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Off-axis electron holography is a powerful technique that involves the formation of an interference pattern in a transmission electron microscope (TEM) by overlapping two parts of an electron wave, one of which has passed through a region of interest on a specimen and the other is a reference wave. The resulting off-axis electron hologram can be analyzed digitally to recover the phase difference between the two parts of the electron wave, which can then be interpreted to provide quantitative information about local variations in electrostatic potential and magnetic induction within and around the specimen. Off-axis electron holograms can be recorded while a specimen is subjected to external stimuli such as elevated or reduced temperature, voltage, or light. The protocol that is presented here describes the practical steps that are required to record, analyze, and interpret off-axis electron holograms, with a primary focus on the measurement of magnetic fields within and around nanoscale materials and devices. Presented here are the steps involved in the recording, analysis, and processing of off-axis electron holograms, as well as the reconstruction and interpretation of phase images and visualization of the results. Also discussed are the need for optimization of the specimen geometry, the electron optical configuration of the microscope, and the electron hologram acquisition parameters, as well as the need for the use of information from multiple holograms to extract the desired magnetic contributions from the recorded signal. The steps are illustrated through a study of specimens of B20-type FeGe, which contain magnetic skyrmions and were prepared with focused ion beams (FIBs). Prospects for the future development of the technique are discussed.

The study of the paleomagnetic signal recorded by rocks allows scientists to understand Earth's past magnetic field and the formation of the geodynamo. The magnetic recording fidelity of this signal is dependent on the magnetic domain state it adopts. The most prevalent example found in nature is the pseudo-single-domain (PSD) structure, yet its recording fidelity is poorly understood. Here, the thermoremanent behavior of PSD magnetite (Fe3O4) particles, which dominate the magnetic signatures of many rock lithologies, is investigated using electron holography. This study provides spatially resolved magnetic information from individual Fe3O4 grains as a function of temperature, which has been previously inaccessible. A small exemplar Fe3O4 grain (~150 nm) exhibits dynamic movement of its magnetic vortex structure above 400°C, recovering its original state upon cooling, whereas a larger exemplar Fe3O4 grain (~250 nm) is shown to retain its vortex state on heating to 550°C, close to the Curie temperature of 580°C. Hence, we demonstrate that Fe3O4 grains containing vortex structures are indeed reliable recorders of paleodirectional and paleointensity information, and the presence of PSD magnetic signals does not preclude the successful recovery of paleomagnetic signals.

Inline holography in the transmission electron microscope is a versatile technique which provides real-space phase information that can be used for the correction of imaging aberrations, as well as for measuring electric and magnetic fields and strain distributions. It is able to recover high-spatial-frequency contributions of the phase effectively but suffers from the weak transfer of low-spatial-frequency information, as well as from incoherent scattering. Here, we combine gradient flipping and phase prediction in an iterative flux-preserving focal series reconstruction algorithm with incoherent background subtraction that gives extensive access to the missing low spatial frequencies. A procedure for optimizing the reconstruction parameters is presented, and results from Fe-filled C nanospheres, and MgO cubes are compared with phase images obtained using off-axis holography. [ABSTRACT FROM AUTHOR]

We have combined a flip-chip high-Tc dcSQUIDmagnetometer with a ferromagnetic flux antenna made from 250 insulated 25-μm-thick stripes of amorphous soft magnetic Vitrovac 6025 foil inserted through the pick-up loop of the superconducting flux transformer. The ferromagnetic flux antenna provides improved magnetic coupling of the high-Tc SQUID to magnetic fields of ~0.4 nT/Φ0 to ~0.18 nT/Φ0 . The orientation of the stripes was chosen to be normal to the foil tape rolling direction in order to minimize contributions from Barkhausen noise. A magnetic field resolution of ~2 fT√Hz at 1 kHz and 77 K was achieved. Details of the technology and noise spectra of the novel composite high-Tc SQUID sensor are presented and their prospective applications for biomagnetic research and nondestructive evaluation are discussed. [ABSTRACT FROM AUTHOR]

