Optically Controlled Spin-Flipping of Charge Carriers in Conjugated

Article pubs.acs.org/JPCC

Optically Controlled Spin-Flipping of Charge Carriers in Conjugated Polymers Bing Di,† Shansong Yang,† Yalin Zhang,† Zhong An,*,† and Xin Sun*,‡ †

College of Physics and Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang 050024, China Department of Physics, Fudan University, Shanghai 200433, China

‡

ABSTRACT: On the basis of the dynamics of polaron relaxation in conjugated polymers, it is found theoretically that the spin of an injected electron, which converts to a negative polaron in a conjugated polymer, is reversed by photoexcitation. This effect of photoinduced spin-flipping in polymers can be used to design a device of an optically controlled spin valve for organic spintronics. Here the spin-flipping is driven by the electric dipole transition rather than the magnetic dipole transition, and it consequently has a much higher efficiency.

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INTRODUCTION Organic spintronics not only is an intriguing interdisciplinary field of research where physics, chemistry, and electrical engineering inevitably meet but also offers the possibility of adding magnetic functionality to organic semiconductor materials or plastic devices.1−3 With the development of organic spintronics, spin-coherent transport in organic materials that are suitable for spintronics has attracted much attention because of the extremely weak spin−orbit coupling interaction and hyperfine interaction, which result in an especially long spin relaxation time in organic material.4,5 Considering that they are cheap, involve only easy processing, have almost infinite chemical tunability, and in particular have applications in mediating or controlling a spin-polarized signal, organic materials have become very appealing alternatives to the materials currently used in spintronics. To date, several new organic spin-dependent devices have been fabricated, including an organic spin valve (OSV)6−8 and an organic magnetoresistance transistor.9,10 The canonical OSV device consists of two ferromagnetic electrodes (FEs) used as the spin injector and spin detector. They are separated by a nonmagnetic organic transport spacer that allows spin carriers to be transported from one electrode to the other.6 The OSV switch primarily depends on the relative orientation of the spin magnetization of the two FEs. The relative orientation can be tuned by an external magnetic field between the antiparallel and parallel configurations. Thus, spin direction tuning is a key process in an OSV. This paper discusses optically controlled spin-flipping as an alternative to manipulating the spin orientation of carriers in polymers. In contrast to inorganic materials, conjugated polymers possess characteristic low-dimensional instability. The electron−phonon coupling not only results in its carriers being © 2013 American Chemical Society

composite particles, such as charged spin polarons or charged spinless bipolarons with an internal structure characterized by lattice distortion,11−16 but also makes the carriers very sensitive to external excitations, such as photoexcitation. In fact, photoexcitation dynamics in conjugated polymers have been studied well, and many interesting photoinduced phenomena have been found in recent years,17−21 for example, photoinduced polarization reversion,18 charge flipping of carriers,19 and fission of charged spin polarons and charged spinless bipolarons.20,21 These photoinduced effects have become a useful method for controlling the properties of charge carriers in organic materials. Thus, it is also expected that the spin orientation of charge carriers in conjugated polymers may be controlled by photoexcitation. If so, then it may be possible to design and realize high-efficiency organic devices for spin control. In this paper, a photoinduced spin-flipping phenomenon in conjugated polymers is simulated using a molecular dynamics method. When a spin-up polaron is photoexcited to an excited state, both its charge and spin distribution will evolve, accompanying the lattice relaxation due to self-trapping effects in polymers. Note, however, that the photoexcitation itself occurs via an electric dipole transition (EDT), which cannot directly change the spin of the polaron. Eventually, the excited polaron splits into a triplet exciton and a normal polaron that has its spin in the direction opposite that of the original polaron. The details of this dynamical process are discussed below. This split comes from the dynamical symmetry breaking caused by the nonlinearity in the self-trapping process.20 In this Received: May 13, 2013 Revised: August 15, 2013 Published: August 21, 2013 18675

dx.doi.org/10.1021/jp4046885 | J. Phys. Chem. C 2013, 117, 18675−18680

The Journal of Physical Chemistry C

Article

Figure 1. Lattice configuration (a), spin distribution and charge distribution (b), and electronic spectrum (c) of a spin-up negative polaron in a polymer.

