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Probing long-range carrier-pair spin-spin interactions in a conjugated polymer by detuning of electrically detected spin beating.

van Schooten KJ, Baird DL, Limes ME, Lupton JM, Boehme C - Nat Commun (2015)

Bottom Line: Spin pairs exhibit persistent spin coherence, allowing minute magnetic fields to perturb spin precession and thus recombination rates and photoreaction yields, giving rise to a range of magneto-optoelectronic effects in devices.Little is known, however, about interparticle magnetic interactions within such pairs.The deviation from uncoupled precession frequencies quantifies both the exchange (<30 neV) and dipolar (23.5±1.5 neV) interaction energies responsible for the pair's zero-field splitting, implying quantum mechanical entanglement of charge-carrier spins over distances of 2.1±0.1 nm.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of Utah, 115 South 1400 East, Salt Lake City, Utah 84112-0830, USA.

ABSTRACT

Unlabelled: Weakly coupled electron spin pairs that experience weak spin-orbit interaction can control electronic transitions in molecular and solid-state systems. Known to determine radical pair reactions, they have been invoked to explain phenomena ranging from avian magnetoreception to spin-dependent charge-carrier recombination and transport. Spin pairs exhibit persistent spin coherence, allowing minute magnetic fields to perturb spin precession and thus recombination rates and photoreaction yields, giving rise to a range of magneto-optoelectronic effects in devices. Little is known, however, about interparticle magnetic interactions within such pairs. Here we present pulsed electrically detected electron spin resonance experiments on poly(styrene-sulfonate)-doped poly(3,4-ethylenedioxythiophene) (

Pedot: PSS) devices, which show how interparticle spin-spin interactions (magnetic-dipolar and spin-exchange) between charge-carrier spin pairs can be probed through the detuning of spin-Rabi oscillations. The deviation from uncoupled precession frequencies quantifies both the exchange (<30 neV) and dipolar (23.5±1.5 neV) interaction energies responsible for the pair's zero-field splitting, implying quantum mechanical entanglement of charge-carrier spins over distances of 2.1±0.1 nm.

No MeSH data available.


Rabi spin-beat oscillations as a function of B0-detuning in the frequency domain.(a) Rabi frequency components in the on-resonance raw data of Fig. 3a obtained from the Fourier transform of the total charge Q (that is, not the baseline-corrected data ΔQ displayed in Fig. 3). The harmonic is about twice the fundamental frequency, confirming the presence of a strongly driven pair process, where both spins are resonant in the B1 field. A frequency peak due to the difference-beat oscillation is also observed close to the origin. (b) Frequency components under detuning off resonance (obtained from the raw data Q). Fundamental and harmonic shift to higher frequencies under detuning, with the intensity of the harmonic diminishing as only one carrier remains strongly driven. (c) The relative change in frequency and amplitude for continuous detuning. (d) Simulation based on the stochastic Liouville formalism, utilizing the radical pair spin Hamiltonian given in Supplementary Note 1.
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f4: Rabi spin-beat oscillations as a function of B0-detuning in the frequency domain.(a) Rabi frequency components in the on-resonance raw data of Fig. 3a obtained from the Fourier transform of the total charge Q (that is, not the baseline-corrected data ΔQ displayed in Fig. 3). The harmonic is about twice the fundamental frequency, confirming the presence of a strongly driven pair process, where both spins are resonant in the B1 field. A frequency peak due to the difference-beat oscillation is also observed close to the origin. (b) Frequency components under detuning off resonance (obtained from the raw data Q). Fundamental and harmonic shift to higher frequencies under detuning, with the intensity of the harmonic diminishing as only one carrier remains strongly driven. (c) The relative change in frequency and amplitude for continuous detuning. (d) Simulation based on the stochastic Liouville formalism, utilizing the radical pair spin Hamiltonian given in Supplementary Note 1.

