Hyperfine Coupling Constants of Photoinduced Axial Symmetry NV Centers in a 6H Silicon Carbide: DFT and High-Field ENDOR Spectroscopy Study

Abstract

Solid-state spin centers are at the forefront of developing advanced quantum technologies, engaging in applications of sensing, communication and computing. A semiconductor host matrix compatible with existing silicon technology provides a robust platform for holding spin defects and an opportunity for external manipulation. In this article, negatively charged nitrogen-vacancy (NV) centers in the hexagonal hh position in a 6H polytype silicon carbide crystal was studied using high-frequency (94 GHz) electron paramagnetic (EPR) and electron nuclear double resonances (ENDOR) spectroscopy. Experimentally determined values of hyperfine and quadrupole interactions of ¹⁴N were compared with the values obtained for the centers in NV_k2k1 positions. The distribution of spin density of the defect within a supercell of the SiC crystal lattice was calculated using the density functional theory approach. The theoretical estimation of electron-nuclear interaction constants turned out to be in close agreement with the experimental values, which allows us to refine the microscopic model of a point defect. The temperature dependence of the spin Hamiltonian values (δA/δT ≅ 180 Hz/K) was studied with the possibility of observing the ¹⁴N NMR signal at room temperature. The fundamental knowledge gained about interactions’ parameters’ behavior lays the foundation for the creation of promising quantum platforms.

1. Introduction

Semiconductor crystals, due to their wide band gap (>3 eV), have firmly established themselves as reliable host matrices for high-spin point defects, which can serve as quantum bits [1,2]. Various ways of forming stable defects/centers with specified and repeatable properties are associated with local disruption of the integrity of the crystal structure of the sample by high-energy irradiation, ion implantation, or femtosecond laser action [3]. The most common point defects are of a vacant nature, where the resulting atomic deficit can act as an isolated center or be coordinated with another impurity unit. As a rule, photoactive spin defects significantly change the optical properties of the substance in the visible and near-IR ranges, which led to the emergence of their more classical name—color centers. A feature of optically active spin defects is their sensitivity or flexibility to external influences in the form of laser and microwave (MW) quanta, as well as radiofrequency (RF) radiation, which together affect the final energy state.

Well-studied nitrogen-vacancy (NV) centers in diamond, despite decades of ongoing research, remain at the center of scientific attention, presenting new achievements in the field of quantum applications [4,5]. Recently, there has been growing interest among researchers in the silicon carbide (SiC) crystal, which, unlike diamond (a dielectric), has a greater proximity to existing semiconductor integrated circuits and devices [6]. Various defects with fundamentally different microstructures and properties can be formed in SiC; nevertheless, they “obtain along” together within one ensemble (C = 10¹⁷–10¹⁸ particles/cm³) medium. SiC crystals have a structural polymorphic variability or polytypism, which affects the order of “stacking” of Si and C atoms along the “c” axis (quantity and location). Thus, now, more than 250 modifications are known, where among the most phase-homogeneous, stable, and highly crystalline samples are 3C (with the band gap value of 2.6 eV), 4H (3.23 eV), and 6H (3.06 eV) polytypes. Silicon vacancy with electron spin S = 3/2 was presented first as an electron qubit with optical excitation at 808 nm and relaxation times of several ms at 297 K [7].

The particular hexagonal structure of 6H-SiC results in three non-equivalent sites for vacancy-type defects and dopants: one hexagonal site and two cubic-like sites called quasi-cubic position, in contrast to 4H-SiC or 3C-SiC, which have two and one non-equivalent sites, correspondingly [8]. The unique electrical and optical properties of 6H-SiC make it suitable for specific light-based applications, including LED substrates and optical sensors [9]. 6H-SiC offers excellent thermal stability and is used in devices that must operate in high-temperature environments. While 4H-SiC has been considered by researchers as a medium for power electronics due to the higher electron mobility and breakdown voltages, the distinct stacking sequence and resulting defect properties of 6H-SiC are now being explored for their potential in quantum technologies like sensing, networking, and computing [10]. The diverse defect configurations in 6H-SiC provide a unique platform for quantum technology research, potentially yielding different spin qubits and IR-band single-photon emitters compared to the more commonly studied 3C- or 4H-SiC [11]. Divacancy, which is a pair complex of two nearest vacancies in silicon and carbon, due to its interesting spin-optical characteristics, has received no less recognition in the development of a material base for quantum systems [12].

