Superconducting Effects in Optimization of Magnetic Penetration Thermometers for X-Ray Microcalorimeters

We have made high-resolution X-ray microcalorimeters using superconducting MoAu bilayers and Nb meander coils. The temperature sensor is a magnetic penetration thermometer. Operation is similar to metallic magnetic calorimeters, but instead of the magnetic susceptibility of a paramagnetic alloy, we use the diamagnetic response of the superconducting MoAu to sense temperature changes in an X-ray absorber. Flux-temperature responsivity can be large for small sensor heat capacity, with enough dynamic range for applications. We find that models of observed flux-temperature curves require several effects to explain flux penetration or expulsion in the microscopic devices. The superconductor is nonlocal, with large coherence length and weak pinning of flux. At the lowest temperatures, behavior is dominated by screening currents that vary as a result of the temperature dependence of the magnetic penetration depth, modified by the effect of the nonuniformity of the applied field occurring on a scale comparable to the coherence length. In the temperature regime where responsivity is greatest, spatial variations in the order parameter become important: both local variations as flux enters/leaves the film and an intermediate state is formed, and globally as changing stability of the electrical circuit creates a Meissner transition and flux is expelled/penetrates to minimize free energy.