Superhyperfine induced photon-echo collapse of erbium in Y2SiO5

We investigate the decoherence of ${\mathrm{Er}}³⁺$ in ${\mathrm{Y}}₂\mathrm{Si}{\mathrm{O}}₅$ at low magnetic fields using the photon-echo technique. We reproduce accurately a variety of the decay curves with a unique coherence time by considering the so-called superhyperfine modulation induced by a large number of neighboring spins. There is no need to invoke any characteristic time of the spin fluctuations to reproduce very different decay curves. The number of involved nuclei increases when the magnetic is lowered. The experiment is compared with a model associating 100 surrounding ions with their exact positions in the crystal frame. We also derive an approximate spherical model (angular averaging) to interpret the main feature the observed decay curves close to zero field.