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 part
icularly useful for 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 an MgB$_2$ single crystal cut in the $ac$ plane by focussed ion beam milling and tilted to $45^circ$ with respect to the electron beam about its $a$ axis. A new method was developed to simulate these images which accounted for vortices with a non-zero 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 $Lambda_{ab}=100pm 35$ nm and $Lambda_c=120pm 15$ nm at 10.8 K in a field of 4.8 mT. The large error in $Lambda_{ab}$ is a consequence of tilting the sample about $a$ and had it been tilted about $c$, the errors 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, we obtained a more precise value using a sample cut in the $ab$ plane. Using this value gives $Lambda_{ab}=107pm 8$ nm, $Lambda_c=120pm 15$ nm, $xi_{ab}=39pm 11$ nm and $xi_c=35pm 10$ 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: $30times 15$ microns and 200 nm thick so this method could prove useful for characterising new superconductors where only small single crystals are available.
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 simulatio
ns. 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.
Neutron diffraction has been used to investigate antiferromagnetism since 1949. Here we show that antiferromagnetic reflections can also be seen in transmission electron diffraction patterns from NiO. The diffraction patterns taken here came from reg
ions as small as 10.5 nm and such patterns could be used to form an image of the antiferromagnetic structure with a nanometre resolution.
Flux vortices in superconductors can be imaged using transmission electron microscopy because the electron beam is deflected by the magnetic flux associated with the vortices. This technique has a better spatial and temporal resolution than many othe
r imaging techniques and is sensitive to the magnetic flux density within each vortex not simply the fields at the sample surface. Despite these advantages, only two groups have successfully employed the technique using specially adapted instruments. Here we demonstrate that vortices can be imaged with a modern, commercial transmission electron microscope operating at 300 kV equipped with a field emission gun, Lorentz lens and a liquid helium cooled sample holder. We introduce superconductivity for non-specialists and discuss techniques for simulating and optimising images of flux vortices. Sample preparation is discussed in detail as the requirement for samples with very large (>10um), flat areas so that the image is not dominated by diffraction contrast is the main difficulty with the technique. We have imaged vortices in superconducting Bi2Sr2CaCu2O8+d and use correlation functions to investigate the ordered arrangements they adopt as a function of applied magnetic field.