effective approach for investigating photoexcitation dynamics in conjugated polymers.17 The lattice configuration is described by the staggered bond order parameter δn ≡ (−1)n(2un − un+1 − un−1)/4; the charge distribution is represented as ρn = 1 − ∑k,sψsk*(n,t)f k,sψsk(n,t), and the spin distribution is given by Sn = −s ℏ/2[∑kψsk*(n,t)f k,sψsk(n,t) − ∑kψ−s k *(n,t)f k,−sψk (n,t)]. In the equations described above, ψsk(n,t) is the electron wave function that is the solution to the time-dependent Schrödinger equation, and f k,s(=0,1) denotes the time-independent distribution function and is determined by the initial occupation state.

process, the total spin does not change, but the polaron’s spin is reversed. This spin-flipping of carriers is produced by the EDT rather than the magnetic dipole transition (MDT) and is therefore highly efficient. On the basis of this photoinduced spin-flipping phenomenon, an optically controlled OSV with high efficiency is proposed.

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MODEL AND NUMERICAL METHOD The system can be described by the one-dimensional Su− Schrieffer−Heeger (SSH) tight-binding model with a Brazoskii−Kirova-type symmetry-breaking term22 HSSH =

∑

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s n cn†, shnn ′cn ′ , s + Hlatt = − ∑ [tn , n + 1 + ( − 1) te]

n,n′,s

(cn†+ 1, scn , s + hc) +

RESULTS AND DISCUSSION The proposed structure consists of a quasi-one-dimensional polymer chain inserted between two ferromagnetic electrodes. Once the carrier is injected into the polymer from the cathode, a spin-up negative polaron is formed. There has been a considerable amount of research devoted to the study of the structure and dynamics of the polaron in the conjugated polymer.11−16,22,24−28 The lattice configuration, charge distribution, spin distribution, and electronic spectrum of the spin-up negative polaron are shown in Figure 1. Figure 1c shows that a distorted polaron lattice produces two localized states, Φu and Φd, in the gap, where the upper level, Φu, is occupied by only one spin-up electron and the lower level, Φd, is doubly occupied. Meanwhile, the conduction bands are empty. Under certain photoexcitation processes, for example, STIRAP (stimulated Raman adiabatic passage) or an external laser pump,20,21,29,30 the spin-down electron, localized initially in state Φd of the negative polaron, can be excited into the bottom of the conduction band. Note that this excitation occurs via an EDT rather than an MDT. Because of the self-trapping effect in conjugated polymers, the original lattice configuration for the excited state is unstable, and a process of lattice relaxation begins, with the electron distribution following the lattice changes. The time-dependent staggered bond order parameter δn is shown in Figure 2 during the relaxation process following the photoexcitation. The results show that the lattice undergoes different transient distortions at different times after the photoexcitation. In the early stages, the lattice configuration of the original excited polaron is contained in one local deformation corresponding to a single valleylike structure. As the relaxation process continues, the original excited polaron gradually begins to develop two valleylike structures with two independent local deformations, which indicates that the

n,s

K 2

∑ (un+ 1 − un)2 + n

M 2

∑ uṅ 2 n

(1)

