Optical and microstructural characterization of Er³⁺ doped epitaxial cerium oxide on silicon

Erbium (Er) doped solid-state hosts present a quality candidate for developing quantum memories,^1–3 due to the intrinsic spin–photon interface and long coherence times of Er.⁴ In addition, the compatibility of Er with the telecom C-band,⁵ due to its 1.53 μm optical transition and the versatility of solid-state hosts,⁵ has recently motivated several investigations into a multitude of erbium-doped host materials—such as Er:TiO₂,^6–8 Er:Y₂O₃,^9,10 Er:CaWO₄,^11,12 Er:Y₂SiO₅,¹³ Er:MgO,¹⁴ Er:YVO₄,¹⁵ Er:LiNbO₃,¹⁶ and Er:Si^17,18—in order to explore various desired characteristics.

Optimizing the electron spin coherence of Er³⁺ for quantum memory applications necessitates the selection of an environment with minimal decoherence sources, and for high-quality wide-bandgap crystals at cryogenic temperatures, the leading factor of decoherence is nearby nuclear spins within the host material.¹⁹ A recent computational study identified that cerium dioxide (CeO₂) is an optimal host for maximizing electron spin coherence,¹⁹ due to the near-zero natural abundance of nuclear spins in its constituent elements.²⁰ CeO₂ is additionally attractive as a host since its lattice constant (5.41 Å) is close to the lattice constant of Si (5.43 Å).²¹ This leads to a low lattice mismatch of −0.4% when CeO₂ is epitaxially grown on Si substrates (irrespective of its orientation). Heteroepitaxy on silicon then provides an avenue for scalability and future integration with photonic and electronic quantum devices.

In this work, we benchmark Er-doped CeO₂ (Er:CeO₂) thin films grown on Si(111) by molecular beam epitaxy (MBE) for use as a telecom-wavelength interfaced spin qubit platform. Previous work on CeO₂/Si epitaxy has focused mostly on microstructural studies.^22–25 Inaba et al.²⁶ have examined Er:CeO₂/Si down to 10 000 parts per million (ppm) Er and reported preliminary Er³⁺ optical characterization results at 4 K, including an optical excited state lifetime (T₁) of 1.5 ms at 1512 nm. We have focused on significantly lower Er concentrations (2–130 ppm) than have been studied previously in CeO₂. This regime is of interest for quantum applications since typically below 10 ppm, the effects of inter-dopant dipolar interactions are reduced such that, taking into account only the Er dopants themselves, dephasing times—which are important for quantum applications—should primarily be limited by the radiative lifetime.⁴ 

We conduct a detailed study of the MBE-grown Er:CeO₂/Si(111) system, starting with a microstructural study of the thin film where we confirm that CeO₂ grows epitaxially on the Si(111) substrate with appropriate Ce⁴⁺ valency. Examining the spin properties of the Er doped into the CeO₂ system by electron paramagnetic resonance (EPR), we identify results consistent with Er³⁺ substituting into the cubic Ce⁴⁺ site and observe a narrow EPR linewidth of 245(1) MHz at concentrations of 2–3 ppm.

In addition, we examine the optical properties of the trivalent Er³⁺ dopants at 3.5 K, and we identify an optical inhomogeneous linewidth of 9.5(2) GHz, a spectral diffusion linewidth as narrow as 4.8(3) MHz, and an optical lifetime as long as 3.5(1) ms at 2–3 ppm doping levels. Of particular note is that the spectral diffusion linewidths found here via transient spectral hole burning—though broader than in bulk or with nanostructures built upon bulk samples as measured by spectral hole burning²⁷ or photon echo^12,28,29—are narrower by an order of magnitude than other reports of spectral diffusion in thin film or nanostructured Er-doped oxides on silicon.^6–8 To elaborate upon our study, we identify the trends by which the EPR, optical inhomogeneous, and spectral diffusion linewidths narrow and the excited state lifetime increases as a function of decreasing Er concentration.

Finally, we examine the effect of annealing the Er:CeO₂ films up to 900 °C, which yields narrowing of the inhomogeneous linewidth by 20% and lengthening of the excited state lifetime by 40%.

Er:CeO₂ thin films are grown epitaxially on Si(111) ±0.5° substrates using a Riber C21 DZ Cluster molecular beam epitaxy (MBE) system. Growths are carried out between 665 and 675 °C²⁶ and initiated on a 7 × 7 reconstructed Si(111) surface. When used as a substrate, Si(111) is known to lead to epitaxial single crystal growth of CeO₂.^22–26 Meanwhile, the Si(100) substrate orientation has been known to lead to mixed domain growths.^30,31 There is one exception reported in the literature,³² which explores a two-stage deposition process and identifies single crystal CeO₂(001) growth of thick layers, but a detailed defect analysis via electron microscopy of such layers was not provided.

