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Physical Review Materials

Distinguishing erbium dopants in Y2O3 by site symmetry: Ab initio theory of two spin-photon interfaces

Churna Bhandari, Cüneyt Şahin, Durga Paudyal, Michael E. Flatté

Published Dec 27, 2023• 4 citations
Publisher

Abstract

We present a first-principles study of the defect formation and electronic structure of erbium (Er)--doped yttria $({\mathrm{Y}}_{2}{\mathrm{O}}_{3})$. This is an emerging material for spin-photon interfaces in quantum information science due to the narrow-linewidth optical emission from Er dopants at standard telecommunication wavelengths and their potential for quantum memories and transducers. We calculate formation energies of neutral and negatively and positively charged Er dopants and find the charge-neutral configuration to be the most stable, consistent with experiment. Of the two substitutional sites of Er for Y, the ${C}_{2}$ (more relevant for quantum memories) and ${C}_{3i}$ (more relevant for quantum transduction), we identify the former as possessing the lowest formation energy. The electronic properties are calculated using the Perdew-Burke-Ernzerhof functional along with the Hubbard $U$ parameter and spin-orbit coupling, which yields a $\ensuremath{\sim}6\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ orbital and a $\ensuremath{\sim}3\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}$ spin magnetic moment, and 11 electrons in the Er $4f$ shell, confirming the formation of charge-neutral ${\mathrm{Er}}^{3+}$. This standard density functional theory approach underestimates the band gap of the host and lacks a first-principles justification for $U$. To overcome these issues we performed screened hybrid functional calculations, including a negative $U$ for the $4f$ orbitals, with mixing $(\ensuremath{\alpha})$ and screening $(w)$ parameters. These produced robust electronic features with slight modifications in the band gap and the $4f$ splittings depending on the choice of tuning parameters. We also computed the many-particle electronic excitation energies and compared them with experimental values from photoluminescence.