Much less attention has been paid to the recently discovered NV centers in SiC, which are microstructural analogs of nitrogen-centered carbon vacancies in diamond [13]. The interaction of the electron spin of the vacancy with the ¹⁴N isotope with a nuclear spin of I = 1 opens additional channels/routes for the transfer and processing of quantum information. Hyperfine coupling is a unique native mechanism for selective addressing of qubits based on electron and nuclear spins, with the possibility of demonstrating two-qubit gates and violation of Bell’s inequality [14,15]. Moreover, hyperfine detuning allows the creation of high-precision conditional rotation gates based on selective resonant excitation [16]. The distributed spin density within the unit cell allows the formation of a hyperfine connection with several nuclei simultaneously, opening up the possibility of creating a quantum register consisting of electron and nuclear spins. The electronic subsystem of the register can be a high-speed link between external optical radiation (photon) carrying quantum information and spin magnetization formed by photoinduced spin polarization. Due to longer relaxation times, the nuclear spin subsystem can act as a cell for storing information, which was first shown on ensembles of ³¹P donors in isotopically purified ²⁸Si, and with a coherent time at room temperature of more than 39 min [17]. Therefore, nuclear spins, which are still poorly understood as a medium for quantum information, have enormous development potential and require further research.

The first quantum operations on electron and nuclear spins were carried out using pulse sequences of electron paramagnetic resonance EPR and nuclear magnetic resonance NMR spectroscopy, which are the most convenient experimental approaches for studying the features/properties of spin defects. Using EPR, long-lived electron Rabi oscillations were obtained for silicon vacancies and NV centers in SiC, even at room temperature [18]. The combination of both electron and nuclear resonance transitions allows a more in-depth study of the spin system together with the local environment, position, and defect′s microstructure, establishing the values of hyperfine and quadrupole interactions. In the case of NV centers in diamond, the experimental values of the hyperfine interaction of an electron spin (S = 1) with nitrogen nuclei ¹⁴N (I = 1) were found to be approximately A_|| = −2.14 MHz or −2.2 MHz and A_⊥ = −2.70 MHz, where the nuclear quadrupole splitting is reported to be around 5.0 MHz [19]. Electron-nuclear interactions for NV centers in silicon carbide have been well studied primarily for the 4H polytype, where interaction parameters were determined for both axially C_3v symmetric and basal C_h1 centers. The constant of hyperfine interaction for axial centers is 1.14–1.16 MHz, and for basal centers it is 0.97 and 0.65 MHz. The quadrupole coupling constant for both types of NV centers is between 1.8 and 1.9 MHz [20]. Electron-nuclear interactions in 6H-SiC polytype have been studied in detail for the axial NV center in the k₂k₁ position, apart from the isotropic Fermi interaction a_iso = −1.125 MHz was found due to the specific distribution of NV’s spin density [21]. Theoretical simulations have successfully predicted the mentioned values for the hyperfine and quadrupole tensors, which facilitated the confirmation of the defect′s microscopic structure.

