Vortex Imaging Research Articles

Measurement of the penetration depth and coherence length ofMgB2in all directions using transmission electron microscopy

We demonstrate that images of flux vortices in a superconductor taken with a transmission electron microscope can be used to measure the penetration depth and coherence length in all directions at the same temperature and magnetic field. This is particularly useful for $\mathrm{MgB}{}_{2}$, where these quantities vary with the applied magnetic field and values are difficult to obtain at low field or in the $c$ direction. We obtained images of flux vortices from a $\mathrm{MgB}{}_{2}$ single crystal cut in the $ac$ plane by focused ion beam milling and tilted to ${45}^{\ensuremath{\circ}}$ with respect to the electron beam about the crystallographic $a$ axis. A new method was developed to simulate these images that accounted for vortices with a nonzero core in a thin, anisotropic superconductor and a simplex algorithm was used to make a quantitative comparison between the images and simulations to measure the penetration depths and coherence lengths. This gave penetration depths ${\ensuremath{\Lambda}}_{ab}=100\ifmmode\pm\else\textpm\fi{}35$ nm and ${\ensuremath{\Lambda}}_{c}=120\ifmmode\pm\else\textpm\fi{}15$ nm at 10.8 K in a field of 4.8 mT. The large error in ${\ensuremath{\Lambda}}_{ab}$ is a consequence of tilting the sample about $a$ and had it been tilted about $c$, the errors on ${\ensuremath{\Lambda}}_{ab}$ and ${\ensuremath{\Lambda}}_{c}$ would be reversed. Thus obtaining the most precise values requires taking images of the flux lattice with the sample tilted in more than one direction. In a previous paper [J. C. Loudon et al., Phys. Rev. B 87, 144515 (2013)], we obtained a more precise value for ${\ensuremath{\Lambda}}_{ab}$ using a sample cut in the $ab$ plane. Using this value gives ${\ensuremath{\Lambda}}_{ab}=107\ifmmode\pm\else\textpm\fi{}8$ nm, ${\ensuremath{\Lambda}}_{c}=120\ifmmode\pm\else\textpm\fi{}15$ nm, ${\ensuremath{\xi}}_{ab}=39\ifmmode\pm\else\textpm\fi{}11$ nm, and ${\ensuremath{\xi}}_{c}=35\ifmmode\pm\else\textpm\fi{}10$ nm, which agree well with measurements made using other techniques. The experiment required two days to conduct and does not require large-scale facilities. It was performed on a very small sample, $30\ifmmode\times\else\texttimes\fi{}15 \ensuremath{\mu}\mathrm{m}$ and 200-nm thick, so this method could prove useful for superconductors where only small single crystals are available, as is the case for some iron-based superconductors.

Mechanotransduction mechanisms for intraventricular diastolic vortex forces and myocardial deformations: part 1.

Epigenetic mechanisms are fundamental in cardiac adaptations, remodeling, reverse remodeling, and disease. This two-article series proposes that variable forces associated with diastolic RV/LV rotatory intraventricular flows can exert physiologically and clinically important, albeit still unappreciated, epigenetic actions influencing functional and morphological cardiac adaptations and/or maladaptations. Taken in toto, the two-part survey formulates a new paradigm in which intraventricular diastolic filling vortex-associated forces play a fundamental epigenetic role, and examines how heart cells react to these forces. The objectives are to provide a perspective on vortical epigenetic effects, to introduce emerging ideas, andto suggest directions of multidisciplinary translational research. The main goal is to make pertinent biophysics and cytomechanical dynamic systems concepts accessible to interested translational and clinical cardiologists. I recognize that the diversity of the epigenetic problems can give rise to a diversity of approaches and multifaceted specialized research undertakings. Specificity may dominate the picture. However, I take a contrasting approach. Are there concepts that are central enough that they should be developed in some detail? Broadness competes with specificity. Would, however, this viewpoint allow for a more encompassing view that may otherwise be lost by generation of fragmented results? Part 1 serves as a general introduction, focusing on background concepts, on intracardiac vortex imaging methods, and on diastolic filling vortex-associated forces acting epigenetically on RV/LV endocardium and myocardium. Part 2 will describe pertinent available pluridisciplinary knowledge/research relating to mechanotransduction mechanisms for intraventricular diastolic vortex forces and myocardial deformations and to their epigenetic actions on myocardial and ventricular function and adaptations.

