By using the stripline Microwave Vector-Network Analyser Ferromagnetic Resonance and Pulsed Inductive Microwave Magnetometry spectroscopy techniques, we study a strong coupling regime of magnons to microwave photons in the planar geometry of a lithographically formed split-ring resonator (SRR) loaded by a single-crystal epitaxial yttrium-iron-garnet (YIG) film. Strong anti-crossing of the photon modes of SRR and of the magnon modes of the YIG film is observed in the applied-magnetic-field resolved measurements. The coupling strength extracted from the experimental data reaches 9% at 3 GHz.Theoretically, we propose an equivalent circuit model of the SRR loaded by a magnetic film. This model follows from the results of our numerical simulations of the microwave field structure of the SRR and of the magnetisation dynamics in the YIG film driven by the microwave currents in the SRR. The equivalent-circuit model is in good agreement with the experiment. It provides simple physical explanation of the process of mode anti-crossing.Our findings are important for future applications in microwave quantum photonic devices as well as in nonlinear and magnetically tuneable metamaterials exploiting the strong coupling of magnons to microwave photons.

We report the experimental demonstration of an abnormal, opposite anti-crossing effect in a photon-magnon-coupled system that consists of an Yttrium Iron Garnet film and an inverted pattern of split-ring resonator structure (noted as ISRR) in a planar geometry. It is found that the normal shape of anti-crossing dispersion typically observed in photon-magnon coupling is changed to its opposite anti-crossing shape just by changing the position/orientation of the ISRR's split gap with respect to the microstrip line axis along which ac microwave currents are applied. Characteristic features of the opposite anti-crossing dispersion and its linewidth evolution are analyzed with the help of analytical derivations based on electromagnetic interactions. The observed opposite anti-crossing dispersion is ascribed to the compensation of both intrinsic damping and coupling-induced damping in the magnon modes. This compensation is achievable by controlling the relative strength and phase of oscillating magnetic fields generated from the ISRR's split gap and the microstrip feeding line. The position/orientation of an ISRR's split gap provides a robust means of controlling the dispersion shape of anti-crossing and its damping in a photon-magnon coupling, thereby offering more opportunity for advanced designs of microwave devices. a) Correspondence and requests for materials should be addressed to S.-K. K sangkoog@snu.ac.kr

We experimentally demonstrate strongly enhanced coupling between excited magnons in an Yttrium Iron Garnet (YIG) film and microwave photons in an inverted pattern of split-ring resonator (noted as ISRR). The anti-crossing effects of the ISRR’s photon mode and the YIG’s magnon modes were found from |S21|-versus-frequency measurements for different strengths and directions of externally applied magnetic fields. The spin-number-normalized coupling strength (i.e. single spin-photon coupling) was determined to 0.194 Hz ( = 90 MHz) at 3.7 GHz frequency. Furthermore, we found that additional fine features in the anti-crossing region originate from the excitation of different spin-wave modes (such as the magnetostatic surface and the backward-volume magnetostatic spin-waves) rather than the Kittel-type mode. These spin-wave modes, as coupled with the ISRR mode, modify the anti-crossing effect as well as their coupling strength. An equivalent circuit model very accurately reproduced the observed anti-crossing effect and its coupling strength variation with the magnetic field direction in the planar-geometry ISRR/YIG hybrid system. This work paves the way for the design of new types of high-gain magnon-photon coupling systems in planar geometry.

Yttrium iron garnet (YIG:Y3Fe5O12) thin films were grown on (111) gadolinium gallium garnet (Gd3Ga5O12, GGG) substrates using pulsed-laser deposition under several different deposition and annealing conditions. X-ray diffraction measurements revealed that the crystallographical orientation of the YIG films is pseudomorphic to and the same as that of the GGG substrate, with a slight rhombohedral distortion along the surface normal. Furthermore, X-ray reciprocal space mapping evidenced that in-situ annealed YIG films during film growth are under compressive strain, whereas ex-situ annealed films have two different regions under compressive and tensile strain. The saturation magnetization (4πMS) of the films was found to vary, according to the deposition conditions, within the range of 1350 to 1740 G, with a very low coercivity of HC < 5 Oe. From ferromagnetic resonance (FMR) measurements, we estimated the effective saturation magnetization (4πMeff) to be 1810 to 2530 G, which are larger than that of single crystalline bulk YIG (∼1750 G). Such high values of 4πMeff are attributable to the negative anisotropy field (HU) that increases in size with increasing compressive in-plane strain induced in YIG films. The damping constant (αG) of the grown YIG films was found to be quite sensitive to the strain employed. The lowest value of αG obtained was 2.8 × 10−4 for the case of negligible strain. These results suggest a means of tailoring HU and αG in the grown YIG films by the engineering of strain for applications in spintronics and magneto-optical devices.