Recordings of magnetic fields, thought to be crucial to our solar system's rapid accretion, are potentially retained in unaltered nanometric low-Ni kamacite (~metallic Fe) grains encased within dusty olivine crystals, found in the chondrules of unequilibrated chondrites. However, most of these kamacite grains are magnetically non-uniform, so their ability to retain four- billion-year-old magnetic recordings cannot be estimated by previous theories, which assume only uniform magnetization. Here, we demonstrate that non-uniformly magnetized nano-metric kamacite grains are stable over solar system timescales and likely the primary carrier of remanence in dusty olivine. By performing in-situ temperature-dependent nanometric magnetic measurements using off-axis electron holography, we demonstrate the thermal stability of multi-vortex kamacite grains from the chondritic Bishunpur meteorite. Combined with numerical micromagnetic modeling, we determine the stability of the magnetization of these grains. Our study shows that dusty olivine kamacite grains are capable of retaining magnetic recordings from the accreting solar system. [ABSTRACT FROM AUTHOR]

Electron waves give an unprecedented enhancement to the field of microscopy by providing higher resolving power compared to their optical counterpart. Further information about a specimen, such as electric and magnetic features, can be revealed in electron microscopy because electrons possess both a magnetic moment and charge. In-plane magnetic structures in materials can be studied experimentally using the effect of the Lorentz force. On the other hand, full mapping of the magnetic field has hitherto remained challenging. Here we measure a nanoscale out-of-plane magnetic field by interfering a highly twisted electron vortex beam with a reference wave. We implement a recently developed holographic technique to manipulate the electron wavefunction, which gives free electrons an additional unbounded quantized magnetic moment along their propagation direction. Our finding demonstrates that full reconstruction of all three components of nanoscale magnetic fields is possible without tilting the specimen. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses the advanced optical magnetic imaging technique used to study the three-dimensional magnetic fields that originate from chains of magnetic nanocrystals inside the living cells of magnetotactic bacteria.

An approach is presented that allows independent determination of the mean inner potential contribution to a phase image of a highly doped layer in a semiconductor measured using off-axis electron holography, in order to quantify the contribution to the recorded phase from the dopant potential alone. The method takes into account the possible presence of both substitutional and interstitial dopant atoms and is used here to analyse an experimental phase image of 12 delta-doped B layers in Si that are separated from each other by <6 nm. [ABSTRACT FROM PUBLISHER]

Electron holography is a powerful technique for characterizing electrostatic potentials, charge distributions, electric and magnetic fields, strain distributions and semiconductor dopant distributions with sub-nm spatial resolution. Mapping internal electrostatic and magnetic fields within nanoparticles and other low-dimensional materials by TEM requires both high spatial resolution and high phase sensitivity. Carrying out such an analysis fully quantitatively is even more challenging, since artefacts such as dynamical electron scattering may strongly affect the measurement. In-line electron holography, one of the variants of electron holography, features high phase sensitivity at high spatial frequencies, but suffers from inefficient phase recovery at low spatial frequencies. Off-axis electron holography, in contrast, can recover low spatial frequency phase information much more reliably, but is less effective in retrieving phase information at high spatial frequencies when compared to in-line holography. We investigate gold nanoparticles using hybrid electron holography at both atomic-resolution and intermediate magnification. Hybrid electron holography is a novel technique that synergistically combines off-axis and in-line electron holography, allowing the measurement of the complex wave function describing the scattered electrons with excellent signal-to-noise properties at both high and low spatial frequencies. The effect of dynamical electron scattering is minimized by beam tilt averaging. [ABSTRACT FROM AUTHOR]

Abstract: An approach that can be used to measure the magnetic moment of a magnetized nanoparticle or nanostructure from an electron-optical phase image is introduced. The measurement scheme is based on integration of the gradient of the measured phase image within a circular boundary that contains the structure of interest. The quantity obtained is found to be directly proportional to the magnetic moment of the particle, with a constant of proportionality that does not depend on the particle''s shape or magnetization state. The measurement of magnetic moments from both simulated and experimental phase images is demonstrated, and strategies are presented that can be utilized to overcome sources of error associated with, for example, the presence of neighboring magnetic particles and the perturbation of the holographic reference wave. [Copyright &y& Elsevier]

Off-axis electron holography allows both the amplitude and the phase shift of an electron wavefield propagating through a specimen in a transmission electron microscope to be recovered. The technique requires the use of an electron biprism to deflect an object wave and a reference wave to form an interference pattern. Here, we introduce an approach based on semiconductor processing technology to fabricate fine electron biprisms with rectangular cross-sections. By performing electrostatic calculations and preliminary experiments, we demonstrate that such biprisms promise improved performance for electron holography experiments. [ABSTRACT FROM AUTHOR]

