Surface-Symmetry-Driven Dzyaloshinskii-Moriya Interaction and Canted Ferrimagnetism in Collinear Magnetoelectric Antiferromagnet Cr_{2}O_{3}.

Antiferromagnets are normally thought of as materials with compensated magnetic sublattices. This adds to their technological advantages but complicates readout of the antiferromagnetic state. We demonstrate theoretically the existence of a Dzyaloshinskii-Moriya interaction (DMI), which is determined by the magnetic symmetry classes of Cr_{2}O_{3} surfaces with an in-plane magnetic easy axis. The DMI explains a previously predicted out-of-plane magnetization at the nominally compensated surfaces of chromia, leading to a surface-localized canted ferrimagnetism. This is in agreement with magnetotransport measurements and with density functional theory predictions that further allow us to quantify the strength of DMI. The temperature dependence of the transversal resistance for these planes shows distinct behavior in comparison with that of the Cr_{2}O_{3} c plane, which we attribute to the influence of DMI. Our Letter provides a framework to analyze surface-driven phenomena in antiferromagnets, and motivates the use of nominally compensated chromia surfaces for antiferromagnetic spintronics and magnonics.

Kinetically controlled metal-elastomer nanophases for environmentally resilient stretchable electronics.

Nanophase mixtures, leveraging the complementary strengths of each component, are vital for composites to overcome limitations posed by single elemental materials. Among these, metal-elastomer nanophases are particularly important, holding various practical applications for stretchable electronics. However, the methodology and understanding of nanophase mixing metals and elastomers are limited due to difficulties in blending caused by thermodynamic incompatibility. Here, we present a controlled method using kinetics to mix metal atoms with elastomeric chains on the nanoscale. We find that the chain migration flux and metal deposition rate are key factors, allowing the formation of reticular nanophases when kinetically in-phase. Moreover, we observe spontaneous structural evolution, resulting in gyrified structures akin to the human brain. The hybridized gyrified reticular nanophases exhibit strain-invariant metallic electrical conductivity up to 156% areal strain, unparalleled durability in organic solvents and aqueous environments with pH 2-13, and high mechanical robustness, a prerequisite for environmentally resilient devices.

Three-dimensional magnetic nanotextures with high-order vorticity in soft magnetic wireframes.

Additive nanotechnology enable curvilinear and three-dimensional (3D) magnetic architectures with tunable topology and functionalities surpassing their planar counterparts. Here, we experimentally reveal that 3D soft magnetic wireframe structures resemble compact manifolds and accommodate magnetic textures of high order vorticity determined by the Euler characteristic, χ. We demonstrate that self-standing magnetic tetrapods (homeomorphic to a sphere; χ = + 2) support six surface topological solitons, namely four vortices and two antivortices, with a total vorticity of + 2 equal to its Euler characteristic. Alternatively, wireframe structures with one loop (homeomorphic to a torus; χ = 0) possess equal number of vortices and antivortices, which is relevant for spin-wave splitters and 3D magnonics. Subsequent introduction of n holes into the wireframe geometry (homeomorphic to an n-torus; χ < 0) enables the accommodation of a virtually unlimited number of antivortices, which suggests their usefulness for non-conventional (e.g., reservoir) computation. Furthermore, complex stray-field topologies around these objects are of interest for superconducting electronics, particle trapping and biomedical applications.

Chirality coupling in topological magnetic textures with multiple magnetochiral parameters.

Chiral effects originate from the lack of inversion symmetry within the lattice unit cell or sample's shape. Being mapped onto magnetic ordering, chirality enables topologically non-trivial textures with a given handedness. Here, we demonstrate the existence of a static 3D texture characterized by two magnetochiral parameters being magnetic helicity of the vortex and geometrical chirality of the core string itself in geometrically curved asymmetric permalloy cap with a size of 80 nm and a vortex ground state. We experimentally validate the nonlocal chiral symmetry breaking effect in this object, which leads to the geometric deformation of the vortex string into a helix with curvature 3 µm-1 and torsion 11 µm-1. The geometric chirality of the vortex string is determined by the magnetic helicity of the vortex texture, constituting coupling of two chiral parameters within the same texture. Beyond the vortex state, we anticipate that complex curvilinear objects hosting 3D magnetic textures like curved skyrmion tubes and hopfions can be characterized by multiple coupled magnetochiral parameters, that influence their statics and field- or current-driven dynamics for spin-orbitronics and magnonics.

