Strong Coupling between Microwave Photons and Nanomagnet Magnons

Coupled microwave photon-magnon hybrid systems offer promising applications by harnessing various magnon physics. At present, in order to realize high coupling strength between the two subsystems, bulky ferromagnets with large spin numbers are utilized, which limits their potential applications for scalable quantum information processing. By enhancing single spin coupling strength using lithographically defined superconducting resonators, we report high cooperativities between a resonator mode and a Kittel mode in nanometer thick Permalloy wires. The on-chip, lithographically scalable, and superconducting quantum circuit compatible design provides a direct route towards realizing hybrid quantum systems with nanomagnets, whose coupling strength can be precisely engineered and dynamic properties can be controlled by various mechanisms derived from spintronic studies.

Figure 1

(a) Photo of a CPW resonator device with $100\mu \mathrm{m}\times 8\mu \mathrm{m}\times 50\mathrm{nm}$ $\mathrm{MgO}/\mathrm{Py}/\mathrm{Pt}$ stripe deposited at the center of the signal line. The distance $l=12\mathrm{mm}$ between the two open gaps at the ends of signal line defines the fundamental resonant frequency to be 4.96 GHz. (b) Microwave transmissions at 1.5 K with zero applied field before and after Py is deposited, exhibiting resonance signals with quality factors 1570 and 760, respectively. With Py, the resonator mode is blue detuned due to residual coupling to the magnon mode. (c) Microwave transmission as a function of frequency and in-plane magnetic field at 1.5 K for a sample with $500\mu \mathrm{m}\times 8\mu \mathrm{m}\times 50\mathrm{nm}$ Py showing the characteristic anticrossing of magnon-photon coupling. [The data from (b) and (c) are taken from different samples.] (d) Theoretical microwave transmission spectrum calculated using input-output theory with parameters obtained from the experiment.

Figure 2

(a) Image of a low-impedance lumped element resonator device with $40\mu \mathrm{m}\times 2\mu \mathrm{m}\times 10\mathrm{nm}$ $\mathrm{MgO}/\mathrm{Py}/\mathrm{Ta}$ stripe deposited at the center of the $4\mu \mathrm{m}$ wide inductive wire. (b) (Left panels) Microwave transmission of the low-impedance resonator obtained from experiment and simulation. Two modes are observed as transmission minima due to photon absorption from the signal line. (Right panels) Simulation of current density distribution of the resonant modes, respectively. Red and blue areas indicate regions with strong and weak current densities, respectively. The first harmonic mode exhibits large current density at the central inductive wire which enhances coupling. (c) Microwave transmission as a function of frequency and in-plane magnetic field at 1.5 K. ${\mu }_0{M}_s=1.1\mathrm{T}$ and $g/2\pi =74.5\mathrm{MHz}$ are determined from the fitting shown in dashed line. Minimum transmission shows up under resonant conditions.

Figure 3

Magnon-photon coupling strength $g$ as a function of magnetic volume and spin number. The dashed lines represent fittings of the scaling rule $g=g_s\sqrt{N}$. The single spin coupling strength for two resonators in this Letter are determined to be $g_s^{\mathrm{CPW}}/2\pi =18\mathrm{Hz}$ and $g_s^{\mathrm{LE}}/2\pi =263\mathrm{Hz}$ in CPW resonators and lumped element resonators, respectively.