Experimental evaluation of the 'transport-of-intensity' equation for magnetic phase reconstruction in Lorentz transmission electron microscopy

Mean inner potential of elemental crystals from density-functional theory calculations: Efficient computation and trends

The mean inner potential (V0) of crystals plays an important role in electron microscopy. In a few cases, it has been measured experimentally, using mostly electron holography; however, it is not uncommon to find reports that disagree by a few volts regarding the mean inner potential of the same material. Different levels of theory have also been used to estimate its value, often by building the crystal as a superposition of isolated atoms or ions-an independent-atom approximation that does not take bonding into account. In a few cases, density-functional theory (DFT) calculations were done to capture such bonding, frequently using computer-intensive all-electron approaches. In this article, we describe in detail a faster implementation based on postprocessing files produced by a DFT code that relies on the projector-augmented wave method. We deployed this approach to compute values of V0 for 44 elemental solids, and we provide the first quantum-mechanical calculation of the mean inner potential beyond the independent-atom approximation for many of them. We also report instances in which different surface terminations for the same material led to differences in V0 of more than 3 V, highlighting the dependence of the mean inner potential on the boundary conditions of the sample. Finally, by comparing our values of V0 with other material properties, we show that it correlates mostly linearly with the mass density, that it can be used to compute a good approximation to the orbital diamagnetic contribution to the magnetic susceptibility, and that it provides a simple route to compute atomic scattering amplitudes for forward scattering of electrons.

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.

The Mean Inner Potential of Hematite α-Fe2O3 Across the Morin Transition

We measure the mean inner potential (MIP) of hematite, α-Fe2O3, using electron holography and transmission electron microscopy. Since the MIP is sensitive to valence electrons, we propose its use as a chemical bonding parameter for solids. Hematite can test the sensitivity of the MIP as a bonding parameter because of the Morin magnetic phase transition. Across this transition temperature, no change in the corundum crystal structure can be distinguished, while a change in hybridized Fe-3d and O-2p states was reported, affecting ionic bonding. For a given crystallographic phase, the change in the MIP with temperature is expected to be minor due to thermal expansion. Indeed, we measure the temperature dependence in corundum α-Al2O3(112¯0) between 95 and 295 K showing a constant MIP value of ∼16.8 V within the measurement accuracy of 0.45 V. Thus, our objectives are as follows: measure the MIP of hematite as a function of temperature and examine the sensitivity of the MIP as a bonding parameter for crystals. Measured MIPs of α-Fe2O3(112¯0) above the Morin transition are equal, 17.85 ± 0.50 V, 17.93 ± 0.50 V, at 295 K, 230 K, respectively. Below the Morin transition, at 95 K, a significant reduction of ∼1.3 V is measured to 16.56 ± 0.46 V. We show that this reduction follows charge redistribution resulting in increased ionic bonding.

Spontaneous Topological States and Their Mutual Transformations in a Rare-Earth Ferrimagnet

Nontrivial chiral spin textures with nanometric sizes and novel characteristics (e.g., magnetic skyrmions) are promising for encoding information bits in future energy-efficient and high-density spintronic devices. Because of antiferromagnetic exchange coupling, skyrmions in ferrimagnetic materials exhibit many advantages in terms of size and efficient manipulation, which allow them to overcome the limitations of ferromagnetic skyrmions. Despite recent progress, ferrimagnetic skyrmions have been observed only in few films in the presence of external fields, while those in ferrimagnetic bulks remain elusive. This study reports on spontaneously generated zero-field ground-state magnetic skyrmions and their subsequent transformation into traditional magnetic bubbles via intermediate states of (bi-)target bubbles during a magnetic anisotropy change in the rare-earth ferrimagnetic crystal DyFe₁₁ Ti. Spontaneous reversible topological transformation driven by a temperature-induced spin reorientation transition is directly distinguished using Lorentz transmission electron microscopy. The spontaneous generation of magnetic skyrmions and successive topological transformations in ferrimagnetic DyFe₁₁ Ti are expected to advance the design of topological spin textures with versatile properties and potential applications in rare-earth magnets.

Transport of intensity equation method and its applications

A phase retrieval technique based on a transport of intensity equation (TIE) is one of the defocus series reconstruction techniques in microscopy. Since it does not require any dedicated devices like a biprism, and only three defocus images are enough to retrieve phase information, it has been applied to observe magnetic fields, magnetic domains, electrostatic potentials and strains. It is also used to improve image resolution by correcting spherical aberration. This technique is simple and easy to use, but some artifacts often appear in the retrieved phase map. One should pay careful attention to the experimental conditions and the algorithms and boundary conditions used to solve the TIE. This paper reviews the principle of the TIE method, the algorithms used to solve it and application results in materials science.

Measuring the mean inner potential of Al2O3 sapphire using off-axis electron holography

The mean inner potential (MIP) of a single crystal α-Al₂O₃ sapphire was measured using off-axis electron holography. To measure the MIP, we use mechanically polished wedge specimens for transmission electron microscopy (TEM). This approach also enabled us to measure the plasmon mean free path for inelastic scattering (IMFP). The wedge specimen, chosen here at an angle of approximately 45°, allows to determine the MIP by measuring the gradient of phase variations of the reconstructed electron wave over extended regions across the sample. The angle of the wedge was measured to an accuracy of better than 1° by two methods: first, perpendicular sectioning in a focused ion beam for direct measurement by TEM and second, by a non-destructive approach of confocal optical microscopy. The validity of this methodology was examined on a single crystal Si(001) sample showing that the mechanically polished wedge approach can be applied to a wide range of materials. Our measurements concluded that the MIP of sapphire is V₀ = 16.90 ± 0.36 V. Furthermore, the IMFP of sapphire was measured at 136 ± 2 nm for 197 keV electrons with a collection angle of 18mrad. The measured MIP of sapphire reflects its degree of ionicity, which lies between theoretical calculations based on electron scattering factors of charged and neutral isolated atoms obtained by Dirac-Fock calculations. Our MIP measurements tend to the expected value for this predominantly ionic material. To account for chemical bonding and the role of the crystallographic plane at the surface of the sample, we compared the experimental measurements to density-functional-theory calculations of the MIP. Calculations of α-Al₂O₃ slabs cut along (0001) and (1-100) planes obtained MIP values of 15.7 V and 16.7 V, respectively.

Observation of stable Néel skyrmions in cobalt/palladium multilayers with Lorentz transmission electron microscopy

Néel skyrmions are of high interest due to their potential applications in a variety of spintronic devices, currently accessible in ultrathin heavy metal/ferromagnetic bilayers and multilayers with a strong Dzyaloshinskii–Moriya interaction. Here we report on the direct imaging of chiral spin structures including skyrmions in an exchange-coupled cobalt/palladium multilayer at room temperature with Lorentz transmission electron microscopy, a high-resolution technique previously suggested to exhibit no Néel skyrmion contrast. Phase retrieval methods allow us to map the internal spin structure of the skyrmion core, identifying a 25 nm central region of uniform magnetization followed by a larger region characterized by rotation from in- to out-of-plane. The formation and resolution of the internal spin structure of room temperature skyrmions without a stabilizing out-of-plane field in thick magnetic multilayers opens up a new set of tools and materials to study the physics and device applications associated with chiral ordering and skyrmions.

Néel skyrmions are spin textures with a magnetization that rotates from in- to out-of-plane with distance from its centre. Here, the authors show that Lorentz transmission electron microscopy can be used to directly image Néel skyrmions with high resolution in thick exchange-coupled magnetic multilayers.