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<p>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<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(^3\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> MgZn ferrite sample, in fair agreement with theoretical predictions. Our oscillator, with a thermal noise limit on the order of 10<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(^{-12}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mo>-</mo> <mn>12</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> N/<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sqrt{\text {Hz}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msqrt> <mtext>Hz</mtext> </msqrt> </math></EquationSource> </InlineEquation>, 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.</p>

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

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  • 发表日期：

    2026年7月29日

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  • Matt Dwyer,
  • Devan Shoemaker,
  • John T. Markert

摘要

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 \(^3\) 3 MgZn ferrite sample, in fair agreement with theoretical predictions. Our oscillator, with a thermal noise limit on the order of 10 \(^{-12}\) - 12 N/ \(\sqrt{\text {Hz}}\) 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.