Double-resonance techniques’ abilities allow direct experimental observation of temperature-induced changes in the electron-nuclear coupling values for the NV defect in diamond [22,23,24]. In this work, we studied the electron-nuclear interactions of axial NV centers in the hexagonal structural position hh in the 6H-SiC sample using EPR and double electron-nuclear resonance (ENDOR). The experiments were carried out in the high-frequency region of the EPR spectrometer (94 GHz) to achieve greater spectroscopic resolution and reduce the second-order contributions of the perturbation theory. The established values of the spin Hamiltonian were evaluated for their dependence on the crystal temperature. Using the density functional theory method, theoretical values of the spin Hamiltonian parameters and the nature of the defect spin density distribution were derived. The experimental outcomes were compared with the results obtained for NV centers in the quasi-cubic k₂k₁ position.

2. Materials and Methods

2.1. Sample

6H-SiC crystals enriched with ²⁸Si (I = 0) atoms were grown by high-temperature sublimation from the gas phase using physical vapor transport technology, utilizing a precursor that contained up to approximately 99% of the ²⁸Si isotope. The nitrogen atom concentration in the studied crystal was equal to C ≈ 10¹⁷ cm⁻³. 6H-²⁸SiC samples were irradiated by high-energy (2 MeV) electrons with particle flux density (fluence) of 4 × 10¹⁸ cm⁻² in order to form vacancy defects. To create stable negatively charged nitrogen-vacancy complexes, the irradiated crystals were annealed at T = 900 °C in an argon atmosphere for 2 h. The sample investigated for the W-band EPR with dimensions of 450 × 450 × 670 μm³ was placed in a capillary and securely held in the resonator space by the holder collet.

2.2. Experimental Approaches

The magnetic resonance measurements were performed using a Bruker Elexsys E680 spectrometer (Bruker, Karlsruhe, Germany) operating at the microwave frequency of ν = 94 GHz. The EPR data were collected in pulse mode through electron spin echo (ESE) integration as a magnetic field function by Hahn pulse sequence π_MW/2–τ—π_MW—τ—ESE, where π_MW/2 = 40 ns and τ = 1500 ns. The Mims pulse sequence (π_MW/2–τ—π_MW/2–π_RF—π_MW/2–τ—ESE) was used for ENDOR spectra detection, where π_RF = 72 µs. An additional RF source (1–250 MHz) with an output power of 150 kW was necessary to initiate NMR transitions. Low-temperature experiments were conducted using a flow helium cryostat from Oxford Instruments (Abingdon, Oxfordshire, UK). Optical excitation of the samples was implemented by the solid-state diode-pumped lasers (λ = 980 nm) with an output power up to 500 mW. The pulse programmer used allowed the effective laser power to be reduced to a nominal 50 mW. Given the studied sample’s volume and SiC heat capacity, the crystal could heat up by 1.5 K during a 5 ms optical pulse. The high helium flow in the cryostat ensured effective rejection of the optically induced heating of the sample, resulting in negligible deviations and an experimental error for ENDOR results of less than <1%.

2.3. Computational Method

The configuration of paramagnetic impurities and parameters of the electron-ion interactions were determined by the density functional theory method using the Perdew–Burk–Ernzerhof (PBE) [25] exchange-correlation functional in the Quantum ESPRESSO version 7.4.1 software package (PWscf module). The calculations were carried out using a supercell, which is an atomic structure consisting of 36 6H-SiC unit cells (Figure 1). The proposed structure was optimized while preserving the boundaries of the supercell (using the “relax” calculation type) using a Monkhorst–Pack k-point grid of 1 × 1 × 1 size. Structural optimization was carried out with a plane wave kinetic energy cut-off value of 50 Ry and an electron density cut-off value of 200 Ry. Quantum ESPRESSO’s GIPAW module was used to calculate electron-nuclear interaction parameters, including hyperfine and quadrupole interactions [26]. ENDOR spectra were simulated using the Matlab EasySpin 5.2.36 software package [27].

