Magnomechanical cross-correlation thermometry

The development of hybrid quantum technologies has driven a need for low-temperature environments such as dilution refrigerators. In these cryogenic environments, accurate thermometry can be difficult to implement, expensive, and often requires calibration to an external reference. We propose a thermometric measurement of a hybrid system consisting of phonons coupled via the magnetostrictive interaction to magnons within a ferromagnetic sphere. Our approach is based on a cross-correlation measurement which is calibration-free and low temperature compatible. We demonstrate the ability to distinguish thermomechanical motion from the magnon induced back-action. Furthermore, the spectrum of back-action driven motion can be used to scale the thermomechanical motion, providing a direct measurement of the phonon temperature, independent of experimental parameters.