Self-healable printed magnetic field sensors using alternating magnetic fields.

We employ alternating magnetic fields (AMF) to drive magnetic fillers actively and guide the formation and self-healing of percolation networks. Relying on AMF, we fabricate printable magnetoresistive sensors revealing an enhancement in sensitivity and figure of merit of more than one and two orders of magnitude relative to previous reports. These sensors display low noise, high resolution, and are readily processable using various printing techniques that can be applied to different substrates. The AMF-mediated self-healing has six characteristics: 100% performance recovery; repeatable healing over multiple cycles; room-temperature operation; healing in seconds; no need for manual reassembly; humidity insensitivity. It is found that the above advantages arise from the AMF-induced attraction of magnetic microparticles and the determinative oscillation that work synergistically to improve the quantity and quality of filler contacts. By virtue of these advantages, the AMF-mediated sensors are used in safety application, medical therapy, and human-machine interfaces for augmented reality.

Flexomagnetism and vertically graded Néel temperature of antiferromagnetic Cr2O3 thin films.

Antiferromagnetic insulators are a prospective materials platform for magnonics, spin superfluidity, THz spintronics, and non-volatile data storage. A magnetomechanical coupling in antiferromagnets offers vast advantages in the control and manipulation of the primary order parameter yet remains largely unexplored. Here, we discover a new member in the family of flexoeffects in thin films of Cr2O3. We demonstrate that a gradient of mechanical strain can impact the magnetic phase transition resulting in the distribution of the Néel temperature along the thickness of a 50-nm-thick film. The inhomogeneous reduction of the antiferromagnetic order parameter induces a flexomagnetic coefficient of about 15 µB nm-2. The antiferromagnetic ordering in the inhomogeneously strained films can persist up to 100 °C, rendering Cr2O3 relevant for industrial electronics applications. Strain gradient in Cr2O3 thin films enables fundamental research on magnetomechanics and thermodynamics of antiferromagnetic solitons, spin waves and artificial spin ice systems in magnetic materials with continuously graded parameters.

Defect Nanostructure and its Impact on Magnetism of α-Cr2 O3 Thin Films.

Thin films of the magnetoelectric insulator α-Cr2 O3 are technologically relevant for energy-efficient magnetic memory devices controlled by electric fields. In contrast to single crystals, the quality of thin Cr2 O3 films is usually compromised by the presence of point defects and their agglomerations at grain boundaries, putting into question their application potential. Here, the impact of the defect nanostructure, including sparse small-volume defects and their complexes is studied on the magnetic properties of Cr2 O3 thin films. By tuning the deposition temperature, the type, size, and relative concentration of defects is tailored, which is analyzed using the positron annihilation spectroscopy complemented with electron microscopy studies. The structural characterization is correlated with magnetotransport measurements and nitrogen-vacancy microscopy of antiferromagnetic domain patterns. Defects pin antiferromagnetic domain walls and stabilize complex multidomain states with a domain size in the sub-micrometer range. Despite their influence on the domain configuration, neither small open-volume defects nor grain boundaries in Cr2 O3 thin films affect the Néel temperature in a broad range of deposition parameters. The results pave the way toward the realization of spin-orbitronic devices where magnetic domain patterns can be tailored based on defect nanostructures without affecting their operation temperature.

Fundamentals of Curvilinear Ferromagnetism: Statics and Dynamics of Geometrically Curved Wires and Narrow Ribbons.

Low-dimensional magnetic architectures including wires and thin films are key enablers of prospective ultrafast and energy efficient memory, logic, and sensor devices relying on spin-orbitronic and magnonic concepts. Curvilinear magnetism emerged as a novel approach in material science, which allows tailoring of the fundamental anisotropic and chiral responses relying on the geometrical curvature of magnetic architectures. Much attention is dedicated to magnetic wires of Möbius, helical, or DNA-like double helical shapes, which act as prototypical objects for the exploration of the fundamentals of curvilinear magnetism. Although there is a bulk number of original publications covering fabrication, characterization, and theory of magnetic wires, there is no comprehensive review of the theoretical framework of how to describe these architectures. Here, theoretical activities on the topic of curvilinear magnetic wires and narrow nanoribbons are summarized, providing a systematic review of the emergent interactions and novel physical effects caused by the curvature. Prospective research directions of curvilinear spintronics and spin-orbitronics are discussed, the fundamental framework for curvilinear magnonics are outlined, and mechanically flexible curvilinear architectures for soft robotics are introduced.