3. Results and Discussion

NV centers in the crystal under study are characterized by intense microwave absorption consisting of two fine structure components due to the electron spin S = 1 and splitting in a zero magnetic field of 1300 MHz between the levels M_S = 0 and M_S = ±1. Photoinduced EPR spectra of the NV centers in the 6H-SiC crystal at T = 150 K are shown in Figure 1b. The recorded signal is photoinduced under the action of continuous optical radiation, since in the “dark” mode, the signal level is negligibly small. The high-field component of the fine structure is phase inverted since optical excitation leads to a preferential population of the state with M_S = 0, called spin alignment or polarization. The resulting optically induced spin population inversion creates a condition for radiation under the action of a microwave source, as in masers.

The EPR spectra in the temperature range of 297 K and 150 K consist of three contributions with a characteristic triplet type, which is due to the presence of structurally nonequivalent positions of NV centers: k₁k₂, hh, and k₂k₁ configurations [28]. Each of the axial positions is distinguished by a local environment, which is reflected in the value of D value. Recorded in detail, the components of the NV centers in three different positions consist of three additional sub-splitting. One of the reasons for the appearance of equidistant lines with the same intensities is the hyperfine interaction of the defect with the nuclear spin of nitrogen ¹⁴N. To confirm this assumption, the resonant absorption spectra of the NV centers in the radio frequency region were obtained using the ENDOR spectroscopy method. Corresponding spectra are presented in Figure 2. NMR-induced transitions lead to the observation of four narrow lines with a width of 4–5 kHz. The nature of these lines is associated with the isotope ¹⁴N with a nuclear spin of I = 1, which, due to the hyperfine and quadrupole interactions, leads to the splitting of spin sublevels with different energies (energy scheme).

The following spin Hamiltonian to describe the signals of the defect centers with electron spin S = 1 is used:

$$H=g{\mu }_B\mathit{B}·\mathit{S}+D\left(S_z^2-S(S+1)\right)+{ A}_{\left|\right|}{S}_z{I}_z+A_{\perp }\left(S_x{I}_x+S_y{\mathrm{I}}_y\right)+Q\left(I_z^2-I(I+1)\right)$$

(1)

where $g$ is the spectroscopic splitting factor (gravity center of the EPR spectrum), ${\mu }_B$ is the boron magneton, D (axial symmetry) is the zero-field splitting (ZFS) value, and S_x,y,z and I_x,y,z are the quantum projections of the electron and nuclear spins; A and Q are the values of the tensors of hyperfine and quadrupole interactions.

In the course of describing the experiment (Figure 2a), for the parallel orientation of the crystal c axis relative to B₀, the contributions of the hyperfine (A) splitting and the quadrupole coupling constants (Cq) were determined using the spin Hamiltonian (1). The ENDOR spectra were also obtained for the high-field EPR component, where the NMR lines have a mirror reflection relative to the Larmor frequency of ¹⁴N. The nuclear Larmor frequency of ¹⁴N is ν_L = 10.2 MHz with a gyromagnetic ratio of 3.077 MHz/T, which corresponds to a magnetic field of 3.4 T.

In order to clarify the symmetry of the interaction tensors and contributions to the electron-nuclear splitting, a series of experiments with successive rotation of the crystal relative to B₀ was carried out. Figure 3 shows the dependence of the NMR lines’ position on the angle between the external magnetic field and the c-axis of the crystal (experiment, dots). The theoretical description is carried out using Equation (1) and taking into account the following three contributions: isotropic Fermi interaction, dipole–dipole coupling, and nuclear quadrupole splitting. The established data are presented in

Table 1. Experimental and theoretical values of hyperfine and quadrupole interactions of the NV center in 6H-SiC for the hh position at T = 150 K. The theoretical estimate is obtained using the quantum-mechanical approach of density functional theory. For comparison with k₂k₁ position (exp): a_iso = −1.125 MHz, b < 50 kHz and C_q = 2.530 MHz; (dft): a_iso = −1.118 MHz, b = 64 kHz and C_q = −2.695 MHz.