STXM observation and quantitative study of magnetic vortex structure

Magnetic recording has now played an important role in the development of non-volatile information storage technologies, so it becomes essential to quantitatively understand the magnetization distribution in magnetic microstructures. In ferromagnetic disks, squares and triangles with submicron sizes, it is energetically favorable for the magnetization to form a closed in-plane vortex and a perpendicular vortex core at the center. This vortex magnetic structure is a new candidate for future magnetic memory device because both the vortex chirality and the core polarity can be manipulated by applying an external magnetic field or a spin-polarized current. Further development of vortex-based memory devices requires quantitative measurement of vortex domain structures, which is still lacking.In this paper, magnetization configuration in a vortex structure has been quantitatively studied by scanning transmission X-ray microscope (STXM) utilizing X-ray magnetic circular dichroism (XMCD) effect in Shanghai Synchrotron Radiation Facility. Samples have been fabricated on the 100 nm silicon-nitride membranes. The patterns are first transferred to PMMA photoresist using e-beam lithography, then a 50 nm thick Ni80Fe20 film is deposited by e-beam evaporation. Magnetic vortex configurations are characterized with the X-ray energy at Fe L3 absorption edge and Ni L3 absorption edge, respectively. The image taken at Fe edge shows greater contrast than that at Ni edge. Experimental results indicate that the magnetic vortex state remains stable in permalloy circle, square and triangle structures with diameters from 2 to 5 m. The STXM images indicate that the magnetization in circular geometry changes continuously along the concentric circles without clear domain boundaries. In contrast, magnetization in square geometry consists of four distinct domains with clear diagonal domain boundaries. Similarly, three domains can be observed in triangle geometry. In order to quantify the in-plane magnetization configuration in magnetic vortices, we also use micromagnetic simulation to calculate the magnetization distributions of these three geometries. By extracting Mx along the circular profiles in both experimental and simulated vortex images, we find that the experimental magnetic profiles in the STXM images are consistent with the simulation data quantitatively. These magnetic structures are also studied by magnetic force microscopy (MFM). Since MFM is only sensitive to the dipolar magnetic field around the domain boundary, the MFM images show different configurations from the STXM images.

Superfluid 3He, a two-fluid system, with the normal-fluid dynamics dominated by Andreev reflection

As a specific offering towards his festschrift, we present a review the various properties of the excitation gas in superfluid 3He, which depend on Andreev reflection. This phenomenon dominates many of the properties of the normal fluid, especially at the lowest temperatures. We outline the ideas behind this dominance and describe a sample of the many experiments in this system which the operation of Andreev reflection has made possible, from temperature measurement, particle detection, vortex imaging to cosmological analogues.

Influence of the Reynolds number on the instant flow evolution of a turbulent rectangular free jet of air

The paper is aimed at investigating the influence of the Reynolds number on the instant flow evolution of a rectangular free jet of air in the range of Reynolds numbers from Re=35,300 to Re=2,200, where the Reynolds number, Re, is defined according to the hydraulic diameter, D, of a rectangular slot of height H, equal to about D=2H. The Particle Image Velocimetry (PIV) technique allows obtaining the instant PIV visualizations on the central symmetry section of the rectangular jet. The visual inspection of the instant frames with one and two vortices, except for Re=35,300 where only one vortex images are detected, shows that after the jet exit is present the Flow with Constant Instant Height, with a length LCIH which increases with the decrease of the Reynolds number, from a ratio LCIH/H equal to LCIH/H=0.9 at Re=35,300 to LCIH/H=4.0 at Re=2,200. The instant PIV measurements, carried out at several distances from the jet exit, show that the variations of the ratio U/U‾0 of the centerline instant velocity, U, to the exit average velocity, U‾0, remain below ±4% for a length LCIV, defining the Flow with Constant Instant Velocity on the centerline. The ratio LCIV/H increases from LCIV/H=1.1 at Re=35,300 to LCIV/H=4.1 at Re=2,200 and is quite similar to LCIH/H. The instant PIV measurements of the centerline turbulence intensity, Tu, show that its variations remain below ±4% for a length LCIT, defining the Flow with Constant Instant Turbulence on the centerline. The ratio LCIT/H is equal to LCIV/H. The instant PIV velocity profiles in the transverse direction, are practically unchanged for a length LUVP which defines the flow with Unchanged Velocity Profile. The four lengths LUVP=LCIH=LCIV=LCIT are considered equal, defining the Flow with Negligible Disturbances, with length LND, or first type of flow, L1, which is in agreement with the average length of the flow with Constant Height, LCH, in the turbulent and laminar regime, and with the average length of the Undisturbed flow, LU, in the turbulent regime. The instant PIV frames show the presence, after the flow with negligible disturbances, of the Flow with Small Variations of the Height, where the jet height varies slightly without forming the vortex. The length of the flow with Small Variation of the Height is LSVH, and the first vortex appears after the total length (LND+LSVH). The variations of the instant PIV measurements of the centerline turbulence intensity, Tu, increase after the length LCIT, but remaining below ±5–9% for a length LSVT, which defines the Flow with Small Variation of the Turbulence. The total length (LCIT+LSVT) is comparable to (LCIH+LSVH) in the turbulent and laminar regimes, and can be assumed equal to the sum of the lengths of the flows with negligible and small disturbances, LND+LSD=L2, which is in agreement with the average length of the undisturbed flow, LU, in the laminar regime. The instant PIV frames show the flow with Coherent Vortices after L2, with a length LCV, followed by the vortices breakdown. The instant PIV frames allow visualizing the end of the flow with Coherent Vortices, defining the total length of the flows with negligible and small disturbances, and coherent vortices, as LND+LSD+LCV=L3, which is in good agreement with the average length of the potential core, LP.

