Elucidating magnetic structure with optical dopants: erbium-doped Gd$_2$SiO$_5$

Abstract

The narrowness of the optical transitions of rare-earth-ion dopants makes them highly sensitive probes of their environment. We measured the optical transitions Er$^{3+}$ dopants to determine the previously unknown magnetic ordering of Gd$_{2}$SiO$_{5}$ -- a promising host for quantum applications of rare-earth dopants. By measuring the transitions' magnetic-field dependence we determined an antiferromagnetic ordering with spins oriented along or slightly canted from the crystal's $a^*$ axis. The optical transitions are narrower than the coupling to gadolinium spins revealing information about the coupling strengths. We further optically measured a N\'eel temperature of $1.86\pm0.01_\mathrm{stat.}\pm0.07_\mathrm{syst.}$ K, and assembled a phase diagram in applied field and temperature showcasing a triple point where two gadolinium sites order semi-independently from each other. At high applied field the erbium dopants show long optical coherence times up to 0.4 ms at 3 T; at low fields these are probably limited by three low-frequency magnon modes below 10 GHz, observed directly. This study can be used to benchmark a method of magnetic structure determination.