A charge transfer mechanism for optically addressable solid-state spin pairs

TL;DR

The paper addresses the lack of a microscopic origin for ODMR in hBN spin defects by combining spin- and time-resolved PL measurements with a radical-pair–inspired optical-spin defect pair (OSDP) model. It shows that two nearby defects form a metastable spin pair whose spin-selective charge-transfer transitions produce ODMR via selection rules, with the observable ODMR contrast depending on the relative spin-selectivity of creation and recombination. First-principles calculations identify carbon-based donor-acceptor pairs as plausible candidates for the defects, predicting a $49\ \mathrm{MHz}$ ODMR linewidth and ZPLs spanning the visible to near-IR, consistent with GaN observations. The work provides a universal framework for engineering and discovering optically addressable spin pairs in wide-bandgap materials and suggests clear paths to tailor spin dynamics in two-dimensional hosts like hBN.

Abstract

Optically detected magnetic resonance (ODMR) with no resolvable zero-field splitting has been observed from emitters in hexagonal boron nitride across a broad range of wavelengths, but so far an understanding of their microscopic structure and the physical origin of ODMR has been lacking. Here we perform comprehensive measurements and modelling of the spin-resolved photodynamics of ensembles and single emitters, and uncover a universal model that accounts, and provides an intuitive physical explanation, for all key experimental features. The model, inspired by the radical-pair mechanism from spin chemistry, assumes a pair of nearby point defects -- a primary optically active defect and a secondary defect. Charge transfer between the two defects creates a metastable weakly coupled spin pair with ODMR naturally arising from selection rules. Using first-principle calculations, we show that simple defect pairs made of common carbon defects provide a plausible microscopic explanation. Our optical-spin defect pair (OSDP) model resolves several previously open questions including the asymmetric envelope of the Rabi oscillations, the large variability in ODMR contrast amplitude and sign, and the wide spread in emission wavelength. It may also explain similar phenomena observed in other wide bandgap semiconductors such as GaN. The presented framework will be instrumental in guiding future theoretical and experimental efforts to study and engineer solid-state spin pairs.

Figures (30)

• Figure 1: Spin-active visible-band emitters in hBN. (a) Schematic of the experiment. (b) PL spectrum of a single emitter excited with a 532 nm laser. Inset: corresponding auto-correlation function indicating single photon emission. (c) CW ODMR spectrum of the emitter in (b), obtained at $B_0\approx75$ mT. Inset: ODMR spectrum of another emitter featuring a 60% contrast. (d) PL spectrum of a large ensemble of emitters. Inset: PL decay trace (red) following a short laser pulse, from which the excited-state lifetime $\tau_e$ is estimated via a stretched exponential fit (black dashed line). (e) Series of CW ODMR spectra of the ensemble at different field strengths $B_0\approx18 - 196$ mT. (f) Magnetic field dependence of the resonance frequency extracted from (e). Dashed line is a linear fit, indicating $g = 2.0(1)$. (g) Schematic of a weakly coupled spin pair and the resultant energy level structure. The eigenstates are $T_+=\left| \uparrow\uparrow \right\rangle$, $T_-=\left| \downarrow\downarrow \right\rangle$, and mixtures of $\left| \uparrow\downarrow \right\rangle$ and $\left| \downarrow\uparrow \right\rangle$, or equivalently of $S=(\left| \uparrow\downarrow \right\rangle-\left| \downarrow\uparrow \right\rangle)/\sqrt{2}$ and $T_0=(\left| \uparrow\downarrow \right\rangle+\left| \downarrow\uparrow \right\rangle)/\sqrt{2}$Boehme2003. Energy splitting between the two mixed states is assumed negligible (weakly coupled approximation).
• Figure 2: Spin-resolved photodynamics. (a) Pulse sequence for the spin-resolved PL measurements. An initial 1-ms laser pulse is applied to polarise the spin. The second laser pulse reads out the PL from the polarised spin following a 1-$\mu$s dark time (top sequence), or from the unpolarised spin following a 1-$\mu$s MW pulse (bottom). (b) PL trace for the entire 1-ms laser pulse. Throughout, the PL amplitude is normalised to the steady-state PL. (c) PL trace during the first $10\,\mu$s of the readout laser pulse with (blue, $F_2$) and without (orange, $F_1$) the applied MW pulse, for the same single emitter as in Fig. \ref{['fig1']}(b,c). Inset: Relative difference between the two traces. The dashed lines are monoexponential fits. (d) Same as (c) but for a large ensemble of emitters. Here the dashed lines are stretched exponential fits.
• Figure 3: Optical readout of spin dynamics. (a) Rabi measurement sequence with 5-$\mu$s gated regions at the front of the readout laser pulse following a MW pulse of variable duration $\tau$ (blue, $F_2$) or a dark time of duration $\tau$ (red, $F_1$). (b) Top: PL averaged over gated regions indicated in (a), as a function of $\tau$. The solid lines are simulations based on the three-level model depicted in inset, fit to the experimental data. Rabi driving at rate $\Omega$ occurs between pure triplet ($T_\pm$) and mixed singlet-triplet ($ST_0$) states which decay at different rates ($k_{\rm rec}^T$ and $k_{\rm rec}^S$ respectively) to a pure singlet ($S$) state. Bottom: Normalised Rabi measurement ($F_2-F_1$) and corresponding simulation. (c) Sequence for the spin contrast decay measurement. The readout laser pulse follows a variable dark time $\tau$ with or without a final 1-$\mu$s MW pulse. (d) Top: PL averaged over 5-$\mu$s gated regions indicated in (c), as a function of $\tau$. Bottom: Difference between the two traces ($F_2-F_1$), fit with a monoexponential to estimate the average spin polarisation lifetime.
• Figure 4: PL settling-recovery dynamics. (a) Pulse sequence consisting of 10-ms laser pulses separated by a variable dark time $\tau$ which allows the system to relax. PL readout is taken from the front ($F$) and back ($B$) of the pulse. (b) Example PL traces for increasing dark time $\tau$, recorded for an ensemble of emitters. (c) Integrated PL ($F$, $B$) versus $\tau$. The signal trace $F$ (first 10 $\mu$s of each laser pulse) is fit with a stretched exponential. The flat reference trace $B$ (last 10 $\mu$s of each laser pulse) confirms the system is reset to the same state after each pulse independent of $\tau$. (d) PL traces after $\tau=50$ ms (ensuring most populations have decayed back to the initial state) plotted on a log time scale, for three laser intensities: $P_{\rm L}=1.2 \times 10^2$, $P_{\rm L}=1.2 \times 10^3$, and $P_{\rm L}=1.2 \times 10^4$ W/cm$^2$ (from lighter to darker green). Black dashed lines are stretched exponential fits from which the settling rate $k_{\rm sett}$ is extracted. Inset: Settling rate as a function of $P_{\rm L}$. The dashed line corresponds to the model presented in Fig. \ref{['fig5']}(c), with parameters discussed in SI Sec. \ref{['sec:ensemble']}.
• Figure 5: Proposed electronic structure. (a) Single-particle picture for two point defects occupied by two electrons. The green/red arrows represent optical transitions. The black arrow represents a charge transfer from defect B to defect A. (b) Pictorial representation in the hBN lattice. The two electrons are either co-localised on defect A forming a spin-singlet system (left), or localised on one defect each forming a degenerate singlet-triplet system (right). (c) Many-body picture of the two-defect system. The four states of the spin pair [see Fig. \ref{['fig1']}(g)] are treated as a simplified two-level system (states denoted as $ST_0$ and $T_\pm$) split by $g\mu_{\rm B} B_0$. Spin driving is only enabled between these two states.