The development of a new era of quantum devices requires an understanding of how paramagnetic dopants or impurity spins behave in crystal hosts. Here, we describe a spectroscopic technique which uses traditional electron spin resonance (ESR) combined with the measurement of a large population of electromagnetic whispering gallery modes. This allows the characterization of the physical parameters of paramagnetic impurity ions in the crystal at low temperatures. We present measurements of two ultrahigh-purity sapphires cooled to 20 mK in temperature, and determine the concentration of Fe${}^{3+}$ ions and their frequency sensitivity to a dc magnetic field. Our method is different from ESR in that it is possible to track the resonant frequency of the ion from zero applied magnetic field to any arbitrary value, allowing excellent measurement precision. This high precision reveals anisotropic behavior of the Zeeman splitting. In both crystals, each Zeeman component demonstrates a different $g$ factor.

• Received 29 October 2012

DOI:https://doi.org/10.1103/PhysRevB.87.094412