Magnetic Skyrmion Formation at Lattice Defects and Grain Boundaries Studied by Quantitative Off-Axis Electron Holography

Geometric phase analysis of magnetic skyrmion lattices in Lorentz transmission electron microscopy images

Magnetic skyrmions are quasi-particles with a swirling spin texture that form two-dimensional lattices. Skyrmion lattices can exhibit defects in response to geometric constraints, variations of temperature or applied magnetic fields. Measuring deformations in skyrmion lattices is important to understand the interplay between the lattice structure and external influences. Geometric phase analysis (GPA) is a Fourier-based image processing method that is used to measure deformation fields in high resolution transmission electron microscopy (TEM) images of crystalline materials. Here, we show that GPA can be applied quantitatively to Lorentz TEM images of two-dimensional skyrmion lattices obtained from a chiral magnet of FeGe. First, GPA is used to map deformation fields around a 5-7 dislocation and the results are compared with the linear theory of elasticity. Second, rotation angles between skyrmion crystal grains are measured and compared with angles calculated from the density of dislocations. Third, an orientational order parameter and the corresponding correlation function are calculated to describe the evolution of the disorder as a function of applied magnetic field. The influence of sources of artifacts such as geometric distortions and large defoci are also discussed.

Accelerating Quantum Materials Development with Advances in Transmission Electron Microscopy

Quantum materials are driving a technology revolution in sensing, communication, and computing, while simultaneously testing many core theories of the past century. Materials such as topological insulators, complex oxides, superconductors, quantum dots, color center-hosting semiconductors, and other types of strongly correlated materials can exhibit exotic properties such as edge conductivity, multiferroicity, magnetoresistance, superconductivity, single photon emission, and optical-spin locking. These emergent properties arise and depend strongly on the material's detailed atomic-scale structure, including atomic defects, dopants, and lattice stacking. In this review, we describe how progress in the field of electron microscopy (EM), including in situ and in operando EM, can accelerate advances in quantum materials and quantum excitations. We begin by describing fundamental EM principles and operation modes. We then discuss various EM methods such as (i) EM spectroscopies, including electron energy loss spectroscopy (EELS), cathodoluminescence (CL), and electron energy gain spectroscopy (EEGS); (ii) four-dimensional scanning transmission electron microscopy (4D-STEM); (iii) dynamic and ultrafast EM (UEM); (iv) complementary ultrafast spectroscopies (UED, XFEL); and (v) atomic electron tomography (AET). We describe how these methods could inform structure-function relations in quantum materials down to the picometer scale and femtosecond time resolution, and how they enable precision positioning of atomic defects and high-resolution manipulation of quantum materials. For each method, we also describe existing limitations to solve open quantum mechanical questions, and how they might be addressed to accelerate progress. Among numerous notable results, our review highlights how EM is enabling identification of the 3D structure of quantum defects; measuring reversible and metastable dynamics of quantum excitations; mapping exciton states and single photon emission; measuring nanoscale thermal transport and coupled excitation dynamics; and measuring the internal electric field and charge density distribution of quantum heterointerfaces- all at the quantum materials' intrinsic atomic and near atomic-length scale. We conclude by describing open challenges for the future, including achieving stable sample holders for ultralow temperature (below 10K) atomic-scale spatial resolution, stable spectrometers that enable meV energy resolution, and high-resolution, dynamic mapping of magnetic and spin fields. With atomic manipulation and ultrafast characterization enabled by EM, quantum materials will be poised to integrate into many of the sustainable and energy-efficient technologies needed for the 21st century.

Confinement of Skyrmions in Nanoscale FeGe Device-like Structures

Skyrmion-based devices have been proposed as a promising solution for low-energy data storage. These devices include racetrack or logic structures and require skyrmions to be confined in regions with dimensions comparable to the size of a single skyrmion. Here we examine skyrmions in FeGe device shapes using Lorentz transmission electron microscopy to reveal the consequences of skyrmion confinement in a device-like structure. Dumbbell-shaped elements were created by focused ion beam milling to provide regions where single skyrmions are confined adjacent to areas containing a skyrmion lattice. Simple block shapes of equivalent dimensions were also prepared to allow a direct comparison with skyrmion formation in a less complex, yet still confined, device geometry. The impact of applying a magnetic field and varying the temperature on the formation of skyrmions within the shapes was examined. This revealed that it is not just confinement within a small device structure that controls the position and number of skyrmions but that a complex device geometry changes the skyrmion behavior, including allowing skyrmions to form at lower applied magnetic fields than in simple shapes. The impact of edges in complex shapes is observed to be significant in changing the behavior of the magnetic textures formed. This could allow methods to be developed to control both the position and number of skyrmions within device structures.

