It is well known that a magnetic field produces a phase change proportional to the in plane magnetic field B . Alas the out of plane magnetic field is more elusive. The only measurement that so far seems to produce any out of plane information is the magnetic dichroism  as it actually measures the out of plane magnetization.
Unfortunately magnetic dichroism experiment is still a complicated experiment that requires a considerable control of the condition and of the material; moreover the measures of the magnetization , often with the objective on, is not directly a measure of the magnetic field itself.
However while a plane wave along the optical axis has no significant interaction with a magnetic field along z , vortex beams with winding number l do feel such field through a Larmor phase effect .
We will demonstrate here that through the use of large vortex beams  we are able, for the first time, to measure the out of plane magnetic field generated by a magnetic pillar of Co .
We placed the vortex around the pillar ensuring as much as possible an axial symmetry and observed the phase effect. The result is in good agreement with the typical magnetization expected for the pillar with an average field at surface of about 2T.
Fig 1 illustrates the A and B field produced by a magnetic pillar. The actual magnetic pillar fabricated by EBID deposition is illustrated in fig 1b. Fig 2 depicts the vortex beam density with L=200 as imaged in its focal plane. Thanks to an interferometric approach we were able to measure the magnetic phase contribution and bind it to the magnetic field in proximity of the sample. The magnetic phase is visible in the inset of fig 2 showing approximate axial symmetry.
The technique has been carried on in Low Mag mode with the main objective lens off but there are no principle limitation to the application in conventional (S) TEM mode.
Moreover this promises to be one of the best recognition of the importance of vortex beams in microscopy for material science.
 R E. Dunin-Borkowski, M. R. McCartney et al Science 282 (1998) 1868
 P. Schattschneider, S. Rubino Nature 441 (2006) 486
 J. Verbeeck, H. Tian P. Schattschneider Nature 467 (2010) 301
 B. J. McMorran, A. Agrawal et al. Science 331 (2011) 192
 V. Grillo et al . Phys Rev Lett 114, 034801 (2015)
 G. Pozzi, C. B. Boothroyd Appl. Phys. Lett. 108, 083108 (2016)
To cite this abstract:Vincenzo Grillo, Tyler Harvey, Jordan Pierce, Federico Venturi, Roberto Balboni, Gian Carlo Gazzadi, Stefano Frabboni, Benjamin McMorran, Robert Boyd, Ebrahim Karimi; The measurement of off-plane magnetic field through electron vortex beams. The 16th European Microscopy Congress, Lyon, France. https://emc-proceedings.com/abstract/the-measurement-of-off-plane-magnetic-field-through-electron-vortex-beams/. Accessed: December 2, 2023
EMC Abstracts - https://emc-proceedings.com/abstract/the-measurement-of-off-plane-magnetic-field-through-electron-vortex-beams/