Spin-strain interaction in nitrogen-vacancy centers in diamond

The interaction of solid-state electronic spins with deformations of their host crystal is an important ingredient in many experiments realizing quantum information processing schemes. Here, we theoretically characterize that interaction for a nitrogen-vacancy (NV) center in diamond. We derive the symmetry-allowed Hamiltonian describing the interaction between the ground-state spin-triplet electronic configuration and the local strain. We numerically calculate the six coupling-strength parameters of the Hamiltonian using density functional theory, and propose an experimental setup for measuring those coupling strengths. The importance of this interaction is highlighted by the fact that it enables to drive spin transitions, both magnetically allowed and forbidden, via mechanically or electrically driven spin resonance. This means that the ac magnetic field routinely used in a wide range of spin-resonance experiments with NV centers could in principle be replaced by ac strain or ac electric field, potentially offering lower power requirements, simplified device layouts, faster spin control, and local addressability of electronic spin qubits.

Figure 1

Nitrogen-vacancy (NV) center in the diamond lattice (Bravais cell depicted as a cube in black). $\{X,Y,Z\}$ defines the cubic reference frame and $\{x,y,z\}$ defines the NV reference frame. Deformation of the diamond crystal is visualized in red for ${\varepsilon }_{xx}=0.1$ strain component. We use this high strain only for sake of clarity.

Figure 2

Level structure of the ${}^{14}\mathrm{NV}$ at the GSLAC as a function of the axial magnetic field $B_z$. All transverse magnetic field components and stress are zero, $B_x=B_y=0,\sigma =0$. The circle marks the crossing that serves to identify the stress coupling coefficients $g_{25},g_{26}$. The levels coupled by the hyperfine interaction are shown with the same color (red solid; light blue dashed). The arrows indicate the bright radio-frequency magnetic transitions at the corresponding values of the magnetic field. In the absence of mechanical stress, the dashed lines are invisible in optically detected magnetic resonance.

Figure 3

Effect of mechanical stress on the photoluminescence contrast in optically detected magnetic resonance of an ${}^{14}\mathrm{NV}$ center. Black: no stress, orange: ${\sigma }_{zz}=1\text{GPa}$. The curves show the dependence of hyperfine transition frequencies as function of the axial magnetic field $B_z$ in the vicinity of the GSLAC. The thickness of each curve is proportional to the photoluminescence contrast $C$ [Eq. (13)]; maximal thickness corresponds to $C=1$. (a) High-energy transitions to $|1e\rangle$ spin states. (b) Low-energy transitions within the subspace of $|0e\rangle$ and $|-1e\rangle$.

Figure 4

Strain dependence of the zero-field splitting matrix element $D_{xy}$. Data points show the DFT results for the matrix element $D_{xy}$, as a function of the strain component ${\varepsilon }_{xy}$, with all other strain components set to zero. Solid line shows a linear fit, with a slope of $9832\pm 9\mathrm{MHz}/\mathrm{strain}$, allowing to obtain the coupling-strength parameter $h_{16}$ via Eq. (B2).