Volume 11, Issue 14 p. 3040-3058
Review
Free Access

Coherent Spin Manipulation in Molecular Semiconductors: Getting a Handle on Organic Spintronics

Prof. John M. Lupton

Prof. John M. Lupton

Department of Physics and Astronomy, University of Utah, 115 South 1400 East, Salt Lake City, UT 84112-0830 (USA), Fax: (+1) 801-581-4801

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Dr. Dane R. McCamey

Dr. Dane R. McCamey

Department of Physics and Astronomy, University of Utah, 115 South 1400 East, Salt Lake City, UT 84112-0830 (USA), Fax: (+1) 801-581-4801

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Prof. Christoph Boehme

Prof. Christoph Boehme

Department of Physics and Astronomy, University of Utah, 115 South 1400 East, Salt Lake City, UT 84112-0830 (USA), Fax: (+1) 801-581-4801

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First published: 02 July 2010
Citations: 65

Graphical Abstract

“Messy” organic semiconductors seem the least likely materials for high-resolution physics experiments. Yet their unique material properties open a route to explore fundamental aspects of spin physics in the condensed phase. The control of the spin population in organic light-emitting diodes (OLEDs; see picture) may herald a new device concept: quantum mechanically coherent organic spintronics.

Abstract

Organic semiconductors offer expansive grounds to explore fundamental questions of spin physics in condensed matter systems. With the emergence of organic spintronics and renewed interest in magnetoresistive effects, which exploit the electron spin degree of freedom to encode and transmit information, there is much need to illuminate the underlying properties of spins in molecular electronic materials. For example, one may wish to identify over what length of time a spin maintains its orientation with respect to an external reference field. In addition, it is crucial to understand how adjacent spins arising, for example, in electrostatically coupled charge-carrier pairs, interact with each other. A periodic perturbation of the field may cause the spins to precess or oscillate, akin to a spinning top experiencing a torque. The quantum mechanical characteristic of the spin is then defined as the coherence time, the time over which an oscillating spin, or spin pair, maintains a fixed phase with respect to the driving field. Electron spins in organic semiconductors provide a remarkable route to performing “hands-on” quantum mechanics since permutation symmetries are controlled directly. Herein, we review some of the recent advances in organic spintronics and organic magnetoresistance, and offer an introductory description of the concept of pulsed, electrically detected magnetic resonance as a technique to manipulate and thus characterize the fundamental properties of electron spins. Spin-dependent dissociation and recombination allow the observation of coherent spin motion in a working device, such as an organic light-emitting diode. Remarkably, it is possible to distinguish between electron and hole spin resonances. The ubiquitous presence of hydrogen nuclei gives rise to strong hyperfine interactions, which appear to provide the basis for many of the magnetoresistive effects observed in these materials. Since hyperfine coupling causes quantum spin beating in electron–hole pairs, an extraordinarily sensitive probe for hyperfine fields in such pairs is given.

1. Introduction

Most publications on organic semiconductors from the past 25 years introduce the subject by praising the unique device capabilities of these materials: flexible, solution processable, lightweight, and tunable.1 An astonishing amount of this early promise is becoming reality, with meticulous research and development activities promoting organic light-emitting diodes (OLEDs), solar cells, and transistor applications into ever-expanding market segments. One may therefore be forgiven for overlooking some of the extraordinary intrinsic physical and chemical properties of π-conjugated macromolecules. However, in the long run, the field of organic electronics benefits tremendously from clear identification and articulation of the unique terrain for scientific exploration opened up by engaging with these compounds. The appeal of research into organic electronics can be enhanced by identifying the overlap with seemingly disparate research fields. Examples of the academic diversity of the field include: elucidation of elementary charge- and energy-transfer phenomena, which are crucial to many biophysical processes such as light harvesting in photosynthesis;2 the conformational diversity of macromolecules, in particular conjugated polymers, which relates to questions of protein folding and polymer physics in general;3 quantum optical phenomena enabled by the characteristically high oscillator strength of molecular transitions, bridging to elementary atomic quantum optics;4, 5 electronic localization phenomena, which underlie optical transitions in semiconductor quantum structures;6 stochastic processes emerging from the interplay between homogeneous and inhomogeneous disorder broadening,7 with potential applications to larger-scale questions of stochastic resonance;8 and elementary spin physics of weakly spin–orbit coupled systems,912 which is presently gaining particular interest with the flurry of research directed to carbon nanotubes and graphene.13, 14

The spin degree of freedom in organic semiconductors has recently attracted particular attention, with the possibility of encoding and transporting information in the spin—rather than merely in the charge—of a carrier.15 For example, organic semiconductors have been used as active materials in spin valves.1618 In such a device, a ferromagnetic electrode injects spin-polarized charge carriers into the organic semiconductor. A second electrode collects the charges again, but only if the direction of magnetization of the electrode matches the orientation of spins migrating through the transport layer. Inorganic spin valves are used widely as magnetic field sensors in high-density magnetic storage devices.19 Although it is unlikely that organic spin valves will displace conventional compounds from most applications, it has come as a significant surprise that an effect exists at all: charge transport in organic semiconductors occurs by hopping, which one may anticipate to be detrimental to maintaining a spin-polarized charge current. However, spin–orbit coupling in these low atomic order number (Z) materials is also very weak, so that the spin information is not readily perturbed. While earlier investigations into mere spin valve effects as determined by magnetic-field-induced changes in current were hard to disentangle from simple magnetoresistance phenomena,20 a host of elaborate spectroscopic techniques have now established the presence of spin currents in organic semiconductors.21, 22 With this avenue to new “spintronic” (or more precisely, spin electronic) devices open, it is absolutely imperative to develop cutting-edge spectroscopic methods to not only quantify spin polarization and spin-dependent processes, but also to manipulate these in a controlled way.

An electron spin in a magnetic field constitutes the prototypical quantum two-level system. Indeed, much of early quantum mechanics was tested on well-defined spin systems, with the emergence of magnetic resonance techniques. Over the years, attention moved to investigating different energy, frequency, and intensity domains: electron and nuclear spin resonance gave way to atomic quantum optics, from which, in turn, solid-state quantum optics branched off. For electron spin resonance to probe pure quantum states, weak spin–orbit coupling is required, thus limiting the applicability of the technique in the context of conventional semiconducting materials used in spintronics, such as GaAs.19 With increasing interest in the fundamental spin physics of carbon-based compounds, however, a close look at what electron spin resonance-based techniques can reveal about the underlying nature of spin excitations is called for. As is so often the case, this exploration is driven not wholly by intellectual curiosity alone. The accurate preparation, preservation, and manipulation of quantum states, along with the controlled interaction between these states, form the backbone of quantum information processing. Maybe the future for organic semiconductors lies in quantum computing?23

Herein, we review some of the recent progress in studying and exploiting the fundamental spin physics of organic semiconductors, focusing on coherent control of the spin population in an OLED by means of pulsed, electrically detected magnetic resonance, with the aim of making readers with only a peripheral interest in spin resonance techniques aware of the potential of these emerging spectroscopic tools. We begin by discussing some of the elementary aspects of spin excitations in organic semiconductors, such as the formation of tightly bound excitations (excitons) of singlet and triplet spin multiplicity. Following a brief introduction to the general technique of electron spin resonance, we describe some of the applications of this methodology to questions in organic electronics. Electron spin resonance opens a unique pathway to coherent control of spin populations and thus of observables in a device, such as the current. We offer a brief overview of some of the routes to implementing coherent control of excitation populations in optoelectronic devices, before exploring the spin route in more detail. We demonstrate coherent manipulation of the device current through selective spin resonance of either one carrier or two carrier pairs. The latter case leads to the unique phenomenon of spin beating, as electron and hole spins in the device respond to the driving electromagnetic field slightly differently. This effect provides direct access to hyperfine interactions, which are clearly dominant in these hydrocarbon-based materials and are not readily controlled in more conventional semiconducting spin systems.