Winglet design and optimization for a MALE UAV using CFD

In this study, a winglet optimization procedure for a Medium-Altitude-Long-Endurance (MALE) Unmanned-Aerial-Vehicle (UAV) is presented. The UAV layout, aerodynamic and performance parameters were defined during the conceptual and preliminary design phases, where a first winglet configuration was also designed. The winglet optimization procedure was a part of the detail design phase. The flow around several winglet configurations was investigated, using CFD. Reynolds-Averaged-Navier–Stokes (RANS) were employed and coupled with the Spalart–Allmaras turbulence model. At first, only the flow around the wing-winglet part of the UAV was investigated, in order to determine the optimal design, by comparing the lift and drag coefficients, the lift-to-drag (L/D) ratios, the stalling characteristics and the root bending moment. Then, the airflow around the entire aircraft was studied, at loiter conditions for the first and the optimal winglet configuration, in order to compare the overall UAV aerodynamic performance. Lift, drag and pitching moment coefficient charts, along with vorticity contours and tip vortex images, are presented, and appropriate conclusions are drawn. The calculations showed a considerable improvement in the aircraft's aerodynamic performance after installing the optimized winglet; this in turn provided an increase in total flight time by approximately 10%.

Geometrical Confinement Effects in Layered Mesoscopic Vortex Matter

We study the geometrical confinement effect in Bi $$_{2}$$ Sr $$_{2}$$ CaCu $$_{2}$$ O $$_{8 +\delta }$$ mesoscopic vortex matter with edge-to-surface ratio of 7–12 %. Samples have in-plane square and circular edges, 30 $$\upmu $$ m widths, and $$\sim $$ 2 $$\upmu $$ m thickness. Direct vortex imaging reveals the compact planes of the structure align with the sample edge by introducing topological defects. The defect density is larger for circular than for square edges. Molecular dynamics simulations suggest that this density is not an out-of-equilibrium property but rather determined by the geometrical confinement.

Vortex energy landscape from real space imaging analysis of YBa2Cu3O7 with different defect structures

A methodology based on real space vortex image analysis is presented able to estimate semi-quantitatively the relevant energy densities of an arbitrary array of vortices, map the interaction energy distributions and evaluate the pinning energy associated to particular defects. The combined study using nanostructuration tools, a vortex visualization technique and the energy method is seen as an opportunity to estimate vortex pinning potentials strengths. Particularly, spatial distributions of vortex energy densities induced by surface nanoindented scratches are evaluated and compared to those of twin boundaries. This comparative study underlines the remarkable role of surface nanoscratches in pinning vortices and its potentiality in the design of novel devices for pinning and guiding vortex motion.

Ptychographical imaging of the phase vortices in the x-ray beam formed by nanofocusing lenses

We present the ptychographical reconstruction of the x-ray beam formed by nanofocusing lenses (NFLs) containing a number of phase singularities (vortices) in the vicinity of the focal plane. As a test object Siemens star pattern was used with the finest features of 50 nm for ptychographical measurements. The extended ptychographical iterative engine (ePIE) algorithm was applied to retrieve both complex illumination and object functions from the set of diffraction patterns. The reconstruction revealed the focus size of 91.4±1.1 nm in horizontal and 70±0.3 nm in vertical direction at full width at half maximum (FWHM). The complex probe function was propagated along the optical axis of the beam revealing the evolution of the phase singularities.

