For initial characterization of Mo transitions in 6H-SiC and 4H-SiC we used PL and PLE spectroscopy (Methods). Figure 1c shows the PL emission spectrum of the 6H-SiC sample at 3.5 K, measured using an 892.7 nm laser for excitation. The ZPL transition of the Mo defect visible in this spectrum will be studied in detail throughout this work. The shaded region indicates the emission of phonon replicas related to this ZPL.41,42 While we could not perform a detailed analysis, the peak area of the ZPL in comparison with that of the phonon replicas indicates that the ZPL carries clearly more than a few percent of the full PL emission. Similar PL data from Mo in the 4H-SiC sample, together with a study of the temperature dependence of the PL, can be found in Supplementary Information (Fig. S1).

For a more detailed study of the ZPL of the Mo defects, PLE was used. In PLE measurements, the photon energy of a narrow-linewidth excitation laser is scanned across the ZPL part of the spectrum, while resulting PL of phonon-sideband (phonon-replica) emission is detected (Fig. 1b, we used filters to keep light from the excitation laser from reaching the detector, Methods). The inset of Fig. 1c shows the resulting ZPL for Mo in 6H-SiC at 1.1057 eV (1121.3 nm). For 4H-SiC we measured the ZPL at 1.1521 eV (1076.2 nm, Supplementary Information). Both are in close agreement with literature.41,42 Temperature dependence of the PLE from the Mo defects in both 4H-SiC and 6H-SiC can be found in Supplementary Information (Fig. S2).

The width of the ZPL is governed by the inhomogeneous broadening of the electronic transition throughout the ensemble of Mo impurities, which is typically caused by non-uniform strain in the crystal. For Mo in 6H-SiC we observe a broadening of 24 ± 1 GHz FWHM, and 23 ± 1 GHz for 4H-SiC. This inhomogeneous broadening is larger than the anticipated electronic spin splittings,33 and it thus masks signatures of spin levels in optical transitions between the ground and excited state.

In order to characterize the spin-related fine structure of the Mo defects, a two-laser spectroscopy technique was employed.28,43,44 We introduce this for the four-level system sketched in Fig. 2a. A laser fixed at frequency f 0 is resonant with one possible transition from ground to excited state (for the example in Fig. 2a |g 2 〉 to |e 2 〉), and causes PL from a sequence of excitation and emission events. However, if the system decays from the state |e 2 〉 to |g 1 〉, the laser field at frequency f 0 is no longer resonantly driving optical excitations (the system goes dark due to optical pumping). In this situation, the PL is limited by the (typically long) lifetime of the |g 1 〉 state. Addressing the system with a second laser field, in frequency detuned from the first by an amount δ, counteracts optical pumping into off-resonant energy levels if the detuning δ equals the splitting Δ g between the ground-state sublevels. Thus, for specific two-laser detuning values corresponding to the energy spacings between ground-state and excited-state sublevels the PL response of the ensemble is greatly increased. Notably, this technique gives a clear signal for sublevel splittings that are smaller than the inhomogeneous broadening of the optical transition, and the spectral features now reflect the homogeneous linewidth of optical transitions.28,47

Fig. 2 Two-laser spectroscopy results for Mo in 6H-SiC. a Working principle of two-laser spectroscopy: one laser at frequency f 0 is resonant with the |g 2 〉 − |e 2 〉 transition, the second laser is detuned from the first laser by δ. If δ is such that the second laser becomes resonant with another transition (here sketched for |g 1 〉 − |e 2 〉) the photoluminescence will increase since optical spin-pumping by the first laser is counteracted by the second and vice versa. b–d Photoluminescence excitation (PLE) signals as a function of two-laser detuning at 4 K. b Magnetic field dependence with field parallel to the c-axis (ϕ = 1°). For clarity, data in the plot have been magnified by a factor 10 right from the dashed line. Two peaks are visible, labeled L 1 and L 2 (the small peak at 3300 MHz is an artefact from the Fabry-Pérot interferometer in the setup). c Magnetic field dependence with the field nearly perpendicular to the c-axis (ϕ = 87°). Three peaks and a dip (enlarged in the inset) are visible. These four features are labeled L 1 through L 4 . The peak positions as a function of field in b, c coincide with straight lines through the origin (within 0.2% error). d Angle dependence of the PLE signal at 300 mT (angles accurate within 2°). Peaks L 1 and L 4 move to the left with increasing angle, whereas L 2 moves to the right. The data in b–d are offset vertically for clarity Full size image