Metallic Er, Ce, and molecular O₂ beams are used with a beam equivalent O₂:Ce flux ratio of 20. Growths are observed in situ using a reflection high-energy electron diffraction (RHEED) system operated at 15 kV. We grow with erbium doping levels between 2 and 130 ppm (well below the reported solubility limit of 9% Er in CeO₂³³) and thicknesses between 200 and 940 nm. Following deposition, films are cooled in the presence of oxygen flux. Further details are described in the supplementary material.

Cross-sectional transmission electron microscopy (XTEM) studies are carried out using a Thermo Fisher Spectra 200 operated at 200 keV in the scanning transmission electron microscopy (STEM) mode. The same beam conditions are used for energy-dispersive x-ray (EDX) spectroscopy. Specimens for XTEM and EDX are prepared using focused ion beam (FIB) milling.³⁴ A four-circle Rigaku SmartLab diffractometer is used for x-ray diffraction (XRD) scans, along with x-ray absorption spectroscopy (XAS) performed on Beamline 29 ID-D of the Advanced Photon Source at Argonne National Laboratory. All microstructural measurements are conducted at room temperature.

Continuous wave (CW) X-band (9.5 GHz) EPR experiments are carried out using a Bruker ELEXSYS II E500 EPR spectrometer (Bruker BioSpin), equipped with a TE₁₀₂ rectangular EPR resonator (Bruker ER 4102ST). Field modulation at 100 kHz in combination with lock-in detection leads to first derivative-type CW EPR spectra. The measurements are performed at cryogenic temperatures between 4.0 and 4.2 K, with temperature governed by a helium gas-flow cryostat (ICE Oxford) and an ITC (Oxford Instruments). The Er:CeO₂ samples are mounted with the static magnetic field parallel to the Si⟨110⟩ axis. The data are collected using a field modulation of 1 mT, a microwave power attenuation of 35 dB (from 200 mW), and a field step size of 0.2 mT.

The optical characterization is performed in a custom confocal microscopy setup designed for telecom C-band spectroscopy, with samples mounted in a cryostat at 3.5 K (s50 Cryostation, Montana Instruments). Time-resolved photoluminescence excitation (PLE) spectroscopy is performed with 1.5 ms excitation pulses shaped by acousto-optic modulators (AOMs) and 7 ms collection intervals subsequent to the excitation pulses. The PLE signal is detected by a Quantum Opus superconducting nanowire single photon detector (SNSPD). The transient spectral hole burning (TSHB) measurements are enabled by the addition of a phase electro-optic modulator to the excitation path, yielding sidebands with a specific detuning from the laser carrier. The photoluminescence (PL) measurements are performed in the same setup with an alternative collection path routed to a low-noise InGaAs camera (PyLoN IR, Princeton Instruments) and the excitation laser operated continuously. Additional details of this setup are described elsewhere.⁸ 

Figure 1(a) shows the RHEED pattern of the surface of a 3 ppm Er, 940 nm thick CeO₂ film on Si(111) immediately following growth, with the electron beam incident along the Si⟨110⟩ azimuth. No significant changes in RHEED patterns are noted during growth or for different Er doping concentrations. The streaky pattern indicates a smooth, single-crystalline surface and is consistent with an epitaxial CeO₂(111)/Si(111) alignment between the epilayer and substrate. This is further confirmed by XTEM studies. Figure 1(b) shows a representative high-resolution bright field XTEM image with diffraction patterns shown in the insets. A 4 nm thick amorphous layer is observed at the CeO₂/Si interface. We identified a mixed CeO_x–SiO_y composition across this layer via EDX [Fig. 1(c)]. Similar interfacial oxide layers have been observed in CeO₂/Si previously²⁶ and are a well-known phenomenon in ionic oxides grown on Si,^9,35 resulting from oxygen diffusion followed by catalytic oxidation of the buried silicon interface.

Low-magnification bright field XTEM (see Fig. S1 of the supplementary material for an example) shows an epilayer threading dislocation density of $∼109$ cm⁻². Similar threading defects can be seen in the XTEM studies of CeO₂/Si by Inaba et al.²⁶ Threading segments do not relieve lattice mismatch strain, and we ascribe the formation of these threading defects to the initial stages of epitaxial growth of CeO₂, possibly due to the formation of localized patches of oxidized silicon due to the catalytic effects of the deposited CeO₂.

