Electron holography observation of vortex lattices in a superconductor

Enhancing performance of electron holography with mathematical and machine learning-based denoising techniques

Electron holography is a useful tool for analyzing functional properties, such as electromagnetic fields and strains of materials and devices. The performance of electron holography is limited by the 'shot noise' inherent in electron micrographs (holograms), which are composed of a finite number of electrons. A promising approach for addressing this issue is to use mathematical and machine learning-based image-processing techniques for hologram denoising. With the advancement of information science, denoising methods have become capable of extracting signals that are completely buried in noise, and they are being applied to electron microscopy, including electron holography. However, these advanced denoising methods are complex and have many parameters to be tuned; therefore, it is necessary to understand their principles in depth and use them carefully. Herein, we present an overview of the principles and usage of sparse coding, the wavelet hidden Markov model and tensor decomposition, which have been applied to electron holography. We also present evaluation results for the denoising performance of these methods obtained through their application to simulated and experimentally recorded holograms. Our analysis, review and comparison of the methods clarify the impact of denoising on electron holography research.

Observation of magnetic vortex configuration in non-stoichiometric Fe3O4 nanospheres

Theoretical and micromagnetic simulation studies of magnetic nanospheres with vortex configurations suggest that such nanostructured materials have technological advantages over conventional nanosystems for applications based on high-power-rate absorption and subsequent emission. However, full experimental evidence of magnetic vortex configurations in spheres of submicrometer size is still lacking. Here, we report the microwave irradiation fabrication of Fe3O4 nanospheres and establish their magnetic vortex configuration based on experimental results, theoretical analysis, and micromagnetic simulations. Detailed magnetic and electrical measurements, together with Mössbauer spectroscopy data, provide evidence of a loss of stoichiometry in vortex nanospheres owing to the presence of a surface oxide layer, defects, and a higher concentration of cation vacancies. The results indicate that the magnetic vortex spin configuration can be established in bulk spherical magnetite materials. This study provides crucial information that can aid the synthesis of magnetic nanospheres with magnetically tailored properties; consequently, they may be promising candidates for future technological applications based on three-dimensional magnetic vortex structures.

Electron holography for observing magnetic bubbles and stripe-shaped domains in magnetic fields

An electron holography optical system was developed for relatively high magnetic fields up to 500 mT. The objective lens worked as a magnetic field generator for the specimen and the first intermediate lens worked for imaging as one of the pair lens composed of the objective lens. Specimen images were first formed on the object plane of the second intermediate lens. Electron biprism for conventional holography was installed under the second intermediate lens. Reconstruction of phase distributions was performed by the Fourier transform method and the vector maps were used to clarify small phase modulations. By using the developed system, magnetic characteristics of hexaferrite magnets (BaFe_12-x-δSc_xMg_δO₁₉), such as magnetic bubbles and stripe-shaped magnetic domains, were observed at smaller than 200 mT. Their magnetization structures and their interactions are demonstrated with the experimental results.

Phase-shifting electron holography for accurate measurement of potential distributions in organic and inorganic semiconductors

Phase-shifting electron holography (PS-EH) is an interference transmission electron microscopy technique that accurately visualizes potential distributions in functional materials, such as semiconductors. In this paper, we briefly introduce the features of the PS-EH that overcome some of the issues facing the conventional EH based on Fourier transformation. Then, we present a high-precision PS-EH technique with multiple electron biprisms and a sample preparation technique using a cryo-focused-ion-beam, which are important techniques for the accurate phase measurement of semiconductors. We present several applications of PS-EH to demonstrate the potential in organic and inorganic semiconductors and then discuss the differences by comparing them with previous reports on the conventional EH. We show that in situ biasing PS-EH was able to observe not only electric potential distribution but also electric field and charge density at a GaAs p-n junction and clarify how local band structures, depletion layer widths and space charges changed depending on the biasing conditions. Moreover, the PS-EH clearly visualized the local potential distributions of two-dimensional electron gas layers formed at AlGaN/GaN interfaces with different Al compositions. We also report the results of our PS-EH application for organic electroluminescence multilayers and point out the significant potential changes in the layers. The proposed PS-EH enables more precise phase measurement compared to the conventional EH, and our findings introduced in this paper will contribute to the future research and development of high-performance semiconductor materials and devices.

Interference and interferometry in electron holography

This paper reviews the basics of electron holography as an introduction of the holography part of this special issue in Microscopy. We discuss the general principle of holography and interferometry regarding measurements and analyses of phase distributions, first using the optical holography. Next, we discuss physical phenomena peculiar to electron waves that cannot be realized by light waves and principles of electromagnetic field detection and observation methods. Furthermore, we discuss the interference optical systems of the electron waves and their features, and methods of reconstruction of the phase information from electron holograms, which are essential for realization of practical electron holography. We note that following this review application of electron holography will be discussed in detail in the papers of this special issue.