In our measurements a 200 μW continuous-wave control and probe laser were made to overlap in the sample. For investigating Mo in 6H-SiC the control beam was tuned to the ZPL at 1121.32 nm (f control = f 0 = 267.3567 THz), the probe beam was detuned from f 0 by a variable detuning δ (i.e., f probe = f 0 + δ). In addition, a 100 μW pulsed 770 nm re-pump laser was focused onto the defects to counteract bleaching of the Mo impurities due to charge-state switching28,48,49 (which we observed to only occur partially without re-pump laser). All three lasers were parallel to within 3° inside the sample. A magnetic field was applied to ensure that the spin sublevels were at non-degenerate energies. Finally, we observed that the spectral signatures due to spin disappear in a broad background signal above a temperature of ~10 K (Fig. S4), and we thus performed measurements at 4 K (unless stated otherwise).

Figure 2b shows the dependence of the PLE on the two-laser detuning for the 6H-SiC sample (4H-SiC data in Supplementary Information Fig. S6), for a range of magnitudes of the magnetic field (here aligned close to parallel with the c-axis, ϕ = 1°). Two emission peaks can be distinguished, labeled line L 1 and L 2 . The emission (peak height) of L 2 is much stronger than that of L 1 . Figure 2c shows the results of a similar measurement with the magnetic field nearly orthogonal to the crystal c-axis (ϕ = 87°), where four spin-related emission signatures are visible, labeled as lines L 1 through L 4 (a very small peak feature left from L 1 , at half its detuning, is an artifact that occurs due to a leakage effect in the spectral filtering that is used for beam preparation, see Methods). The two-laser detuning frequencies corresponding to all four lines emerge from the origin (B = 0, δ = 0) and evolve linearly with magnetic field (we checked this up to 1.2 T). The slopes of all four lines (in Hertz per Tesla) are smaller in Fig. 2c than in Fig. 2b. In contrast to lines L 1 , L 2 , and L 4 , which are peaks in the PLE spectrum, L 3 shows a dip.

In order to identify the lines at various angles ϕ between the magnetic field and the c-axis, we follow how each line evolves with increasing angle. Figure 2d shows that as ϕ increases, L 1 , L 3 , and L 4 move to the left, whereas L 2 moves to the right. Near 86°, L 2 and L 1 cross. At this angle, the left-to-right order of the emission lines is swapped, justifying the assignment of L 1 , L 2 , L 3 , and L 4 as in Fig. 2b, c. Supplementary Information presents further results from two-laser magneto-spectroscopy at intermediate angles ϕ (section 2a).

We show below that the results in Fig. 2 indicate that the Mo impurities have electronic spin S = 1/2 for the ground and excited state. This contradicts predictions and interpretations of initial results.33,38,41,42 Theoretically, it was predicted that the defect associated with the ZPL under study here is a Mo impurity in the asymmetric split-vacancy configuration (Mo impurity asymmetrically located inside a Si–C divacancy), where it would have a spin S = 1 ground state with zero-field splittings of about 3–6 GHz.33,38,41,42 However, this would lead to the observation of additional emission lines in our measurements. Particularly, in the presence of a zero-field splitting, we would expect to observe two-laser spectroscopy lines emerging from a non-zero detuning.28 We have measured near zero fields and up to 1.2 T, as well as from 100 MHz to 21 GHz detuning (Supplementary Information section 2c), but found no more peaks than the four present in Fig. 2c. A larger splitting would have been visible as a splitting of the ZPL in measurements as presented in the inset of Fig. 1c, which was not observed in scans up to 1000 GHz. Additionally, a zero-field splitting and corresponding avoided crossings at certain magnetic fields would result in curved behavior for the positions of lines in magneto-spectroscopy. Thus, our observations rule out that there is a zero-field splitting for the ground-state and excited-state spin sublevels. In this case the effective spin-Hamiltonian50 can only take the form of a Zeeman term

$$H_{g(e)} = \mu _Bg_{g(e)}{\mathbf{B}} \cdot {\tilde{\mathbf S}},$$ (1)

where g g(e) is the g-factor for the electronic ground (excited) state (both assumed positive), μ B the Bohr magneton, B the magnetic field vector of an externally applied field, and \({\tilde{\mathbf S}}\) the effective spin vector. The observation of four emission lines can be explained, in the simplest manner, by a system with spin S = 1/2 (doublet) in both the ground and excited state.