The transfer integral between site n and site n + 1 is given by tn,n+1 = t0 − α(un+1 − un), where t0 represents the transfer integral of π-electrons in a regular lattice. α is the electron− lattice coupling constant, and un is the lattice displacement of the nth site from its equidistant position. The quantity te is a symmetry-breaking parameter introduced to remove the ground-state degeneracy for nondegenerate polymers. The operator c†n,s (cn,s) creates (annihilates) a π-electron with spin s at the nth site. K is the elastic constant, and M is the mass of a CH group. The model parameters in the calculation are chosen on the basis of conventional values used in previous research of electroluminescence and photoexcitation polymers (t0 = 2.5 eV, α = 4.1 eV/Å, te = 0.05 eV, K = 21 eV/Å2, and M = 1349.14 eV fs2 Å−2),11,15−18 and the results are expected to be qualitatively valid for most conjugated polymers. Initially, the polymer chain contains a spin-up negative polaron in the center of the chain. The initial bond configuration and electron structure can be obtained by solving the self-consistent equations for the bond configuration {un} and all the electron wave functions {ϕsk(n)}. Once the polaron undergoes photoexcitation, the temporal evolution of the lattice configuration, charge distribution, and spin distribution are determined by the coupling between the equation of motion for the atom displacements and the time-dependent Schrödinger equation. The solution is obtained using the same techniques as in previous work, i.e., the Runge−Kutta method of order 8 with step-size control.23 This method has been shown to be an 18676



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exciton state while the right one is a negative polaron state. Thus, a negative polaron is split into an exciton and a negative polaron by photoexcitation and subsequent relaxation. To further identify the nature of the two kinds of particles, the evolution of the spin distribution can be compared with the relaxation of the charge distribution. The bottom row in Figure 3 shows the spin distribution at the same three times that were used with the charge distribution. Remarkably, not only is the charge distribution localized in the redistributed lattice deformations, but the original single spin-up distribution is changed. Corresponding to the charge distribution evolution described in the top row in Figure 3, two positive spins have shifted to the left side, leaving a negative spin on the right side. The nature of two kinds of particles can also be obviously confirmed by the numerical calculations of the time evolution of total spin SL in the left half-chain and SR in the right halfchain, as shown in Figure 4. In the initial stages, SL is equal to

Figure 2. Temporal evolution of δn (note that the vertical scale is reversed) of the original negative polaron following photoexcitation.

polaron is starting to split. After ∼100 fs, the two local deformations basically do not change further, which means that the original polaron is fully divided into two separated particles. This dynamic relaxation can also be described by following the evolution of the charge distribution during the relaxation of the lattice configuration. Via comparison of the evolution of the lattice configuration with that of the charge distribution, it can be seen that the lattice configuration and charge distribution coincide with each other in both space and time. As an example, the charge distributions at three different instants in time are shown in Figure 3 (top row) and may be compared with the lattice configurations shown in Figure 2. Along with the relaxation of the lattice configuration, although the amount of charge localized in the polymer is not changed, the charge is redistributed so that it is no longer symmetric about the center. For example, near 50 fs, the original negative charge distribution develops a profile with two valleys of negative charge. The more negative charge shifts to the right side, and simultaneously, a slight negative charge emerges on the left side. As this relaxation continues, a valley with a negative charge is established on the right side, while there is no charge on the left side. Subsequently, the main features of this charge distribution remain stable. Given the charge distributions, we may anticipate that the left composite particle is likely an

Figure 4. Evolution of total spin SL in the left half-polymer chain and SR in the right half-polymer chain.

SR with a value of ℏ/4, and the system has inversion symmetry. As the relaxation process continues, the inversion symmetry of the system is broken, and it can be seen that SL approaches ℏ, while SR reaches −ℏ/2. The result can be easily understood as a

Figure 3. Charge distribution (top row) and spin distribution (bottom row) at three different times, compared with the lattice configuration evolution shown in Figure 2. 18677



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spin in the direction opposite that of the original negative polaron. Additionally, it should be stated that the up-spin electron localized in Φd can also be excited. In this case, a singlet exciton and a polaron with the same spin as the original one are generated. The singlet exciton will be recombined to emit a photon with an energy lower than the original excitation energy; it is nothing but the photoluminescence with a Stokes shift. Actually, the excitation of up spin and the excitation of down spin are two independent channels. One channel with down spin gives spin-flipping, and another channel with up spin just wastes energy. As described above, relaxation takes place with no electric field. If an electric field is present, the two new composite particles that have been formed by photoexcitation relaxation will separate completely under the influence of the electric field. For example, when an external electric field is applied along with the polymer chain with an E of 0.15 mV/Å, the electric field drives the spin-reversed negative polaron in the same direction as the original negative polaron. The whole evolution process is shown in Figure 7. The triplet exciton will decay

spin-up negative polaron being split by photoexcitation into a spin-down negative polaron and an S = 1 triplet exciton. The electronic characteristics of the two new particles are also reflected in the eigenenergy levels. The evolution of the eigenlevels with time is plotted in Figure 5. One can see that