Moving Pearl Vortices in Thin-Film Superconductors

The magnetic field hz of a moving Pearl vortex in a superconducting thin-film in (x,y) plane is studied with the help of the time-dependent London equation. It is found that for a vortex at the origin moving in +x direction, hz(x,y) is suppressed in front of the vortex, x>0, and enhanced behind (x<0). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.

Visualization of different carrier concentrations in n-type-GaN semiconductors by phase-shifting electron holography with multiple electron biprisms

Phase-shifting electron holography (PS-EH) using a transmission electron microscope (TEM) was applied to visualize layers with different concentrations of carriers activated by Si (at dopant levels of 1019, 1018, 1017 and 1016 atoms cm-3) in n-type GaN semiconductors. To precisely measure the reconstructed phase profiles in the GaN sample, three electron biprisms were used to obtain a series of high-contrast holograms without Fresnel fringes generated by a biprism filament, and a cryo-focused-ion-beam (cryo-FIB) was used to prepare a uniform TEM sample with less distortion in the wide field of view. All layers in a 350-nm-thick TEM sample were distinguished with 1.8-nm spatial resolution and 0.02-rad phase-resolution, and variations of step width in the phase profile (corresponding to depletion width) at the interfaces between the layers were also measured. Thicknesses of the active and inactive layers at each dopant level were estimated from the observed phase profile and the simulation of theoretical band structure. Ratio of active-layer thickness to total thickness of the TEM sample significantly decreased as dopant concentration decreased; thus, a thicker TEM sample is necessary to visualize lower carrier concentrations; for example, to distinguish layers with dopant concentrations of 1016 and 1015 atoms cm-3. It was estimated that sample thickness must be more than 700 nm to make it be possible to detect sub-layers by the combination of PS-EH and cryo-FIB.

Imaging of magnetic and electric fields by electron microscopy

Nanostructured materials become more and more a part of our daily life, partly as self-assembled particles or artificially patterned. These nanostructures often possess intrinsic magnetic and/or electric fields which determine (at least partially) their physical properties. Therefore it is important to be able to measure these fields reliably on a nanometre scale. A rather common instrument for the investigation of these fields is the transmission electron microscope as it offers high spatial resolution. The use of an electron microscope to image electric and magnetic fields on a micron down to sub-nanometre scale is treated in detail for transmission electron microscopes (TEM) and scanning transmission electron microscopes (STEM). The formation of contrast is described for the most common imaging modes, the specific advantages and disadvantages of each technique are discussed and examples are given. In addition, the experimental requirements for the use of the techniques described are listed and explained.

Visualizing the morphology of vortex lattice domains in a bulk type-II superconductor

Alike materials in the solid state, the phase diagram of type-II superconductors exhibit crystalline, amorphous, liquid and spatially inhomogeneous phases. The multitude of different phases of vortex matter has thence proven to act as almost ideal model system for the study of both the underlying properties of superconductivity but also of general phenomena such as domain nucleation and morphology. Here we show how neutron grating interferometry yields detailed information on the vortex lattice and its domain structure in the intermediate mixed state of a type-II niobium superconductor. In particular, we identify the nucleation regions, how the intermediate mixed state expands, and where it finally evolves into the Shubnikov phase. Moreover, we complement the results obtained from neutron grating interferometry by small-angle neutron scattering that confirm the spatially resolved morphology found in the intermediate mixed state, and very small-angle neutron scattering that confirm the domain structure of the vortex lattice.

The phase diagram of type-II superconductors exhibits a multitude of different phases, whose study can shed light on domain nucleation and morphology. Here the authors use neutron grating interferometry to investigate the nucleation and phase changes of an intermediate mixed state in a niobium superconductor.

Diagnosing nanoelectronic components using coherent electrons

We present the direct observation, using off-axis electron holography (EH), of the electric potential distribution in the vicinity of a single carbon nanotube electrically biased by two closely spaced contacts. When our results are combined with finite element modeling, we demonstrate the ability to separately observe the electrostatic potential drops across the metal contacts at the interface with the nanotube and along the length of the nanotube itself. We demonstrate that the uneven resistivity of different contacts can cause an asymmetric EH phase shift, which can readily be identified and quantified. EH thus offers a unique and precise approach for in-depth understanding and quick diagnosis of many similar nanoscale electronic devices.

