Measurement of Phonon Angular Momentum via the Einstein-de Haas Effect, Fiber-Optic Interferometry, and a Single-Crystal Silicon Torsional Oscillator

In this study, we report direct force measurements of the temperature-dependent macroscopic phonon angular momentum, using a fiber-optic interferometer and a torsional crystal oscillator. An oscillating magnetic field was applied to an insulating ferromagnet attached to a single-crystal silicon double-torsional oscillator. By the Einstein-de Haas effect, oscillator displacement measurements between low temperatures and those closer to the Debye temperature allow observation of the changing phonon angular momentum. A force change of approximately 60 nN was detected between 77 K and 300 K for a 0.3 mm ³ MgZn ferrite sample, in fair agreement with theoretical predictions. Our oscillator, with a thermal noise limit on the order of 10 ⁻¹² N/ √Hz , allows the possibility of high-accuracy detection. Competing effects were minimized; for example, induced eddy current momentum can overwhelm the phonon effect for metallic ferromagnets, and careful temperature-dependent force calibrations were required.