Quantifying the Topology of Magnetic Skyrmions in three Dimensions

Magnetic skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number describing the rotation of spins across the skyrmion. However, in real systems with a finite thickness of the material being larger than the magnetic exchange length, the skyrmion spin texture extends into the third dimension and cannot be assumed as homogeneous. Using soft x-ray laminography we reconstruct with about 20nm spatial (voxel) resolution the full three-dimensional spin texture of a skyrmion in an 800 nm diameter and 95 nm thin disk patterned into a trilayer [Ir/Co/Pt] thin film structure. A quantitative analysis finds that the evolution of the radial profile of the topological skyrmion number and the chirality is non-uniform across the thickness of the disk. Estimates of local micromagnetic energy densities suggest that the changes in topological profile are related to non-uniform competing energetic interactions. Theoretical calculations and micromagnetic simulations are consistent with the experimental findings. Our results provide the foundation for nanoscale magnetic metrology for future tailored spintronics devices using topology as a design parameter, and have the potential to reverse-engineer a spin Hamiltonian from macroscopic data, tying theory more closely to experiment.Comment: 18 pages, 4 figure

Controlled Ordering of Room-Temperature Magnetic Skyrmions in a Polar Van der Waals Magnet

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, Van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the $\mu$m scale, showing control over this order-disorder transition on scales relevant for device applications.Comment: 26 pages; 5 main text, 8 supplementary figure

Imaging the magnetic nanowire cross-section and magnetic ordering within a suspended 3D artificial spin-ice

Artificial spin-ice systems are patterned arrays of magnetic nanoislands arranged into frustrated geometries and provide insight into the physics of ordering and emergence. The majority of these systems have been realized in two-dimensions, mainly due to the ease of fabrication, but with recent developments in advanced nanolithography, three-dimensional artificial spin ice (ASI) structures have become possible, providing a new paradigm in their study. Such artificially engineered 3D systems provide new opportunities in realizing tunable ground states, new domain wall topologies, monopole propagation, and advanced device concepts, such as magnetic racetrack memory. Direct imaging of 3DASI structures with magnetic force microscopy has thus far been key to probing the physics of these systems but is limited in both the depth of measurement and resolution, ultimately restricting measurement to the uppermost layers of the system. In this work, a method is developed to fabricate 3DASI lattices over an aperture using two-photon lithography, thermal evaporation, and oxygen plasma exposure, allowing the probe of element-specific structural and magnetic information using soft x-ray microscopy with x-ray magnetic circular dichroism (XMCD) as magnetic contrast. The suspended polymer–permalloy lattices are found to be stable under repeated soft x-ray exposure. Analysis of the x-ray absorption signal allows the complex cross section of the magnetic nanowires to be reconstructed and demonstrates a crescent-shaped geometry. Measurement of the XMCD images after the application of an in-plane field suggests a decrease in magnetic moment on the lattice surface due to oxidation, while a measurable signal is retained on sub-lattices below the surface

Field-Driven Dynamics of Magnetic Hopfions.

We present micromagnetic simulations on resonant spin wave modes of magnetic Hopfions up to 15 GHz driven by external magnetic fields. A sharp transition is found around 66 mT coinciding with a transition from Hopfions to magnetic torons. The modes exhibit characteristic amplitudes in frequency space accompanied by unique localization patterns in real space and are found to be robust to damping around topological features, particularly vortex lines in Hopfions and Bloch points in torons. The marked differences in spin wave spectra between Hopfions, torons, and target skyrmions can serve as fingerprints in future experimental validation studies of these novel 3D topological spin textures

