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 Er³⁺:Y₂SiO₅, 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 Er³⁺:CaWO₄, Er³⁺:LiNbO₃ and Nd³⁺:Y₂SiO₅ at different concentrations.