An ω–2θ XRD scan of a 3 ppm Er, 940 nm thick CeO₂ sample, as shown in Fig. 2(a), is carried out to further examine the as-grown crystal structure. The scan yields a CeO₂(111) peak with a full width at half maximum (FWHM) of 630 arcsec, qualitatively consistent with the threading dislocation density observed. The peak separation between the Si(111) and CeO₂(111) peaks is ∼700 arcsec, indicating that most of the misfit strain remains elastically stored in the film.

To corroborate the crystal structure identified by XRD, XAS of the Ce M-edge on a 35 ppm Er, 240 nm thick CeO₂ on Si sample shows two sets of peaks related to the M5 and M4 transitions of electrons from 3d core orbitals to unoccupied p- and f-like symmetry orbitals, as shown in Fig. 2(b). The positions of the main peaks at 883 eV (M5) and 901 eV (M4) relate to the electric-dipole allowed transitions to 4f states^36–38 and are consistent with the Ce⁴⁺ valence state and the formation of CeO₂ (as opposed to Ce³⁺ and Ce₂O₃). The satellite peaks at 889 eV (Y′) and 906.5 (Y) result from the transition to 4f states in the condition band and are additional indicators of predominately Ce⁴⁺ valency.^39,40 Overall, spectral shape and peak separation are consistent with the Ce⁴⁺ oxidation state, and peaks corresponding to Ce³⁺ are not identifiable within the spectrum. These data together with the XRD and XTEM studies suggest that we have a CeO₂ film where the Ce³⁺ concentration is likely less than 1%, beyond the detection limit of the experimental setup.

In the effective spin-1/2 Hamiltonian H [Eq. (1)], the first term covers the Zeeman splitting of the electron spin states S proportional to the Bohr magneton μ_B, the applied magnetic field B, and the effective g-factor produced by the local structure. The second term accounts for the hyperfine interaction between the electron spin S and the nuclear spin I for Er isotopes with a non-zero nuclear spin, governed by the hyperfine splitting tensor A.

Figure 3(a) shows a representative example of an EPR spectrum (blue dots) obtained from the 3 ppm Er, 940 nm thick CeO₂ sample. We identify a primary resonance peak near 100 mT surrounded by a set of lower-intensity resonance peaks. The primary peak arises from the absorption of the Er³⁺ electron spin transition for the 77% of naturally abundant nuclear spin I = 0 Er isotopes (primarily ¹⁶⁶Er, ¹⁶⁸Er, and ¹⁷⁰Er). The lower-intensity peaks arise from the hyperfine interaction between the electron spins and the remaining naturally abundant nuclear spin I = 7/2 isotope (¹⁶⁷Er), which yields eight hyperfine peaks. Seven hyperfine peaks are easily identifiable adjacent to the primary peak; the eighth hyperfine peak is obscured by the primary peak.⁴¹ 

The measured EPR spectrum is fitted [Fig. 3(a), magenta dashed line] to the energy structure defined by Eq. (1) to extract effective g-values, hyperfine parameters A, and EPR linewidths. Resonance peaks are described with the first derivatives of Lorentzians, and the hyperfine peak locations are identified accounting for the second-order perturbation in nuclear spin.⁴² We extract an effective value g = 6.812(5) and a hyperfine splitting of A = 687(1) MHz for the displayed sample. This g-factor is consistent with the theoretical study of Er³⁺ residing in a cubic crystal field symmetry⁴³ and is additionally consistent with the experimental study of Er:CeO₂ in bulk and nanocrystal forms.^43,44 Based on the cubic symmetry sites available in CeO₂ and the comparable size of the Ce⁴⁺ and Er³⁺ ions (for coordination number 8, ionic radii of 0.97 Å and 1.004 Å, respectively⁴⁵), we note that the Er ion likely substitutes into the Ce site^46,47 under this growth method.

