Real-space observation of magnetic excitations and avalanche behavior in artificial quasicrystal lattices.

Artificial spin ice lattices have emerged as model systems for studying magnetic frustration in recent years. Most work to date has looked at periodic artificial spin ice lattices. In this paper, we observe frustration effects in quasicrystal artificial spin ice lattices that lack translational symmetry and contain vertices with different numbers of interacting elements. We find that as the lattice state changes following demagnetizing and annealing, specific vertex motifs retain low-energy configurations, which excites other motifs into higher energy configurations. Additionally, we find that unlike the magnetization reversal process for periodic artificial spin ice lattices, which occurs through 1D avalanches, quasicrystal lattices undergo reversal through a dendritic 2D avalanche mechanism.

Creation of artificial skyrmions and antiskyrmions by anisotropy engineering.

Topologically non-trivial spin textures form a fundamental paradigm in solid-state physics and present unique opportunities to explore exciting phenomena such as the topological Hall effect. One such texture is a skyrmion, in which the spins can be mapped to point in all directions wrapping around a sphere. Understanding the formation of these spin textures, and their energetic stability, is crucial in order to control their behavior. In this work, we report on controlling the perpendicular anisotropy of continuous Co/Pt multilayer films with ion irradiation to form unique spin configurations of artificial skyrmions and antiskyrmions that are stabilized by their demagnetization energy. We elucidate their behavior using aberration-corrected Lorentz transmission electron microscopy. We also discuss the energetic stability of these structures studied through in-situ magnetizing experiments performed at room temperature, combined with micromagnetic simulations that successfully reproduce the spin textures and behavior. This research offers new opportunities towards creation of artificial skyrmion or antiskyrmion lattices that can be used to investigate not only fundamental properties of their interaction with electron currents but also technological applications such as artificial magnonic crystals.

Quantitative 3D electromagnetic field determination of 1D nanostructures from single projection.

One-dimensional (1D) nanostructures have been regarded as the most promising building blocks for nanoelectronics and nanocomposite material systems as well as for alternative energy applications. Although they result in confinement of a material, their properties and interactions with other nanostructures are still very much three-dimensional (3D) in nature. In this work, we present a novel method for quantitative determination of the 3D electromagnetic fields in and around 1D nanostructures using a single electron wave phase image, thereby eliminating the cumbersome acquisition of tomographic data. Using symmetry arguments, we have reconstructed the 3D magnetic field of a nickel nanowire as well as the 3D electric field around a carbon nanotube field emitter, from one single projection. The accuracy of quantitative values determined here is shown to be a better fit to the physics at play than the value obtained by conventional analysis. Moreover the 3D reconstructions can then directly be visualized and used in the design of functional 3D architectures built using 1D nanostructures.

Iterative reconstruction of magnetic induction using Lorentz transmission electron tomography.

Intense ongoing research on complex nanomagnetic structures requires a fundamental understanding of the 3D magnetization and the stray fields around the nano-objects. 3D visualization of such fields offers the best way to achieve this. Lorentz transmission electron microscopy provides a suitable combination of high resolution and ability to quantitatively visualize the magnetization vectors using phase retrieval methods. In this paper, we present a formalism to represent the magnetic phase shift of electrons as a Radon transform of the magnetic induction of the sample. Using this formalism, we then present the application of common tomographic methods particularly the iterative methods, to reconstruct the 3D components of the vector field. We present an analysis of the effect of missing wedge and the limited angular sampling as well as reconstruction of complex 3D magnetization in a nanowire using simulations.

Separation of electrostatic and magnetic phase shifts using a modified transport-of-intensity equation.

We introduce a new approach for the separation of the electrostatic and magnetic components of the electron wave phase shift, based on the transport-of-intensity equation (TIE) formalism. We derive two separate TIE-like equations, one for each of the phase shift components. We use experimental results on FeCoB and Permalloy patterned islands to illustrate how the magnetic and electrostatic longitudinal derivatives can be computed. The main advantage of this new approach is the fact that the differences in the power spectra of the two phase components (electrostatic phase shifts often have significant power in the higher frequencies) can be accommodated by the selection of two different Tikhonov regularization parameters for the two phase reconstructions. The extra computational demands of the method are more than compensated by the improved phase reconstruction results.

Direct observation of unconventional topological spin structure in coupled magnetic discs.

Confined magnetic thin films are known to exhibit a variety of fascinating topological spin states such as Skyrmions, vortices, and antivortices. Such topological excitations are fundamentally important to our understanding of quantum critical phenomenon and related phase transitions. Here we report on the direct observation of an unconventional topological spin state and its behavior in antiferromagnetically coupled NiFe discs at room temperature. The observed spin structure is similar to the theoretically predicted merons which have not yet been observed directly. We have used in situ Lorentz microscopy magnetizing experiments combined with micromagnetic simulations to follow the stability and the behavior of the meron state. The work presented in this paper will open new opportunities for direct experimental investigation of various topological states that can provide insights into the fundamental physics of their interactions.

Determination of magnetic vortex polarity from a single Lorentz Fresnel image.

Nanoscale confinement of the magnetization in a magnetic element often results in the creation of a vortex structure. The vortex equilibrium state is characterized by the curling of the in-plane magnetization (chirality) and an out-of-plane core magnetization. The polarity of the vortex core can point up or down, independent of the chirality, and, thus, magnetic elements with a vortex core are interesting as four-state logic elements. We present an easy-to-use, quantitative method for the determination of both chirality and polarity from a single Fresnel image. This method offers direct evidence of the three-dimensional structure of a magnetic vortex and has significant advantages over the more complex methods currently in use.

Vector field electron tomography of magnetic materials: theoretical development.

The theory of vector field electron tomography, the reconstruction of the three-dimensional magnetic induction around a magnetized object, is derived within the framework of Lorentz transmission electron microscopy. The tomographic reconstruction method uses as input two orthogonal tilt series of magnetic phase maps and is based on the vector slice theorem. An analytical reconstruction of the magnetic induction of a single magnetic dipole is presented as a proof-of-concept. The method is compared to two previously reported approaches: a reconstruction starting from the gradient of the magnetic phase maps, and a direct reconstruction of the magnetic vector potential. Numerical examples as well as estimates of the reconstruction errors for a range of magnetic particle shapes are reported.