetic van der Waals (vdW) materials have emerged as promising candidates for spintronics applications, especially after the recent discovery of intrinsic ferromagnetism in monolayer vdW materials. There has been a critical need for tunable ferromagnetic vdW materials beyond room temperature. Here, we report a real-space imaging study of itinerant ferromagnet Fe3GeTe2 and the enhancement of its Curie temperature well above ambient temperature. We find that the magnetic long-range order in Fe3GeTe2 is characterized by an unconventional out-of-plane stripe-domain phase. In Fe3GeTe2 microstructures patterned by a focused ion beam, the out-of-plane stripe domain phase undergoes a surprising transition at 230 K to an in-plane vortex phase that persists beyond room temperature. The discovery of tunable ferromagnetism in Fe3GeTe2 materials opens up vast opportunities for utilizing vdW magnets in room-temperature spintronics devices.

Influence of Nonuniform Micron-Scale Strain Distributions on the Electrical Reorientation of Magnetic Microstructures in a Composite Multiferroic Heterostructure.

Composite multiferroic systems, consisting of a piezoelectric substrate coupled with a ferromagnetic thin film, are of great interest from a technological point of view because they offer a path toward the development of ultralow power magnetoelectric devices. The key aspect of those systems is the possibility to control magnetization via an electric field, relying on the magneto-elastic coupling at the interface between the piezoelectric and the ferromagnetic components. Accordingly, a direct measurement of both the electrically induced magnetic behavior and of the piezo-strain driving such behavior is crucial for better understanding and further developing these materials systems. In this work, we measure and characterize the micron-scale strain and magnetic response, as a function of an applied electric field, in a composite multiferroic system composed of 1 and 2 µm squares of Ni fabricated on a prepoled [Pb(Mg1/3Nb2/3)O3]0.69-[PbTiO3]0.31 (PMN-PT) single crystal substrate by X-ray microdiffraction and X-ray photoemission electron microscopy, respectively. These two complementary measurements of the same area on the sample indicate the presence of a nonuniform strain which strongly influences the reorientation of the magnetic state within identical Ni microstructures along the surface of the sample. Micromagnetic simulations confirm these experimental observations. This study emphasizes the critical importance of surface and interface engineering on the micron-scale in composite multiferroic structures and introduces a robust method to characterize future devices on these length scales.

Author Correction: Nanoscale control of competing interactions and geometrical frustration in a dipolar trident lattice.

The original version of this article contained an error in the legend to Figure 4. The yellow scale bar should have been defined as '~600 nm', not '~600 µm'. This has now been corrected in both the PDF and HTML versions of the article.

Nanoscale control of competing interactions and geometrical frustration in a dipolar trident lattice.

Geometrical frustration occurs when entities in a system, subject to given lattice constraints, are hindered to simultaneously minimize their local interactions. In magnetism, systems incorporating geometrical frustration are fascinating, as their behavior is not only hard to predict, but also leads to the emergence of exotic states of matter. Here, we provide a first look into an artificial frustrated system, the dipolar trident lattice, where the balance of competing interactions between nearest-neighbor magnetic moments can be directly controlled, thus allowing versatile tuning of geometrical frustration and manipulation of ground state configurations. Our findings not only provide the basis for future studies on the low-temperature physics of the dipolar trident lattice, but also demonstrate how this frustration-by-design concept can deliver magnetically frustrated metamaterials.Artificial magnetic nanostructures enable the study of competing frustrated interactions with more control over the system parameters than is possible in magnetic materials. Farhan et al. present a two-dimensional lattice geometry where the frustration can be controlled by tuning the unit cell parameters.

Emergent dynamic chirality in a thermally driven artificial spin ratchet.

Modern nanofabrication techniques have opened the possibility to create novel functional materials, whose properties transcend those of their constituent elements. In particular, tuning the magnetostatic interactions in geometrically frustrated arrangements of nanoelements called artificial spin ice can lead to specific collective behaviour, including emergent magnetic monopoles, charge screening and transport, as well as magnonic response. Here, we demonstrate a spin-ice-based active material in which energy is converted into unidirectional dynamics. Using X-ray photoemission electron microscopy we show that the collective rotation of the average magnetization proceeds in a unique sense during thermal relaxation. Our simulations demonstrate that this emergent chiral behaviour is driven by the topology of the magnetostatic field at the edges of the nanomagnet array, resulting in an asymmetric energy landscape. In addition, a bias field can be used to modify the sense of rotation of the average magnetization. This opens the possibility of implementing a magnetic Brownian ratchet, which may find applications in novel nanoscale devices, such as magnetic nanomotors, actuators, sensors or memory cells.

