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 MgB2, 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 MgB2 single crystal cut in the ac plane by
focussed ion beam milling and tilted to 45◦ with respect to the electron beam about the crystallographic
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 Λab = 100 ± 35 nm and Λc = 120 ± 15 nm
at 10.8 K in a field of 4.8 mT. The large error in Λab is a consequence of tilting the sample about
a and had it been tilted about c, the errors on Λab and Λc 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 [Phys. Rev. B 87, 144515, 2013], we obtained a more
precise value for Λab using a sample cut in the ab plane. Using this value gives Λab = 107 ± 8 nm,
Λc = 120 ± 15 nm, ξab = 39 ± 11 nm and ξc = 35 ± 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× 15 µm 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.This work was funded by the Royal Society. Work at
Eidgenossische Technische Hochschule, Zürich was supported
by the Swiss National Science Foundation and the National
Center of Competence in Research programme “Materials
with Novel Electronic Properties.”This is the accepted manuscript for a paper published in Physical Review B, 91, 054505, 5 February 2015, DOI: 10.1103/PhysRevB.91.05450
