Magnon Kerr effect in a strongly coupled cavity-magnon system

We experimentally demonstrate magnon Kerr effect in a cavity-magnon system where magnons in a small yttrium iron garnet (YIG) sphere are strongly but dispersively coupled to the photons in a three-dimensional cavity. When the YIG sphere is pumped to generate considerable magnons, the Kerr effect yields a perceptible shift of the cavity's central frequency and more appreciable shifts of the magnon modes. We derive an analytical relation between the magnon frequency shift and the drive power for the uniformly magnetized YIG sphere and find that it agrees very well with the experimental results of the Kittel mode. Our study paves the way to explore nonlinear effects in the cavity-magnon system.

Figure 1

Schematic of the experiment setup. The 3D cavity is placed in the uniform magnetic field created by a superconducting magnet. Ports 1 and 2 are used for transmission spectroscopy, and port 3 is for driving the YIG sphere via a superconducting microwave line with a loop antenna at its end. The total attenuation of the input port is 99 dB. The right part shows the magnetic-field distribution of the cavity-mode ${\mathrm{TE}}_{102}$. The bias magnetic field, the drive magnetic field, and the magnetic field of the ${\mathrm{TE}}_{102}$ mode are mutually perpendicular at the site of the YIG sphere where the magnetic field of the ${\mathrm{TE}}_{102}$ mode is maximal.

Figure 2

(a) Transmission spectrum for the normal-mode splitting measured as a function of the bias magnetic field and the probe microwave frequency. The large anticrossing indicates strong coupling between the Kittel mode and the cavity-mode ${\mathrm{TE}}_{102}$. The small splittings are due to the MS modes coupled with the cavity mode. (b) Transmission spectrum at three values of the bias magnetic field. The curves are offset vertically for clarity.

Figure 3

(a) Central frequency shift of the cavity-mode ${\mathrm{TE}}_{102}$ when the drive field is on (red curve) and off (black curve), respectively. (b) Transmission spectrum of the cavity measured as a function of the drive-field frequency. The blue arrow indicates the response of the Kittel mode, whereas the orange and purple arrows indicate the MS modes 1 and 2, respectively. (c) Transmission spectrum of the cavity measured as a function of the drive frequency by successively increasing the driving power. The probe field is fixed at 10.1035 GHz in both (b) and (c).

Figure 4

(a) Frequency shift of the Kittel mode (blue square) and the central frequency shift of the cavity mode ${\mathrm{TE}}_{102}$ (red circle) measured at various values of the drive power. The blue fitting curve for the Kittel mode is obtained using Eq. (6). (b) Frequency shifts of MS mode 1 (orange up-triangle) and MS mode 2 (purple down-triangle) measured at various values of the drive power. The corresponding orange and purple fitting curves also are obtained using Eq. (6). The frequency shifts of the Kittel mode, MS mode 1, and MS mode 2 are here referenced from 9.5526, 9.4758, and 9.6174 GHz, respectively.

Figure 5

(a) The 3D cavity, which is made of oxygen-free copper and plated with gold. (b) The drive antenna, which is connected to a superconducting microwave line that goes into the cavity via port 3. (c) The small YIG sphere, which has a diameter of 1 mm and is placed near the antenna and glued on the inner wall of the cavity.