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arXiv:2603.12603

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

Luke S. Trainor, Masaya Hiraishi, J. -R. Soh, Jevon J. Longdell

cond-mat.str-elquant-phSubmitted Mar 13, 2026• Announced Mar 16, 2026• 0 citations
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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 Néel 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.

Comments
17 pages, 11 figures

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In many important situations, the dominant dephasing mechanism in cryogenic rare-earth-metal-ion--doped systems is due to magnetic field fluctuations from spins in the host crystal. Operating at a magnetic field where a transition has a zero first-order Zeeman (ZEFOZ) shift can greatly reduce this dephasing. Here we identify the location of transitions with a zero first-order Zeeman shift for optical transitions in Pr3+{}^{3+}3+:YAG and for spin transitions in Er3+{}^{3+}3+:Y2{}_{2}2​SiO5{}_{5}5​. The long coherence times that ZEFOZ can enable would make Pr3+{}^{3+}3+:YAG a strong candidate for achieving the strong-coupling regime of cavity QED, and would be an important step forward in creating long-lived telecommunications wavelength quantum memories in Er3+{}^{3+}3+:Y2{}_{2}2​SiO5{}_{5}5​. This work relies mostly on published spin-Hamiltonian parameters, but Raman heterodyne spectroscopy was performed on Pr3+{}^{3+}3+:YAG to measure the parameters for the excited state.
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Experimental observations of rare-earth ions doped into an antiferromagnetic crystal show an enriched optical spectrum. In this paper we present a cluster-based model to describe erbium ions doped into a gadolinium vanadate (Er:GdVO4_44​) host crystal, wherein the erbium ion couples directly to its four nearest neighbour gadolinium ions, which in turn couple to the mean field of the rest of the crystal. Compared to previous models in the literature, the parameters used to fit this model are fewer in number, with clearer physical origins. Agreement with the experimentally observed optical spectrum of Er:GdVO4_44​ suggests that our model succeeds in capturing the most important interactions of the system, suggesting that it may be useful for predicting microwave-to-optical transduction in future experiments.
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Rare-earth ions in solid-state hosts exhibit low homogeneous broadening and long spin coherence at cryogenic temperatures thus making them a promising candidate for optical quantum memories [1], optical-microwave transducers [2] and single dopant-based devices such as single photon emitters operating at the telecommunication wavelengths [3]. Here, we present an overview of the spin and optical properties of Er ensembles in Si accessed via resonant photoluminescence excitation (PLE) spectroscopy [4]. Samples were positioned directly on top of tailor-fabricated superconducting single photon detectors, placed in a dilution refrigerator unit and resonantly excited using fiber optics. Our method provided high collection efficiency and allowed spectral measurements of low Er density samples. The observed Er PLE spectra were strongly affected by the presence of co-dopants such as O, B or P reflecting their influence on the formation of optically active Er sites and corresponding Er optical transition energies. Higher O densities resulted in especially rich PLE spectra suggesting that a variety of Er-O complexes formed due to O doping. Lowering the O concentration, we achieved PLE spectra dominated by a single Er site in P doped samples. Interestingly, the Er spin relaxation and optical coherence properties were barely affected by the employed co-dopants and mainly depended on the Er concentration. By lowering the Er concentration from relatively high (1018cm-3) to low densities (1016cm-3), we were able to increase Er spin lifetimes from ~0.1 s to ~30 s. Long spin relaxation times allowed us to identify PLE spectra of new Er sites in Si. In both concentration regimes, we observed sub-MHz transient spectral holes suggesting long optical coherence times. Furthermore, we observed sub-MHz spin transitions in both natural and isotopically purified Si and achieved spin coherence times above 1 ms in isotopically purified Si. Narrow optical linewidths and long transverse and longitudinal spin relaxation times show that Er in Si is an excellent candidate for future quantum information and communication applications.