2. Spin in Organic Semiconductors

Electron spin plays a key role in organic semiconductor devices. To exemplify the problem, we focus our discussion on the case of OLEDs. Figure 1 a shows a schematic structure of an OLED: a conducting, luminescent organic material is sandwiched between a cathode and an anode, from which electrons and holes are injected, respectively. There is no magnetic field present, so neither electron nor hole has any preferential spin orientation. The charge carriers migrate through the device until they are separated by the Onsager radius, and Coulombic capture occurs: the electrostatic attraction between electron and hole exceeds the thermal energy.24 Ultimately, electron and hole meet on one molecular segment, and recombine to form an exciton. Now, the carrier spins become defined, as the electron spin interacts with the hole spin, and vice versa. As both carriers are indistinguishable spin-1/2 particles, recombination has to be treated as a quantum mechanical superposition of the individual spin states: the combined carrier spin wavefunctions are a prototypical example of quantum mechanical entanglement. As befits a system of fermions, the total carrier pair wavefunction must be antisymmetric in the exchange of two particles. The wavefunction is made up of the product of a spatial and a spin part: a symmetric spatial wavefunction necessitates an antisymmetric spin wavefunction; an antisymmetric spatial wavefunction goes in hand with a symmetric spin wavefunction. The resulting combinations of spin pairs are shown in Figure 1 a: there is one singlet state, and correspondingly three triplet states exist. In other words, if such simple spin statistics hold and the probability of formation of excitons of either singlet or triplet character is the same, only 25 % of excitons are formed in the singlet channel. Most organic hydrocarbon materials only show radiative recombination from the singlet state, so that high triplet formation rates form a formidable loss channel in light-emitting devices.25

Details are in the caption following the image

Elementary processes of charge recombination in an OLED. a) Electrons and holes are injected from opposite electrodes, cathode and anode. As each charge carries a spin, recombination can result in a total of four different spin configurations. b) As the injected electron and hole approach each other, the correlation energy of the carrier pair increases. For distant carriers, the charges can be viewed either as free polarons or extended polaron pairs, which break up and form randomly. Once the electrostatic correlation energy exceeds the thermal energy at a critical radius of rC, persistently bound polaron pairs are formed. In this limit, charge carriers recombine and dissociate following degenerate spin statistics, that is, according to a singlet/triplet ratio of 1:3. Below a charge-pair separation of rX, exchange interactions begin to contribute to the energetics of the spin pair so that singlet and triplet are no longer degenerate. Ultimately, singlet and triplet excitations are formed on one molecular unit. Optical excitation (photoluminescence, PL) generates singlet excitons, which can either dissociate, recombine radiatively or nonradiatively, or undergo intersystem crossing (ISC) down to the triplet exciton level. EL=electroluminescence. Reproduced with permission from ref. 110. Copyright 2007, Wiley-VCH.

The carrier capture process itself is not a trivial phenomenon and several microscopic details still remain unknown. For example, when does the isotropic bulk electrostatic interaction break down to an anisotropic interaction resulting from the inherent electronic anisotropy of the extended π system of a conjugated polymer? Figure 1 b illustrates schematically the main steps in carrier capture. The Coulombic (1/r) interaction potential between the two charges is plotted as a function of distance r between the charges. The potential is negative due to the binding nature of the oppositely charged particles. For large separations, the charges can be considered free. This situation applies when the thermal energy exceeds the interaction potential. Below the Coulombic capture radius rC, the carriers are electrostatically bound, but the electron spins do not necessarily interact. Once the carriers become very close, the wavefunctions begin to overlap so that exchange interactions become non-negligible. The critical radius for this phenomenon is defined as rX. Note that at slightly larger radii, spin–dipolar interactions between the carrier spins will occur. We are not aware of any experimental evidence for such interactions in organic semiconductors. The spin–dipolar interaction increases more weakly than the exponentially growing exchange interaction for small pair radii, but drops off faster than the Coulomb interaction for large separations. Strongly localized polaronic states would therefore be necessary to make this interaction dominant in any regime. The final carrier-capture step sees electron and hole situated on the same molecule, or molecule-like unit of the polymer chain, to form an exciton of either singlet or triplet configuration. Note that conjugated polymers are generally subdivided into chromophoric units with some molecule-like electronic properties. A charge-carrier pair may thus form within one single polymer chain, but still have a spatial separation that exceeds the size of a molecular exciton.

The reverse process of recombination—dissociation of the molecular exciton—is also labeled in Figure 1 b. It is important to note that intersystem crossing, an electron spin-flip arising from spin–orbit coupling, may occur, thus transforming the singlet exciton into a triplet exciton. This process is generally rather weak in pure low-Z materials, although particular molecular symmetries occurring in the most planar structures can enhance the effect.26 Because of the strong exchange interaction within the molecular excitation, triplet energy levels are lower than those of singlets. In homogeneous molecular systems this energy splitting can lie between 0.5 and 1 eV.27

Several techniques exist to visualize triplet excitons in an OLED, such as studying the optical absorption induced by the presence of the triplet.2831 Although the triplet itself is not dipole coupled to the singlet ground state of the molecule, transitions can occur from the triplet excited state to higher-lying states within the triplet excited-state manifold. However, there are generally other absorbing species present in an OLED, such as charge carriers (polarons), which themselves introduce efficient subgap optical transitions, so that a clear assignment to triplet excitations is not always straightforward. A facile way to reveal triplet excitations directly lies in actually enabling radiative emission from the triplet excited state. This process is known as phosphorescence.27 Incorporation of a heavy-metal atom into the organic complex can dramatically enhance spin–orbit coupling, effectively mixing singlet and triplet levels. The triplet–singlet excited state–ground state (T1→S0) transition becomes less dipole forbidden. This effect is generally achieved by incorporating phosphorescent molecules into a fluorescent, singlet-emitting matrix.32 As each optically active unit of the material contains a heavy-metal atom, intersystem crossing is also enhanced from the singlet to the triplet (S1→T1), which results in very little direct fluorescence from the excited singlet state.33, 34

An alternative approach to generating phosphorescence in an organic material lies in the fact that, in the absence of radiative recombination, nonradiative decay of the triplet is very slow, often occurring on the timescale of microseconds or longer. In contrast, singlet excitons decay radiatively within a nanosecond.35 As a consequence, triplet excitons can potentially migrate farther than singlet excitons. A sparse population of heavy-metal atom sites within an otherwise homogeneous organic material can therefore dramatically increase T1→S0 coupling, without affecting S1→T1 transitions.36 Exploitation of this effect has opened a unique window on triplet excitations in OLEDs.12, 37 Figure 2 shows a comparison of the electroluminescence and photoluminescence of such a material, a thin film of a phenyl-substituted ladder-type poly(para-phenylene) with a minute concentration of palladium atoms covalently bound to the backbone. The concentration of palladium is of the order of 100 ppm, which corresponds to less than one atom per polymer chain. The photoluminescence spectrum shows a clear signature of the singlet exciton at 460 nm, followed by a well-defined vibronic progression.6 The same spectral feature is observed under electrical excitation of the film, but now a further emission band is seen at 600 nm, with a similar vibronic progression. This additional emission corresponds to phosphorescence, radiative recombination from the triplet state, which is only populated very inefficiently under optical excitation of the film.

Details are in the caption following the image

Resolving singlet and triplet excitons in an OLED. A conjugated polymer with a vanishingly small concentration of heavy-metal atoms enables highly local spin–orbit coupling, which induces singlet–triplet spin mixing and opens the pathway for radiative triplet recombination in the form of phosphorescence. The solid line shows the polymer film emission under optical excitation. In this case, only emission from singlet excitons is observed, which peaks at 460 nm and is followed by a well-defined vibronic progression. Under electrical excitation (dashed line) the same singlet feature is seen, but now an additional characteristic appears at 600 nm which can be assigned to phosphorescence from the triplet state. In the case of electrical injection, spin pairs are formed randomly, so that 75 % of the pairs end up in the triplet state. Reproduced with permission from ref. 110. Copyright 2007, Wiley-VCH.

The direct observation of singlet and triplet excitons in an OLED proves that the simple spin picture drawn above basically holds true. However, what about the spin state of the electron–hole pair before it recombines within one molecular unit? Is it meaningful to assign singlet and triplet configuration to an intermolecular charge-carrier pair, a charge-transfer state, or a polaron pair?38 Obviously, electron spin resonance provides direct insight into this question, and was used early on to argue in favor of the existence of polaron pairs of both singlet and triplet character.3941 The remainder of the present article will deal with this discussion. It is worth noting, however, that the direct visualization of singlet and triplet excitons in organic semiconductors by fluorescence and phosphorescence, respectively, can be used to prove the presence of both singlet and triplet polaron pairs.12 The further electron and hole are separated, the greater the effect of an external electric field will be on their mutual correlation. Realistic electric fields do not quench triplet excitons, which have a total binding energy in excess of 1 eV. However, under certain conditions, a strong modulation of the phosphorescence signal can be observed in the presence of an electric field, thus proving the presence of spin triplet polaron pair species, which are much more polarizable than the ultimate triplet exciton.12, 35

Triplet and singlet excitons are not isoenergetic, so from simple arguments of energy conservation one would not necessarily expect the rate of exciton formation to be the same for the two spin species.25 There are several further arguments that can be invoked, which relate to the electronic structure and the spatial distribution of electron and hole wavefunctions under singlet and triplet spin configurations.25 Figure 3 illustrates the basic spin-dependent processes involving charge carriers in an organic optoelectronic device, be it an OLED or a photodiode.10 Free charge carriers are either injected into the device, or generated through dissociation of an electrostatically bound polaron pair of either singlet or triplet multiplicity (PPS or PPT). The dissociation rates equation image and equation imageof these carrier pairs are spin dependent, so that a measured photocurrent will depend on the original spin state of the polaron pair. The polaron pair can change its spin configuration between singlet and triplet either randomly, through spin–lattice relaxation (also referred to as a T1 process in the context of magnetic resonance spectroscopy, seeing that the transition is irreversible); or a crossover can be driven coherently by an external electromagnetic field, as occurs in electron spin resonance. Such a coherent manipulation of the spin state requires that the individual electron or hole spin remains phase coherent with the driving field. Loss of phase coherence, which may be due to the intrinsic (homogeneous) properties of the spin system, or extrinsic (inhomogeneous) characteristics arising from, for example, disorder or local field distortions, is broadly referred to as a T2 (homogeneous) or T2* (inhomogeneous) process, respectively.