The broadening of resonance peaks in EPR may result from a variety of factors, including magnetic dipole–dipole interactions (e.g., Er–Er) and strain due to defects (e.g., threading dislocations, vacancies, and unintentional dopants). Focusing on the nuclear spin zero peak, we find that the EPR linewidth increases linearly with Er³⁺ doping, as shown in Fig. 3(b) for a series of Er:CeO₂/Si samples (with thicknesses between 740 and 940 nm and Er doping levels between 2 and 130 ppm—see the supplementary material for a table of sample details). A linear increase in linewidth with doping concentration may be associated with broadening due to magnetic dipole–dipole interactions between spins, but we find that broadening due solely to the concentration of Er³⁺ ions, Γ_d–d, calculated based on the Er concentration and measured g-factor,⁴⁸ would have the values Γ_d–d(2 ppm Er) = 0.2 MHz and Γ_d–d(130 ppm Er) = 15.2 MHz. Both of these values are significantly less than the observed linewidths from the EPR measurement of those doping levels of 245(1) MHz and 1450(25) MHz, respectively. The reason for this discrepancy remains unclear but suggests that there are other potential dopant-driven broadening mechanisms at play.

We then proceed to characterizing the optical interface presented by the Er:CeO₂ system. The Er³⁺ ground state ⁴I_15/2 (referred to as Z) and the first excited state ⁴I_13/2 (referred to as Y) each split into five levels due to the cubic symmetry of the host CeO₂ structure,⁴⁹ which was confirmed by EPR. A diagram of the expected crystal field-split level structure is shown in Fig. 4(a).

The spectrum in Fig. 4(a) shows the PL emission of the 3 ppm Er, 940 nm thick CeO₂ sample excited with 1473 nm light, to the top of the Y states. After excitation, a fast non-radiative decay process moves the excited population to Y₁.⁵⁰ Radiative decay from Y₁ to the Z levels allows us to observe four Y₁–Z_i transitions, consistent with the maximum five Z levels allowed by cubic symmetry. The highest energy transition, in this case Y₁–Z₁, is found to be at 1530.74(5) nm⁵¹ within the telecom C-band.

For additional optical characterization, we focus on the Z₁–Y₁ transition due to its technological relevance at low temperatures, with the readily accessible spin interface in Z₁ as discussed in the EPR section and the absence of the non-radiative processes found in Y_>1. We probe the Z₁–Y₁ transition with a higher spectral resolution using PLE as a function of Er doping density, using the same series of samples as used for the EPR study (see the supplementary material for sample details).

The inhomogeneous linewidth Γ_inh of the absorption line as shown in Fig. 4(b) ranges from 11.1(4) GHz at 2 ppm Er and 9.5(2) GHz at 3 ppm Er to 41(7) GHz at 130 ppm Er. This linewidth is influenced by the presence of electric fields caused by charged defects or strain in the vicinity of the optically active Er³⁺ sites. Such defects can include (1) other Er³⁺ ions since the aliovalent Er³⁺ on a Ce⁴⁺ site will result in a negatively charged point defect $ErCe′$ (per Kröger–Vink notation⁵²), (2) charge compensating defects such as positively charged oxygen vacancies,⁴⁶ and (3) “grown-in” imperfections during crystal growth. For a defect density n, one expects Γ_inh ∝ n^2/3 for dipoles interacting with nearby charge defects and Γ_inh ∝ n for broadening due to strain, dipoles interacting with random electric field gradients, or dipole–dipole interactions.⁵³ 

Taking n ∼ n_Er, where n_Er is the concentration of $ErCe′$ defects, we fit the two described cases to the Er-concentration dependent inhomogeneous linewidth. Both scenarios follow the generic trend of the data, with the n^2/3 dependence [Fig. 4(b), red dashed line] yielding a slightly better fit than the linear case [Fig. 4(b), blue dotted line]. While the overall behavior is captured, we make no definite inference of the broadening defect’s nature at this stage. In either case, we find $∼10$ GHz of residual inhomogeneous broadening even at low Er concentrations of 2–3 ppm, likely due to grown-in crystalline imperfections (see the supplementary material for an extended discussion).

Continuing our optical study, we find that increasing the Er³⁺ concentration leads to a decrease in the optical excited state lifetime T₁, as shown in Fig. 4(c) (black dots), from 3.5(1) ms at 2–3 ppm to $∼2.7$ ms at 130 ppm. These results are consistent with the presence of defects adding non-radiative or quenching pathways according to the Inokuti–Hirayama theory,⁵⁴ though the exact nature of these defects cannot be inferred at this time. (Additional details on this analysis are presented in the supplementary material.) Concordantly, the longer millisecond-scale lifetimes of the Er optical transition (compared to other defect qubits such as vanadium in silicon carbide⁵⁵ or NV centers in diamond⁵⁶) are a consequence of the forbidden ⁴I_15/2 −⁴I_13/2 transition.⁴ However, our longest lifetimes at low doping are lower by a factor of $∼3$ compared to the longest Er lifetimes reported in the literature for doping in bulk host crystals grown from the melt under near-equilibrium conditions, such as in yttrium orthosilicate.^27,57 This is likely due to the higher defect densities and the presence of proximal interfaces in our thin film materials grown under non-equilibrium conditions.