Phase contrast image simulations for electron holography of magnetic and electric fields

The research on flux line lattices and pancake vortices in superconducting materials, carried out within a long and fruitful collaboration with Akira Tonomura and his group at the Hitachi Advanced Research Laboratory, led us to develop a mathematical framework, based on the reciprocal representation of the magnetic vector potential, that enables us to simulate realistic phase images of fluxons. The aim of this paper is to review the main ideas underpinning our computational framework and the results we have obtained throughout the collaboration. Furthermore, we outline how to generalize the approach to model other samples and structures of interest, in particular thin ferromagnetic films, ferromagnetic nanoparticles and p-n junctions.

Twin-electron biprism

In order to obtain a large deflection angle without increasing the applied voltage to an electron biprism, we have developed a 'twin-electron biprism' (TBP), which is composed of two filament electrodes and a pair of ground plates. The observed interference-fringe spacing revealed that the deflection angle created by a TBP was about twice larger than that by a 'conventional electron biprism'. Also, we have suggested, in a double-electron biprism interferometry, the optimal disposition of a TBP for reducing the intensity of Fresnel fringes recorded in an electron hologram.

Electron tomography and holography in materials science

The rapid development of electron tomography, in particular the introduction of novel tomographic imaging modes, has led to the visualization and analysis of three-dimensional structural and chemical information from materials at the nanometre level. In addition, the phase information revealed in electron holograms allows electrostatic and magnetic potentials to be mapped quantitatively with high spatial resolution and, when combined with tomography, in three dimensions. Here we present an overview of the techniques of electron tomography and electron holography and demonstrate their capabilities with the aid of case studies that span materials science and the interface between the physical sciences and the life sciences.

The Aharonov-Bohm effect and its applications to electron phase microscopy

The Aharonov-Bohm effect was conclusively established by a series of our electron interference experiments, with the help of some advanced techniques, such as coherent field-emission electron beams and microlithography. Using this fundamental principle behind the interaction of an electron wave with electromagnetic fields, new observation techniques were developed to directly observe microscopic objects and quantum phenomena previously unobservable.

Direct observation of thitherto unobservable quantum phenomena by using electrons

Fundamental aspects of quantum mechanics, which were discussed only theoretically as "thought experiments" in the 1920s and 1930s, have begun to frequently show up in nanoscopic regions owing to recent rapid progress in advanced technologies. Quantum phenomena were once regarded as the ultimate factors limiting further miniaturization trends of microstructured electronic devices, but now they have begun to be actively used as the principles for new devices such as quantum computers. To directly observe what had been unobservable quantum phenomena, we have tried to develop bright and monochromatic electron beams for the last 35 years. Every time the brightness of an electron beam improved, fundamental experiments in quantum mechanics became possible, and quantum phenomena became observable by using the wave nature of electrons.

Off-axis electron holography of magnetic nanowires and chains, rings, and planar arrays of magnetic nanoparticles

A selection of recent results illustrating the application of off-axis electron holography to the study of magnetic microstructure in closely-spaced nanoparticles and nanowires is reviewed. Examples are taken from the characterization of FeNi nanoparticle chains, Co nanoparticle rings, two-dimensional arrays of naturally occurring magnetite crystals in minerals, and single crystalline Co nanowires. Approaches that can be used to separate the magnetic signal of interest from the mean inner potential contribution to the measured holographic phase shift are described, and the spatial and phase resolution that can be achieved are discussed.

Phase imaging and nanoscale currents in phase objects imaged with fast electrons

We derive the magnetic transport-of-intensity equation (MTIE) that links defocused contrast of magnetic nanoobjects imaged by partially coherent electron waves to their micromagnetic parameters. This provides Maxwell's explanation for observable contrast in terms of the Z component of currents existing around vortices in superconductors and domain vortices and walls in ferromagnets. The solution of the MTIE via Fourier transform is used for quantitative mapping of magnetic flux and projected induction in magnetic and superconducting materials imaged by Lorentz microscopy.

An introduction to off-axis electron holography

The technique of off-axis electron holography is introduced and reviewed. The history of the topic is discussed briefly looking at the origin of electron holography and the reasons for its growth in recent years around the world. The formation and numerical reconstruction of the hologram is discussed in detail on a theoretical and practical level. The spread of holography is illustrated through a number of applications ranging from ultra high resolution studies of crystal structures, the imaging of magnetic and electric fields, the determination of sample composition and morphology and the use of holography for imaging biological specimens.

Direct Observation of Vortex Dynamics in Superconducting Films with Regular Arrays of Defects

The microscopic mechanism of the matching effect in a superconductor, which manifested itself as the production of peaks or cusps in the critical current at specific values of the applied magnetic field, was investigated with Lorentz microscopy to allow direct observation of the behavior of vortices in a niobium thin film having a regular array of artificial defects. Vortices were observed to form regular and consequently rigid lattices at the matching magnetic field, at its multiples, and at its fractions. The dynamic observation furthermore revealed that vortices were most difficult to move at the matching field, whereas excess vortices moved easily.