New Dimension in Magnetism and Superconductivity: 3D and Curvilinear Nanoarchitectures.

Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products.

Nematic shells: new insights in topology- and curvature-induced effects.

Within the framework of continuum theory, we draw a parallel between ferromagnetic materials and nematic liquid crystals confined on curved surfaces, which are both characterized by local interaction and anchoring potentials. We show that the extrinsic curvature of the shell combined with the out-of-plane component of the director field gives rise to chirality effects. This interplay produces an effective energy term reminiscent of the chiral term in cholesteric liquid crystals, with the curvature tensor acting as a sort of anisotropic helicity. We discuss also how the different nature of the order parameter, a vector in ferromagnets and a tensor in nematics, yields different textures on surfaces with the same topology as the sphere. In particular, we show that the extrinsic curvature governs the ground state configuration on a nematic spherical shell, favouring two antipodal disclinations of charge +1 on small particles and four +1/2 disclinations of charge located at the vertices of a square inscribed in a great circle on larger particles.

Curvilinear One-Dimensional Antiferromagnets.

Antiferromagnets host exotic quasiparticles, support high frequency excitations and are key enablers of the prospective spintronic and spin-orbitronic technologies. Here, we propose a concept of a curvilinear antiferromagnetism where material responses can be tailored by a geometrical curvature without the need to adjust material parameters. We show that an intrinsically achiral one-dimensional (1D) curvilinear antiferromagnet behaves as a chiral helimagnet with geometrically tunable Dzyaloshinskii-Moriya interaction (DMI) and orientation of the Néel vector. The curvature-induced DMI results in the hybridization of spin wave modes and enables a geometrically driven local minimum of the low-frequency branch. This positions curvilinear 1D antiferromagnets as a novel platform for the realization of geometrically tunable chiral antiferromagnets for antiferromagnetic spin-orbitronics and fundamental discoveries in the formation of coherent magnon condensates in the momentum space.

Rashba Torque Driven Domain Wall Motion in Magnetic Helices.

Manipulation of the domain wall propagation in magnetic wires is a key practical task for a number of devices including racetrack memory and magnetic logic. Recently, curvilinear effects emerged as an efficient mean to impact substantially the statics and dynamics of magnetic textures. Here, we demonstrate that the curvilinear form of the exchange interaction of a magnetic helix results in an effective anisotropy term and Dzyaloshinskii-Moriya interaction with a complete set of Lifshitz invariants for a one-dimensional system. In contrast to their planar counterparts, the geometrically induced modifications of the static magnetic texture of the domain walls in magnetic helices offer unconventional means to control the wall dynamics relying on spin-orbit Rashba torque. The chiral symmetry breaking due to the Dzyaloshinskii-Moriya interaction leads to the opposite directions of the domain wall motion in left- or right-handed helices. Furthermore, for the magnetic helices, the emergent effective anisotropy term and Dzyaloshinskii-Moriya interaction can be attributed to the clear geometrical parameters like curvature and torsion offering intuitive understanding of the complex curvilinear effects in magnetism.

Coupling of chiralities in spin and physical spaces: the Möbius ring as a case study.

We show that the interaction of the magnetic subsystem of a curved magnet with the magnet curvature results in the coupling of a topologically nontrivial magnetization pattern and topology of the object. The mechanism of this coupling is explored and illustrated by an example of a ferromagnetic Möbius ring, where a topologically induced domain wall appears as a ground state in the case of strong easy-normal anisotropy. For the Möbius geometry, the curvilinear form of the exchange interaction produces an additional effective Dzyaloshinskii-like term which leads to the coupling of the magnetochirality of the domain wall and chirality of the Möbius ring. Two types of domain walls are found, transversal and longitudinal, which are oriented across and along the Möbius ring, respectively. In both cases, the effect of magnetochirality symmetry breaking is established. The dependence of the ground state of the Möbius ring on its geometrical parameters and on the value of the easy-normal anisotropy is explored numerically.