Control of structure and spin texture in the van der Waals layered magnet CrSBr

Controlling magnetism at nanometer length scales is essential for realizing high-performance spintronic, magneto-electric and topological devices and creating on-demand spin Hamiltonians probing fundamental concepts in physics. Van der Waals (vdW)-bonded layered magnets offer exceptional opportunities for such spin texture engineering. Here, we demonstrate nanoscale structural control in the layered magnet CrSBr with the potential to create spin patterns without the environmental sensitivity that has hindered such manipulations in other vdW magnets. We drive a local phase transformation using an electron beam that moves atoms and exchanges bond directions, effectively creating regions that have vertical vdW layers embedded within the initial horizontally vdW bonded exfoliated flakes. We calculate that the newly formed two-dimensional structure is ferromagnetically ordered in-plane with an energy gap in the visible spectrum, and weak antiferromagnetism between the planes, suggesting possibilities for creating spin textures and quantum magnetic phases.

Cryogenic Electron Microscopy on Strongly Correlated Quantum Materials

ConspectusQuantum materials refers to a class of materials with exotic properties that arise from the quantum mechanical nature of their constituent electrons, exhibiting, for example, high-temperature superconductivity, colossal magnetoresistivity, multiferroicity, and topological behavior. Quantum materials often have incompletely filled d- or f-electron shells with narrow energy bands, and the conduct of their electrons is strongly correlated. One distinct characteristic of the materials is that their electronic states are often spatially inhomogeneous and thus well suited for study using a spatially resolved electron beam with its great scattering power and sensitivity to atomic ionicity. Furthermore, most of these exotic properties only manifest at very low temperatures, posing a challenge to modern electron microscopy. It requires extraordinarily instrument stabilities at cryogenic temperatures with critical spatial, temporal, and energy resolutions in both static and dynamic manner to probe these materials. On the other hand, the ability to directly visualize the atomic, electronic and spin structures and inhomogeneities of quantum materials and correlate them to their functionalities creates enormous opportunities. At the most elementary levels of condensed matter physics, understanding the competing order of electron, spin, orbital, and lattice and their degrees of freedom, the impacts of defects and interfaces, and the site-specific quantum phenomena and phase transitions that give rise to the emergent behaviors allows us to discover and control novel materials for quantum information science and technologies.In this Account, several of our research examples are selected to highlight the use of cryogenic electron microscopy (cryo-EM) to study strongly correlated quantum materials. We focus on the critical roles of heterogeneity, interfaces, defects, and disorder in crystal structure, magnetic structure, and electronic structure to understand the physical properties of the materials that cryo-EM enables. We show how electron crystallography coupled with Bragg diffraction and diffuse scattering analysis empowers us to reveal the nature of structural modulations, lattice distortion, and phonons and how quantitative electron diffraction can be used to map the distributions of the valence electrons that bond atoms together. We exploit transformative advances in imaging capabilities including the use of femtosecond laser and ultrafast electron diffraction to probe electron-lattice interactions and photoinduced transitions beyond equilibrium of matter. We review our Lorentz phase microscopy studies to illustrate the intriguing transformations among various topological chiral spin states under applied magnetic field at various cryogenic temperatures. Finally, we show that atomically resolved imaging and electron energy-loss spectroscopy at 10 K can be used to understand interface-enhanced superconductivity. The wide range of research and progress on quantum materials at low temperature reported here may inspire and attract more researchers in this ever-expanding field of cryo-EM.

Tilted X-Ray Holography of Magnetic Bubbles in MnNiGa Lamellae

Nanoscopic lamellae of centrosymmetric ferromagnetic alloys have recently been reported to host the biskyrmion spin texture; however, this has been disputed as the misidentication of topologically trivial type-II magnetic bubbles. Here we demonstrate resonant soft X-ray holographic imaging of topological magnetic states in lamellae of the centrosymmetric alloy (Mn_1-xNi_x)_0.65Ga_0.35 (x = 0.5), showing the presence of magnetic stripes evolving into single core magnetic bubbles. We observe rotation of the stripe phase via the nucleation and destruction of disclination defects. This indicates the system behaves as a conventional uniaxial ferromagnet. By utilizing the holography with extended reference by autocorrelation linear differential operator (HERALDO) method, we show tilted holographic images at 30° incidence confirming the presence of type-II magnetic bubbles in this system. This study demonstrates the utility of X-ray imaging techniques in identifying the topology of localized structures in nanoscale magnetism.

