Measurement of Phonon Angular Momentum via the Einstein-de Haas Effect, Fiber-Optic Interferometry, and a High-Q Oscillator

We report the first measurement of the temperature dependent macroscopic phonon angular momentum using a fiber-optic-interferometer and mechanical oscillator system. An oscillating magnetic field was applied to an insulating ferromagnet attached to a single-crystal high-Q 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 on the order of 700 nN was detected between 77 K and 300 K for a 3 mm³ MgZn ferrite sample, in fair agreement with recent theoretical predictions¹. Our oscillator, with resonances at 1.3, 2.1, 9.4, and 12.4 kHz has a thermal noise limit on the order of 10^-14 N/√Hz, allowing 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.