Figure 5. Evolution of the localized electronic energy levels with time, corresponding to the lattice configuration evolution described in Figure 2.

there are four energy levels in the energy gap after the relaxation. Two energy levels, Ψu and Ψd, emerge from the highest occupied molecular orbital (HOMO) level and the lowest unoccupied molecular orbital (LUMO) level, respectively. The four levels are localized electronic states corresponding to the two lattice defects. Φu and Φd are the localized energy levels of the exciton, while Ψu and Ψd are the localized energy levels of the polaron. The whole optically controlled spin-flipping process is illustrated in Figure 6 by a schematic diagram of the energy spectrum. Through photoexcitation, a spin-up negative polaron can be photoexcited to the excited state. Because of self-trapping effects in polymers, the excited polaron state is unstable, and both its charge and spin distributions will evolve with lattice relaxation. Eventually, a spin-up negative polaron is split into two particles. One is an S = 1 triplet exciton, and the other is a negative polaron with its

Figure 7. Temporal evolution of δn (note that the vertical scale is reversed) of the original negative polaron following photoexcitation in the presence of an external electric field (E) of 0.15 mV/Å.

through a nonradiative transition by thermal vibrations or magnetic dipole interactions; its lifetime spans a wide range

Figure 6. Schematic diagram of the energy spectrum evolution of the optically controlled spin-flipping process. 18678



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carriers in the conjugated polymers is therefore reversed. On the basis of this optically controlled spin reversal effect, a highefficiency organic polymer spin valve can be designed.

from a few picoseconds to several microseconds and is much longer than that of the singlet exciton.31,32 On the basis of this optically controlled spin reversal effect in a conjugated polymer, a generic polymer spin valve can be designed as illustrated in Figure 8. A polymer transport spacer

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Project supported by the National Natural Science Foundation of China (11074064) and the Natural Science Fund of Hebei Province of China (A2010000357 and A2012108003). We thank professor N. E. Davison for helpful discussions.

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REFERENCES

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Figure 8. Proposed devices for an optically controlled polymer spin valve.

(PTS) is in contact with a left ferromagnetic electrode (LFE) and a right ferromagnetic electrode (RFE), which have the opposite polarization directions. After the spin-up negative polaron is injected into the PTS from the LFE, the electric field drives this polaron toward the RFE, but the spin-up polaron cannot move into the RFE and remains in the PTS because the polaron and the RFE have antiparallel magnetizations. In this case, the spin valve does not conduct and is turned off. Once the polymer undergoes photoexcitation, the spin-up negative polaron splits to form a spin-down negative polaron that has a spin orientation parallel to that of the RFE. The spin-down negative polaron can then easily migrate from the PTS into the RFE under the effect of the electric field, and the spin valve circuit is therefore turned on. From the dynamical process described above, it may be seen that the spin-flipping of the polaron can be driven by photoexcitation through the EDT between orbital states. This is different from conventional spin-flipping in the PMR (paramagnetic resonance) and NMR (nuclear magnetic resonance), which are both driven by the MDT of the spin. Because the transition probability of the EDT is 2 orders of magnitude larger than that of the MDT, the spin-flipping process studied here possesses a much higher efficiency. It is remarkable that the EDT can also reverse the spin orientation of charge carriers in polymers.

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SUMMARY In summary, by using a molecular dynamics method, the process of optically controlled spin-flipping of charge carriers in conjugated polymers has been demonstrated. With proper photoexcitation, a spin-up negative polaron is split into two new composite particles; one is an S = 1 triplet exciton, and the other is a spin-down negative polaron. The spin orientation of 18679



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Optically Controlled Spin-Flipping of Charge Carriers in Conjugated

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