Details are in the caption following the image

Spin-dependent recombination and dissociation dynamics in an organic semiconductor. Charge-carrier pairs (polaron pairs, labeled PP) can be formed in the singlet or triplet configuration. Conversion between singlet and triplet polaron pairs can either occur incoherently, through random spin–lattice relaxation, or coherently, through manipulation with an external electromagnetic driving field which induces spin precession. Carrier pairs may either dissociate, with spin-dependent rates dPP, or recombine to form singlet (SE) or triplet (TE) excitons with rates kS and kT, respectively. Conjugated polymers generally have a singlet ground state, labeled S0. Reproduced with permission from ref. 10. Copyright 2008, Nature Publishing Group.

Rather than dissociating, the charge-carrier pairs can also recombine to form an exciton of either singlet or triplet multiplicity. Not least because of the energetic difference between singlet and triplet, this recombination process is strongly spin dependent, with transition rates kS and kT, respectively. Singlet and triplet excitons may then decay, radiatively or nonradiatively, to the molecular ground state. Note that we have focused on the key spin-dependent transitions and not indicated the reverse process of singlet exciton formation, the dissociation of an exciton into a polaron pair in a photovoltaic device. Usually, this process involves charge transfer across a heterojunction.1 Even in a nominally homogeneous device, miniscule concentrations of defects may promote exciton dissociation and the formation of polaron pairs.42 This process is trivially spin dependent: for one thing, only singlet excitons are generated under optical excitation in a photovoltaic device; for another, the triplet exciton is much more tightly bound than the singlet so that entirely different energetics apply. In most photoconducting materials the triplet exciton dissociation rate can therefore be assumed to be zero: only singlet excitons contribute to the photocurrent.

3. Electron Spin Resonance Spectroscopy of Organic Semiconductors

The phenomenon of magnetic resonance is based on the Zeeman effect, which describes a splitting of electronic energy levels in an external magnetic field. A free electron, which is a spin-1/2 particle, will split into two states in an external field that correspond to parallel and antiparallel alignment. The energy difference between these two states arises from the fact that the electron spin corresponds to a magnetic moment. Magnetic energy is simply the product of magnetic moment and applied field, so that the total energy of the electron is either lowered or raised by this amount. For typical magnetic fields of order 1 T, this energetic splitting of electrons corresponds to radiation of energy of order 100 μeV, or tens of gigahertz. Generally, microwave radiation is therefore used to probe electron spin resonance. Traditional spin resonance measures the absorption and emission of microwave radiation by the paramagnetic spin ensemble in a sample. As discussed above, the polarization of the spin ensemble may control external observables, such as conductivity or luminescence, so that more sensitive detection routes than mere absorption of the microwave field can be designed to explore the magnetic resonance condition.

Electron spin resonance is used extensively in materials characterization, as it is inherently sensitive to unpaired electrons: dangling bonds, defects, or free radicals. The technique is particularly suited to investigations involving materials with weak spin–orbit coupling, where the differences in lifetime between the three excited-state triplet sublevels give rise to a spin-dependent buildup of macroscopic polarization.4348 In its simplest application, the attenuation of a microwave field is measured by the absorption of radiation resulting from transitions between an electron spin being parallel or antiparallel to an external magnetic field. This technique has been important in studying the effect of doping on the generation of carriers in conducting polymers,4960 but has also been widely used to reveal photogeneration of charge carriers in conjugated semiconducting materials.30, 6183 Such photogeneration of carriers is particularly important in blend systems for photovoltaic applications.8486 However, mere absorption measurements are usually less sensitive than, for example, fluorescence-based investigations. In the former case differential changes over a large background are measured, whereas in the latter case the background can, in principle, be set to zero. Magnetic resonance may therefore be increased phenomenally in sensitivity by recording secondary observables, such as a current or a luminescence recombination signal. By detecting the modulation in fluorescence intensity of a single molecule, at cryogenic temperatures, it has thus been possible to image the spin resonance condition of one electron spin at a time.87, 88 This approach has revealed an amazing heterogeneity in the local magnetic field experienced by a single spin, such as variations arising from single atomic isotopes within the molecule.89 It has also been possible to detect single spins in defect sites in diamond, by using related techniques. Such experiments can even be performed at room temperature.90, 91 Could it, in principle, be possible to track a single charge in an organic electronic device using this technique?

Given a spin-dependent recombination or dissociation channel such as that illustrated in Figure 3, application of the electron magnetic resonance condition will lead to a modification of the device current. Currents down to the femtoampere range are readily measured, so that given sufficient time resolution, in principle it should be possible to identify spin-dependent transport-modifying processes arising from a small number of electrons. Such electrically detected spin resonance has, in combination with optically (photoluminescence or electroluminescence) detected magnetic resonance, in the past been used to gain insight into the nature of charge carriers in organic semiconductors.28, 9296 For example, it is possible to deduce the size of a polaron, and to image charge buildup in a field-effect transistor.5456, 9799

Spin resonance techniques have been particularly powerful in illuminating spin-dependent transitions in organic semiconductors.25, 92, 93 Consider the reaction diagram in Figure 3. If the rate of formation of singlet excitons kS out of singlet polaron pairs is greater than the rate of formation of triplet excitons kT out of triplet polaron pairs, and effective mixing between singlet and triplet polaron pairs occurs, for example due to spin–lattice relaxation, then the overall electroluminescence quantum yield of a singlet-emitting material should exceed 25 %.25 The occurrence of such preferential formation of singlet excitons would clearly be beneficial for OLED applications, but may be detrimental to devices which aim to exploit the spin degree of freedom.15, 17

Vardeny and co-workers developed a sensitive technique to quantify preferential recombination in the singlet channel.25 Their approach is based on the fact that polarons and triplets can be identified through their distinct induced absorption bands, by using the methodology of photoinduced absorption spectroscopy.86 Here, a powerful continuous-wave laser beam generates a large population of singlet excitations. Most of the singlets decay radiatively, but some dissociate into polarons (or polaron pairs), and others undergo intersystem crossing to the triplet excited state. By studying the differential transmission spectrum of a broad probe spectrum, the optically induced absorptions can be revealed. Figure 4 shows the differential transmission spectrum of a film of the conjugated polymer methyl-substituted ladder-type poly(para-phenylene), obtained at a temperature of 10 K. A strong absorption band is observed between 500 and 1000 nm, with evident substructure superimposed. An additional absorption appears in the near-infrared part of the spectrum. Following previous assignments, the absorption features are labeled as being due to polarons (P) or triplet excitons (T). It is now possible to investigate the effect of electron spin resonance on the induced absorption features. Figure 4 b plots the differential photoinduced absorption spectrum arising under the condition of magnetic resonance. The occurrence of magnetic resonance can be inferred from sweeping the magnetic field and measuring the change in differential transmission, as plotted in the inset. Magnetic resonance arises when the photon energy matches the Zeeman splitting, that is, the magnetic energy difference between parallel and antiparallel spins: equation image, where is Planck’s constant times the frequency of the microwave driving field, g is the Landé g-factor, equation imageis the Bohr magneton, and equation image is the applied magnetic field. The change in the photoinduced absorption spectrum corresponds to the occurrence of magnetic resonance of a spin-1/2 species. Plotting the entire differential photoinduced absorption spectrum dramatically improves the spectroscopic resolution, thus allowing a clear separation between polaron and triplet absorption bands. Most importantly, under the condition of resonance both polaron and triplet absorption strengths are reduced. This case is referred to as magnetic resonance quenching. The reduction in the absorption signal is interpreted in terms of a simultaneous lowering of both polaron and triplet exciton populations. The conclusion is then that polaron pairs are preferentially lost to singlet excitons under the condition of magnetic resonance, rather than forming singlet and triplet excitons with comparable probability. The fractional change in polaron-to-triplet exciton populations can be related directly to the ratio between singlet and triplet exciton formation rates, kS/kT. Interestingly, a substantial dependence of this ratio on both the optical gap of the material and the overall conjugation length was reported,92 and has also been studied in detail theoretically.100

Details are in the caption following the image

Photoinduced absorption spectrum and photoinduced absorption-detected magnetic resonance of a conjugated polymer film at 77 K revealing spin-dependent carrier-pair recombination pathways. a) The photoinduced absorption (PA) spectrum measures the change in transmission through the polymer film following photoexcitation with an intense laser beam and shows a distinct peak around 900 nm, which can be attributed to absorption by the triplet excited state. Photoexcitation also generates polarons, with two characteristic absorption bands labeled P1 and P2. b) The photoinduced absorption-detected magnetic resonance (PADMR) measures the change in differential light transmission under the condition of magnetic resonance. As shown in the inset, this condition is verified by detecting the change in differential transmission as a function of applied magnetic field, during illumination of the sample by a microwave field. Under spin resonance, singlet and triplet polaron pairs are mixed randomly, as illustrated in Figure 3. This random mixing of polaron pair spin configuration results in a reduction of the intensity of the polaron and triplet absorption bands: on resonance, the polaron and triplet populations are reduced. Such a reduction on resonance can only arise from increased formation of singlet excitons, or alternatively, increased quenching of triplet excitons by polarons through an Auger-like nonradiative recombination process. It is generally believed that in the case of these data, the former interpretation holds. Reproduced with permission from ref. 25. Copyright 2001, Nature Publishing Group.