Mentions: pEDMR reveals the perturbation of the device current following resonant microwave excitation. The device current is governed by a multi-rate transient as described in the Methods, which arises from spin-dependent carrier-pair dissociation and recombination1844. Figure 2c shows an example of such a transient of current change from the steady state. The initial enhancement of the current over the first 25 μs is followed by a longer-term (∼600 μs) quenching, which reflects the return to steady state after a resonant population transfer between singlet and triplet eigenstates1831. Observation of coherent state manipulation requires time integration over the shaded area, giving the total charge, Q(τ), involved in the resonant transition during the driving time τ. Measuring Q on-resonance while applying microwave fields whose B1 is in excess of the average Larmor separation, 〈ΔωL(B0, Bhyp)〉 (refs 10, 21, 37), leads to Rabi oscillations at the fundamental and the harmonic frequency as shown in Fig. 3a. Note that Fig. 3 displays a baseline-corrected charge ΔQ, that is, a second-order polynomial fit function to the raw data Q was subtracted from Q. This baseline subtraction was introduced solely for improved visualization of the fine structure in Rabi frequency. Since this correction causes a misrepresentation of the low-frequency contributions of the measured data, the quantitative analysis discussed in the following (Fig. 4) was conducted on the raw data Q; the correction procedure and the raw data are given in Supplementary Note 3 and Supplementary Fig. 2. Figure 3a shows that a spin-beat oscillation is maintained for over 20 cycles and 700 ns, indicating that damping of Rabi oscillations in this system is fundamentally restricted by the spin coherence time, T2, rather than . We measured this dephasing time to be 342±2 ns using the spin-echo technique described previously9. The presence of both a fundamental Rabi oscillation and a harmonic feature confirms that the species probed is a spin-½ charge pair29303132. In addition, we are able to resolve the spin-beat difference oscillation (at /ωa−ωb/) in the Fourier transform, as discussed below (see, for example, the peak close to the origin in Fig. 4a). This difference-beat oscillation is masked in MEH-PPV by the strong hyperfine fields1027. The beat oscillation disappears for small B1 driving fields (data not shown), implying that the pair is weakly exchange coupled10212526. To estimate the relative magnitude of interpair spin coupling, spin beats must be measured while detuning B0 since the characteristics of off-resonance oscillation frequency components uniquely fingerprint these interactions28293032.


Probing long-range carrier-pair spin-spin interactions in a conjugated polymer by detuning of electrically detected spin beating.

van Schooten KJ, Baird DL, Limes ME, Lupton JM, Boehme C - Nat Commun (2015)

Rabi spin-beat oscillations as a function of B0-detuning in the frequency domain.(a) Rabi frequency components in the on-resonance raw data of Fig. 3a obtained from the Fourier transform of the total charge Q (that is, not the baseline-corrected data ΔQ displayed in Fig. 3). The harmonic is about twice the fundamental frequency, confirming the presence of a strongly driven pair process, where both spins are resonant in the B1 field. A frequency peak due to the difference-beat oscillation is also observed close to the origin. (b) Frequency components under detuning off resonance (obtained from the raw data Q). Fundamental and harmonic shift to higher frequencies under detuning, with the intensity of the harmonic diminishing as only one carrier remains strongly driven. (c) The relative change in frequency and amplitude for continuous detuning. (d) Simulation based on the stochastic Liouville formalism, utilizing the radical pair spin Hamiltonian given in Supplementary Note 1.
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Related In: Results  -  Collection

