Optically detected spin states in SiC
To generate defect ensembles in , we began with semi-insulating (SI), n-type and undoped substrates. In substrates with a low intrinsic defect concentration, we then used carbon ion implantation followed by an annealing process designed to join vacancies into complexes (see Methods and Supplementary Note 1). The 3C-SiC samples consist of single and polycrystalline epitaxial films grown on substrates, while the 4H- and 6H-SiC substrates are bulk single crystals.
Our optically detected magnetic resonance (ODMR) measurements show that all three measured polytypes host a number of optically addressable defect spins. These ODMR measurements rely on spin-dependent optical cycles both to polarize spins with laser illumination and to measure those spin states through changes in the photoluminescence (PL) intensity. We focus on defect optical transitions with zero-phonon lines in the 1.08–1.2 eV range. These can be observed as peaks in the PL spectrum when the samples are illuminated with higher energy laser excitation (Fig. 1a). In addition to these sharp peaks, much of the PL from these defects is emitted in broad phonon sidebands at lower energies, which we also collect.
The ODMR spectra (
Fig. 1b–d) are obtained by measuring the fractional change in PL intensity (Δ
IPL/
IPL) under continuous wave laser illumination as a function of both an applied out-of-plane DC magnetic field (
B) and the frequency (
f) of an applied radiofrequency (RF) magnetic field. Spin flips produce a Δ
IPL/
IPL signature and occur when
f is resonant with one of the defect’s spin transitions, which can all be tuned by varying
B. The large number of observed ODMR lines demonstrates the versatility of as a host for optically addressable spin states.
In each polytype, wavelength-resolved ODMR measurements associate the various ODMR features with specific PL lines (see Koehl
et al.3 and Carlos
et al. for 4H-SiC and Supplementary Fig. S1for 6H- and 3C-SiC). Some of the defects in 4H-SiC (PL1-PL4) have been identified as spin-1 neutral divacancies
9. The defects responsible for the other spin transitions observed (compiled in Supplementary Table S1) have similar spin and optical properties to the neutral divacancies but have not been conclusively identified.
Spin coherence at cryogenic and room temperatures
Long-lived spin coherence, an important prerequisite for quantum information and sensing technologies, is a general feature of spins in all three polytypes. Our coherence measurements are based on standard pulsed magnetic resonance techniques including Rabi, Ramsey, Hahn echo, Carl-Purcell-Meiboom-Gill (Fig. 2) and spin relaxation (Supplementary Fig. S2) sequences. At 20 K, the spin relaxation times range from 8 to 24 ms. The Hahn-echo coherence times (T2) range from 10 μs to 360 μs at 20 K, depending on the substrate, with significant dependence on implantation dose and substrate doping type. The longest T2 times we measured were in native neutral divacancies in 4H-SiC that were generated during crystal growth.
All three polytypes exhibit defects whose spin coherence persists up to room temperature (Fig. 3and Supplementary Figs S3–S5). In as-grown 4H-SiC, one neutral divacancy line (PL3) persists up to room temperature as well as three other ODMR lines (PL5–PL7) of unknown origin, all withT2=50±10 μs. Polycrystalline 3C-SiC also exhibits a state with room-temperature spin coherence, although similar states with the same zero-phonon line and ODMR transition in certain other 3C-SiC substrates that we measured did not. In 6H-SiC, the SI and n-type substrates have the same ODMR lines at 20 K, but their room-temperature ODMR signatures are substantially different from each other (Fig. 3b), with several additional ODMR lines in the n-type substrate that do not appear at 20 K or in the SI substrate. The presence of these coherent spin states at room temperature is a particularly promising result for spin-based sensing24 with .
Coherent spin interactions
Ultimately, many spin-based quantum technologies will require not only separately addressable spins with long coherence times but also a means of coupling these spins together. Patterned ion implantation has generated individual and strongly coupled nitrogen-vacancy (NV) centres in diamond
25. We have also patterned spin ensembles in , using ion implantation through poly-(methyl-methacrylate) (PMMA) apertures (Fig. 4a; Supplementary Fig. S6). Though these are not individual spins, this patterning demonstration shows promise for spatially engineering defects. As optical wavelengths significantly exceed the length scale required for strong magnetic coupling between single dipoles (<30 nm for diamond NV centres
25), scaling up a dipole-coupled spin network is a significant challenge. defects in inequivalent lattice sites have distinct RF and optical transition energies, giving complex polytypes of with many inequivalent defect species the possibility of hosting many separately addressable spins in a single confocal volume (Fig. 4b).
As a step towards independently addressable dipole-coupled spins, we measure dipole–dipole spin interactions between inequivalent defect ensembles. The study of these interactions also provides valuable information about the spin density and optical polarization in these defect states. Our measurements use double electron–electron resonance26 (DEER) to flip the spin of one spin ensemble (the ‘drive’ species), while the resulting change in the Larmor precession rate of another ensemble (the ‘sense’ species) is measured. We focused on 6H-SiC for these measurements, which when implanted, had higher spin densities than in our 4H-SiC substrates, and higher DEER-coupling strengths.
The change in precession rate (Δ
f), a measure of the average dipole-coupling strength, is experimentally observed as an additional phase (Δ
θfree) acquired by the sense species over the free precession segment of a Hahn-echo measurement (Fig. 5a). These parameters are related by
, where
tpulse is the delay of the drive pulses relative to the center of the Hahn-echo sequence. This pulse sequence is designed to refocus the sense spins due to all magnetic fields except those due to drive species spin flips. When we drive Rabi oscillations on the drive species, we simultaneously observe DEER oscillations in Δ
θfree of the sense spins (Fig. 5b).
To measure both Δf and the decoherence rate of the sense spins due to drive-spin flips (τ), we vary both tpulse and the phase of the final π/2 pulse in the sense spin Hahn-echo sequence (θHahn). The resulting data (Fig. 5c, left) are well fit by:
For the data at
θHahn=
π/2, the coherent coupling term becomes
in equation (1), providing a sensitive measure of Δ
f, while the data at
θHahn=0 and
θHahn=
π are dominated by the decoherence term, giving a more accurate measure of
τ. The globally fitted values of Δ
f for various drive-spin ensemble species (Fig. 5d and Supplementary Fig. S7) show that the
c-axis-oriented spins (QL1, QL2 and QL6) exhibit Δ
f values in the single kHz range. The lower symmetry of the basal-oriented spins (QL3–QL5) results in eigenstates with smaller magnetic moments, reducing Δ
f for these species (Supplementary Note 2).
We also repeated this experiment with the pulse sequence shown in Fig. 5a modified by the addition of a depolarizing π/2 pulse, which is applied to the drive spins before the sense spins’ Hahn-echo sequence. In this case, because the π pulses applied to the drive-spin population no longer cause a net change in magnetization, Δf vanishes (Fig. 5c, right). Additionally, when the drive spins are depolarized, τ increases slightly. When QL1 is the sense species and QL2 is the drive species, τchanges from 89±3 μs (polarized QL2) to 96±3 μs (unpolarized QL2).