Loop-gap resonators achieving strong magnon-photon coupling in magnetic insulator thin films

TL;DR

This work introduces a three-dimensional modular loop-gap resonator (LGR) engineered to maximize the magnetic filling factor for coupling to ultrathin magnetic-insulator films, enabling strong magnon–photon coupling at room temperature with a 75 nm YIG film. The authors develop both lumped-element and finite-element models to optimize resonance frequency, quality factor, and magnetic vacuum field, achieving a pronounced coupling strength $g$ and cooperativity $\mathcal{C}>1$. They further demonstrate field-differential magneto-spectroscopy to isolate the magnetically coupled mode from parasitic, uncoupled modes, and show coupling to standing spin-wave modes across the film thickness, including perpendicular standing spin-wave (PSSW) modes. The modular resonator design enables scalable, tunable experiments with epitaxial thin films and multilayers, with potential for cryogenic upgrades to reach very high cooperativities and to explore magnon-based quantum technologies and spintronic applications.

Abstract

Magnon-photon hybrid systems consisting of a three-dimensional electromagnetic resonator and a bulk magnetic insulator constitute the standard experimental platform in cavity magnonics. Here, we demonstrate a modular loop-gap resonator design optimized to couple with thin films of magnetic insulators. We achieve the strong-coupling regime using this loop-gap resonator coupled to a 75~nm-thick epitaxial film of yttrium iron garnet at room temperature. We further show how to perform field-differential spectroscopy of the hybrid magnon-photon system, which eliminates the unwanted signal from other loop-gap modes uncoupled to the magnetic film. In addition to the uniform ferromagnetic resonance mode, the loop-gap resonator enables an hybridization with the standing spin-wave modes forming across the thickness of the film. Our approach unlocks the use of epitaxial films and multilayers of magnetic insulators to tune the magnon band structure in cavity magnonics experiments.

Figures (7)

• Figure 1: (a) Photographs of the resonator system: assembled LGR and top half of cylindrical box next to bottom half of cylindrical box; detail of the loops and gaps; coupling antennas with screw system. (b) Schematic representation of the LGR designed in this work: the $E$-field (orange) is mostly confined in the gaps, as shown in zoomed-in view; the $B$-field (purple) is concentrated in the sample loop and is residual in the return-flux loops used for external coupling. (c) Sketch of current lines, and equivalent circuit model of the LGR as symmetrical lumped $R_0$, $L_0$ and $C_0$. (d) Intensity map of the coupling field $B\textsubscript{vac}$ in the sample plane ($yz$), as determined by finite-element simulations. The black rectangles locate the two gaps.
• Figure 2: Intensity maps of the coupling field $B\textsubscript{vac}$ in the sample plane ($yz$), as determined by finite-element simulations, for (a) an LGR same as in Fig. \ref{['fig:01']}d, but $l=25.58mm$, (b) an LGR made of 5 identical modules with $l=5.1mm$, each separated by 0.02mm. The black rectangles locate the two gaps, the dashed lines separate the different LGR modules.
• Figure 3: Microwave transmission $\left|{S_{21}}\right|$ for both LGR1 and LGR2. Blue and orange solid lines correspond to the measured $\left|{S_{21}}\right|$ for the loaded LGR1 and LGR2, respectively, without magnetic field applied. The horizontal dotted line at -6dB represents the transmission at critical coupling conditions. Black dashed lines correspond to the fitted cavity transmission for LGR1 and LGR2. For LGR1, the fit line is decomposed into the contributions from the magnetically coupled main LGR mode (LGR1 magn.) and from the parasitic mode near 12GHz (LGR1 paras.), whose complex sum provides the fitted $S_{21}$.
• Figure 4: Microwave transmission of the loaded LGRs with 75nm-thick YIG film. (a) Amplitude and (b) phase of $S_{21}$ as a function of in-plane field $B_{\rm{y}}$ and measurement frequency $f$, for LGR1 (hollow upper cylindrical box). (c) Amplitude and (d) phase of $S_{21}$ as a function of $B_{\rm{y}}$ and $f$, for LGR2 (cylindrical box with separator). $B_{\rm{m}}$ is the field required to excite the Kittel mode of the film at the cavity resonant frequency.
• Figure 5: Field-derivative microwave transmission of the loaded LGRs with 75nm-thick YIG film. (a) Real and (b) imaginary parts of $\partial{}S_{21}/\partial{}B$ as a function of in-plane field $B_{\rm{y}}$ and measurement frequency $f$, for LGR1 (hollow upper cylindrical box). (c) Real and (d) imaginary parts of $\partial{}S_{21}/\partial{}B$ as a function of $B_{\rm{y}}$ and $f$, for LGR2 (cylindrical box with separator). The sinusoidal modulation field is 40µT.