Strong Coupling between Magnons and Microwave Photons in On-Chip Ferromagnet-Superconductor Thin-Film Devices

We demonstrate strong magnon-photon coupling of a thin-film Permalloy device fabricated on a coplanar superconducting resonator. A coupling strength of 0.152 GHz and a cooperativity of 68 are found for a 30-nm-thick Permalloy stripe. The coupling strength is tunable by rotating the biasing magnetic field or changing the volume of Permalloy. We also observe an enhancement of magnon-photon coupling in the nonlinear regime of the superconducting resonator, which is attributed to the nucleation of dynamic flux vortices. Our results demonstrate a critical step towards future integrated hybrid systems for quantum magnonics and on-chip coherent information transfer.

Figure 1

(a) The microwave circuit of a NbN superconducting resonator with a Py stripe. The green (blue) and red boxes show the capacitive coupling to the external circuit and the Permalloy stripe, respectively. (b) Microwave power transmission of an unloaded superconducting resonator measured at $P_{\mathrm{in}}=-55\mathrm{dBm}$ after zero-field cooling. (c) Hysteresis evolution of ${\omega }_p$ for (b). (d) Ferromagnetic resonance spectra of a Py stripe measured at 1.4 K [38], with the linewidth at ${\omega }_p$ marked by arrows.

Figure 2

Characterization of a 30-nm Py stripe ($L=900\mu \mathrm{m}$) coupled to a NbN superconducting resonator, measured at $P_{\mathrm{in}}=-55\mathrm{dBm}$ and $\theta =0°$. (a)–(b) Microwave transmission spectra $S_{21}=10\log (P_{\mathrm{out}}/P_{\mathrm{in}})$ of (a) the unloaded resonator and (b) the resonator loaded with the Py stripe. (c) Extracted ${\omega }_{mp}$ and (d) $\mathrm{\Delta }{\omega }_{mp}$ from (a)–(b). In (c) the photon modes have been shifted by $-0.12\mathrm{GHz}$ to match the hybrid modes. Dashed lines denote the magnon modes. Solid blue and red curves denote the fits.

Figure 3

Tunable magnon-photon coupling. (a)–(d) Microwave transmission spectra of the NbN superconducting resonator loaded with a Py(30 nm) stripe with $L=900\mu \mathrm{m}$, from $\theta =22.5°$ to 90°. (e) Extracted coupling strength $g$ as a function of $\theta$ with the fit. (f) $\mathrm{\Delta }{\omega }_p$ as a function of ${\mu }_0{H}_B$ with the dashed fits. (g)–(i) Transmission spectra for different Py stripes: (g) $t=50\mathrm{nm}$, $L=900\mu \mathrm{m}$; (h) $t=30\mathrm{nm}$, $L=900\mu \mathrm{m}$; (i) $t=30\mathrm{nm}$, $L=300\mu \mathrm{m}$. (j) Extracted $g$ as a function of $\sqrt{V/V_0}$, where $V_0$ denotes the volume of the Py(30 nm) stripe with $L=900\mu \mathrm{m}$. (k) $\mathrm{\Delta }{\omega }_p$ as a function of ${\mu }_0{H}_B$, with the fitting curve also plotted.

Figure 4

Magnon-photon coupling in the nonlinear regime. (a) Nonlinear resonance line shapes from $P_{\mathrm{in}}=-15\mathrm{dBm}$ to $P_{\mathrm{in}}=5\mathrm{dBm}$ with a step of 2 dB for Py(50 nm) stripe with $L=900\mu \mathrm{m}$. (b) $P_{\mathrm{out}}/P_{\mathrm{in}}$ for $P_{\mathrm{in}}=-55$, $-5$, and 1 dBm. (c) Comparison of peak positions of the hybrid modes between $P_{\mathrm{in}}=1$ and $-55\mathrm{dBm}$.