For such a system, Fig. 3 presents the two-laser optical pumping schemes that correspond to the observed emission lines L 1 through L 4 . Addressing the system with the V-scheme excitation pathways from Fig. 3c leads to increased pumping into a dark ground-state sublevel, since two excited states contribute to decay into the off-resonant ground-state energy level while optical excitation out of the other ground-state level is enhanced. This results in reduced emission observed as the PLE dip feature of L 3 in Fig. 2c (for details see Supplementary Information section 5).

Fig. 3 Two-laser pumping schemes with optical transitions between S = 1/2 ground and excited states. a Λ scheme, responsible for L 1 emission feature: Two lasers are resonant with transitions from both ground states |g 1 〉 (red arrow) and |g 2 〉 (blue arrow) to a common excited state |e 2 〉. This is achieved when the detuning equals the ground-state splitting Δ g . The gray arrows indicate a secondary Λ scheme via |e 1 〉 that is simultaneously driven in an ensemble when it has inhomogeneous values for its optical transition energies. b Π scheme, responsible for L 2 emission feature: Two lasers are resonant with both vertical transitions. This is achieved when the detuning equals the difference between the ground-state and excited-state splittings, |Δ g − Δ e |. c V scheme, responsible for L 3 emission feature: Two lasers are resonant with transitions from a common ground state |g 1 〉 to both excited states |e 1 〉 (blue arrow) and |e 2 〉 (red arrow). This is achieved when the laser detuning equals the excited state splitting Δ e . The gray arrows indicate a secondary V scheme that is simultaneously driven when the optical transition energies are inhomogeneously broadened. d X scheme, responsible for the L 4 emission feature: Two lasers are resonant with the diagonal transitions in the scheme. This is achieved when the detuning is equal to the sum of the ground-state and the excited-state splittings, (Δ g + Δ e ) Full size image

We find that for data as in Fig. 2c the slopes of the emission lines are correlated by a set of sum rules

$$\Theta _{L3} = \Theta _{L1} + \Theta _{L2},$$ (2)

$$\Theta _{L4} = 2\Theta _{L1} + \Theta _{L2},$$ (3)

Here Θ Ln denotes the slope of emission line L n in Hertz per Tesla. The two-laser detuning frequencies for the pumping schemes in Fig. 3a–d are related in the same way, which justifies the assignment of these four schemes to the emission lines L 1 through L 4 , respectively. These schemes and equations directly yield the g-factor values g g and g e for the ground and excited state (Supplementary Information section 2).

We find that the g-factor values g g and g e strongly depend on ϕ, that is, they are highly anisotropic. While this is in accordance with earlier observations for transition metal defects in SiC,33 we did not find a comprehensive report on the underlying physical picture. In Supplementary Information section 7, we present a group-theoretical analysis that explains the anisotropy g g ≈ 1.7 for ϕ = 0° and g g = 0 for ϕ = 90°, and similar behavior for g e (which we also use to identify the orbital character of the ground and excited state). In this scenario the effective Landé g-factor50 is given by

$$g(\phi ) = \sqrt {\left( {g_{||}{\mathrm{cos}}\phi } \right)^2 + \left( {g_ \bot {\mathrm{sin}}\phi } \right)^2},$$ (4)

where g || represents the component of g along the c-axis of the silicon carbide structure and g ⊥ the component in the basal plane. Figure 4 shows the ground and excited state effective g-factors extracted from our two-laser magneto-spectroscopy experiments for 6H-SiC and 4H-SiC (additional experimental data can be found in Supplementary Information). The solid lines represent fits to the Eq. (4) for the effective g-factor. The resulting g || and g ⊥ parameters are given in Table 1.

