Micro-Calorimeter for Heat Capacity Studies of Sub-Microgram Superconducting Crystals

A steady-state ac-temperature micro-calorimeter for heat capacity measurement of sub-microgram superconducting samples is presented. It utilizes thermocouple thermometers nano-patterned onto 150 nm thick Si$_{3}$N$_{4}$ membranes. Theoretical models, mathematical relations describing the operation of the calorimeter and calibration procedures are discussed. The system achieves a resolution of 10$^{-4}$; and allows for measurements from 5 K to room temperature. The calorimeter can be continuously rotated in a split-coil magnet generating up to 8 T. To demonstrate the performance of our device we present measurements of the specific heat of single crystals of SmFeAsO$_{0.85}$F$_{0.15}$ (120 $\mu $m wide and 10 $\mu $m thick, crystal w1) and of BaFe$_{2}$(As$_{1-x}$P$_{x})_{2}$ (150 $\mu $m wide and 30 $\mu $m thick).