A displacement-shifted vision-based hybrid particle tracking velocimetry (PTV) technique

A displacement-shifted approach is introduced to the vision-based particle tracking velocimetry (VB-PTV) technique described in Lei et al. (Exp Fluids 53(5):1251–1268, 2012), using translational and angular displacements. The particle matching algorithm in VB-PTV is based on a proximity matrix, G ij , which favors short distance particle matches over long distance matches. By modifying the formula used in constructing G ij , particles that lie at the expected location of the match are favored. Two displacement-shifted methods are introduced: the first of which relies on particle image velocimetry estimates of particle displacements and the second of which relies on both the expected displacement and direction of the correct match to construct the proximity matrix. These displacement-shifted algorithms improve performance in high gradient (0.3 px/px and above), high displacement flows (upwards of 20 pixels), broadening the range of flows for which VB-PTV can be used. RMS errors in PTV results are reduced by 33 % or more when these displacement-shifted algorithms are made to the VB-PTV algorithm which is used to process Oseen vortex images. Experimental images of shear layer and the wake region of vortex shedding were used to verify the performances of the proposed methods, and the results are in agreement with the synthetic tests.

Vortices at nanoscale: Still some room at the bottom

Vortices as topological defects existon all scales of Nature from cosmicstrings to a dense quark matter.In macroscopic quantum systemslike superconductors, superfluidsand Bose-Einstein condensatesthe vortices are of special interest.There, they are quantized having“normal” cores where the superfluidorder parameter is zero and itsphase usually changes by 2

A scanning superconducting quantum interference device with single electron spin sensitivity

Superconducting quantum interference devices (SQUIDs) can be used to detect weak magnetic fields and have traditionally been the most sensitive magnetometers available. However, because of their relatively large effective size (on the order of 1µm), the devices have so far been unable to achieve the level of sensitivity required to detect the field generated by the spin magnetic moment (μB) of a single electron. Here we show that nanoscale SQUIDs with diameters as small as 46nm can be fabricated on the apex of a sharp tip. The nano-SQUIDs have an extremely low flux noise of 50nΦ0Hz(-1/2) and a spin sensitivity of down to 0.38μBHz(-1/2), which is almost two orders of magnitude better than previous devices. They can also operate over a wide range of magnetic fields, providing a sensitivity of 0.6μBHz(-1/2) at 1T. The unique geometry of our nano-SQUIDs makes them well suited to scanning probe microscopy, and we use the devices to image vortices in a type II superconductor, spaced 120nm apart, and to record magnetic fields due to alternating currents down to 50nT.

Stray-field imaging of magnetic vortices with a single diamond spin

Despite decades of advances in magnetic imaging, obtaining direct, quantitative information with nanometre scale spatial resolution remains an outstanding challenge. Recently, a technique has emerged that employs a single nitrogen-vacancy defect in diamond as an atomic-size magnetometer, which promises significant advances. However, the effectiveness of the technique when applied to magnetic nanostructures remains to be demonstrated. Here we use a scanning nitrogen-vacancy magnetometer to image a magnetic vortex, which is one of the most iconic objects of nanomagnetism, owing to the small size (~10 nm) of the vortex core. We report three-dimensional, vectorial and quantitative measurements of the stray magnetic field emitted by a vortex in a ferromagnetic square dot, including the detection of the vortex core. We find excellent agreement with micromagnetic simulations, both for regular vortex structures and for higher-order magnetization states. These experiments establish scanning nitrogen-vacancy magnetometry as a practical and unique tool for fundamental studies in nanomagnetism.

Quantitative imaging of flux vortices in the type-II superconductor MgB2using cryo-Lorentz transmission electron microscopy

Imaging of flux vortices in high quality MgB$_2$ single crystals has been successfully performed in a commercial Field Emission Gun-based Transmission Electron Microscope. In Cryo-Lorentz Microscopy, the sample quality and the vortex lattice can be monitored simultaneously, allowing one to relate microscopically the surface quality and the vortex dynamics. Such a vortex motion ultimately determines the flow resistivity, $\rho_{f}$, the knowledge of which is indispensable for practical applications such as superconducting magnets or wires for Magnetic Resonance Imaging. The observed patterns have been analyzed and compared with other studies by Cryo-Lorentz Microscopy or Bitter decoration. We find that the vortex lattice arrangement depends strongly on the surface quality obtained during the specimen preparation, and tends to form an hexagonal Abrikosov lattice at a relatively low magnetic field. Stripes or gossamer-like patterns, recently suggested as potential signatures of an unconventional behavior of MgB$_2$, were not observed.