NVhh	A-Tensor Values (MHz)	Cq (MHz)
Experiment	aiso = −1.175; b ≤ 0.02	2.523
Theory	aiso = −1.140; b = 0.088	2.6194

. The orientational anisotropy of the line position is caused mainly by the quadrupole interaction of axial symmetry. Comparison of the isotropic HFI value in this system with the literature data for an isolated nitrogen atom indicates that the spin density of the NV center is localized on the nitrogen nucleus only to an extremely small extent. Most of the spin density is distributed among the nearest carbon and silicon atoms. Taking into account the expressions for calculating the HFI contributions [29], the spin density is about ρ = 0.02%. In the high-frequency range, where the Larmor frequency is greater than the HFI and NQI values, the electron-nuclear interaction is of the “weak coupling” type.

The spin density of the NV defect in the crystal lattice of the 6H-SiC sample under study was calculated using DFT methods. The distribution features are shown in Figure 4. The spin density is distributed predominantly within the planar Si-C plane perpendicular to the crystallographic c-axis, with a slight overlap of the adjacent upper structural layer. The distribution has axial symmetry without rhombic distortion. As can be seen, the spin density of the NV center affects distant coordination spheres, up to the fourth one. Such a dispersed spin density on the nearest and distant nuclei of ¹³C (I = ½, 1.013%) and ²⁸Si (I = ½, 4.28%) is capable of providing a channel for transferring spin magnetization representing quantum information between electron and nuclear sub-ensemble through hyperfine interaction, thereby implementing a multiqubit electron-nuclear register [30,31].

Based on the obtained spin density of NV_hh defects, theoretical values of hyperfine and quadrupole interactions were calculated, where tensor matrix elements of dipole–dipole splitting were also found. A comparative analysis of the values is shown in Table 1. Relatively good agreement with experimental data allows one to be convinced that the optically active paramagnetic center under study is a spin defect consisting of a silicon vacancy and an impurity nitrogen atom in the carbon position. In accordance with the simulation of the ENDOR lines’ angular dependence and DFT calculations, the Fermi contact term HFI turned out to be negative. The spin density is predominantly localized on the three carbon dangling bonds surrounding the silicon vacancy, which polarizes the core states of the nitrogen. Because of the positive sign of the nuclear magnetic moment of ¹⁴N, the resulting value of a_iso = −1.175 MHz is negative [32]. Absolute value and axial symmetry of NQI above 2 MHz also indicated a threefold silicon-coordinated N atom according to sp³—hybridization, confirming conclusively the attribution of the observed EPR and ENDOR spectra to a nearest N_CV_Si pair in a negatively charged ground state [33].

In most cases, ENDOR experiments require low temperatures of the samples studied due to the technical restrictions caused by the electron and nuclear spin subsystems’ relaxation rates. The Mims pulse sequence comprises stimulated electron spin echo, where the maximum allowable interval between microwave pulses required to implement the RF excitation (t_π_RF = 72 μs) is determined by the T_1e time [34]. In this work, in addition to the previous results, signals of the NV centers in the 6H-SiC sample were obtained at room temperature. In order to eliminate overheating of the crystal under the influence of a continuous wave IR laser (λ = 980 nm), a helium flushing was turned on at a T = 275 K, which can easily be achieved using Peltier elements down to 200 K. The relaxation times of the NV centers’ electron spin subsystem at room temperature were T₁ = 100 μs for electron-phonon interactions and T₂ = 25 μs for spin–spin interactions. The ENDOR spectra for both fine structure transitions under natural (297 K) conditions are shown in Figure 5. The signal-to-noise ratio is noticeably smaller; however, the ENDOR spectrum was obtained in a reasonable experimental time of several scans. Radiofrequency radiation absorption at room temperature can find its application for quantum technologies in the field of external RF-sensing and formation of qubit networks [35,36].

