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

We report initial design and use of capacitive and fiber-optic-interferometer systems to measure the predicted^[1] macroscopic phonon angular momentum. An oscillating magnetic field is applied to an insulating ferromagnet attached to our single-crystal high-Q double torsional oscillator. By the Einstein-de Haas effect, oscillator displacement measurements compared between liquid-nitrogen-temperatures and those closer to the Debye temperature allow extraction of the phonon angular momentum. We predict a force change of 5 x 10^-7 N for a 1 mm³ MgZn ferrite sample, which should be easily measurable. Our oscillator, with a resonance at 13.3 kHz, has a thermal noise limit on the order of 10^-15 N/√Hz. With capacitive detection, we achieved a force noise of ~10^-8 N/√Hz, and interferometer detection has improved our force sensitivity to about 10^-11 N/√Hz. Competing effects are being minimized; for example, induced eddy current momentum can overwhelm the phonon effect for metallic ferromagnets.

[1] L. Zhang, and Q. Niu, Phys. Rev. Lett. 112, 085503 (2014)