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f4: Rabi spin-beat oscillations as a function of B0-detuning in the frequency domain.(a) Rabi frequency components in the on-resonance raw data of Fig. 3a obtained from the Fourier transform of the total charge Q (that is, not the baseline-corrected data ΔQ displayed in Fig. 3). The harmonic is about twice the fundamental frequency, confirming the presence of a strongly driven pair process, where both spins are resonant in the B1 field. A frequency peak due to the difference-beat oscillation is also observed close to the origin. (b) Frequency components under detuning off resonance (obtained from the raw data Q). Fundamental and harmonic shift to higher frequencies under detuning, with the intensity of the harmonic diminishing as only one carrier remains strongly driven. (c) The relative change in frequency and amplitude for continuous detuning. (d) Simulation based on the stochastic Liouville formalism, utilizing the radical pair spin Hamiltonian given in Supplementary Note 1.
Mentions: pEDMR reveals the perturbation of the device current following resonant microwave excitation. The device current is governed by a multi-rate transient as described in the Methods, which arises from spin-dependent carrier-pair dissociation and recombination1844. Figure 2c shows an example of such a transient of current change from the steady state. The initial enhancement of the current over the first 25 μs is followed by a longer-term (∼600 μs) quenching, which reflects the return to steady state after a resonant population transfer between singlet and triplet eigenstates1831. Observation of coherent state manipulation requires time integration over the shaded area, giving the total charge, Q(τ), involved in the resonant transition during the driving time τ. Measuring Q on-resonance while applying microwave fields whose B1 is in excess of the average Larmor separation, 〈ΔωL(B0, Bhyp)〉 (refs 10, 21, 37), leads to Rabi oscillations at the fundamental and the harmonic frequency as shown in Fig. 3a. Note that Fig. 3 displays a baseline-corrected charge ΔQ, that is, a second-order polynomial fit function to the raw data Q was subtracted from Q. This baseline subtraction was introduced solely for improved visualization of the fine structure in Rabi frequency. Since this correction causes a misrepresentation of the low-frequency contributions of the measured data, the quantitative analysis discussed in the following (Fig. 4) was conducted on the raw data Q; the correction procedure and the raw data are given in Supplementary Note 3 and Supplementary Fig. 2. Figure 3a shows that a spin-beat oscillation is maintained for over 20 cycles and 700 ns, indicating that damping of Rabi oscillations in this system is fundamentally restricted by the spin coherence time, T2, rather than . We measured this dephasing time to be 342±2 ns using the spin-echo technique described previously9. The presence of both a fundamental Rabi oscillation and a harmonic feature confirms that the species probed is a spin-½ charge pair29303132. In addition, we are able to resolve the spin-beat difference oscillation (at /ωa−ωb/) in the Fourier transform, as discussed below (see, for example, the peak close to the origin in Fig. 4a). This difference-beat oscillation is masked in MEH-PPV by the strong hyperfine fields1027. The beat oscillation disappears for small B1 driving fields (data not shown), implying that the pair is weakly exchange coupled10212526. To estimate the relative magnitude of interpair spin coupling, spin beats must be measured while detuning B0 since the characteristics of off-resonance oscillation frequency components uniquely fingerprint these interactions28293032.

Bottom Line: Spin pairs exhibit persistent spin coherence, allowing minute magnetic fields to perturb spin precession and thus recombination rates and photoreaction yields, giving rise to a range of magneto-optoelectronic effects in devices.Little is known, however, about interparticle magnetic interactions within such pairs.The deviation from uncoupled precession frequencies quantifies both the exchange (<30 neV) and dipolar (23.5±1.5 neV) interaction energies responsible for the pair's zero-field splitting, implying quantum mechanical entanglement of charge-carrier spins over distances of 2.1±0.1 nm.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of Utah, 115 South 1400 East, Salt Lake City, Utah 84112-0830, USA.

ABSTRACT

Unlabelled: Weakly coupled electron spin pairs that experience weak spin-orbit interaction can control electronic transitions in molecular and solid-state systems. Known to determine radical pair reactions, they have been invoked to explain phenomena ranging from avian magnetoreception to spin-dependent charge-carrier recombination and transport. Spin pairs exhibit persistent spin coherence, allowing minute magnetic fields to perturb spin precession and thus recombination rates and photoreaction yields, giving rise to a range of magneto-optoelectronic effects in devices. Little is known, however, about interparticle magnetic interactions within such pairs. Here we present pulsed electrically detected electron spin resonance experiments on poly(styrene-sulfonate)-doped poly(3,4-ethylenedioxythiophene) (

Pedot: PSS) devices, which show how interparticle spin-spin interactions (magnetic-dipolar and spin-exchange) between charge-carrier spin pairs can be probed through the detuning of spin-Rabi oscillations. The deviation from uncoupled precession frequencies quantifies both the exchange (<30 neV) and dipolar (23.5±1.5 neV) interaction energies responsible for the pair's zero-field splitting, implying quantum mechanical entanglement of charge-carrier spins over distances of 2.1±0.1 nm.

No MeSH data available.