Spintronics and magnetic field effects in organic semiconductors and devices

Spintronics and magnetic field effects in organic semiconductors and devices

12

Tho Duc Nguyen*, Eitan Ehrenfreund†, Zeev Valy Vardeny‡ *Department of Physics and Astronomy, University of Georgia, Athens, GA, United States, † Physics Department, Technion—Israel Institute of Technology, Haifa, Israel, ‡Physics and Astronomy Department, University of Utah, Salt Lake City, UT, United States

12.1

Introduction

Over the past two decades, the electron spin has transformed from an exotic subject in classroom lectures to a degree of freedom that materials scientists and engineers exploit in new electronic devices nowadays. This interest has been motivated from the prospect of using the spin degree of freedom, in addition to the charge, as an information-carrying physical quantity in electronic devices, thus changing the device functionality in an entirely new paradigm, which has been dubbed spintronics (Wolf et al., 2001; Zutic et al., 2004). This interest culminated by awarding the 2007 Nobel Prize in Physics to Drs. Albert Fert and Peter Gru˝nberg for the discovery and application of the giant magneto-resistance (GMR). More recently, the spintronics field (also called spin-based electronics) has focused on hybrids of ferromagnetic (FM) electrodes and semiconductors, in particular spin injection and transport in the classical semiconductor gallium arsenide (Awschalom and Flatte, 2007). However, spin injection into semiconductors has been a challenge because of the impedance matching problem between the FM and semiconductor (Yunus et al., 2008). In any case, this research has yielded much original physical insight, but no successful applications yet. For the last few years, interest also has risen in similar phenomena in the organics. The organic spintronics field was launched via two articles by Dediu et al. (2002) that suggested spin injection in organic semiconductors (OSCs), and Xiong et al. (2004), which demonstrated spin-polarized currents in thin films with a small organic molecule (namely, Alq3). OSCs can absorb and emit light while transporting charge, and this leads to optoelectronic devices such as photovoltaic cells (PVCs), organic light-emitting diodes (OLEDs), and organic field-effect transistors (OFETs). It is thus expected that adding control of the electron spin to the multifunctional characteristics of these versatile materials should yield novel magnetic devices in the near future. However, there are serious challenges to be faced in understanding the properties of spin-polarized current in OSCs and obtain high-quality devices. Most important, the approach in studying spin injection and transport in organic thin films is fundamentally different from that used for their inorganic counterparts. Handbook of Organic Materials for Electronic and Photonic Devices. https://doi.org/10.1016/B978-0-08-102284-9.00012-7 © 2019 Elsevier Ltd. All rights reserved.

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OSCs are composed of light elements that have weak spin-orbit interaction; consequently, they should possess long spin relaxation times (Ruden and Smith, 2004; Pramanik, 2007; McCamey, 2008). Moreover, hyperfine interaction (HFI) has been thought to play an important role in organic magneto-transport (Bobbert et al., 2009). For example, if the HFI constant a determines the spin lattice relaxation time, TSL of the injected carriers, and consequently their spin diffusion length in a device setting, then the device performance may be enhanced simply by manipulating the nuclear spins of the organic spacer atoms. Moreover the HFI may also play an important role in other organic magneto-electronic devices such as two-terminal devices (Pulizzi, 2009). In addition to spin-polarized carrier injection into OSCs, another fascinating effect has been observed when applying a small external magnetic field to OLEDs that was dubbed the magnetic field effect (MFE; Hayashi, 2004), in which both the current and electroluminescence (EL) increase by as much as 40% at room temperature in relatively small magnetic fields of about 100 Gauss. In fact, MFE in organics was discovered about four decades ago (Ern and Merrifield, 1968); however, renewed interest in it has recently risen since it was realized that the MFE in OLEDs has tremendous potential applications. In spite of recent research efforts in organic MFE, the underlying mechanism and basic experimental findings remain hotly debated. Finally, HFI can influence other spin response processes such as optically detected magnetic resonance (ODMR) in OSC films (McCamey, 2008). ODMR is actually a magnetic field effect induced by microwave (MW) absorption that mixes the spin sublevels of polaron pair species. Therefore, gaining an understanding of ODMR in organic films and electronic devices may shed light on the organic MFE phenomenon. Moreover, ODMR spectroscopy is unique in that it readily measures the spin relaxation time in OSCs, and thus information may be obtained about the electronic spin interaction strength. Therefore, we have used this technique to obtain HFI strength in the same materials that are used for spin injection and MFE studies. In this chapter, we review some of the research achieved at the University of Utah in the field of organic spintronics (Wang and Vardeny, 2010; Nguyen et al., 2010a,b; Nguyen et al., 2011a,b); Specifically, we investigate the role of HFI in various organic magneto-electronic devices and films by replacing all strongly coupled hydrogen atoms (1H, nuclear spin I ¼ ½ ) in the organic π-conjugated polymer poly(dioctyloxy) phenyl vinylene (DOO-PPV) spacer (dubbed H-polymer in this discussion), with deuterium atoms (2H, I ¼ 1) [hereafter dubbed D-polymer; see Fig. 12.1] having much smaller a—namely, a(D) ¼ a(H)/6.5 (Carrington and McLachlan, 1967). We studied the influence of this hydrogen isotope exchange on the magnetic response of three spin-dependent processes: l

