Spin-wave excitation and critical angles in a hybrid photon-magnon-coupled system

We studied strongly enhanced excitations of magnetostatic spin-waves in a hybrid magnon-photon-coupled system consisting of an inverted split-ring resonator and an yttrium iron garnet film. The backward-volume magnetostatic wave, magnetostatic surface wave, forward-volume magnetostatic wave modes, as well as multiple mixed modes were observed according to the direction of externally applied magnetic fields with respect to the spin-wave propagation direction. From experimental measurements, we found that there exist certain characteristic angles, which is to say, critical angles (theta(c), phi(c)), whereby the group velocity of the excited spin-wave modes reaches zero, along with a single ferromagnetic resonance peak. Furthermore, we analytically derived the critical angles as sin theta(c) = (H-eff/H){2 - (1 + mu M-0(s)=H-eff)sin(2) phi(c)}(-1/2), where H-eff is the effective magnetic-field strength, H the externally applied field strength, and mu M-0(s) is the saturation magnetization. This analytical form is in quantitative agreement with estimations from experimentally observed spin-wave modes. This work not only provides a better understanding of multiple-mode spin-wave excitations in given field directions with the help of photon-magnon coupling, but also offers better coupling controllability based on the change of the external magnetic field direction. Published under license by AIP Publishing.