Modeling the nanoscale linear response of superconducting thin films measured by a scanning probe microwave microscope

A localized and strong RF magnetic field, created by a magnetic write head, is used to examine the linear electrodynamic properties of a Nb superconducting film. The complex reflection coefficient of the write head held in close proximity to the films is measured as a function of sample temperature. A model combining a magnetic circuit (magnetic write head inductively coupled to the sample) and transmission line (microwave circuit) is given to interpret the linear response measurement. Additionally, this reflection linear response measurement can be used to determine the temperature dependence of the magnetic penetration depth on a variety of superconductors.