l

l

Magneto-electroluminescence (MEL) and magneto-conductance (MC) responses in OLEDs, which are presented in Section 12.2. In this section, we also summarize the newly discovered, ultrasmall MFE, such as in MEL and MC at B <1 mT. GMR in organic spin valves (OSVs), where the spin transport in the device determines its performance (Xiong et al., 2004), is presented in Section 12.3. ODMR in thin films, where spin-dependent recombination of photogenerated spin-half polaron pairs is enhanced under magnetic resonance conditions (Yang et al., 2007), which is discussed in Section 12.4.

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Fig. 12.1 Chemical structures of several OSCs that we used for organic spintronics research at the University of Utah: small molecules: (i) tris(8-hydroxyquinolinato)aluminium (Alq3) and fullerene C60; (ii) π-CPs: 2-methoxy-5-(20 -ethylhexyloxy) (MEHPPV); and poly(dioctyloxy) phenylenevinylene that contains hydrogen isotope (H-polymer); deuterated DOOPPV where some hydrogen atoms in the DOOPPV skeleton are replaced by deuterium atoms (D-polymer); and C13-rich DOO-PPV (C13-polymer), where some 12C in the polymer chain backbone was replaced by 13C.

12.2

Magneto-conductance and magnetoelectroluminescence in OLEDs

The MFE involving photoconductivity (PC) in poly-phenylene OLEDs was first conducted by Frankevich et al. (1996). They detected a significant change of a few percent in PC when a relatively small magnetic field of about 100 mT was applied to the device. Later, Kalinowski et al. showed that EL can be modulated in OLEDs made of small molecules such as tris(8-hydroxyquinline aluminum) (Alq3; structure given in Fig. 12.1) by a small applied magnetic field (Kalinowski et al., 2003, 2004). In 2004, Wohlgenannt et al. demonstrated a very large magneto-resistance (MR) up to 10% at a characteristic field of 10 mT in OLEDs made of the polymer poly(9,9dioctylfluorenyl-2,7-diyl) (PFO) (Francis et al., 2004). The effect was dubbed organic magneto-resistance (OMR). Later, they also found that OMR with similar magnitude occurs in small molecules such as Alq3 (Mermer et al., 2005). Because OMR is among the largest obtained magneto-resistive effects in any bulk materials, it has attracted a number of research groups to this novel field. Fig. 12.2 shows a typical OLED structure and the largest reported MEL and MC (which is essentially the inverse of OMR) magnitudes of an OLED (Nguyen et al., 2008). The MEL (MC) response may reach about 60% (30%) at an applied magnetic field of about 100 mT. The effect has been found to be essentially independent of the angle between the film plane and applied magnetic field (Mermer et al., 2005).