It has recently been shown that an electron vortex beam can be generated by the magnetic field surrounding the tip of a dipole-like magnet. This approach can be described using the magnetic Aharonov-Bohm effect and is associated with the fact that the end of a long magnetic rod can be treated approximately as a magnetic monopole. However, it is difficult to vary the magnetisation of the rod in such a setup and the electron beam vorticity is fixed for a given tip shape. Here, we show how a similar behaviour, which has the advantage of easy tuneability, can be achieved by making use of the electrostatic Aharonov-Bohm effect associated with an electrostatic dipole line. We highlight the analogies between the magnetic and electrostatic cases and use simulations of in-focus, Fresnel and Fraunhofer images to show that a device based on two parallel, oppositely charged lines that each have a constant charge density can be used to generate a tuneable electron vortex beam. We assess the effect of using a dipole line that has a finite length and show that if the charge densities on the two lines are different then an additional biprism-like effect is superimposed on the electron-optical phase. [ABSTRACT FROM AUTHOR]

The technique of double exposure electron holography, which is based on the superposition of two off-axis electron holograms, was originally introduced before the availability of digital image processing to allow differences between electron-optical phases encoded in two electron holograms to be visualised directly without the need for holographic reconstruction. Here, we review the original method and show how it can now be extended to permit quantitative studies of phase shifts that oscillate in time. We begin with a description of the theory of off-axis electron hologram formation for a time-dependent electron wave that results from the excitation of a specimen using an external stimulus with a square, sinusoidal, triangular or other temporal dependence. We refer to the more general method as continuous exposure electron holography, present preliminary experimental measurements and discuss how the technique can be used to image electrostatic potentials and magnetic fields during high frequency switching experiments. [ABSTRACT FROM AUTHOR]

Off-axis electron holography provides a direct means of retrieving the phase of the wavefield in a transmission electron microscope, enabling measurement of electric and magnetic fields at length scales from microns to nanometers. To maximise the accuracy of the technique, it is important to acquire holograms using experimental conditions that optimise the phase resolution for a given spatial resolution. These conditions are determined by a number of competing parameters, especially the spatial coherence and the instrument instabilities. Here, we describe a simple, yet accurate, model for predicting the dose rate and exposure time that give the best phase resolution in a single hologram. Experimental studies were undertaken to verify the model of spatial coherence and instrument instabilities that are required for the optimisation. The model is applicable to electron holography in both standard mode and Lorentz mode, and it is relatively simple to apply. [ABSTRACT FROM AUTHOR]

Abstract: The mapping of static electric and magnetic fields using electron probes with a resolution and sensitivity that are sufficient to reveal nanoscale features in materials requires the use of phase-sensitive methods such as the shadow technique, coherent Foucault imaging and the Transport of Intensity Equation. Among these approaches, image-plane off-axis electron holography in the transmission electron microscope has acquired a prominent role thanks to its quantitative capabilities and broad range of applicability. After a brief overview of the main ideas and methods behind field mapping, we focus on theoretical models that form the basis of the quantitative interpretation of electron holographic data. We review the application of electron holography to a variety of samples (including electric fields associated with p–n junctions in semiconductors, quantized magnetic flux in superconductors and magnetization topographies in nanoparticles and other magnetic materials) and electron-optical geometries (including multiple biprism, amplitude and mixed-type set-ups). We conclude by highlighting the emerging perspectives of (i) three-dimensional field mapping using electron holographic tomography and (ii) the model-independent determination of the locations and magnitudes of field sources (electric charges and magnetic dipoles) directly from electron holographic data. [Copyright &y& Elsevier]

The magnetic state, including the stray fields, of a chiral pattern of interacting permalloy nanomagnets is studied using off-axis electron holography in the transmission electron microscope. The projected in-plane magnetisation of the nanomagnets is reconstructed from the experimental magnetic phase shift using model-based iterative reconstruction. The thickness and chemical composition of the nanomagnets are characterised in cross-sectional geometry. The average value of the magnetic polarisation of the permalloy through the thickness of the sample is measured to be 0.73 T. This value is lower than the bulk value of 1 T, likely as a result of a combination of the microstructure, composition and possible oxidation of the nanomagnets. The experimental results are compared to micromagnetic simulations to confirm the magnetic states and to understand the switching processes in the magnetic nanoislands. • Quantitative measurement of magnetic state of permalloy islands in chiral ice using off-axis electron holography. • Structure and chemical composition of sputtered permalloy islands. • Reconstruction of in-plane magnetic polarisation. • Effect of imperfections on magnetisation reversal. [ABSTRACT FROM AUTHOR]