Temperature dependence of the $^{13}\mathrm{C}$ hyperfine structure of the negatively charged nitrogen-vacancy center in diamond

Temperature dependence of the ${}^{13}C$ hyperfine structure of the negatively charged nitrogen-vacancy center in diamond

M. S. J. Barson, P. Reddy, S. Yang, N. B. Manson, J. Wrachtrup, and M. W. Doherty

Phys. Rev. B 99, 094101 – Published 4 March 2019

Abstract

The nitrogen-vacancy (NV) center is a well utilized system for quantum technology, in particular quantum sensing and microscopy. Fully employing the NV center's capabilities for metrology requires a strong understanding of the behavior of the NV center with respect to changing temperature. Here, we probe the NV electronic spin density as the surrounding crystal temperature changes from 10 K to 700 K by examining the hyperfine interactions with a nearest-neighbor ${}^{13}C$ . These results are corroborated with ab initio calculations and demonstrate that the change in hyperfine interaction is small and dominated by a change in the hybridization of the orbitals constituting the spin density, thus indicating that the defect and local crystal geometry is returning towards an undistorted structure at higher temperature.

Received 15 December 2018

DOI:https://doi.org/10.1103/PhysRevB.99.094101

Physics Subject Headings (PhySH)

Fine & hyperfine structure NV centers Quantum metrology

Diamond Nitrogen vacancy centers in diamond

Density functional calculations Optically detected magnetic resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. S. J. Barson¹, P. Reddy¹, S. Yang^2,3, N. B. Manson¹, J. Wrachtrup², and M. W. Doherty¹

¹Laser Physics Centre, Research School of Physics and Engineering, Australian National University, 2601, Australia
²3. Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, Stuttgart, 70569, Germany
³Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

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Vol. 99, Iss. 9 — 1 March 2019

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Figure 1
(a) Unit cell with crystallographic coordinates $(X, Y, Z) = ([100], [010], [100])$ and NV coordinates chosen as $(x, y, z) = ([11 \bar{2}], [\bar{1} 10], [111])$ . (b) Energy levels with the ${}^{13}C$ hyperfine interaction with spin-spin splitting $δ_{h f}$ and hyperfine splitting $Δ_{h f}$ . Due to the nondiagonal components of the hyperfine interaction, for zero or small applied magnetic fields the hyperfine levels are a mixture of spin levels, without simply defined quantum numbers. (c) Depiction of processes occurring during thermal expansion; lattice distortion and resulting redistribution of spin density between atoms and rehybridization (reorientation) of the orbitals comprising the spin density.
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Figure 2
(a) Change in mean position ( $δ_{h f}$ ) of spin resonances with temperature; the dashed line is from the Hamiltonian using the theoretical description for $D (T)$ (see Appendix pp2) and the ab initio determined hyperfine terms. Inset: Example ${}^{13}C$ ODMR spectra from ensemble at $T = 180$ °C; colored lines are Gaussian fits. The upper/lower insets are from lower/higher gain settings on the lock-in amplifier. The ${}^{13}C$ resonance are just visible in the low gain spectra. The central resonance (omitted) saturates the amplifier in the high gain spectra. (b) Change in difference of spin resonances ( $Δ_{h f}$ ) with temperature; dashed-dot line represents the Hamiltonian (shifted in energy to match data) with ab initio temperature dependent hyperfine parameters and the dotted line is with constant hyperfine parameters and $D (T)$ .
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Figure 3
(a) Ab initio results of hyperfine parameters (points) and linear fits (lines) due to changes in lattice constant $a$ . (b) Changes to the dipolar ( $d$ ) and Fermi ( $f$ ) components of the hyperfine interaction with respect to changes in the temperature $T$ . (c),(d) Changes to the spin density $η$ and component of $p$ orbital ${|c_{p}|}^{2}$ . (e) Ab initio results of the positions of atoms at zero temperature. The arrows indicate the shift of the atoms for increasing temperature. The arrows representing displacement are normalized in size; as such, the carbons nearest to the vacancy experience the greatest displacement. The carbon atoms are gray, the vacancy is pink, the nitrogen is green, and the ${}^{13}C$ atom is black. The axes $(X, Y, Z)$ represent the crystallographic coordinate system.
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Figure 4
(a) Volumetric strain vs temperature using expressions from Sato et al. and Reeber et al. Note the divergence for the description by Sato for $T > 300$ K. (b) The descriptions of the temperature dependence of $D (T)$ by Doherty et al., Chen et al., and Toyli et al. with artificial data created by the expressions from Doherty and Toyli ( $D$ ) and the expected result from considering thermal expansion strain only ( $D_{e x}$ ). (c) Refitting over the full temperature range using equation (B1) and the artificial data ( $D$ ).
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Figure 5
(a) The experimental data for the average spin resonances from the high-temperature ensemble measurements for both the central main resonance and the ${}^{13}C$ resonances. The different colors are from separate measurements. (b) The difference in spin resonance of both the central main resonance and the ${}^{13}C$ resonances. Note the nonmonotonic behavior of both spin resonances with increasing temperature. This was repeatable for separate measurements. (c) The separation of the ${}^{13}C$ spin resonances with the temperature dependence of the separation of the main spin resonances subtracted and shifted to match the low temperature data.
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Physical Review B

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Temperature dependence of the ${}^{13}C$ hyperfine structure of the negatively charged nitrogen-vacancy center in diamond

M. S. J. Barson, P. Reddy, S. Yang, N. B. Manson, J. Wrachtrup, and M. W. Doherty

Phys. Rev. B 99, 094101 – Published 4 March 2019

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Physical Review B

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Temperature dependence of the C13 hyperfine structure of the negatively charged nitrogen-vacancy center in diamond

M. S. J. Barson, P. Reddy, S. Yang, N. B. Manson, J. Wrachtrup, and M. W. Doherty

Phys. Rev. B 99, 094101 – Published 4 March 2019

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Temperature dependence of the ${}^{13}C$ hyperfine structure of the negatively charged nitrogen-vacancy center in diamond