Atomically engineered ferroic layers yield a room-temperature magnetoelectric multiferroic.

Materials that exhibit simultaneous order in their electric and magnetic ground states hold promise for use in next-generation memory devices in which electric fields control magnetism. Such materials are exceedingly rare, however, owing to competing requirements for displacive ferroelectricity and magnetism. Despite the recent identification of several new multiferroic materials and magnetoelectric coupling mechanisms, known single-phase multiferroics remain limited by antiferromagnetic or weak ferromagnetic alignments, by a lack of coupling between the order parameters, or by having properties that emerge only well below room temperature, precluding device applications. Here we present a methodology for constructing single-phase multiferroic materials in which ferroelectricity and strong magnetic ordering are coupled near room temperature. Starting with hexagonal LuFeO3-the geometric ferroelectric with the greatest known planar rumpling-we introduce individual monolayers of FeO during growth to construct formula-unit-thick syntactic layers of ferrimagnetic LuFe2O4 (refs 17, 18) within the LuFeO3 matrix, that is, (LuFeO3)m/(LuFe2O4)1 superlattices. The severe rumpling imposed by the neighbouring LuFeO3 drives the ferrimagnetic LuFe2O4 into a simultaneously ferroelectric state, while also reducing the LuFe2O4 spin frustration. This increases the magnetic transition temperature substantially-from 240 kelvin for LuFe2O4 (ref. 18) to 281 kelvin for (LuFeO3)9/(LuFe2O4)1. Moreover, the ferroelectric order couples to the ferrimagnetism, enabling direct electric-field control of magnetism at 200 kelvin. Our results demonstrate a design methodology for creating higher-temperature magnetoelectric multiferroics by exploiting a combination of geometric frustration, lattice distortions and epitaxial engineering.

Tailoring Spin Textures in Complex Oxide Micromagnets.

Engineered topological spin textures with submicron dimensions in magnetic materials have emerged in recent years as the building blocks for various spin-based memory devices. Examples of these magnetic configurations include magnetic skyrmions, vortices, and domain walls. Here, we show the ability to control and characterize the evolution of spin textures in complex oxide micromagnets as a function of temperature through the delicate balance of fundamental materials parameters, micromagnet geometries, and epitaxial strain. These results demonstrate that in order to fully describe the observed spin textures, it is necessary to account for the spatial variation of the magnetic parameters within the micromagnet. This study provides the framework to accurately characterize such structures, leading to efficient design of spin-based memory devices based on complex oxide thin films.

Thermodynamics of emergent magnetic charge screening in artificial spin ice.

Electric charge screening is a fundamental principle governing the behaviour in a variety of systems in nature. Through reconfiguration of the local environment, the Coulomb attraction between electric charges is decreased, leading, for example, to the creation of polaron states in solids or hydration shells around proteins in water. Here, we directly visualize the real-time creation and decay of screened magnetic charge configurations in a two-dimensional artificial spin ice system, the dipolar dice lattice. By comparing the temperature dependent occurrence of screened and unscreened emergent magnetic charge defects, we determine that screened magnetic charges are indeed a result of local energy reduction and appear as a transient minimum energy state before the system relaxes towards the predicted ground state. These results highlight the important role of emergent magnetic charges in artificial spin ice, giving rise to screened charge excitations and the emergence of exotic low-temperature configurations.

Sub-nanosecond signal propagation in anisotropy-engineered nanomagnetic logic chains.

Energy efficient nanomagnetic logic (NML) computing architectures propagate binary information by relying on dipolar field coupling to reorient closely spaced nanoscale magnets. Signal propagation in nanomagnet chains has been previously characterized by static magnetic imaging experiments; however, the mechanisms that determine the final state and their reproducibility over millions of cycles in high-speed operation have yet to be experimentally investigated. Here we present a study of NML operation in a high-speed regime. We perform direct imaging of digital signal propagation in permalloy nanomagnet chains with varying degrees of shape-engineered biaxial anisotropy using full-field magnetic X-ray transmission microscopy and time-resolved photoemission electron microscopy after applying nanosecond magnetic field pulses. An intrinsic switching time of 100 ps per magnet is observed. These experiments, and accompanying macrospin and micromagnetic simulations, reveal the underlying physics of NML architectures repetitively operated on nanosecond timescales and identify relevant engineering parameters to optimize performance and reliability.