DOI
10.1103/physrevmaterials.7.126201

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We present a first-principles study of the defect formation and electronic structure of erbium (Er)--doped yttria (Y2O3)({\mathrm{Y}}_{2}{\mathrm{O}}_{3})(Y2​O3​). This is an emerging material for spin-photon interfaces in quantum information science due to the narrow-linewidth optical emission from Er dopants at standard telecommunication wavelengths and their potential for quantum memories and transducers. We calculate formation energies of neutral and negatively and positively charged Er dopants and find the charge-neutral configuration to be the most stable, consistent with experiment. Of the two substitutional sites of Er for Y, the C2{C}_{2}C2​ (more relevant for quantum memories) and C3i{C}_{3i}C3i​ (more relevant for quantum transduction), we identify the former as possessing the lowest formation energy. The electronic properties are calculated using the Perdew-Burke-Ernzerhof functional along with the Hubbard UUU parameter and spin-orbit coupling, which yields a \ensuremath∼6\ensuremathμB\ensuremath{\sim}6\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}\ensuremath∼6\ensuremathμB​ orbital and a \ensuremath∼3\ensuremathμB\ensuremath{\sim}3\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{B}\ensuremath∼3\ensuremathμB​ spin magnetic moment, and 11 electrons in the Er 4f4f4f shell, confirming the formation of charge-neutral Er3+{\mathrm{Er}}^{3+}Er3+. This standard density functional theory approach underestimates the band gap of the host and lacks a first-principles justification for UUU. To overcome these issues we performed screened hybrid functional calculations, including a negative UUU for the 4f4f4f orbitals, with mixing (\ensuremathα)(\ensuremath{\alpha})(\ensuremathα) and screening (w)(w)(w) parameters. These produced robust electronic features with slight modifications in the band gap and the 4f4f4f splittings depending on the choice of tuning parameters. We also computed the many-particle electronic excitation energies and compared them with experimental values from photoluminescence.
Distinguishing erbium dopants in Y2_22​O3_33​ by site symmetry: \textit{ ab initio} theory of two spin-photon interfaces
We present a first-principles study of defect formation and electronic structure of erbium (Er)-doped yttria (Y2_22​O3_33​). This is an emerging material for spin-photon interfaces in quantum information science due to the narrow linewidth optical emission from Er dopants at standard telecommunication wavelengths and their potential for quantum memories and transducers. We calculate formation energies of neutral, negatively, and positively charged Er dopants and find the charge neutral configuration to be the most stable, consistent with experiment. Of the two substitutional sites of Er for Y, the C2C_2C2​ (more relevant for quantum memories) and C3iC_{3i}C3i​ (more relevant for quantum transduction), we identify the former as possessing the lowest formation energy. The electronic properties are calculated using the Perdew-Burke-Ernzerhof (PBE) functional along with the Hubbard UUU parameter and spin-orbit coupling (SOC), which yields a ∼\sim∼ 6 μBμ_BμB​ orbital and a ∼\sim∼ 3 μBμ_BμB​ spin magnetic moment, and 11 electrons in the Er 4f4f4f shell, confirming the formation of charge-neutral Er3+^{3+}3+. This standard density functional theory (DFT) approach underestimates the band gap of the host and lacks a first-principles justification for UUU. To overcome these issues, we performed screened hybrid functional (HSE) calculations, including a negative UUU for the 4f4f4f orbitals, with mixing (ααα) and screening (www) parameters. These produced robust electronic features with slight modifications in the band gap and the 4f4f4f splittings depending on the choice of tuning parameters. We also computed the many-particle electronic excitation energies and compared them with experimental values from photoluminescence.
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Erbium-doped solids are a promising platform for quantum technology due to the Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ 1.5-\textmu{}m optical transition in the telecom C band that can offer long coherence times. To characterize the intrinsic C2{\mathrm{C}}_{2}C2​ site of Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ in Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ for quantum information and photonic signal-processing applications, absorption and site-selective fluorescence spectroscopy were used to assign the Er3+4I15/2\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}Er3+4I15/2​$\ensuremath{\leftrightarrow}$4I13/2^{4}I_{13/2}4I13/2​ transitions. The lowest-to-lowest transition occurs at 1535.608 nm and laser absorption determined an inhomogeneous linewidth of 780 MHz in a 0.005%-doped crystal at 3.4 K. Time-resolved fluorescence established an upper limit for the excited-state lifetime of 8.5 ms. Angular-dependent Zeeman absorption was used to determine ground- and excited-state ggg tensors. The C2{\mathrm{C}}_{2}C2​-site ggg tensor components for the ground state are gx=1.60{g}_{x}=1.60gx​=1.60, gy=4.71{g}_{y}=4.71gy​=4.71, and gz=11.93{g}_{z}=11.93gz​=11.93 with a tipping angle of \ensuremath{\alpha} = $2.{06}^{\ensuremath{\circ}}$, whereas for the excited state the components are gx=1.08{g}_{x}=1.08gx​=1.08, gy=4.36{g}_{y}=4.36gy​=4.36, and gz=10.07{g}_{z}=10.07gz​=10.07 with a tipping angle of \ensuremath{\alpha} = $\ensuremath{-}11.{7}^{\ensuremath{\circ}}$. Optical decoherence can be suppressed by the application of a magnetic field parallel to $\ensuremath{\langle}111\ensuremath{\rangle}$ crystal axes where all C2{\mathrm{C}}_{2}C2​ sites become nearly magnetically equivalent with large ggg values so that spin flips of neighboring Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ ions can be simultaneously suppressed. Using this magnetic field direction, two-pulse photon echoes gave a homogeneous linewidth of 5 kHz for an applied magnetic field of 0.5 T, narrowing and saturating at 2.5 kHz at 3.5 T. Decoherence over intermediate magnetic fields was described by spectral diffusion due to $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic dipole interactions driven by the direct phonon process. With Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+:Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ absorption at a convenient telecom laser wavelength and the ability to fabricate waveguides, our study suggests that this is a promising material system for quantum information and spectral hole-burning signal-processing applications.
