Optical study of the anisotropic erbium spin flip-flop dynamics

We investigate the erbium flip-flop dynamics as a limiting factor of the electron spin lifetime and more generally as an indirect source of decoherence in rare-earth doped insulators. Despite the random isotropic arrangement of dopants in the host crystal, the dipolar interaction strongly depends on the magnetic field orientation following the strong anisotropy of the \(g\)-factor. In Er\(^{3+}\):Y\(_2\)SiO\(_5\), we observe by transient optical spectroscopy a three orders of magnitude variation of the erbium flip-flop rate (10ppm dopant concentration). The measurements in two different samples, with 10ppm and 50ppm concentrations, are well-supported by our analytic modeling of the dipolar coupling between identical spins with an anisotropic \(g\)-tensor. The model can be applied to other rare-earth doped materials. We extrapolate the calculation to Er\(^{3+}\):CaWO\(_4\), Er\(^{3+}\):LiNbO\(_3\) and Nd\(^{3+}\):Y\(_2\)SiO\(_5\) at different concentrations.