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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.


Related in: MedlinePlus

Deviations of measured spin-pair nutation harmonic frequency from the analytical description allowing for intrapair spin–spin interaction strength and intercharge separation to be quantified.(a) Frequency peaks for the detuning dependency of the fundamental (black) and harmonic (red) frequency components, plotted in Fig. 4c. The blue line shows the analytical solution for the Rabi frequency of a driven pair of weakly coupled spin-½ carriers (that is, for negligible zero-field splitting), given their measured Larmor separation and the known driving field B1 as parameters (see refs 29, 31, 32). (b) Difference, Δ, between measured and computed analytical harmonic frequency as a function of detuning. Since on-resonance, Δ, is a function of exchange J and dipolar coupling strength D, it allows for a direct determination of the intrapair spin–spin interaction strength. (c) Numerical simulation of intrapair spin–spin interaction strength. Plot of possible combinations of J and D that give rise to a shift of the harmonic oscillation frequency in agreement with the measured value Δ. By further simulating the detuning behaviour of all frequency components for each of these combinations and eliminating cases that strongly diverge from observation (grey), bounds are placed on the magnitudes of J and D (red), yielding /J/<30 neV and /D/=23.5±1.5 neV (see associated discussion in Supplementary Notes 5 and 6). Error bars in the simulation arise from the experimental uncertainty in Δ of 60 kHz. Vertical error bars denote simulations where J is fixed and D is varied, and vice versa for horizontal error bars.
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f5: Deviations of measured spin-pair nutation harmonic frequency from the analytical description allowing for intrapair spin–spin interaction strength and intercharge separation to be quantified.(a) Frequency peaks for the detuning dependency of the fundamental (black) and harmonic (red) frequency components, plotted in Fig. 4c. The blue line shows the analytical solution for the Rabi frequency of a driven pair of weakly coupled spin-½ carriers (that is, for negligible zero-field splitting), given their measured Larmor separation and the known driving field B1 as parameters (see refs 29, 31, 32). (b) Difference, Δ, between measured and computed analytical harmonic frequency as a function of detuning. Since on-resonance, Δ, is a function of exchange J and dipolar coupling strength D, it allows for a direct determination of the intrapair spin–spin interaction strength. (c) Numerical simulation of intrapair spin–spin interaction strength. Plot of possible combinations of J and D that give rise to a shift of the harmonic oscillation frequency in agreement with the measured value Δ. By further simulating the detuning behaviour of all frequency components for each of these combinations and eliminating cases that strongly diverge from observation (grey), bounds are placed on the magnitudes of J and D (red), yielding /J/<30 neV and /D/=23.5±1.5 neV (see associated discussion in Supplementary Notes 5 and 6). Error bars in the simulation arise from the experimental uncertainty in Δ of 60 kHz. Vertical error bars denote simulations where J is fixed and D is varied, and vice versa for horizontal error bars.

Mentions: We simulate the detuning behaviour under the given experimental conditions by employing a stochastic Liouville formalism2830313237 (see Methods). The agreement between measurement and simulation, shown in Fig. 4d, is striking, with the primary difference being that the measured data have a reduced frequency resolution due to the finite coherence time of the spin system probed. The specific detuning behaviour allows us to constrain the zero-field splitting parameters J and D since these directly control the Rabi frequency components on detuning28293031 (see, for example, Fig. 5c). Note that hyperfine interactions can be neglected in the spin Hamiltonian used for this simulation since exchange and dipolar interactions are properties of the mutually coupled pair irrespective of the individual hyperfine field experienced by the pair partners. In addition, the spin–orbit interaction is implicitly accounted for by using the measured difference in g-factor for the pair (see Supplementary Note 4 and Supplementary Fig. 3), which enters the spin Hamiltonian of the pair system as a Larmor separation as indicated in Fig. 1c (refs 30, 32).


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)

Deviations of measured spin-pair nutation harmonic frequency from the analytical description allowing for intrapair spin–spin interaction strength and intercharge separation to be quantified.(a) Frequency peaks for the detuning dependency of the fundamental (black) and harmonic (red) frequency components, plotted in Fig. 4c. The blue line shows the analytical solution for the Rabi frequency of a driven pair of weakly coupled spin-½ carriers (that is, for negligible zero-field splitting), given their measured Larmor separation and the known driving field B1 as parameters (see refs 29, 31, 32). (b) Difference, Δ, between measured and computed analytical harmonic frequency as a function of detuning. Since on-resonance, Δ, is a function of exchange J and dipolar coupling strength D, it allows for a direct determination of the intrapair spin–spin interaction strength. (c) Numerical simulation of intrapair spin–spin interaction strength. Plot of possible combinations of J and D that give rise to a shift of the harmonic oscillation frequency in agreement with the measured value Δ. By further simulating the detuning behaviour of all frequency components for each of these combinations and eliminating cases that strongly diverge from observation (grey), bounds are placed on the magnitudes of J and D (red), yielding /J/<30 neV and /D/=23.5±1.5 neV (see associated discussion in Supplementary Notes 5 and 6). Error bars in the simulation arise from the experimental uncertainty in Δ of 60 kHz. Vertical error bars denote simulations where J is fixed and D is varied, and vice versa for horizontal error bars.
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4403378&req=5

f5: Deviations of measured spin-pair nutation harmonic frequency from the analytical description allowing for intrapair spin–spin interaction strength and intercharge separation to be quantified.(a) Frequency peaks for the detuning dependency of the fundamental (black) and harmonic (red) frequency components, plotted in Fig. 4c. The blue line shows the analytical solution for the Rabi frequency of a driven pair of weakly coupled spin-½ carriers (that is, for negligible zero-field splitting), given their measured Larmor separation and the known driving field B1 as parameters (see refs 29, 31, 32). (b) Difference, Δ, between measured and computed analytical harmonic frequency as a function of detuning. Since on-resonance, Δ, is a function of exchange J and dipolar coupling strength D, it allows for a direct determination of the intrapair spin–spin interaction strength. (c) Numerical simulation of intrapair spin–spin interaction strength. Plot of possible combinations of J and D that give rise to a shift of the harmonic oscillation frequency in agreement with the measured value Δ. By further simulating the detuning behaviour of all frequency components for each of these combinations and eliminating cases that strongly diverge from observation (grey), bounds are placed on the magnitudes of J and D (red), yielding /J/<30 neV and /D/=23.5±1.5 neV (see associated discussion in Supplementary Notes 5 and 6). Error bars in the simulation arise from the experimental uncertainty in Δ of 60 kHz. Vertical error bars denote simulations where J is fixed and D is varied, and vice versa for horizontal error bars.
Mentions: We simulate the detuning behaviour under the given experimental conditions by employing a stochastic Liouville formalism2830313237 (see Methods). The agreement between measurement and simulation, shown in Fig. 4d, is striking, with the primary difference being that the measured data have a reduced frequency resolution due to the finite coherence time of the spin system probed. The specific detuning behaviour allows us to constrain the zero-field splitting parameters J and D since these directly control the Rabi frequency components on detuning28293031 (see, for example, Fig. 5c). Note that hyperfine interactions can be neglected in the spin Hamiltonian used for this simulation since exchange and dipolar interactions are properties of the mutually coupled pair irrespective of the individual hyperfine field experienced by the pair partners. In addition, the spin–orbit interaction is implicitly accounted for by using the measured difference in g-factor for the pair (see Supplementary Note 4 and Supplementary Fig. 3), which enters the spin Hamiltonian of the pair system as a Larmor separation as indicated in Fig. 1c (refs 30, 32).

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.


Related in: MedlinePlus