It was determined that the value of the HFI at T = 275 K slightly differs from the line splitting at T = 150 K, so additional experiments were carried out at other crystal temperatures. Figure 6 shows the dependence of the spin Hamiltonian parameters. In a wide temperature range, the splitting values are preserved, which is important for selective controlled stable excitation. Temperature-dependent properties of the defect induced by spin-phonon interaction are important to reveal, as the interaction of the spin system with the environment should be taken into account for high-precision quantum control and ultrasensitive detection [37,38]. The results of the magnetic resonance spectroscopy of the NV ensemble in diamond over a wide temperature range were summarized in refs [39,40], demonstrating nonlinear relationships between the zero–field splitting parameters and temperature. The changes in the values of the spin Hamiltonian in the case of NV centers in 6H-SiC are quite small, remaining within the error limits at the same level. By giving a quantitative assessment, the following values of temperature sensitivity can be obtained: δA/δT = 180 Hz/K whereas the ZFS and Q parameters return practically the same within the temperature range 100–280 K. Since the magnitudes of electron-nuclear interactions are defined by the nature of the defect itself and its local environment, it is obvious that both contributions determining the hyperfine splitting, namely the isotropic Fermi interaction constant and the anisotropic dipole–dipole component, depend on the atoms position in the crystal lattice (distance and mutual angles). However, only theoretical considerations of thermally induced distortion of the crystal lattice and the corresponding rearrangement of atoms did not fully satisfy the experimental observations [41]. In Doherty et al. [42] work, the quadratic spin-phonon interaction was additionally taken into account, which, in fact, brought the model of temperature behavior closer to the discovered unconventional dependences. A temperature change in a defective crystal, leading to volumetric compression or expansion of the lattice, additionally distorts the vacancy center with an impurity nitrogen atom, significantly affecting the orbital levels and the distribution of spin density [43]. Thus, the study of the temperature-dependent nature of the NV center hyperfine interaction values requires a microscopic behavior analysis of the defect itself, which is manifested by a change in the hybridization angles and the fraction of the spin density of the center in the region of the nitrogen nucleus.

For NV centers in diamond, prior studies demonstrated that the temperature dependence of HFI magnitudes does not correlate with the thermal expansion coefficients of the crystal lattice [23]. In the case of SiC polytypes 4H and 6H, the coefficients of thermal expansion tend to change sharply (decrease) in the linear region from 350 K to 200 K, with a transition to a level with extremely insignificant shifts [44].

Since frequency shifts reduce the accuracy of resonant quantum control, the present results demonstrate the need to take temperature fluctuations into account. The transition energies tend to be constant for temperatures below 100 K, indicating higher stability and performance in NV center applications. The small magnitude of these changes (HFI, NQI, and ZFS) is a positive factor for the use of NV spin centers in 6H-SiC in quantum applications at high temperatures, since the positions of the resonance lines will not shift, which reduces the requirement for maintaining a constant device temperature.

4. Conclusions

This paper presents the results of magnetic resonance studies of negatively charged nitrogen vacancy centers (NV) in a SiC crystal of the hexagonal polytype 6H for the hh position. The results of EPR and ENDOR spectroscopy in the high-frequency range, together with the results of calculations in the density functional theory, made it possible to determine the values of the hyperfine and quadrupole interaction tensors. The calculated spin density of the NV-center is predominantly within the planar Si-C plane perpendicular to the crystallographic c-axis. The temperature dependence of the spin Hamiltonian parameters was also measured in the temperature range from 100 to 280 K. It was found that the values of the parameters D and Q remain practically unchanged with temperature, while the hyperfine interaction parameter A has a weak temperature dependence, which must be taken into account when designing quantum devices based on NV centers in a crystal 6H-SiC. The established temperature stability of spin Hamiltonian values is a major practical advantage in the field of quantum technology for information processing and bright single-photon sources functioning. Many known quantum systems rely on cryogenic temperatures to maintain the fragile quantum states of their qubits. Room temperature operation based on NV′s spin defects potentially simplifies device engineering and reduces the energy cost of cooling, making the technology more practical and scalable.