These initial and subsequent studies of polaron pair recombination using electron spin resonance generated some discussion in the literature. An alternative way of interpreting the negative magnetic resonance signal in Figure 4 b is through polaron-induced quenching of triplet excitons. In this model, as put forward by Shinar et al., the interaction between polarons and excitons is enhanced under resonance.101105 This interaction leads to a quenching of singlet excitons by promoting nonradiative decay to the ground state at the expense of a polaron or a triplet exciton.29, 31 One may think of this mechanism in terms of conventional Auger recombination, which occurs in atoms and semiconductors: the energy of an excited electron (or electron–hole pair) is passed on to a further electron, thus creating one particle from three.106, 107 Arguments put forward against this quenching interpretation of the magnetic resonance signal involve the observation of delayed luminescence under spin resonance.93, 108 In addition, the coherent spin manipulation discussed in this Review is consistent with the spin-dependent polaron pair recombination model.911 Needless to say, consistency alone is no scientific proof, and spin-dependent exciton-charge interactions are certainly expected to contribute to the photophysics of organic semiconductors.109

Although the magnetic resonance studies discussed here are consistent with spin-dependent transition rates, subsequent investigations revealed that the mixing between spin configurations of the polaron pair (i.e., spin–lattice relaxation) is actually very weak.12, 94 As a consequence, even a strong imbalance towards singlet exciton formation will not actually lead to more singlet excitons in an OLED, since the actual formation of polaron pairs out of free charge carriers is independent of spin.110 Both optical and spin resonance experiments have indicated very inefficient spin mixing through spin–lattice relaxation.12, 94 It is therefore unlikely that fluorescent singlet-emitting OLEDs will exceed 25 % quantum efficiency. Imbalances in the exciton formation rate only become apparent in the emission of OLEDs based on materials with strong spin–orbit coupling which induces inherent spin mixing.111

4. Coherent Optoelectronics

We generally think of the interaction of light and matter as a perturbative, irreversible process: a photon impinging on an atom in resonance with an electronic transition will either raise the electron from the ground state to the excited state, or not. The electromagnetic perturbation to the Hamiltonian describing the electronic wavefunction is infinitesimally short. Likewise, under relaxation of the excited electron, the process of spontaneous emission is irreversible. However, this simple quantum mechanical picture has a flaw: what if a light beam impinges on the atom with such an intensity that two photons arrive within an infinitesimally short succession of each other? The first photon will be absorbed, raising the electron to the excited state, but the second photon will induce stimulated emission, thus bringing the electron back down to the ground state again. The photon flux on the far side of the atom will thus appear unperturbed, and the atom itself will seem transparent. This phenomenon constitutes the limit of strong light–matter coupling, which itself lies at the heart of both nuclear magnetic and electron spin resonance. Since this general quantum mechanical formulation of nonperturbative transitions by Isidor Rabi, interest has emerged in such strong coupling in a variety of electrodynamic phenomena, including optical transitions in atoms,112 molecules,4, 113, 114 semiconductors,115123 and even superconducting Josephson junctions.124

In the context of our discussion of optoelectronic organic materials, optical manifestations of strong light–matter coupling are particularly interesting. A most illuminating example of such strong coupling occurring in a real optoelectronic device is given in Figure 5, in which the light absorption and resulting photocurrent of a single quantum dot photodiode is shown.125 The sketch in Figure 5 a shows radiation of frequency ω impinging on a two-level system of ground state equation image and excited state equation image. A single photon would simply raise the two-level system from the ground state to the excited state. However, depending on the number of photons comprising the incident radiation, that is, the radiation intensity, the two-level system will cycle between the ground and excited state. The ultimate state of the two-level system will depend on the number of photons impinging on the system. In this case, the two-level system is a quantum dot, which can only give rise to a photocurrent when it is in the excited state. Figure 5 b shows the periodic variation in the single quantum dot photocurrent as a function of excitation amplitude. The current clearly displays a periodic modulation, which is known as the Rabi oscillation. The excited-state population of the single quantum dot photodiode undergoes Rabi flopping between the ground and excited states. Such Rabi flopping requires a coherent interaction between the driving field and the two-level system. For example, if the experiment were performed on a collection of quantum dots, some quantum dots may be in the ground state and others in the excited state. Different quantum dots may respond differently to the driving field, so that the Rabi flopping events of the individual quantum dot population average out. However, one may also measure the net polarization of the system, for example, by focusing only on the magnitude of excitation. Use of coherent spectroscopic techniques that measure the optical polarization of a material, such as degenerate four-wave mixing, allows the observation of polarization Rabi flopping in an ensemble.115

Details are in the caption following the image

Coherent control of the electronic-state population of a single quantum dot photodiode. a) A light pulse of finite duration impinging on a single quantum dot can raise an electron from the ground to the excited state. If the intensity of the light pulse is sufficient, a second photon may arrive after the quantum dot has been excited, which induces stimulated emission and returns the quantum dot back to the ground state. The outcome of an absorption experiment therefore depends on the pulse intensity, which is defined by the amplitude of excitation. b) Measured and calculated photocurrent of a single quantum dot photodiode as a function of excitation amplitude. The photocurrent depends on the occupation probability of the excited state, which forms the precursor to optical charge generation. As the excited-state population is depleted again with increasing field amplitude, oscillations in the photocurrent are observed. These oscillations are a signature of coherent nonperturbative interactions of the driving field with the absorbing object, and are generally referred to as Rabi oscillations. Reproduced with permission from ref. 125. Copyright 2002, Nature Publishing Group.

The physics of this experiment on a two-level system can be translated directly to the case of electron spins (or nuclear spins for nuclear magnetic resonance). An external magnetic field B0 creates a macroscopic magnetization in the paramagnetic ensemble of spins, which is perturbed by a periodically varying field B1, usually applied perpendicular to B0. Here, the strength of the microwave absorption controls the excited-state population. The oscillation of the incident microwave field, which corresponds to a perturbing magnetic field of magnitude B1, drives the polarization. As long as all spins are the same, that is, respond in the same way to the perturbing B1 field, coherence can be established between the spin polarization and the driving field: the collection of spins in effect acts as a single two-level system, in analogy to the depiction in Figure 5. Much of the following discussion relating to electron spin resonance can be generalized for the case of electrodynamic interactions in the framework of the so-called optical Bloch equations.

Under an applied magnetic field B0, an electron spin′s energy is split into two levels, which correspond to parallel and antiparallel orientation. The total sum of all individual spin vectors in a sample corresponds to the macroscopic magnetization. The torque experienced by a magnetic moment in a magnetic field is proportional to the rate of its change and thus the change of magnetization, which allows the classical formulation of the equation of motion of spins. These equations are known as the Bloch equations. Due to the nonclassical nature of the spin degree of freedom, the Bloch equations must then be solved using quantum mechanics.

The problem bears analogies to a classical top spinning about its axis with an overall angular momentum of L. The Bloch equations simply relate angular momentum to overall magnetization, so that the equation of motion is written in terms of the rate of change of magnetization. Application of a force orthogonal to the axis of rotation results in a torque initially parallel to the angular momentum axis, in turn displacing the L axis. Due to angular momentum conservation, a force that displaces a top from its axis of rotation gives rise to a secondary contribution to the angular momentum, known as a precession of the top’s axis of rotation. In effect, in a magnetic resonance experiment, the B1 field corresponds to a force applied orthogonal to the direction of net magnetization. As long as this field is present, the magnetization precesses around the original equilibrium axis. It is this spin precession that controls the overall spin population, which in turn becomes apparent through spin-dependent processes involving external observables, such as microwave absorption, current flow, or light emission. Observation of strong coupling of the driving microwave field to the spin population requires precise control of the duration over which the perturbation (torque) is applied. One therefore refers to the technique as pulsed electron spin resonance,126 as the microwave field is delivered to the sample in pulses to control the overall spin precession.

While the remainder of this Review will focus on coherent manipulations of spin populations in organic semiconductors, it is stimulating to note that the underlying physics of strong electromagnetic coupling is highly relevant to a range of phenomena in organic semiconductors. We will focus on discussing time-domain manifestations of Rabi flopping, which lead to an oscillation in excited-state population. However, time- and frequency-domain physics are equivalent. Strong coupling can also be thought of in terms of a coherent superposition of electronic and photonic state, enabled by an interaction Hamiltonian which is large compared to the energy difference between the photon and the electronic state. This energy difference is referred to as the detuning. In a pictorial representation, this situation can be visualized as two adjacent quantum wells with a finite coupling (i.e. a finite tunneling barrier) between them. The wavefunction of the combined two-well system is a linear combination of the two eigenstates of the individual quantum wells. The coupling (through tunneling) lifts the degeneracy between odd and even parity solutions of the wavefunction. The stronger the coupling, the greater the energetic splitting between the lower-energy even (bonding) and odd (antibonding) wavefunctions. The coupling Hamiltonian results in a particle in the double quantum well being in a superposition state. Such superpositions are characterized by the fact that they are not stationary in time: the maximum probability of detecting the particle oscillates from one well to the other. One can state that the coupled quantum system oscillates between the two eigenstates with a frequency that corresponds precisely to the energy splitting between the two, bonding and antibonding, superposition states.

