Angular dependant micro-ESR characterization of a locally doped Gd$^{3+}$:Al$_{2}$O$_{3}$ hybrid system for quantum applications

Rare-earth doped crystals interfaced with superconducting quantum circuitry are an attractive platform for quantum memory and transducer applications. Here we present a detailed characterization of a locally implanted Gd$^{3+}$ in Al$_{2}$O$_{3}$ system coupled to a superconducting micro-resonator, by performing angular dependent micro-electron-spin-resonance (micro-ESR) measurements at mK temperatures. The device is fabricated using a hard Si$_{3}$N$_{4}$ mask to facilitate a local ion-implantation technique for precision control of the dopant location. The technique is found not to degrade the internal quality factor of the resonators which remains above $10^{5}$ (1). We find the measured angular dependence of the micro-ESR spectra to be in excellent agreement with the modelled Hamiltonian, supporting the conclusion that the dopant ions are successfully integrated into their relevant lattice sites whilst maintaining crystalline symmetries. Furthermore, we observe clear contributions from individual microwave field components of our micro-resonator, emphasising the need for controllable local implantation. $1)$ Wisby et al. Appl. Phys. Lett. \textbf{105}, 102601 (2014)