Hyperfine-Field-Mediated Spin Beating in Electrostatically Bound Charge Carrier Pairs

Organic semiconductors offer a unique environment to probe the hyperfine coupling of electronic spins to a nuclear spin bath. We explore the interaction of spins in electron-hole pairs in the presence of inhomogeneous hyperfine fields by monitoring the modulation of the current through an organic light emitting diode under coherent spin-resonant excitation. At weak driving fields, only one of the two spins in the pair precesses. As the driving field exceeds the difference in local hyperfine field experienced by electron and hole, both spins precess, leading to pronounced spin beating in the transient Rabi flopping of the current. We use this effect to measure the magnitude and spatial variation in hyperfine field on the scale of single carrier pairs, as required for evaluating models of organic magnetoresistance, improving organic spintronics devices, and illuminating spin decoherence mechanisms.

Figure 1

Observation of the two spin partners in an electrostatically bound carrier pair in an OLED. The pair can be shuttled between the singlet and triplet manifold by coherently manipulating the orientation of one of the two electron spins within the pair (inset). The change in current through a MEH-PPV OLED $10.2\mu \mathrm{s}$ after a microwave pulse is plotted as a function of external magnetic field $B_0$. The spectrum is described by two Gaussian lines, which we assign to the two spins in the carrier pair. Further fit possibilities are discussed and discounted in the supporting information [31, 33].

Figure 2

(a) Coherent oscillations of the ensemble of spin pairs, observed by measuring the change in OLED current $7.2\mu \mathrm{s}$ after application of resonant microwave pulses of increasing length. The fit with an exponentially damped sinusoidal function with components at both ${\Omega }_{\mathrm{Rabi}}$ and $2{\Omega }_{\mathrm{Rabi}}$ is shown (solid red line), as is a fit with only a single frequency component ${\Omega }_{\mathrm{Rabi}}$ (dashed blue line). (b) Sample Fourier transform spectra of Rabi nutation traces obtained at different $B_1$ field strengths. The frequency of the two peaks was determined, and plotted as a function of $B_1$.

Figure 3

Beating of spin precession following compensation of the difference in intrapair hyperfine fields. (a) As the driving field is increased, the current modulation frequency changes from the Rabi frequency ${\Omega }_{\mathrm{Rabi}}$ to twice the Rabi frequency. This doubling arises because the difference in intrapair hyperfine fields is overcome and both spins are simultaneously in resonance. (b) Relative fraction of pairs with $\Omega ={\Omega }_{\mathrm{Rabi}}$ (not beating) (△) and $\Omega =2{\Omega }_{\mathrm{Rabi}}$ (beating) (○). The solid lines show the expected form of the distribution, the crossover of which gives a measure of $⟨|\Delta B_{\mathrm{hyp}}|⟩=1.1(1)\mathrm{mT}$.