Dispersive readout of ferromagnetic resonance for strongly coupled magnons and microwave photons

We demonstrate the dispersive measurement of ferromagnetic resonance in a yttrium iron garnet sphere embedded within a microwave cavity. The reduction in the longitudinal magnetization at resonance is measured as a frequency shift in the cavity mode coupled to the sphere. This measurement is a result of the intrinsic nonlinearity in magnetization dynamics, indicating a promising route towards experiments in magnon cavity quantum electrodynamics.

Figure 1

(a) Schematic of the semirigid coaxial resonator with YIG sphere inside. (b) Circuit equivalent diagram of the measurement setup and cavity. The probe tone ${\omega }_p$ and mixing are provided by a vector network analyzer (blue) while FMR drive tone ${\omega }_d$ is from a separate microwave source (red). (c) Transmission $|S_{21}|$ through cavity as a function of magnetic field, demonstrating the strong coupling of the uniform FMR mode (blue arrow) to the $\lambda /2$ cavity mode (red arrow). In addition, a number of other spin wave modes in the sphere couple to the cavity; the strongest is indicated by the green arrow. Inset shows a reference map of the measurement region over the modes of the system (only the uniform FMR mode is shown).

Figure 2

Dispersive measurement. (a) Phase shift of the probe tone ${\omega }_p$ $(-10$ dBm) at the resonant frequency of the cavity as a function of the drive frequency ${\omega }_d$, for input drive power 25 dBm (off resonance with the cavity a large amount of power is reflected). The field is fixed at $\mu H_0=1800$ G. A slow time-dependent phase drift and field-independent background have been subtracted. The dashed line is a fit to the square of a Lorentzian [square of Eq. (2)], appropriate since we are sensitive to the square of the transverse magnetization. The fit gives the magnon decay rate $\gamma /2\pi =6$ MHz. (b) Phase shift as a function of magnetic field and drive frequency. Probe frequency tracks the resonance frequency of the cavity, $\approx 3.55$ GHz, as a function of field.

Figure 3

Dependence of measurements on detuning between cavity and FMR mode frequencies. (a) Change in cavity frequency due to FMR, taken from peak amplitude in phase change plotted in Fig. 2. (b) Change in cavity frequency due to the equilibrium susceptibility of the sphere from that when $\chi =0$. The value of ${\omega }_{c}0$ is obtained from the offset in the $1/\Delta$ fit. (c) For reference, the calculated general form of dispersive and dissipative susceptibility of the sphere as a function of detuning from the FMR resonance, from Eqs. (1) and (2), for low damping $\alpha$.

Figure 4

Percentage change in longitudinal magnetization $M_z$ as a function of detuning.

Figure 5

(a) Dependence of the cavity frequency shift on the FMR driving microwave power at fixed static magnetic field ${\mu }_0{H}_0=180$ mT. A linear fit to the data is shown. (b) Power dependence of the cavity frequency shift as a function of probe power at the cavity resonance frequency for the same static field.