Fig. 4 Effective g-factors for the spin of Mo impurities in SiC. Angular dependence of the g-factor for the S = 1/2 ground (g g ) and excited states (g e ) of the Mo impurity in 4H-SiC and 6H-SiC. The solid lines indicate fits of Eq. (4) to the data points extracted from two-laser magneto-spectroscopy measurements as in Fig. 2b,c Full size image

Table 1 Components of the g-factors for the spin of Mo impurities in SiC Full size table

The reason why diagonal transitions (in Fig. 3a, c), and thus the Λ and V scheme are allowed, lies in the different behavior of g e and g g . When the magnetic field direction coincides with the internal quantization axis of the defect, the spin states in both the ground and excited state are given by the basis of the S z operator, where the z-axis is defined along the c-axis. This means that the spin-state overlap for vertical transitions, e.g., from |g 1 〉 to |e 1 〉, is unity. In such cases, diagonal transitions are forbidden as the overlap between e.g., |g 1 〉 and |e 2 〉 is zero. Tilting the magnetic field away from the internal quantization axis introduces mixing of the spin states. The amount of mixing depends on the g-factor, such that it differs for the ground and excited state. This results in a tunable non-zero overlap for all transitions, allowing all four schemes to be observed (as in Fig. 2b where ϕ = 87°). This reasoning also explains the suppression of all emission lines except L 2 in Fig. 2b, where the magnetic field is nearly along the c-axis. A detailed analysis of the relative peak heights in Fig. 2b, c compared to wave function overlap can be found in Supplementary Information (section 4).

The Λ driving scheme depicted in Fig. 3a, where both ground states are coupled to a common excited state, is of particular interest. In such cases it is possible to achieve all-optical coherent population trapping (CPT),45 which is of great significance in quantum-optical operations that use ground-state spin coherence. This phenomenon occurs when two lasers address a Λ system at exact two-photon resonance, i.e., when the two-laser detuning matches the ground-state splitting. The ground-state spin system is then driven toward a superposition state that approaches \(\left| {\Psi _{{\rm CPT}}} \right\rangle \propto {\mathrm{\Omega }}_2\left| {g_1} \right\rangle - {\mathrm{\Omega }}_1\left| {g_2} \right\rangle\) for ideal spin coherence. Here \(\left| {{\mathrm{\Omega }}_n} \right\rangle\) is the Rabi frequency for the driven transition from the \(\left| {g_n} \right\rangle\) state to the common excited state. Since the system is now coherently trapped in the ground state, the photoluminescence decreases.

In order to study the occurrence of CPT, we focus on the two-laser PLE features that result from a Λ scheme. A probe field with variable two-laser detuning relative to a fixed control laser was scanned across this line in frequency steps of 50 kHz, at 200 μW. The control laser power was varied between 200 μW and 5 mW. This indeed yields signatures of CPT, as presented in Fig. 5. A clear power dependence is visible: when the control beam power is increased, the depth of the CPT dip increases (and can fully develop at higher laser powers or by concentrating laser fields in SiC waveguides47). This observation of CPT confirms our earlier interpretation of lines L 1 –L 4 , in that it confirms that L 1 results from a Λ scheme. It also strengthens the conclusion that this system is S = 1/2, since otherwise optical spin-pumping into the additional (dark) energy levels of the ground state would be detrimental for the observation of CPT.

Fig. 5 Signatures of coherent population trapping of Mo spin states in 6H-SiC. Two-laser spectroscopy of the L 1 peak in the PLE signals reveals a dipped structure in the peak at several combinations of probe-beam and control-beam power. This results from coherent population trapping (CPT) upon Λ-scheme driving. Temperature, magnetic field orientation and magnitude, and laser powers, were as labeled. The data are offset vertically for clarity. Solid lines are fits of a theoretical model of CPT (see main text). The inset shows the normalized CPT feature depths Full size image

Using a standard model for CPT,45 adapted to account for strong inhomogeneous broadening of the optical transitions47 (see also Supplementary Information section 6) we extract an inhomogeneous spin dephasing time \(T_2^ \ast\) of 0.32 ± 0.08 μs and an optical lifetime of the excited state of 56 ± 8 ns. The optical lifetime is about a factor two longer than that of the nitrogen-vacancy defect in diamond,12,51 indicating that the Mo defects can be applied as bright emitters (although we were not able to measure their quantum efficiency). The value of \(T_2^ \ast\) is relatively short but sufficient for applications based on CPT.45 Moreover, the EPR studies by Baur et al.33 on various transition-metal impurities show that the inhomogeneity probably has a strong static contribution from an effect linked to the spread in mass for Mo isotopes in natural abundance (nearly absent for the mentioned vanadium case), compatible with elongating spin coherence via spin-echo techniques. In addition, their work showed that the hyperfine coupling to the impurity nuclear spin can be resolved. There is thus clearly a prospect for storage times in quantum memory applications that are considerably longer than \(T_2^ \ast\).