Real-space imaging of confined magnetic skyrmion tubes

Magnetic skyrmions are topologically nontrivial particles with a potential application as information elements in future spintronic device architectures. While they are commonly portrayed as two dimensional objects, in reality magnetic skyrmions are thought to exist as elongated, tube-like objects extending through the thickness of the host material. The study of this skyrmion tube state (SkT) is vital for furthering the understanding of skyrmion formation and dynamics for future applications. However, direct experimental imaging of skyrmion tubes has yet to be reported. Here, we demonstrate the real-space observation of skyrmion tubes in a lamella of FeGe using resonant magnetic x-ray imaging and comparative micromagnetic simulations, confirming their extended structure. The formation of these structures at the edge of the sample highlights the importance of confinement and edge effects in the stabilisation of the SkT state, opening the door to further investigation into this unexplored dimension of the skyrmion spin texture.

Elliptical Bloch skyrmion chiral twins in an antiskyrmion system

Skyrmions and antiskyrmions are distinct topological chiral spin textures that have been observed in various material systems depending on the symmetry of the crystal structure. Here we show, using Lorentz transmission electron microscopy, that arrays of skyrmions can be stabilized in a tetragonal inverse Heusler with D_2d symmetry whose Dzyaloshinskii-Moriya interaction (DMI) otherwise supports antiskyrmions. These skyrmions can be distinguished from those previously found in several B20 systems which have only one chirality and are circular in shape. We find Bloch-type elliptical skyrmions with opposite chiralities whose major axis is oriented along two specific crystal directions: [010] and [100]. These structures are metastable over a wide temperature range and we show that they are stabilized by long-range dipole-dipole interactions. The possibility of forming two distinct chiral spin textures with opposite topological charges of ±1 in one material makes the family of D_2d materials exceptional.

Skyrmions and anti-skyrmions often exist in distinct material systems. Here, the authors observe elliptical skyrmions and anti-skyrmions with opposite topological charges in one tetragonal Heusler compound Mn_1.4Pt_0.9Pd_0.1Sn with D_2d symmetry.

Topological Defects with Distinct Dipole Configurations in PbTiO_{3}/SrTiO_{3} Multilayer Films

Distinct and novel features of nanometric electric topological defects, including dipole waves and dipole disclinations, are presently revealed in the PbTiO_{3} layers of PbTiO_{3}/SrTiO_{3} multilayer films by means of quantitative high-resolution scanning transmission electron microscopy. These original dipole configurations are confirmed and explained by atomistic simulations and have the potential to act as functional elements in future electronics.

Quantification of Magnetic Surface and Edge States in an FeGe Nanostripe by Off-Axis Electron Holography

Whereas theoretical investigations have revealed the significant influence of magnetic surface and edge states on Skyrmonic spin texture in chiral magnets, experimental studies of such chiral states remain elusive. Here, we study chiral edge states in an FeGe nanostripe experimentally using off-axis electron holography. Our results reveal the magnetic-field-driven formation of chiral edge states and their penetration lengths at 95 and 240 K. We determine values of saturation magnetization M_{S} by analyzing the projected in-plane magnetization distributions of helices and Skyrmions. Values of M_{S} inferred for Skyrmions are lower by a few percent than those for helices. We attribute this difference to the presence of chiral surface states, which are predicted theoretically in a three-dimensional Skyrmion model. Our experiments provide direct quantitative measurements of magnetic chiral boundary states and highlight the applicability of state-of-the-art electron holography for the study of complex spin textures in nanostructures.

Absolute Scale Quantitative Off-Axis Electron Holography at Atomic Resolution

An absolute scale match between experiment and simulation in atomic-resolution off-axis electron holography is demonstrated, with unknown experimental parameters determined directly from the recorded electron wave function using an automated numerical algorithm. We show that the local thickness and tilt of a pristine thin WSe_{2} flake can be measured uniquely, whereas some electron optical aberrations cannot be determined unambiguously for a periodic object. The ability to determine local specimen and imaging parameters directly from electron wave functions is of great importance for quantitative studies of electrostatic potentials in nanoscale materials, in particular when performing in situ experiments and considering that aberrations change over time.

Endotaxial growth of FexGe single-crystals on Ge(001) substrates

Through a 3D diffraction method combined with HRTEM images, we have successfully determined the specific phase of each Fe_xGe island grown on the Ge substrate.