A particularly intriguing manifestation of this strong coupling in the optical regime of organic semiconductors is found in certain molecules deposited inside high quality factor microcavities, which are used to tune the photon mode precisely. In such strongly coupled microcavities, dressed exciton–photon states arise, which are characterized by the excitonic transition energy shifting to both higher and lower energy according to the magnitude of Rabi splitting.4, 113 The hybrid exciton–photon superposition particles are referred to as polaritons. Such strongly coupled systems have even been used to generate electroluminescence.127

5. Pulsed Electrically Detected Magnetic Resonance

5.1. How to Expose an OLED to a Strong Microwave Field

To gain insight into the elementary charge generation and recombination pathways in organic semiconductor devices such as OLEDs and photodiodes, we need to place an OLED sandwich structure inside a microwave field. There are two important experimental aspects to consider. First, the microwave field is localized to a resonator cavity, where a standing wave is formed. A standing wave is necessary to ensure that the sample is always exposed to the maximum amplitude of the time-varying B1 driving field. Typical resonator geometries are of the order of centimeters. It is therefore crucial to ensure that the OLED structure does not distort the incident microwave field. Electrical leads to the device within the resonator need to be chosen such that the thickness is well below the skin depth for electromagnetic penetration of the microwave radiation: the device leads effectively need to be transparent to the microwaves. Second, to carry out coherent control of the spin population in an OLED, much like the coherent control of quantum dot population illustrated in Figure 5, it is crucial to be able to vary the duration and amplitude of the microwave radiation. Microwave pulses as short as a few nanoseconds are required to effectively control the rapidly moving spin ensemble in the OLED. Such short pulses necessitate large pulse amplitudes, which lead to overall microwave powers of the order of kilowatts. As an analogy, the reader may wish to contemplate placing a conventional OLED in a domestic microwave oven without causing the induction of electric currents when the microwave field is turned on.

Figure 6 shows the structure of the OLED geometry employed for coherent spin manipulation in a strong microwave field. To prevent sparking, the OLED active area is contacted with evaporated metal strips rather than with wires.9, 10 The strips are more than an order of magnitude thinner (<100 nm) than the skin depth (≈2 μm for Al at T=10 K) of the metal for microwave radiation, so that they appear effectively transparent to the microwaves. In this way, the OLED can be mounted inside the dielectric microwave resonator with minimal perturbation of the electromagnetic field. The sample itself can be immersed in liquid helium within the microwave resonator, which further increases device stability and thus signal-to-noise ratio. Indium tin oxide (ITO) serves as the anode of the device, with calcium/aluminum forming the cathode. An optional layer of hole-injecting poly(3,4-ethylenedioxythiophene) (PEDOT) is inserted between the anode and the active material. Note that due to the low conductivity of ITO, the conducting oxide only serves as a poor lead to connect to the OLED. The ITO is therefore covered with a metal layer. Cathode and anode strip leads are separated vertically by a silicon nitride layer. Although only one pixel is contacted at a time, the advantage of the setup lies in the fact that well-defined OLED templates can be fabricated reproducibly and contacted in a cryostat through a simple clip arrangement. Figure 6 a shows a photograph of a fully functional single-pixel OLED structure mounted onto the cryostat sample rod. Note the absence of wires, which would lead to significant inhomogeneities of the B1 field by shorting the electric field that in turn generates the magnetic field.

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Device design for pulsed electrically detected magnetic resonance of OLEDs. Standard OLED geometries, in the configuration ITO/PEDOT/MEH–PPV/Ca/Al, have to be placed within a low quality factor microwave resonator, where they are exposed to high microwave powers. To prevent electrical discharge and distortion of the microwave field in the resonator, all contacts to the device are fabricated with evaporated thin films, which are thinner than the skin depth for microwaves. a) Photograph of a functional OLED structure mounted onto the sample rod. b) Device schematics. Reproduced with permission from ref. 9. Copyright 2009, Wiley-VCH.

5.2. Time-Resolving Spin-Dependent Transitions

Given the suitable OLED geometry, it is now possible to investigate the effect of spin resonance on the current passing through an OLED. There are two principal approaches to performing the experiment: either under zero bias conditions, that is, where an OLED is short circuited and a current is generated under illumination according to the photovoltaic effect; or under forward bias conditions, where charge carriers are injected from the opposite electrodes. Both situations follow the elementary schematics outlined in Figure 3. The only fundamental difference between these two cases is the relative population of polaron pairs in the singlet and triplet manifold: whereas optical excitation will generate polaron pairs predominantly of singlet spin multiplicity, electrical injection of carriers leads to the formation of both singlets and triplets. Provided the condition for spin resonance is met, both carrier-pair species can undergo transitions from one to the other, thus leading to a mixing of spin populations in the polaron pairs. Consequently, it is only the initial and not the final spin population of polaron pairs (i.e., singlet or triplet pairs) that is affected by the choice of the excitation condition.

There are two primary experimental parameters which can be used to explore the effect of spin resonance on the device current in pulsed electron spin resonance: the magnetic field strength B0, which controls the Zeeman splitting of the spin states, and the time following electromagnetic perturbation of the spin configuration. In effect, we apply a strong microwave pulse to mix singlet and triplet polaron pair spin configurations. We then record the current transient as a function of time following this initial perturbation. Figure 7 shows the variation of device current of an OLED structure operated at zero bias (i.e., in photovoltaic mode). The change in the device current is plotted on a color scale as a function of applied magnetic field B0 and time t following application of a microwave pulse of frequency ∼9.7 GHz (the so-called X-band), duration 160 ns, and power 125 W. Two effects are noted in the transient. First, there is a clear resonance in the current which occurs around 347.3 mT. This resonance starts out as a negative current change (current quenching) and finishes off as a positive signal (current enhancement): at short times, the current is reduced due to the occurrence of the spin resonance condition; at longer times, it is increased. Two representative time slices of the current, which show current quenching and enhancement, respectively, are plotted as a function of field B0 in Figure 7 b, extracted at the times marked by the vertical dashed lines in Figure 7 a.

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Electrically detected magnetic resonance in an MEH–PPV OLED at 4 K following irradiation with a microwave pulse of power 125 W and duration 170 ns. a) Change in the closed-circuit photocurrent of an MEH–PPV OLED as a function of time after perturbation of the current by a microwave pulse and in dependence on the applied magnetic field B0. Two distinct signals are observed at 347.3 mT, which correspond to quenching of the photocurrent at around 10 μs and enhancement of the current at around 30 μs. b) Vertical slices of the current map in (a) at the two times indicated by vertical dashed lines. At 10 μs after the microwave perturbation, quenching of the device current is observed, whereas at 30 μs a current increase arises. c) Transient of the device current on resonance [i.e. at the B0 field marked by a dashed line in (a)], which shows the total quenching and enhancement. The effect of the perturbing microwave field can be quantified by integrating the total quenching current to yield the overall charge ΔQ removed from the photocurrent channel due to the microwave-induced spin mixing. The current quenching is not observed instantaneously due to the time limitation in the response of the current amplifier. d) Magnitude of the current transient plotted on a logarithmic scale, which shows a biexponential form that arises due to the time constants associated with spin-dependent carrier dissociation and recombination. The response of the current amplifier leads to a deviation from the exponential law at very short times. Adapted with permission from ref. 10. Copyright 2008, Nature Publishing Group.

The interplay between current quenching and enhancement is shown on the current transient recorded at optimal magnetic field B0 in Figure 7 c. A total current quenching amplitude can be defined by integrating the transient: this integral ΔQ corresponds to the total number of charge carriers removed from the conduction pathway due to the occurrence of the resonance condition. The current transient can be plotted on a logarithmic scale as shown in Figure 7 d, by considering only the modulus of the current variation. It is found that the current transient exhibits a clearly biexponential recovery form, so that the current returns to its equilibrium value long after electromagnetic perturbation of the spin statistics. The shortest-timescale dynamics of the transient are governed by the rise time of the amplifiers employed, and can be clearly separated out of the data in careful control measurements.

The dynamics in the device current can be modeled by a simple statistical picture, by referring back to Figure 3. Application of the microwave radiation pulse under the condition of resonance (i.e., when the energetic splitting of the Zeeman sublevels matches the incident photon energy) leads to a mixing of the spin configuration between singlet and triplet manifolds. Singlet and triplet polaron pairs will have different energies with respect to each other to accommodate the energetic gain associated with parallel spins in the triplet manifold. In addition, singlet and triplet excitons differ in energy by typically ∼0.7 eV.128 Conversion of a triplet polaron pair into a triplet exciton therefore requires substantially more energy dissipation than conversion of a singlet polaron pair into a singlet exciton. Consequently, exciton formation by carrier recombination is spin dependent. Such exciton formation out of the polaron pairs formed optically constitutes the main loss channel in the present device situation: when a polaron pair forms an exciton, it can no longer dissociate and will therefore not contribute to the photocurrent. Increased exciton formation, which may arise by conversion of triplet polaron pairs into singlet polaron pairs, will therefore lead to current quenching. However, in the present configuration (optical excitation), in which the initial polaron pair population is most likely made up in the singlet manifold (see Figure 2), increased recombination is unlikely to account for the observed initial reduction in the device current.

