Hyperfine and nuclear quadrupole splitting of the ${\mathrm{NV}}^{\ensuremath{-}}$ ground state in $4H$-SiC

Hyperfine and nuclear quadrupole splitting of the ${NV}^{-}$ ground state in $4 H$ -SiC

F. F. Murzakhanov, B. V. Yavkin, G. V. Mamin, S. B. Orlinskii, H. J. von Bardeleben, T. Biktagirov, U. Gerstmann, and V. A. Soltamov

Phys. Rev. B 103, 245203 – Published 21 June 2021

Abstract

Optically addressable spin-triplet defects in silicon carbide, such as divacancies and negatively charged nitrogen vacancy $({NV}^{-})$ allow to develop modern quantum technologies operating in the near-infrared range based on the well-developed semiconductor material. Here, by means of both high-frequency (94 GHz) pulsed electron paramagnetic resonance (EPR) and electron-nuclear double Rresonance (ENDOR) techniques the ground state properties of the negatively charged ${NV}^{-}$ defect in $4 H$ -SiC were studied. We experimentally determined the ordering of the ground state spin sublevels and established the sign of the zero-field splitting to be positive as predicted by theory. Analysis of nuclear magnetic resonance transitions in ENDOR spectra allowed to determine the sign, symmetry, and absolute values of the hyperfine interaction of the ${NV}^{-}$ defect electron spin with ${}^{14}N$ nuclear spin as $A_{∥} = - 1.142 MHz$ and $A_{⊥} = - 1.184 MHz$ . The absolute value of the nuclear quadrupole interaction constant reflecting an interaction between the ${}^{14}N$ nuclear electric quadrupole moment with the electric field gradient was determined to be $| C_{q} | = 2.44 MHz$ . This large value is compatible with a threefold coordinated ${}^{14}N$ nucleus with uniaxial symmetry and proves conclusively the existence of a nearestneighbor $N_{C} V_{Si}$ pair in the material. For this ${NV}^{-}$ defect, an ensemble (Hahn-echo) coherence time of $T_{2} = 49 μ s$ was measured, a value which is in the range previously reported for silicon vacancy spin ensembles and slightly longer than $T_{2} = 40 μ s$ measured here on the divacancy spin ensemble.

Received 18 February 2021
Accepted 8 June 2021

DOI:https://doi.org/10.1103/PhysRevB.103.245203

Physics Subject Headings (PhySH)

Color centers Defects NV centers

Density functional theory Electron nuclear double resonance Electron paramagnetic resonance Electron spin resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

F. F. Murzakhanov ¹, B. V. Yavkin ¹, G. V. Mamin ¹, S. B. Orlinskii¹, H. J. von Bardeleben², T. Biktagirov³, U. Gerstmann ^3,*, and V. A. Soltamov ^1,†

¹Kazan Federal University, Kazan 420008, Russia
²Sorbonne Université, Campus Pierre et Marie Curie, Institut des Nanosciences de Paris, 4, place Jussieu, 75005 Paris, France
³Lehrstuhl für Theoretische Materialphysik, Universität Paderborn, 33098 Paderborn, Germany

^*uwe.gerstmann@upb.de
^†victrosoltamov@gmail.com

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Vol. 103, Iss. 24 — 15 June 2021

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Figure 1
(a) Models of the divacancies ${VV}_{h h}$ , ${VV}_{k k}$ together with ${NV}_{k k}$ defect (highlighted by rectangles) in the $4 H$ -SiC. Si and C vacancies are shown with dashed circles. 1.89 Å is the Si-C bond length along the $c$ axis. 3.08 Å is the distance between basal C atoms. (b) (Top) Optically induced EPR spectrum of axial triplet centers in the $4 H$ -SiC sample measured at temperature $T = 100$ K. Arrows show fine structure lines of the ${VV}_{h h}$ , ${VV}_{k k}$ , and ${NV}_{k k}$ centers. The inset demonstrates optically induced predominant population of the $m_{S} = 0$ in the triplet ground state. (Bottom) EPR signals of ${VV}_{k k}$ and ${NV}_{k k}$ centers (marked with the asterisks) now measured at $T = 10$ and 7 K in the dark. Red-dashed line shows the simulated amplitude of the $T = 7 K$ fine-structure lines. White-dashed line stress the difference in the EPR magnitudes. (c) Scheme of the Zeeman levels population due to Boltzmann distribution. Thick arrows show the $m_{S} = - 1 \to m_{S} = 0$ transitions, depending on the sign of $D$ value.
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Figure 2
(a). The scheme of the ${NV}_{k k}$ ground state energy levels including nuclear Zeeman, hyperfine and quadrupole interactions with one ${}^{14}N$ nuclei. Expected ENDOR transitions for the fine-structure components $m_{S} = 0 \to + 1$ (left panel) and $m_{S} = 0 \to - 1$ (right panel) are shown with red and black bars, respectively. (b) ENDOR spectrum detected on the $m_{S} = 0 \to + 1$ component, $ν_{1} − ν_{4}$ transitions denoted in correspondence with the left panel of the scheme. Insets show the transitions in the enlarged scale, arrow indicates transitions due to the quadrupole splitting. (c) ENDOR spectrum detected on the $m_{S} = 0 \to - 1$ ESE line, $ν_{5} − ν_{8}$ transitions denoted as on the right panel of the scheme.
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Figure 3
ENDOR spectra detected in the ( $B ∥ c$ ) (bottom, $θ = 0^{\circ}$ ) and $B ⊥ c$ (top, $θ = 90^{\circ}$ ) orientations represented in high-resolution coordinates, i.e., $f - ν_{L}$ . Measured angular dependence of the ENDOR frequencies is shown in between by rad and gray balls together with its fit obtained using Eq. (2) with parameters $a = - 1.170 MHz$ , $b = 0.014 MHz$ , and $P = 1.81 MHz$ . Quadrupole splitting parameter $P$ and hyperfine interaction constant ( $A_{∥}$ ) are shown by arrows.
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Figure 4
Coherence times $T_{2}$ measured on the ensemble of optically polarized spins of ${VV}_{k k}$ divacancies (green squares) and ${NV}_{k k}$ centers (orange cicles). Single exponential fit of the experimental relaxation curves (black solid lines) with characteristic decay times $T_{2} = 40 μ s$ and $T_{2} = 49 μ s$ for the ${VV}_{k k}$ and ${NV}_{k k}$ centers, respectively. Inset illustrates the mw pulse sequence used in the current experiment. Relaxation curve measured on the ${VV}_{h h}$ centers follows roughly the same exponential decay with $T_{2} = 41 μ s$ as for the ${VV}_{k k}$ (not shown for clarity).
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Physical Review B

covering condensed matter and materials physics

Hyperfine and nuclear quadrupole splitting of the ${NV}^{-}$ ground state in $4 H$ -SiC

F. F. Murzakhanov, B. V. Yavkin, G. V. Mamin, S. B. Orlinskii, H. J. von Bardeleben, T. Biktagirov, U. Gerstmann, and V. A. Soltamov

Phys. Rev. B 103, 245203 – Published 21 June 2021

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Physical Review B

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Hyperfine and nuclear quadrupole splitting of the NV− ground state in 4H-SiC

F. F. Murzakhanov, B. V. Yavkin, G. V. Mamin, S. B. Orlinskii, H. J. von Bardeleben, T. Biktagirov, U. Gerstmann, and V. A. Soltamov

Phys. Rev. B 103, 245203 – Published 21 June 2021

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Hyperfine and nuclear quadrupole splitting of the ${NV}^{-}$ ground state in $4 H$ -SiC