Investigation of Surface Magnetic Noise by Shallow Spins in Diamond

We present measurements of spin relaxation times ($T_1$, $T_{1\rho }$, $T_2$) on very shallow ($\lesssim 5\mathrm{nm}$) nitrogen-vacancy centers in high-purity diamond single crystals. We find a reduction of spin relaxation times up to 30 times compared to bulk values, indicating the presence of ubiquitous magnetic impurities associated with the surface. Our measurements yield a density of $0.01–0.1{\mu }_B/{\mathrm{nm}}^2$ and a characteristic correlation time of 0.28(3) ns of surface states, with little variation between samples and chemical surface terminations. A low temperature measurement further confirms that fluctuations are thermally activated. The data support the atomistic picture where impurities are associated with the top carbon layers, and not with terminating surface atoms or adsorbate molecules. The low spin density implies that the presence of a single surface impurity is sufficient to cause spin relaxation of a shallow nitrogen-vacancy center.

Figure 1

(a),(b) Energy level diagram of the NV center’s spin $S=1$ system, indicating allowed spin transitions (red solid arrows) and associated transition rates $r_0$ and $r_1$. Blue brackets indicate the energy gaps between states. ${\omega }_0$ is the Larmor frequency ($\sim 2.9\mathrm{GHz}$) and ${\omega }_1$ is the Rabi frequency ($\sim 10\mathrm{MHz}$). A small bias field ($B_0\sim 10\mathrm{mT}$) lifts the degeneracy between $|\pm 1⟩$ [32, 33]. Diagram (a) shows transitions relevant for the $T_1$ measurement and diagram (b) shows transitions relevant for the $T_{1\rho }$ measurement. Dashed levels and arrows in (b) symbolize the superposition between $|0⟩$ and $|-1⟩$. (c) Basic picture of diamond surface magnetic impurities. Surface states are represented by a two-dimensional bath of electron spins that produce a fluctuating magnetic field. A nearby shallow NV center is used as a local probe to pick up the magnetic noise and analyze the spectral characteristics.

Figure 2

Pulse-timing diagrams and example decay curves for measurements of (a) the spin-lattice relaxation time $T_1$ and (b) the rotating-frame relaxation time $T_{1\rho }$. Green “pump/probe” blocks symbolize laser pulses ($\sim 1\mu \mathrm{s}$) and red other blocks symbolize microwave pulses. Red dotted block and “$\pm x$” denote phase cycling for the differential measurement. Curves are exponential fits and dots represent experimental values. Data shown is for NV No. 8 in Fig. 3 measured on sample $A$.

Figure 3

Spin relaxation time measurements of 13 shallow NV centers for different samples and surface terminations. (a) $T_1$, $T_{1\rho }$, and $T_2$ times organized in a two-dimensional correlation plot. Observed relaxation times are $T_1=0.3–9\mathrm{ms}$, $T_{1\rho }=0.02–3\mathrm{ms}$, and $T_2=22–80\mu \mathrm{s}$. Dots represent sample $A$ and triangles represent sample $B$. Bulk $T_1^{\text{bulk}}=12(2)\mathrm{ms}$ (sample $A$) is indicated by a dashed line. (b) Autocorrelation time ${\tau }_c$ of surface fluctuations for the same NV centers, organized by sample and surface termination. (c) rms magnetic field $B_{\mathrm{rms}}$ for each NV center. (d) Density of surface impurities ${\rho }_A$ for samples and surface terminations. (e) Histogram of depth values (upper bound) of NV centers inferred from $B_{\mathrm{rms}}$. Errors are propagated from fits to $T_1$ and $T_{1\rho }$ decay curves. Numerical data are provided as Supplemental Material [36].

Figure 4

(a) Temperature dependence of $T_1$ for a shallow NV center (Sample $A$, red dots) and for bulk NV centers (from Ref. [32], Fig. 2, curve S8). (b) $T_1$ for the same NV center, showing no significant change in $T_1$ with exposure to different oxygen pressures.