A similar argument can be applied to the dissociation of polaron pairs into free charge carriers. If triplet polaron pairs are slightly more tightly bound—they are said to be localized in the exchange hole—then a greater energy barrier has to be surmounted to convert a triplet polaron pair into a detectable (free carrier) current than a singlet polaron pair. The dissociation rates of polaron pairs, just like the recombination rates, are therefore inherently spin dependent. If the initial population of polaron pairs is made up in the singlet spin manifold, then electromagnetic perturbation of the system will convert some singlet polaron pairs to triplet polaron pairs. This process will lower the overall pair dissociation rate when compared to the equilibrium situation, thus reducing the measured current. While the quenching of the photocurrent is due to a quenched singlet polaron pair density, the enhancement of the triplet density simultaneously causes a weaker current enhancement. Immediately after the magnetic resonant change of the two densities, the quenching of the photocurrent is dominant. In contrast, at a later time, when the singlet densities have recovered to the steady state but the triplet densities have not yet recovered, the current enhancement will dominate.

Given this interpretation, the current transient in Figure 7 d therefore provides an estimate of the spin-dependent exciton formation and polaron pair dissociation rates. In addition, we can note that the model considerations only hold for the case in which spin–lattice relaxation does not return the polaron pair spin population back to a random thermal equilibrium. The current transient therefore provides direct experimental access to a lower limit for random spin mixing in the carrier pair, which is often referred to as intersystem crossing. In this context it is crucial to note that such a random, incoherent conversion between spin manifolds is dramatically slowed down on intermolecular excitations when compared to intramolecular excitations. This effect was recently investigated in detail theoretically.129 Intersystem crossing in excitons is usually driven by exciton diffusion through the bulk film:35, 36 in solid films, the probability for an excitation to undergo spin conversion can be of the order of a percent,130 whereas it can become so improbable on the level of an isolated single molecule that excursions to the triplet do not occur within the photochemical lifetime of the molecule (i.e., several billion excitation cycles).3

Following the above discussion, it is still crucial to note that the fact that a model may explain the experimental observation does not necessarily imply that the model is actually correct. Alternative interpretations, such as the formation of multiply charged excitations (e.g., trions)74 and the occurrence of charge–exciton quenching processes,102 may also be invoked to explain some of the observations made. Nevertheless, two crucial statements can be derived unambiguously from the experimental insight gained: the spin resonance condition serves to modify the device current such that a biexponential recovery form arises; this form of the current transient (quenching followed by enhancement) implies that the intrinsic spin dynamics (spin–lattice relaxation) occur on much longer timescales than the observed initial current transient. A memory of the electromagnetic perturbation exists several hundred microseconds after the actual perturbation.10

Operating the OLED in forward bias under current injection leads to the predicated behavior.9 Now the imbalance between singlet and triplet polaron pairs in the initial population is exchanged, so that the primary function of the microwave pulse is to convert triplet pairs to singlet pairs. The polaron pair dissociation rate is thus increased, which results in an initial current enhancement. At longer times, due to the initial loss of carrier pairs to the free polaron conduction channel, fewer pairs are available than in the equilibrium situation, thus resulting in a reduction in the current. Again, a transient in the form of a biexponential recovery is observed (not shown), with initial current enhancement followed by current quenching before the transient returns to equilibrium.9

5.3. Coherent Control of Spin Populations

So far, we have not actually demonstrated the occurrence of coherent manipulations of spin populations, in analogy to the coherent control of the excitation of a single quantum dot described in Figure 5. One could argue that the changes in the device current shown in Figure 7 simply result from an arbitrary reshuffling of the spin configuration. To prove actual coherent control of the polaron pair spin state in an OLED, it is necessary to record the response of the system as a function of the duration and intensity of the electromagnetic driving field, the B1 field. Coherent control of the spin population will manifest itself in a reversible change in the macroscopic observable, which in this case is the device current. The most effective metric to record the perturbation in the OLED current induced by the B1 field is the total number of electrons removed from or added to the conduction channel of the system due to enhanced recombination or reduced dissociation: the total charge ΔQ as labeled in Figure 7 c.

Figure 8 plots the total quenched charge as a function of the duration of the applied microwave pulse τ. We shall focus on the uppermost curve (squares), recorded at a power of 16 W. As the pulse length increases, the magnitude of ΔQ increases until τ reaches roughly 100 ns. Subsequently, the number of electrons depleted decreases again, and displays a distinct periodic oscillation with τ. The oscillations become clearer for increasing microwave power, and also exhibit a rise in frequency. The cartoons at the top of Figure 8 display the underlying physics in the picture of rotating reference frame Bloch spheres, where the spin polarization precesses around the vector describing the driving field.10 The external magnetic field, B0, defines the direction of the initial spin polarization S. Application of a B1 driving field orthogonal to S results in an effective torque acting on S, which induces spin precession. The duration of application of the torque defines the final spin polarization: the ultimate orientation of S. An electromagnetic pulse of a duration such that a 180° change in the orientation of S is induced is referred to as a π pulse; doubling the duration results in a 2 π pulse so that the polarization is returned to its original configuration. These oscillations in the spin polarization are referred to as spin Rabi flopping.

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Coherent spin Rabi flopping in the photocurrent of an MEH–PPV OLED. The change in the total quenched charge ΔQ (see Figure 7) is plotted as a function of microwave pulse duration τ for different microwave powers. A periodic oscillation of the quenched charge is observed with increasing pulse duration. The oscillation frequency rises with increasing microwave power (which depends on the square of the field amplitude B1), as shown in the inset. The diagrams at the top illustrate the precession of the charge-carrier spin S in response to the driving field B1, in analogy to a spinning precessing top. As the direction of the driving field B1 is plotted to be constant, this pictorial representation in form of Bloch spheres is referred to as the rotating reference frame. The spin population and thus the current returns almost to its original state following perturbation by a driving pulse of a characteristic duration, which is referred to as a 2 π pulse. Reproduced with permission from ref. 10. Copyright 2008, Nature Publishing Group.

As in the case of a classical spinning top, the frequency of precession depends on the magnitude of the torque applied. In analogy, increasing the power of the driving field (which depends on the square of the amplitude of the field B1) lowers the precession period. As expected, the inset in Figure 8 shows how the Rabi frequency ΩR depends linearly on the magnitude of B1.

5.4. From the Hyperfine Field to Coherent Spin Beating

In the discussion so far, we have not explicitly identified which charge-carrier species causes the magnetic resonance effect in the current. Close inspection of the line shape (i.e., the resonance spectra shown in Figure 7 b) in steady-state magnetic resonance has indicated that the spectrum can be best described by a superposition of two Gaussians.11 Such a superposition could be interpreted as arising from contributions to the spin resonance spectrum of two distinct species—electrons and holes. Indeed, single-carrier devices (e.g., OLEDs, in which the work functions of the electrodes are chosen such that only holes or electrons are injected) have revealed that the line shapes tend towards a single Gaussian.131133 Obviously, mere fitting of spectral lines is no proof of a particular model: exchange, hyperfine, spin–orbit, or spin–dipolar interactions could all contribute to the observed line shape, and may depend sensitively on the particular device configuration under investigation.11, 134137 The most obvious aspect to focus on is the hyperfine interaction, which describes the effect of the nuclear magnetic moment on the electron spin. The hyperfine interaction depends on the spin of the nucleus, which in turn is controlled by the particular isotope. Most of the carbon in organic semiconductors consists of 12C, which has a nuclear spin of zero. In contrast, the hydrogen nuclei carry a spin of 1/2. Therefore, pure carbon compounds, such as carbon nanotubes, graphite, or graphene, will only show extremely weak hyperfine fields due to the presence of 13C isotopes (the natural abundance of this isotope is 1.1 %).138 Hyperfine fields can be generated by producing isotope-pure carbon-based structures.139 Organic semiconductors, in contrast, are full of hydrogen nuclei, and therefore exhibit significant hyperfine fields. These fields can be modified, for example, by deuteration of the compounds (the overall hyperfine coupling strength of deuterium is approximately a factor of 7 weaker than that of hydrogen, although the nuclear spin of deuterium is 1).140

Hyperfine field effects have long been considered to be important in the physics of organic semiconductors and molecular electronic reactions in general.89, 141148 Possibly the most remarkable manifestation of the effect of hyperfine fields in electron-transfer reactions is found in the mechanism governing the migration ability of birds. Some avian species incorporate highly magnetic field-dependent ocular sensory elements, which provide visual guidance with respect to the Earth’s magnetic field.149 More recently, hyperfine fields have been invoked to explain some of the intriguing magnetic field effects observed in OLED structures.150 It was shown that identical diode structures made with (nuclear spin-free) C60 molecules do not display magnetoresistive effects, when compared to devices containing conventional organic semiconductors.151

Hyperfine fields will affect the effective magnetic resonance of a single carrier, as defined by the Landé g-factor:152 a local magnetic field arising from the nuclei in the vicinity of the electron or hole spin will serve to broaden the selection criteria for allowed microwave photon energies. Following the central limit theorem and assuming isotropic fields, this broadening depends inversely on the number of nuclei contributing randomly to the local field experienced by the carrier spin. The more nuclear magnetic moments are felt by the polaron, the smaller the overall average effect. Figure 9 displays the elementary microscopic picture of a polaron pair in an MEH–PPV film. The electron and hole wavefunctions are sketched to be delocalized along the backbone of the polymer chain. The centers of the wavefunctions are separated by a distance r, which controls the intrapair exchange and dipole–dipole coupling. Each polaron experiences a local magnetic field due to the hyperfine interaction arising from the nuclear spins labeled in Figure 9. There is no correlation between these nuclear spins, so that the dipole orientations are random. The more nuclear spins contribute to the effective field felt by the polaron, the smaller the standard deviation in nuclear magnetic moment orientation. A carrier described by a smaller wavefunction will feel an effectively larger local field than a larger wavefunction. Considering that there is no reason for electron and hole wavefunctions, which in turn relate to the lowest unoccupied and highest occupied molecular orbitals, to have the same degree of spatial delocalization, it is reasonable to propose that the effective average hyperfine field experienced by the electron and hole polaron differs slightly.