The road to 3-dim nanomagnetism: Steep curves and architectured crosswalks

Nanoscience and its associated nanotechnology started several decades ago to discover and harness properties and behavior of materials that occur due to lowering their dimensionality. Nanomagnetism, which is the branch of nanoscience to investigate magnetic properties of materials down to fundamental length and time scales led to the discovery of a plethora of novel nanoscale spin phenomena and has further laid the groundwork for spintronics, which has become the primary enabler for the most advanced information technologies, including magnetic storage and sensor devices.So far, low-dimensional magnetic systems have been confined to zero (quantum dots), one (nanowires), and two (thin films) dimensions, however, recently research with artificially designed three-dimensional magnetic systems is emerging as it opens the path to novel scientifically exciting phenomena with enormous technological potential to advance spintronics further towards ultrasmall, ultrafast and most importantly low-power electronics.These three-dimensional structures harness the scientific achievements from traditional nanomagnetism, but expand them in a tailored way into the third dimension. Local curvature, particular when defined in a rather broad sense, including geometrical curvature adds to a traditional 2D film a third dimension and proximity effects drawing upon the 3D environment are among the design principles for those 3D magnetic systems.This critical focus article reviews briefly the current state-of-the-art of the emerging research topic with 3D nanomagnetic materials, and describes some of the challenges that the research community needs to address in terms of synthesis and fabrication, theory and modelling, as well as characterization and validation to ultimately bring to bear potential applications with 3D nanomagnetic devices.D.R. and P.F. acknowledge the support by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DE-AC02-05-CH11231 within the Non-Equilibrium Magnetism program (MSMAG). A.H.-R. acknowledges the support from the Spanish MICIN under grant PID2019-104604RB/AEI/10.13039/501100011033 and from the Principality of Asturias FICYT under grant AYUD/2021/51185 with the support of FEDER funds. A.F-P. acknowledges funding from the European Community (under the Horizon 2020 Program, Contract No. 101001290, 3DNANOMAG), the MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1), and the Aragon Government through the Project Q-MAD.Peer reviewe

Three-dimensional magnetic textures in strongly coupled cylindrical nanowires

Resumen del trabajo presentado al Joint European Magnetic Symposia (JEMS), celebrado en Warsaw (Poland) del 24 al 29 de julio de 2022.N

Ordering of room-temperature magnetic skyrmions in a polar van der Waals magnet.

Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications

Curvature-mediated spin textures in magnetic multi-layered nanotubes

The scientific and technological exploration of artificially designed three-dimensional magnetic nanostructures opens the path to exciting novel physical phenomena, originating from the increased complexity in spin textures, topology, and frustration in three dimensions. Theory predicts that the equilibrium magnetic ground state of two-dimensional systems which reflects the competition between symmetric (Heisenberg) and antisymmetric (Dzyaloshinskii-Moriya interaction (DMI)) exchange interaction is significantly modified on curved surfaces when the radius of local curvature becomes comparable to fundamental magnetic length scales. Here, we present an experimental study of the spin texture in an 8 nm thin magnetic multilayer with growth-induced in-plane anisotropy and DMI deposited onto the curved surface of a 1.8 {\mu}m long non-magnetic carbon nanowire with a 67 nm radius. Using magnetic soft x-ray tomography the three-dimensional spin configuration in this nanotube was retrieved with about 30nm spatial resolution. The transition between two vortex configurations on the two ends of the nanotube with opposite circulation occurs through a domain wall that is aligned at an inclined angle relative to the wire axis. Three-dimensional micromagnetic simulations support the experimental observations and represent a visualization of the curvature-mediated DMI. They also allow a quantitative estimate of the DMI value for the magnetic multilayered nanotube

Ordering of room-temperature magnetic skyrmions in a polar van der Waals magnet

Abstract Control and understanding of ensembles of skyrmions is important for realization of future technologies. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionalities. To date, skyrmion ensembles have been primarily studied in bulk crystals, or as isolated skyrmions in thin film devices. Here, we investigate the condensation of the skyrmion phase at room temperature and zero field in a polar, van der Waals magnet. We demonstrate that we can engineer an ordered skyrmion crystal through structural confinement on the μm scale, showing control over this order-disorder transition on scales relevant for device applications