Research ArticleAPPLIED PHYSICS

Cavity magnomechanics

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Science Advances  18 Mar 2016:
Vol. 2, no. 3, e1501286
DOI: 10.1126/sciadv.1501286
  • Fig. 1 Device schematic and measurement setup.

    (A) Schematic of the device that consists of a three-dimensional copper cavity (only bottom half is shown) and a YIG sphere. The YIG sphere is placed near the maximum microwave magnetic field (along the y direction) of the cavity TE011 mode. A uniform external magnetic field (H) is applied along the z direction to bias the YIG sphere for magnon-photon coupling. (B) Optical image of the highly polished 250-μm-diameter YIG sphere that is glued to a 125-μm-diameter supporting silica fiber. The gluing area is minimized to reduce the contact damping to the phonon mode. Scale bar, 100 μm. (C) Simulated mechanical displacement (u) of the S1,2,2 phonon mode in the YIG sphere that has the strongest magnomechanical interaction with the uniform magnon mode. (D) An intuitive illustration of the magnomechanical coupling. Top panel shows the uniform magnon excitation in the YIG sphere. Bottom panel illustrates how the dynamic magnetization of magnon (vertical black arrows) causes the deformation (compression along the y direction) of the YIG sphere (and vice versa), which rotates at the magnon frequency. The color scale represents the corresponding volumetric strain fields induced by the dynamic magnetization of magnon. In our experiments, we excite the magnon at gigahertz frequencies and the phonon mode is actuated parametrically, that is, at the beating frequencies (megahertz) of two magnon modes. (E) Schematic illustration of the measurement setup. VNA, vector network analyzer; SRC, microwave source for driving; AMP, microwave amplifier; BPF, bandpass filter; PWR, microwave power meter; CIR, circulator; BSF, bandstop filter; DUT, device under test. (F) Black curve: Cavity reflection spectrum when magnon is on-resonance with the cavity photon mode. The two dips represent the maximum hybridized modes Embedded Image. Red and blue vertical lines indicate the applied drive and probe, respectively. The probe is swept across the hybrid mode resonance. Δsd, two-photon (probe-drive) detuning; Δd–, drive-resonance detuning.

  • Fig. 2 Analysis of the phonon modes and magnetostrictive coupling strengths.

    (A) Simulated displacement profiles of the low-order phonon modes in the YIG sphere (with a small supporting fiber). Embedded Image represents the spheroidal mode with a radial mode number of 1, an angular mode number of l, and an azimuthal mode number of ma. (B) Theoretical prediction of the magnomechanical coupling strength as a function of YIG sphere diameter for the S1,2,0 (black) and S1,2,2 modes (red and blue, corresponding to different bias field directions). Solid lines are numerical calculations, whereas symbols are analytical fittings. (C) Phonon mode frequency as a function of the YIG sphere diameter. Solid lines are the theoretical calculations, showing an inverse proportional dependence, whereas red circles are the measurement results. (D) Simulated phonon linewidth due to clamping loss as a function of the supporting fiber diameter for the Embedded Image modes. Black dot indicates the experiment parameter, showing an anchor loss–limited linewidth of 20 Hz.

  • Fig. 3 Tunable MMIT/MMIA.

    (A) Measured reflection spectra near the lower hybrid mode  as a function of the two-photon detuning Δsd for a series of different bias magnetic fields. The broad dip corresponds to the lower hybrid mode resonance, whose line shape changes with bias magnetic field because of the change in the ratio between magnon and photon components. A strong (26 dBm) microwave drive is red-detuned with a fixed driving frequency ωd. A Fano-like narrow resonance line shows up inside the hybrid mode, which turns into a Lorentzian transparency peak when Δd– = –ωb. Zoom-in shows detailed spectra of the magnomechanically induced resonances [shaded area in (A)]. (B) Measured reflection spectra near the upper hybrid mode Â+ with a blue-detuned strong drive (22 dBm) for various bias magnetic fields. When Δd+ = ωb, the magnomechanically induced narrow resonance shows up as a Lorentzian absorption dip. Zoom-in shows detailed spectra of the shaded area in (B). (C) Reflection spectra of the hybrid magnon-photon modes at various bias magnetic fields. The crosses indicate the drive frequency and bias magnetic field used for each data point in (D). (D) The magnomechanical cooperativity as a function of bias magnetic field. For each measurement, the microwave drive is detuned from the hybrid mode by Δ = ±ωb, while the probe is swept across the hybrid mode resonance. Red squares (blue circles) are for the red (blue) detuning situation. Solid lines in (D) and in the zoom-in of (A) and (B) are theoretical calculations using only a single-fitting parameter gmb.

  • Fig. 4 Enhanced magnomechanical coupling in the triple-resonant system.

    (A) MMIT signal for a red-detuned drive at various driving powers. (B) MMIA and MMPA signal for a blue-detuned drive at various driving powers. (C) The linewidth of the magnomechanically induced resonance as a function of the drive power. (D) Magnomechanical interaction–modified on-resonance reflectivity of the hybrid mode as a function of the drive power. Shaded area indicates the instable regime. Inset: Measured power of the Stokes sideband of the driving signal. The threshold behavior indicates the onset of phonon lasing. (E) Magnomechanical parametric gain as a function of the drive power in an overcoupled hybrid system. Inset: Measured reflection spectrum that shows a 25-dB gain. In the main panels of (C) to (E), blue circles (red squares) are for the blue (red) detuning and solid lines are theoretical calculations.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/3/e1501286/DC1

    Magnomechanical interaction through magnetostrictive forces

    Magnon modes of the YIG sphere

    Coherent cavity magnomechanical coupling

    Thermal instability

    Table S1. Definitions and meanings of symbols.

    Fig. S1. Magnetically induced transparency/absorption at various drive frequencies.

    Fig. S2. Magnomechanical resonance line shape and parameter space diagram.

    Fig. S3. Cascade transparency/absorption.

    References (4352)

  • Supplementary Materials

    This PDF file includes:

    • Magnomechanical interaction through magnetostrictive forces
    • Magnon modes of the YIG sphere
    • Coherent cavity magnomechanical coupling
    • Thermal instability
    • Table S1. Definitions and meanings of symbols.
    • Fig. S1. Magnetically induced transparency/absorption at various drive
      frequencies.
    • Fig. S2. Magnomechanical resonance line shape and parameter space diagram.
    • Fig. S3. Cascade transparency/absorption.
    • References (43–52)

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    Files in this Data Supplement:

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