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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.

Magnetoelectric coupling at room temperature in multiferroic materials, such as BiFeO3, is one of the leading candidates to develop low-power spintronics and emerging memory technologies. Although extensive research activity has been devoted recently to exploring the physical properties, especially focusing on ferroelectricity and antiferromagnetism in chemically modified BiFeO3, a concrete understanding of the magnetoelectric coupling is yet to be fulfilled. We have discovered that La substitutions at the Bi-site lead to a progressive increase in the degeneracy of the potential energy landscape of the BiFeO3 system exemplified by a rotation of the polar axis away from the 〈111〉pc towards the 〈112〉pc discretion. This is accompanied by corresponding rotation of the antiferromagnetic axis as well, thus maintaining the right-handed vectorial relationship between ferroelectric polarization, antiferromagnetic vector and the Dzyaloshinskii-Moriya vector. As a consequence, La-BiFeO3 films exhibit a magnetoelectric coupling that is distinctly different from the undoped BiFeO3 films.

We have studied low-energy configurations in two-dimensional arrays consisting of Ising-type dipolar coupled nanomagnets lithographically defined onto a two-dimensional Cairo lattice, thus dubbed the dipolar Cairo lattice. Employing synchrotron-based photoemission electron microscopy (PEEM), we perform real-space imaging of moment configurations achieved after thermal annealing. These states are then characterized in terms of vertex populations, spin- and emergent magnetic charge correlations, and a topology-enforced emergent ice rule. The results reveal a strong dominance of short-range correlations and the absence of long-range order, reflecting the high degree of geometrical spin frustration present in this example of an artificial frustrated spin system.

We explore the thermodynamics in two-dimensional arrays consisting of Ising-type nanomagnets lithographically arranged onto random sites and angular orientations. Introducing these basic spin-glass ingredients, we study the characteristic features of the low-energy states achieved, following thermal-annealing protocols. From direct visualization of real-time dynamics, we record relaxation timescales together with magnetic susceptibility variations over temperature, revealing trends towards short-range order as randomness is increased, but falling short of pure spin-glass behavior. Our work provides a route towards the realization of artificial Ising spin-glass systems.

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.

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.

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.

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.

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. [ABSTRACT FROM AUTHOR]

Author(s): Julia A. Mundy [1]; Charles M. Brooks [2]; Megan E. Holtz [1]; Jarrett A. Moyer [3]; Hena Das [1]; Alejandro F. Rbola [1]; John T. Heron [2, 4]; James [...]

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. To fully exploit the potential of multiferroic materials the control of their intrinsic degrees of freedom is a prerequisite. Here, the control of spin orientation in strained BiFeO3 films is demonstrated elucidating the microscopic mechanism of the complex interplay of polar and magnetic order. [ABSTRACT FROM AUTHOR]

The transition from planar (2D) 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 parts. The first section 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 Lorentz electron Ptychography provide sub-nanometer 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 section 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 section 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.&#xD., (Creative Commons Attribution license.)

Electric-field control of magnetism requires deterministic control of the magnetic order and understanding of the magnetoelectric coupling in multiferroics like BiFeO 3 and EuTiO 3 . Despite this critical need, there are few studies on the strain evolution of magnetic order in BiFeO 3 films. Here, in (110)-oriented BiFeO 3 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 BiFeO 3 and the ferromagnet Co 0.9 Fe 0.1 exists such that the magnetic anisotropy of the ferromagnet can be effectively controlled by engineering the orientation of the antiferromagnetic-spin axis.