Finally, Fig. 4(d) shows the dependence of the spectral diffusion-limited homogeneous linewidth Γ_SD as measured by transient spectral hole burning (TSHB), henceforth referred to as the spectral diffusion linewidth Γ_SD, as a function of Er doping (black dots). The spectral diffusion linewidth scales linearly with the Er concentration, from 4.8(3) MHz at 2 ppm to 1465(66) MHz at 130 ppm. (Details on the linear fit may be found in the supplementary material.) This is consistent with the instantaneous spectral diffusion from dipole–dipole interactions with nearby excited Er ions, which causes linear broadening in response to an increase in excited ion density.⁵⁸ We emphasize this strong relationship between the doping density and spectral diffusion linewidth, with the data potentially suggesting lower linewidths at sub-ppm Er concentrations, particularly since at our examined lowest doping levels of 2–3 ppm, we see spectral diffusion linewidths of ∼5 MHz for a millisecond-timescale TSHB measurement conducted at 3.5 K.

Though we are careful not to assume the nature of the defects leading to broadening and quenching in the doping series results, we speculate that these defects may be partially mitigated by post-growth annealing. For example, oxygen vacancy-related defects can result from non-equilibrium growth processes such as in MBE, and may be removed by annealing.

To study the effect of annealing, we anneal a 200 nm thick, 3 ppm Er:CeO₂ film on Si for 12 h in 1 atm of 20% O₂/Ar at different temperatures from 300 to 1000 °C using an MTI OTF-1200X tube furnace. The film roughened substantially at 1000 °C, so we constrain our discussion to a maximum annealing temperature of 900 °C where the physical integrity of the samples remains intact. Figure 5 shows the dependencies of the measured inhomogeneous linewidth, excited state lifetime, and spectral diffusion linewidth of the Z₁–Y₁ transition as a function of the annealing temperature between 300 and 900 °C. Annealing in this range leads to improvements in Γ_inh and T₁ of 20% and 40%, respectively, from their as-grown values. We ascribe these improvements to the annealing out of “grown-in” crystal defects in the thin films. However, the spectral diffusion linewidth worsens at moderate temperatures and returns to the as-grown linewidth at the maximum temperature studied, and the process driving this behavior is unclear.

The trends in the inhomogeneous linewidth (Γ_inh) and the excited state lifetime (T₁) as a function of annealing temperature (T) can be captured by assuming (i) a first-order reaction rate-limited process of thermally activated annihilation of the grown-in defects that affect the optical properties and (ii) the suitability of the previously described power law relation and the Inokuti–Hirayama approach, respectively, for the defect concentration dependence upon Γ_inh and T₁. Details extending these models for annealing are given in the supplementary material. We find that an Arrhenius-like activation energy E_A in the range of 0.65–0.75 eV for the temperature-dependent first-order reaction rate constant leads to good fits for both Γ_inh [Fig. 5(a), red dashed line] and T₁ [Fig. 5(b), red dashed line]. This points to a density of grown-in, optically relevant defects that are being annihilated via thermally activated processes.

The question then is the nature of the defect being manipulated during annealing, thus leading to the improvement in the inhomogeneous linewidth and excited state lifetime. Positively charged oxygen vacancies (⁠$VO••$⁠) are a well-known defect in CeO₂, whose concentration can be increased by substituting aliovalent dopants (such as Er³⁺) into Ce⁴⁺ sites^59,60 (⁠$ErCe′$⁠). Charge neutrality in the film is maintained by $2[ErCe′]=[VO••]$⁠, where the brackets indicate the concentration. The oxygen vacancies may affect the Er luminescence via strain or electric field interactions, whose strength would depend upon the distance between the Er and vacancy positions. Since we do not expect the Er concentration to change as a function of annealing temperature up to 900 °C, we would not expect the net $VO••$ concentration to change for reasons of film charge neutrality. It is, however, possible that annealing can lead to diffusion-induced redistribution of oxygen vacancies, leading to their clustering (to form complexes) or gettering by grain boundaries, altering the Er–V_O interactions. This may lead to improvements in the optical properties as observed.

