Determination of the spatial length scale of the magnetic-field distribution in the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ ceramic by surface EPR

We have measured the EPR linewidth of a free-radical layer as a function of height (0.28–10 μm) above the surface of an ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ superconducting ceramic. Using Laplace equation, we can determine from this measurement the second moment of the field distribution (30±10 G) and the wave vector q (1/q=7±0.1 μm) characterizing its spatial scale at the surface. This result rules out the Abrikosov vortex lattice as the main source of surface EPR broadening, which we rather attribute to the grain structure, as suggested by Rakvin. The main consequence of this work is that the calculated width of the field distribution as deduced from the muon-spin-rotation depolarization rate may involve a sizeable contribution not related to the Abrikosov vortex lattice. Our method offers a means to investigate the field distribution at a surface down to wavelengths of a few hundreds of nanometers and widths up to tens of gauss.