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Pictorial representation of the influence of hyperfine fields on the polaron pair spin. Hyperfine fields arise from the nuclear magnetic moment of the proximal hydrogen atoms. Electron and hole wavefunctions are separated by a distance r and typically reside on different chains within the bulk film. A small difference in size of the two wavefunctions results in both carrier spins experiencing slightly different local hyperfine fields. As the orientation of the nuclear spins is random, an infinitely large wavefunction will experience a hyperfine field of zero; the smaller the wavefunction extension, the larger the local hyperfine field effect. Differences in the electron–hole wavefunction delocalization enable a clear distinction of the two carrier species in magnetic resonance experiments.

Assuming the electron and hole within the polaron pair experience small differences in the effective local hyperfine field, one may expect to be able to distinguish the two carrier species in their magnetic resonance response to a driving field B1. At low fields B1, only one of the carrier species can be in resonance with the driving field, since the average difference in local (hyperfine) magnetic field magnitude, |ΔBhyp|, exceeds B1. Once this condition is reversed (i.e., |ΔBhyp|<B1), both carrier spins can experience magnetic resonance. The consequence on the electromagnetically controlled spin dynamics is profound. Figure 10 a displays this situation schematically. As long as the average magnitude of the difference between hyperfine fields experienced by electron and hole exceeds the driving field B1, only one carrier spin will precess, in analogy to the situation discussed in Figures 7 and 8. The oscillation frequency of the carrier spin polarization is defined as the Rabi frequency ΩRabi. Once the driving field exceeds the effective hyperfine field difference, as shown in Figure 10 b, both electron and hole spins can precess. This double precession results in a halving of the period in which the polaron pair mutates from the triplet to the singlet and back to the triplet manifold. The frequency is doubled to 2 ΩRabi.136, 137 Rather than observing periodic Rabi flopping of a single frequency, as shown in Figure 8, this latter case of joint electron–hole precession at large B1 fields will lead to spin precession at two frequencies, ΩRabi and 2 ΩRabi, within an ensemble of spins with a distribution of differences in hyperfine fields. Figure 10 c displays the integrated change in current flowing through an OLED operated in forward bias under electrical injection conditions as a function of time. The points correspond to the measured data whereas the dotted line exhibits the trace of a single periodic oscillation. In contrast to the situation shown in Figure 8, a total of 17 Rabi flopping periods can be resolved in the current transient. Close inspection of the graph reveals a saw-tooth form characteristic of a beating oscillation. Indeed, further analysis of the current evolution by Fourier transformation uncovers two distinct precession frequencies, which both change linearly with increasing driving field B1, as discussed for the case in Figure 8.

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Coherent spin beating of electron and hole spins mediated by the averaging effect induced by the local hyperfine fields. a) For low microwave powers, where the driving field B1 is smaller than the magnitude of the average difference in hyperfine fields experienced by electron and hole, either electron or hole spin will precess. This precession results in the spin pair undergoing transitions between singlet and triplet configurations with a total period of ΩRabi. b) Once the driving field exceeds the random local hyperfine field difference, both electron and hole spins precess simultaneously, which results in a doubling of the Rabi oscillation frequency to 2 ΩRabi. c) As electron and hole spins precess at slightly different frequencies, owing to the miniscule difference in local magnetic field experienced, a beating oscillation of the spins occurs. This oscillation is readily seen in the transient variation of the device current. In this situation, the change in the OLED current is measured under operation in forward bias. Because of an improved device and resonator geometry, and also because of the higher applied B1 fields, more Rabi oscillations are observed than in the situation depicted in Figure 8. The change in device current with microwave pulse length can be accurately described by a superposition of two oscillations, which leads to pronounced beating. For comparison, a single oscillation is plotted as a dotted line, which evidently does not fit the data. The two frequencies ΩRabi and 2 ΩRabi are clearly discerned in a Fourier transformation of the oscillation. Reproduced with permission from ref. 11. Copyright 2010, American Physical Society.

Careful analysis of the spin Rabi flopping observed in the current transient allows extraction of the magnitude of the driving field B1 above which spin beating occurs, that is, both electron and hole spins precess in conjunction. Remarkably, this magnitude of B1 has been found to correspond directly to the average difference in peak position when fitting two Gaussians to a dual-carrier OLED magnetic resonance spectrum. One may conclude that the average difference between hyperfine fields experienced by electron and hole in MEH–PPV is of the order of 1.1 mT. It is this effective difference in local fields that defines how the current through a device will respond to a static external magnetic field.155

In view of the present interest in unraveling mechanisms underlying magnetoresistive effects in organic semiconductors,142, 153, 154 it is crucial to note that electron spin resonance techniques can indeed provide unprecedented accurate insight into the magnitude and nature of hyperfine interactions, as revealed by the occurrence of coherent spin beating effects.11 This insight is gained under static magnetic fields which are two orders of magnitude larger than the hyperfine fields (B0B1), thus demonstrating that, contrary to prior speculation,142 the external field does not shield the hyperfine fields. Magnetoresistive effects are usually considered in the low field regime, of the order of the hyperfine field.154 In intermediate field regimes, it has been proposed that Zeeman splitting of the spin sublevels and subsequent spin mixing gives rise to magnetoresistance due to the occurrence of spin-dependent exciton formation and dissociation.142 However, direct measurements of the exciton population clearly reveal that magnetic field effects in the current and electroluminescence do not appear with changes in the singlet/triplet exciton ratio.12, 155, 156 Even at intermediate to large fields, orders of magnitude larger than local hyperfine fields, the effect of the hyperfine fields on spin-dependent transport is still critically important.11

5.5. Open Questions

Although there is a long history of studying the properties of spins in organic semiconductors and molecular materials in general, the advent of the ability to perform coherent spectroscopy in real device structures marks a new depth in terms of the spectroscopic detail obtainable with these materials. Coherent spin resonance phenomena have been studied optically in molecules for over 30 years, yet it was long believed that charge carriers in organic semiconductors should not exhibit significant spin coherence times.100 Indeed, estimates of spin–lattice relaxation times, which by necessity pose an upper limit to the spin coherence time, have previously been formulated to be as short as nanoseconds.25 The fact that spin coherence phenomena are clearly observed underlines that intrinsic spin mixing is extremely weak, and implies that carrier recombination generally follows spin statistics in OLEDs. The experimental technique of pulsed electrically detected magnetic resonance of OLEDs now offers a new route to exploring the potential of materials-based avenues to actually induce spin mixing. It is conceivable, for example, that high carrier densities or the inclusion of magnetic nanoparticles could promote spin mixing. It is therefore crucial to explore the effect of carrier density, temperature, electric field, and external impurities on the coherence transients observed. It will be of particular importance to identify the influence of strong spin–orbit coupling on the magnetic resonance and spin coherence signal. Intuitively, one would expect strong spin–orbit coupling to remove any spin coherence effect. However, this assumption was previously also made in the context of inorganic semiconductors, where it came as a surprise to measure long spin diffusion distances in GaAs.157, 158 Considering the variety of metal–organic materials for organic electronics, such as iridium-based triplet emitters, coherent spin spectroscopy may provide an avenue to study the subtleties of ligand–metal interactions which appear to strongly affect the properties of a particular triplet emitter.