The Er:CeO₂/Si system presents an attractive combination of benefits, as it is an ideal host oxide for a spin defect with its very low nuclear noise environment, and has low lattice mismatch for epitaxial growth on silicon. In this work, we have carried out a detailed microstructural and optical study of MBE-grown epitaxial Er:CeO₂/Si in the 2–130 ppm Er doping range, yielding results relevant for development in quantum coherent device applications. We establish a baseline for this material in the context of key metrics for rare-earth doped oxide systems: as-grown films at 2–3 ppm Er doping show EPR linewidths as narrow as 245(1) MHz, optical inhomogeneous linewidths down to 9.5(2) GHz, an optical excited state lifetime as long as 3.5(1) ms, and a spectral diffusion-limited homogeneous linewidth as narrow as 4.8(3) MHz. Post-growth annealing up to 900 °C yields an improvement in the optical inhomogeneous linewidth and excited state lifetime by 20% and 40%, respectively.

In studying the spin and optical parameters as a function of Er doping, we show that the functional dependence is consistent with a charge dipole-based interaction model. We find that the linewidths for our thin films are broader than the corresponding linewidths in high-quality Er-doped bulk samples, likely due to the thin film nature—and, therefore, proximity to interfaces—and non-equilibrium growth process of our material system, with the latter leading to a larger number of grown-in defects. Future research is, therefore, targeted at reducing grown-in defect densities via growth process optimization. That said, the $∼5$ MHz spectral diffusion linewidth in the as-grown films is sufficiently narrow to indicate the potential for long optical coherence in the hundreds of nanoseconds, enabling the exploration of measurement techniques, such as photon echo,⁵¹ to directly probe the optical coherence of Er³⁺ in CeO₂.

See the supplementary material for additional details on MBE growth methods, threading dislocation measurement, and optical characterization analysis.

The authors would like to thank Dr. Jasleen K. Bindra for assistance with EPR measurements. This work was primarily supported by Q-NEXT, a U.S. Department of Energy Office of Science National Quantum Information Science Research Centers under Award No. DE-FOA-0002253. Additional support for cryogenic and optical infrastructure development was provided by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences, and Engineering Division. Use of the Center for Nanoscale Materials, an Office of Science User Facility, use of the Advanced Photon Source at Argonne National Laboratory, and the EPR work in the Chemical Sciences and Engineering Division were supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, through Argonne National Laboratory under Contract No. DE-AC02-06CH11357. This work also made use of the Jerome B. Cohen X-Ray Diffraction Facility supported by the MRSEC program of the National Science Foundation (No. DMR-2308691) at the Materials Research Center of Northwestern University and the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (No. NSF ECCS-1542205).

The authors have no conflicts to disclose.

G.D.G., J.Z., I.M., and S.G. conceived of and designed the experiments. I.M., K.E.S., and G.D.G. carried out sample growth. Y.L. and J.W. carried out TEM characterization. I.M. and S.K. carried out XRD measurements. J.B.M. and J.W.F. carried out XAS measurements. J.N., O.G.P., and J.Z. carried out EPR measurements. G.D.G., J.Z., and S.E.S. carried out optical measurements with input from A.M.D. S.C., G.D.G., and R.C. modeled and analyzed the optical data. Overall interpretation and analysis of the results were led by G.D.G., J.Z., and S.G. All authors contributed to the manuscript.

Gregory D. Grant: Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (lead); Writing – original draft (equal); Writing – review & editing (equal). Jiefei Zhang: Conceptualization (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal). Ignas Masiulionis: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Visualization (supporting). Swarnabha Chattaraj: Formal analysis (equal); Methodology (equal); Visualization (supporting). Kathryn E. Sautter: Investigation (supporting). Sean E. Sullivan: Investigation (supporting). Rishi Chebrolu: Data curation (supporting). Yuzi Liu: Investigation (equal). Jessica B. Martins: Investigation (equal); Visualization (supporting). Jens Niklas: Investigation (equal). Alan M. Dibos: Writing – review & editing (equal). Sumit Kewalramani: Investigation (equal); Resources (equal). John W. Freeland: Investigation (equal); Resources (equal); Visualization (supporting). Jianguo Wen: Investigation (equal); Resources (equal); Visualization (supporting). Oleg G. Poluektov: Investigation (equal); Resources (equal). F. Joseph Heremans: Project administration (equal); Resources (equal); Supervision (supporting). David D. Awschalom: Funding acquisition (equal); Methodology (equal); Resources (equal). Supratik Guha: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Resources (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.