Coherent long-range transfer of angular momentum between magnon Kittel modes by phonons

We report ferromagnetic resonance in the normal configuration of an electrically insulating magnetic bilayer consisting of two yttrium iron garnet (YIG) films epitaxially grown on both sides of a 0.5-mm-thick nonmagnetic gadolinium gallium garnet (GGG) slab. An interference pattern is observed and it is explained as the strong coupling of the magnetization dynamics of the two YIG layers either in phase or out of phase by the standing transverse sound waves, which are excited through a magnetoelastic interaction. This coherent mediation of angular momentum by circularly polarized phonons through a nonmagnetic material over macroscopic distances can be useful for future information technologies.

Figure 1

(a) Schematic and picture of the ferromagnetic resonance (FMR) setup. A butterfly-shaped stripline resonator [31] with 0.3-mm-wide constriction is in contact with the bottom layer of the YIG1($d=200$ nm)$|\text{GGG}$($s=0.5$ mm)$|\text{YIG2}$($d=200$ nm) “dielectric spin-valve” stack. The microwave antenna can be tuned in or out of its fundamental resonance (5.11 GHz) as shown in the reflectivity spectrum (b). (c) Schematic of the coupling between the top (red) and bottom (blue) YIG layers by the exchange of coherent phonons: The magnetic precession $m^{+}$ generates a circular shear deformation $u^{+}$ of the lattice that can be tuned into a coherent motion of all fields. Constructive/destructive interference between the dynamics of the two YIG layers occurs for even/odd mode numbers $n$ causing (d) a contrast $\mathrm{\Delta }$ in the absorbed microwave power ($P_{\text{abs}}$) between tones separated by half a phonon wavelength. (e) Density plot of the spectral modulation of $P_{\text{abs}}$ produced by Eq. (1) when magnetic bilayers are strongly coupled to coherent phonon modes. The orange/green dots indicate the spectral position of the even/odd acoustic resonances.

Figure 2

(a) Microwave absorption spectra of a YIG(200 nm)$|\text{GGG}$(0.5 mm) crystal, revealing a periodic modulation of the intensity interpreted as the avoided crossing between the FMR mode (see blue arrow) at ${\omega }_1=\gamma {\mu }_0(H_0-M_1)$, and the $n\text{th}$ standing (shear) ${\mathrm{AW}}_{\text{n}}$ resonances across the total thickness (horizontal dashed lines in orange and green) at ${\omega }_n=n\pi v/(d+s)$. The right panels [(b)–(d)] show the intensity modulation for three different cuts (blue, magenta, and red) along the gyromagnetic ratio (i.e., parallel to the resonance condition). The solid lines in the four panels are fits by the oscillator model [cf. Eq. (1) with fit values in Table 1].

Figure 3

FMR spectroscopy of the $\text{YIG1}\left|\text{GGG}\right|\text{YIG2}$ trilayer. (a) is a transparent overlay of magnetic field sweeps for frequencies in the interval $5.101\pm 0.008$ GHz by 0.1-MHz steps. Dark lines reveal two acoustic resonances marked by orange and green dots. (b) and (c) show the frequency modulation of the FMR amplitude for respectively the bottom YIG1 layer and the top YIG2 layer, in which a contrast $\mathrm{\Delta }$ appears between neighboring acoustic resonances. The solid lines show the modulation predicted by Eq. (1).

Figure 4

(a) Frequency sweep at fixed field performed on the magnetic bilayer. The fine regular modulation within the FMR envelope is ascribed to the excitation of acoustic shear wave resonances. The acoustic pattern is enhanced in (b) by subtracting the FMR envelope emphasizing the constructive/destructive interferences of the even/odd acoustic resonances in the vicinity of the YIG2 FMR mode. (c) shows on a logarithmic scale the predicted modulation using the experimental parameters of Table 1. (d) shows on a linear scale the corresponding power absorbed by the top magnetic layer only.