When introduced as dopants into Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​, Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ ions replace Y3+{\mathrm{Y}}^{3+}Y3+ ions at two crystallographic sites of C2{\mathrm{C}}_{2}C2​ and C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ point symmetries. The C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ site is particularly interesting, given that the inversion symmetry prohibits static electric-dipole moments and electric-dipole transitions, resulting in 1.5 \textmu{}m optical transitions characterized by purely magnetic-dipole properties. Employing $\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}\ensuremath{\leftrightarrow}^{4}I_{13/2}$ transitions, we examined the inherent C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ site of Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ in Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ for its potential in quantum information science and spectral hole burning applications. Our approach involved absorption and site-selective fluorescence spectroscopy to discern Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ energy levels and revealed an excited-state lifetime of 14.6 ms. High-resolution laser spectroscopy at 3.7 K indicated an inhomogeneous linewidth of 1.3 GHz in our sample. Orientation-dependent Zeeman laser absorption spectroscopy facilitated the determination of the full ggg tensors for both the ground and excited states, confirming the C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ site assignment. Furthermore, it identified a suitable magnetic field direction for mitigating decoherence, a finding corroborated through two-pulse photon echo spectroscopy. Our study presents photon echo coherent transient measurements related to magnetic-dipole-allowed rare-earth ion transitions at the C3i{\mathrm{C}}_{3\mathrm{i}}C3i​ site. The observed decoherence, attributed to spectral diffusion arising from $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic-dipole interactions, underscores the complex spin dynamics at play in systems with multiple inequivalent dopant sites. Coupled with the practicality of telecom laser wavelengths, our investigation highlights the promise of magnetic-dipole transitions in advancing quantum information science and spectral hole burning applications.
Rare-earth ions (REIs) have incomplete 4f shells and possess narrow optical intra-4f transitions due to shielding from electrons in the 5s and 5p orbitals, making them good candidates for solid-state optical quantum memory. The emission of Er3+ in the telecom C-band (1530 nm–1565 nm) makes it especially attractive for this application. In order to build practical, scalable devices, the REI needs to be embedded in a non-interacting host material, preferably one that can be integrated with silicon. In this paper, we show that Er3+ can be isovalently incorporated into epitaxial Y2O3 thin films on Si (111). We report on the synthesis of epitaxial, single-crystalline Er:Y2O3 on Si with a narrow inhomogeneous linewidth in the photoluminescence (PL) spectra, 5.1 GHz (<100 mK), and an optical excited state lifetime of 8.1 ms. The choice of Y2O3 was driven by its low nuclear spin and small lattice mismatch with Si. Using PL and electron paramagnetic resonance, we show that Er3+ substitutes for Y in the crystal lattice. The role of interfacial SiOx, diffusion of silicon into the film, and the effect of buffer layers on the inhomogeneous PL linewidth are examined. We also find that the linewidth decreased monotonically with film thickness but surprisingly exhibits no correlation with the film crystalline quality, as measured by the x-ray rocking curve scans, suggesting other factors at play that limit the inhomogeneous broadening in Y2O3 films.
Atomic layer deposited (ALD) Y 2 O 3 thin films have been thoroughly investigated for optical or electronic applications. The coherent spectroscopy of lanthanide ions doped into this material has also recently attracted increasing interest in the field of quantum technologies for which they are considered promising candidates in quantum memories or as spin–photon interfaces. However, these most demanding applications require a deep control over the local positioning of the ions and their close environment in the crystalline matrix. This study focuses on the structural as well as optical properties of Eu 3+ and Er 3+ dopants in Y 2 O 3 using photoluminescence (PL), luminescence decay times, and inhomogeneous line width (Γ inh ) measurements within this particular context. While as-grown ALD films do not provide an ideal host for the emitters, we demonstrate that by optimizing the deposition conditions and using appropriate annealing post treatments narrow inhomogeneous lines can be obtained for the 7 F 0 ↔ 5 D 0 transition of Eu 3+ even for nanoscale films. Furthermore, about 1.5 ms lifetime has been measured for the infrared telecom transition of Er in ultrathin films (<10 nm), which is an order of magnitude higher than in nanoparticles of the same size. These results validate optimized rare-earth-doped ALD Y 2 O 3 films as a suitable platform for photonics applications where few-nanometer-thick films with well-localized emitters are mandatory. This approach provides the first building blocks toward the development of more complex devices for quantum sensing or hybrid structures coupled with other systems such as two-dimensional materials.