In this Review, we have focused mainly on the new technique of coherent electrically detected magnetic resonance. A complete understanding of the spin physics of organic semiconductors will necessitate comparisons of this technique with other detection schemes under similar driving conditions. For example, rather than detecting the outcome of failed recombination and promoted dissociation (i.e., transport), one should observe similar effects when recording the recombination channel directly (i.e., luminescence). Such optically detected magnetic resonance is expected to reveal similar coherent dynamics to those observed in the transport channel. Given the fact that, under certain conditions, singlet and triplet recombination channels can be separated out spectrally as fluorescence and phosphorescence (see Figure 2), spectrally resolved electroluminescence-detected magnetic resonance should provide a direct handle on spin-dependent recombination channels in OLEDs. Such an approach would enable coherent spin optics to be accessed directly in the frequency domain, whereas conventional inorganic semiconductor structures typically measure the degree of circular polarization to quantify overall spin polarization.19 In this context it is worth noting the wealth of literature from the early days of molecular magnetic resonance spectroscopy, which can readily be related to present-day problems in organic electronics. Examples include the demonstration of a variety of coherent phosphorescence (triplet exciton)-detected magnetic resonance effects,4347, 114 such as coherent spin polarization beating.159

The contribution of hyperfine fields to charge-carrier dynamics in organic semiconductors has long been considered to be important.146 Electron spin resonance spectroscopy provides a direct window to assess the magnitude of such hyperfine interactions,141 and to explore the potential impact of hyperfine fields on, for example, charge-carrier pair separation and recombination. An obvious route to explore hyperfine interactions in more detail is to control the nuclear spin by changing the isotopes comprising the organic material. For example, one may substitute some or all of the hydrogen atoms for deuterium. It is astounding how little work has been reported in the literature on the effect of deuteration of organic semiconductors on electronic and magnetic properties.140, 160 In relation to the schematics outlined in Figure 9, we anticipate that it will be possible to tune the overall hyperfine field experienced by electron and hole separately, and to measure this directly using the electrical spin resonance readout. A precise, microscopic control of hyperfine interactions may give rise to solid-state magnetic field sensors of unprecedented sensitivity, in analogy to hyperfine-modulated recombination reactions occurring in nature.141, 149 In addition, the hyperfine interaction in organic semiconductors may provide a pathway to electrically read out or even write nuclear spin polarization, as has been demonstrated for GaAs-based structures.161 Nuclear spins are much more isolated from the environment than electron spins and do not change their orientation readily. To probe coupling between nuclear and electron spins it will be necessary to carry out nuclear magnetic resonance spectroscopy, in which the incident microwave photon energy is matched to the spin resonance of the nucleus rather than to that of the electron. If nuclear spin resonance is found to have an impact on the spin-dependent electron transport due to the hyperfine interaction, ultimately the opposite process may become possible: storing electronic spin information in the nuclear spin. Ferromagnetic electrodes appear to enable the injection of polarized spins in an organic semiconductor, an effect exploited in spin valves with high magnetic field sensitivity.15, 17 Nuclear magnetic resonance spectroscopy may reveal how much of this electronic spin polarization is transferred to the nucleus, where it could potentially be stored for an extended time period. It is likely that many of the remarkable nuclear-electronic spin-transfer effects observed in low-Z materials such as silicon will ultimately become attainable in organic semiconductors.162

Many analogies exist between the spin dynamics underlying organic semiconductors and those studied in more conventional mesoscopic systems such as quantum dots. Whereas carrier pairs—a coherent quantum mechanical superposition of spin states—are often created in coupled quantum dots,163 such entangled excitations arise naturally in molecular materials. Much of the insight gained into controlling and exploiting the interaction of single spin excitations with the spin bath in mesoscopic materials164166 could be applied to problems relating to organic semiconductors. Due to the weak dielectric screening in molecular materials, the Coulombic well experienced by carrier pairs is much steeper than in inorganic materials. As a consequence, it is possible to strongly perturb intercarrier separation by means of electric fields.167 This electrostatic control over carrier separation, most directly manifested in the transient storage of excitation energy,12 allows tuning of the magnitude of the exchange interaction. In quantum dots, it has been demonstrated that such an exchange tuning can enable programming of the excitation in a particular spin state.168170 One may expect that electrostatic manipulation of the carrier-pair exchange interaction in an organic semiconductor could form the basis for similar controlled programming of a spin state when combined with spin-resonant perturbation of the spin density. For example, an excitation could be generated optically, the charge separated and stored using an electric field, manipulated coherently using spin-resonant excitation, and subsequently brought to recombination in a controlled spin channel by removal of the stabilizing electric field. In this context, perhaps the most astounding observation made in Figure 8 is that the experimental technique is sensitive to changes in charge transport through the OLED involving only a few hundred electrons.10 The sensitivity of the differential charge measurement can be enhanced by reducing the overall device current, achieved by shrinking the device area. OLEDs with micrometer-sized electrodes should therefore readily allow the controlled manipulation and detection of single charge spin recombination or dissociation events. Such electrical readout of a single spin has previously been demonstrated in silicon devices,171 but could be expanded with greater versatility in organic materials. A controlled readout of the state of a single electron spin is imperative to designing elementary building blocks for quantum information processing. Quantum computation requires both the preparation of quantum mechanical “qubits” of information, and controlled operations. The exchange interaction between two carrier spins offers a suitable basis for generating quantum mechanical entanglement. Electrical tuning of the exchange by controlled carrier separation could then provide the mechanism for performing logic operations involving two or more spin qubits.

Finally, it is worth noting that the techniques discussed in this Review are not limited in any way to organic semiconductors. Indeed, much of the earlier work on electrically detected magnetic resonance was performed on silicon structures, by using both recombination centers in crystalline silicon172175 and spin-dependent recombination and transport through amorphous silicon.176 Coherent pulsed optically or electrically detected magnetic resonance could offer a unique route to accessing charge localization dynamics in nanostructured materials, such as semiconductor nanocrystal quantum dots.177 In such compounds, charge trapping can give rise to a range of dynamic optical and electrical effects, the most prominent of which is known as luminescence blinking178 (the microscopic origins of blinking—charge separation—have been studied in depth in single organic molecules using spin resonance techniques179). Recombination in quantum dot materials such as CdSe is inherently spin dependent, and leads to a range of remarkable fluorescence dynamics.180, 181 Initial continuous-wave magnetic resonance spectroscopic investigations of CdSe nanocrystals have indicated rather broad resonances.177 These broad resonances may arise not only from the intrinsically strong spin–orbit coupling, but also from the underlying dispersity of the system. Pulsed magnetic resonance may offer a route to select a particular spin subset within the ensemble and to reduce the effect of spin–orbit coupling by temporal gating. In this context it is intriguing to note that persistent spin polarization transfer has been observed in coupled CdSe nanocrystals by means of time-resolved Faraday rotation spectroscopy.182 Other nanoscale optically and electrically active systems, such as metal nanoparticle aggregates, which display a range of random optical phenomena indicative of photoinduced charge generation,183 may also offer unlikely grounds for further exploration of the possibilities of coherent time-resolved magnetic resonance spectroscopy.

6. Conclusions

Organic semiconductors offer an astonishing test bed to perform hands-on quantum mechanics with electron spins. A coherent superposition of an electromagnetic driving field can be formed with the spin polarization in an organic device, and read out directly and very sensitively using spin-dependent recombination and dissociation channels. Such experiments provide unique access to the fundamental material parameters, such as spin dephasing times, spin relaxation times, and local magnetic field perturbations, arising from hyperfine interactions. In combination with methods of polarizing the spin population in an organic device by direct spin-polarized injection, one could envisage constructing a coherent spin transistor. In such a device, the spin current between two electrodes is manipulated by the perturbing electromagnetic field, which acts as a gate. Besides fundamental aspects in materials characterization, such a device may ultimately have real applications. High local magnetic fields, which are achievable through g-factor engineering of the material,184 could raise the photon energy on resonance, thus allowing the construction of sensitive detectors of terahertz radiation. With increasing interest in terahertz imaging technologies for security applications, new opportunities for organic spintronics devices are likely to arise. The organic electronics mantras of flexibility, processability, and scalability may yet have impacts on technologies we are only just able to glimpse.

Acknowledgements

We are deeply indebted to a team of dedicated researchers, including William Baker, Nicholas Borys, Sang-Yun Lee, Seo-Young Paik, Kipp van Schooten, and Manfred Walter. We gratefully acknowledge collaborative funding for this work by the Department of Energy (Award #DESC0000909). J.M.L. is supported by a David & Lucile Packard Foundation Fellowship for Science and Engineering. C.B. is supported by a CAREER project of the National Science Foundation (Award #0953225).

    Biographical Information

    John Lupton is a Professor in the Department of Physics and Astronomy at the University of Utah in Salt Lake City. Having completed his doctoral studies at the University of Durham (UK) in 2000, he pursued several engagements at the University of St. Andrews, the Max Planck Institute for Polymer Research in Mainz, and the Ludwig Maximilians University of Munich before moving to Utah in 2006. His main research interests lie in optical spectroscopy of nanostructures, such as macromolecules, colloidal semiconductors, and metal nanoparticles, and spin physics of organic semiconductors.

    Biographical Information

    Dane McCamey is a Research Assistant Professor in the Department of Physics and Astronomy at the University of Utah. He completed his PhD at the University of New South Wales in Sydney, Australia, in 2007. His main research interests lie in understanding how coherent spin manipulation impacts the electrical properties of semiconductors, exploiting this understanding to investigate fundamental spin physics, and investigating possible technological applications.

    Biographical Information

    Christoph Boehme is an Associate Professor at the Department of Physics and Astronomy of the University of Utah.. He received his PhD in Physics from Philipps Universität of Marburg (Germany) in 2003. He worked from 2000 to 2005 as a researcher at the Hahn-Meitner-Institut Berlin. His main research is focused on electrical detection schemes of spin coherence in semiconductors and their applications for spin spectroscopy for materials research and spin electronics.