Magnetic structure of individual flux vortices in superconducting MgB2derived using transmission electron microscopy

Images of flux vortices in superconductors acquired by transmission electron microscopy should allow a quantitative determination of their magnetic structure but so far, only visual comparisons have been made between experimental images and simulations. Here, we make a quantitative comparison between Fresnel images and simulations based on the modified London equation to investigate the magnetic structure of flux vortices in MgB2. This technique gives an absolute, low-field (~30 Oe) measurement of the penetration depth from images of single vortices. We found that these simulations gave a good fit to the experimental images and that if all the other parameters in the fit were known, the penetration depth for individual vortices could be measured with an accuracy of +/- 5 nm. Averaging over 17 vortices gave a penetration depth in the ab plane of 113 +/- 2 at 10.8 K assuming that the entire thickness of the sample was superconducting. The main uncertainty in this measurement was the proportion of the specimen which was superconducting. Allowing for a non-superconducting layer of up to 50 nm thickness on the specimen surfaces gave a penetration depth in the range 100-115 nm, close to values of 90 +/- 2 nm obtained by small-angle neutron scattering and 118-138 nm obtained by radio-frequency measurements. We also discuss the use of the transport of intensity equation which should, in principle, give a model-independent measure of the magnetic structure of flux vortices.

Vortex imaging in amorphous Mo80Ge20 pentagons

We present the direct observation of vortex configuration in Mo80Ge20 pentagons using the scanning SQUID microscope. Systematic measurements allow us to reveal how vortices are confined in a restricted sample as well as how vortex arrangement evolves with increasing the applied magnetic field. Vortex distribution in pentagon tends to take one of five symmetric axes of pentagon expected from sample geometry. We found that the rule of shell filling is different among various different sizes of the pentagons. For vorticity of six, vortices form a two-shell structure in small pentagon, while single shell structure in larger pentagon. We also demonstrate that the vortex dragging effect can be caused by the superconducting pick-up coil in a weak pinning specimen.

Generalized Hamiltonian point vortex dynamics on arbitrary domains using the method of fundamental solutions

A new algorithm (VOR-MFS) is presented for the solution of a generalized Hamiltonian model of point vortex dynamics in an arbitrary two-dimensional computational domain. The VOR-MFS algorithm utilizes the method of fundamental solutions (MFS) to obtain an approximation to the model Hamiltonian by solution of an appropriate boundary value problem. Unlike standard point vortex methods, VOR-MFS requires knowledge only of the free-space (R2) Green’s function for the problem as opposed to the domain-adapted Green’s function, permitting solution of a much wider range of problems. VOR-MFS is first validated against a vortex image model for the case of (2D Euler) multiple vortex motion in both circular and ‘Neumann-oval’ shaped domains. It is then demonstrated that VOR-MFS can solve for quasi-geostrophic shallow water point vortex motion in the same domains. The exponential convergence of the MFS method is shown to lead to good conservation properties for each of the solutions presented.

Rotating vortex imaging implemented by a quantized spiral phase modulation

We demonstrate both theoretically and experimentally that a spiral mask with a finite number of discrete phase levels allows a defocusing induced rotation of the point spread function in the vortex imaging. Two experimental configurations based on a spiral phase modulation of light and a spiral filtering of the spatial spectrum are studied in a unified theoretical treatment. The rotating point spread functions are analyzed in detail for imaging realized by the vortex lens and the 4-f system used in the spiral phase contrast microscopy. The theoretical results are verified by experiments using a spatial light modulator. The method is applicable to a precise focusing and optical imaging allowing depth estimation from diffracted rotation. Apart from implementation simplicity, the main advantages of the method are high energy efficiency, a possibility to operate with either complex amplitude or spatial spectrum of light and variability allowing a simple control of number of lobes of the point spread function.

Quantitative Imaging of Flux Vortices in Superconductors

Transmission electron microscopy offers the possibility of imaging flux vortices in superconductors quantitatively and at video rate. Here we use the technique to image flux vortices in MgB2 and investigate their magnetic structure.

Selective edge enhancement in three-dimensional vortex imaging with incoherent light

We demonstrate a new imaging method enabling a selective edge contrast enhancement of three-dimensional amplitude objects with spatially incoherent light. The imaging process is achieved in a spiral modification of Fresnel incoherent correlation holography and uses a vortex impulse response function. The correlation recordings of the object are acquired in a one-way interferometer with the wavefront division carried out by a spatial light modulator. Two different methods based on applying a helical reference wave in the hologram recording and a digital spiral phase modulation in image reconstruction are proposed for edge enhancement of amplitude objects. Results of both isotropic and anisotropic spiral imaging are demonstrated in experiments using an LED as an incoherent source of light.