Gating ferromagnetic resonance of magnetic insulators by superconductors via modulating electric field radiation

We predict that ferromagnetic resonance in an insulating magnetic film with in-plane magnetization radiates electric fields polarized along the magnetization with opposite amplitudes at two sides of the magnetic insulator, which can be modulated strongly by adjacent superconductors. With a single superconductor adjacent to the magnetic insulator, this radiated electric field is totally reflected with a $\pi$-phase shift, which thereby vanishes at the superconductor side and causes no influence on the ferromagnetic resonance. When the magnetic insulator is sandwiched by two superconductors, this reflection becomes back and forth, so the electric field exists at both superconductors that drives the Meissner supercurrent, which in turn shifts efficiently the ferromagnetic resonance. We predict an ultrastrong coupling between magnons in the yttrium iron garnet and Cooper-pair supercurrent in NbN with a frequency shift achieving tens of percent of the bare ferromagnetic resonance.

Figure 1

Snapshots of magnetization-radiated electric fields in different heterostructure configurations. The electric field changes linearly across the thickness of the ferromagnetic insulating film. (a) The electric field amplitude is opposite at two sides of the thin magnetic insulator. (b) When fabricating a superconductor thin film on a ferromagnetic insulator, the electric field is suppressed to vanish at the superconductor side but enhanced at the other side of the magnet. When the magnet is sandwiched by two superconductors, the electric field exists but differs at both sides in both symmetric (c) and asymmetric (d) configurations.

Figure 2

S(1)-FI-S(2) heterostructure. The thickness of superconductors above and beneath the thin ferromagnetic insulator of thickness $2d_F$ is $d_S$ and $d_S^{\prime }$, respectively. The driven supercurrents ${\mathbf{J}}_s$ and ${\mathbf{J}}_s^{\prime }$ by FMR flow oppositely along the magnetization direction.

Figure 3

Electric field radiated from the surface magnetization current at the two surfaces of the magnetic insulator.

Figure 4

Radiated electric field of the FI-S heterostructure.

Figure 5

Reflection coefficient $\mathrm{Re}(\mathcal{R}$) as a function of the superconductor thickness $d_S$ with different London's penetration depth $\lambda =100$ nm and $1\mu \mathrm{m}$. We take the frequency $\omega =2\pi \times 4$ GHz.

Figure 6

Radiated electric field of the S-FI-S heterostructure.

Figure 7

Distribution of electric fields in symmetric $d_S=d_S^{\prime }=60$ nm (a) and asymmetric $d_S^{\prime }=2d_S=120$ nm (b) S-FI-S heterostructure. The thickness of the ferromagnetic film $2d_F=120$ nm and London's penetration depth $\lambda (T=0.5T_c)=87.8$ nm.

Figure 8

FMR spectra with the excitation field ${\mu }_0\tilde{H}=0.01$ mT. In (a) and (b), we use the temperature $T=0.5T_c=5.5$ K. (a) Plots the excited electric field amplitude in (one of) the superconductors in the symmetric S-FI-S heterostructure. The amplitude of the resonance electric field $E_z\sim 14$ V/m. (b) The excited amplitudes of the magnetization $M_y$ with and without two adjacent superconductors. $M_x\approx 0.6M_y$ and $0.5M_y$ with and without the superconductors. The frequency shift is as large as $2\pi \times 1.6\mathrm{GHz}\sim {\tilde{\omega }}_{\mathrm{K}}/2$. (c) The temperature dependence of FMR frequency ${\omega }_{\mathrm{K}}$ by solutions with the full calculation (black line) and quasistatic approximation (dashed line). The bare FMR frequency ${\tilde{\omega }}_{\mathrm{K}}=2\pi \times 3.2$ GHz.