Hyperfine interactions of $\text{Er}^{3+}$ ions in $\text{Y}_2\text{SiO}_{5}$: electron paramagnetic resonance in a tunable microwave cavity

Abstract

The hyperfine structure of the ground state of erbium doped yttrium orthosilicate is analyzed with the use of electron paramagnetic resonance experiments in a tunable microwave resonator. This work was prompted by the disagreement between the measurements made in zero magnetic field [Phys. Rev. B, 94, 075117, (2016)] and a previously published spin Hamiltonian, which is derived from standard EPR measurements at 9.5 GHz [Phys. Rev. B, 74, 214409, (2006)]. The ability to vary magnetic field strength, resonator frequency, and the orientation of our sample enabled us to monitor how the frequencies of hyperfine transitions change as a function of a vector magnetic field. Compared to [Phys. Rev. B, 74, 214409, (2006)], we arrived at a different set of spin Hamiltonian parameters, which are also broadly consistent with their data. We discuss the reliability of our new spin Hamiltonian parameters to make predictions outside the magnetic field and frequency regimes of our data. We also discuss why it proved to be difficult to determine spin Hamiltonian parameters for this material, and present data collection strategies that improve the model reliability.