Depth-Resolved Profile of the Magnetic Field beneath the Surface of a Superconductor with a Few nm Resolution

The variation of a magnetic field as a function of depth beneath the surface of an ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ thin film in the Meissner state has been measured using low energy muons. The depth of implantation was varied from 20–150 nm by tuning the energy of the implanted muons from 3–30 keV. These are direct measurements of the penetration of a magnetic field beneath a superconducting surface which illustrate the power of low energy muons for near surface studies in superconductivity and magnetism.