Flux Quantization in Magnetic Nanowires Imaged by Electron Holography

Abstract

Off-axis electron holography has been employed to visualize and measure the magnetic flux leaking from cobalt wires having a radius of 40 nm and a length of a few μm. The magnetic flux of a single nanowire can be understood as the flux of a superposition of magnetic dipoles oriented along the nanowire axis at locations revealed by the phase as well as the amplitude image reconstructed from the hologram. Surprisingly, the reconstructed phase image showed that the total flux of the individual dipoles was always $\frac{h}{e}$, defined as a flux quantum ${\Phi }_0$ and corresponding to a phase change of $2\pi$. We were able to image single nanowires with a flux of $1\Phi$, $2\Phi$, and $3{\Phi }_0$, measured with a precision of $\frac{{\Phi }_0}{32}$.