Handbook of Organic Materials for Electronic and Photonic Devices

V

I

Al C OSEC PEDOT ITO Substrate

(A)

DI/I (dash lines), DEL/EL (solid lines)

388

(B)

0.6

13.8 V

0.5 0.4 13.8 V

0.3

16.6 V

0.2 16.6 V

0.1 0.0

–90 –60 –30

0 30 B (mT)

60

90

Fig. 12.2 (A) A typical OLED device structure. (B) Room-temperature MC (△ I/I) and MEL (△ EL/EL) in an OLED device made of ITO (30 nm)/PEDOT (about 100 nm)/Alq3 (about 100 nm)/Ca (about 30 nm)/Al (30 nm) at two different bias voltages. From Nguyen, T.D., Sheng, Y., Rybicki, J., Wohlgenannt, M., 2008. Magnetic field-effects in bipolar, almost hole-only and almost electron-only tris-(8-hydroxyquinoline) aluminum devices. Phys. Rev. B 77, 235209, with permission.

Various models have been put forward to explain the MFE in OLED devices based on π-conjugated organic solids (Prigodin et al., 2006; Desai et al., 2007b; Bobbert et al., 2007; Hu and Wu, 2007; Wang et al., 2008). These models are based on the role of the HFI between the spin-half of the injected charge carriers and the proton nuclear spins closest to the backbone structure of the active layer. The general understanding is that the spin mixing in bound pairs of charge polarons, dubbed polaronpairs (PPs) in this discussion, becomes less effective as the magnetic field increases, thereby causing an MFE of the measured physical quantity. The PP species consist of negative (P) and positive (P+) polarons, whereas same-charge pairs constitute pairs of P or P+, which may be termed as loosely bound negative or loosely bound positive bipolarons, respectively. Prior to light emissions from exciton recombination in organic light-emitting diodes based on π-CPs, some of the injected free carriers form PP species, which are constituted of P and P+ separated by a distance of a few nanometers, each having a spin of ½. The free carriers and PP excitations are in dynamic equilibrium in the device active layer, which is determined by the processes of formation/dissociation and the recombination of PP via intrachain excitons. A PP excitation can be either in spin-singlet (PPS) or spin-triplet state (PPT), depending on the mutual polarons’ spin configurations. The steady-state PP density depends on the PPS and PPT “effective rate constant” k, which is the sum of the formation, dissociation, and recombination rate constants, as well as triplet-singlet (T-S) mixing via the intersystem crossing (ISC) interaction. If the effective rate kS (for PPS) and kT (for PPT) are not identical, then any disturbance of the T-S mixing rate, such as by the application of an external

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magnetic field, B, would perturb the dynamical steady-state equilibrium that results in MEL and MC. In the absence of an external magnetic field, the T-S mixing is caused by both the exchange interaction between the unpaired spins of the polarons belonging to the PP species, and the HFI between the polaron spin and several adjacent H nuclei. For PP excitation in π-CP chains, where the polarons are separated by a distance of R > about 1–2 nm, the HFI with protons is expected to be dominant and actually determines the ISC rate. The MFE in organic devices is analogous to the MFE observed in chemical and biochemical reactions, where it was explained using the radical pair (RP) mechanism (Brocklehurst and McLauchlan, 1996; Timmel, 1998). In this model, the HFI, Zeeman, and exchange interactions are taken into account. It is assumed that RPs are immobile (and hence the radical diffusion is ignored), but the overall decay rate k of the RP is explicitly taken into account. The steady-state singlet fraction of the RP population (singlet yield ФS) is then calculated from the coherent time evolution of RP wave functions subjected to this interaction. It is clear that when ℏk is much larger than the energy of the HFI and exchange interactions, then the MFE is negligibly small because the pairs disappear before any spin exchange between the spin sublevels can occur. In contrast, for a relatively small decay rate ℏk, the MFE becomes substantially larger, and for a negligible exchange interaction, the singlet yield behaves approximately as ФS  B2/(B20 + B2) (the upside-down Lorentzian function of B), with B0  aHF/gμB, where aHF is the HFI constant. Then, the half-width at halfmaximum (HWHM) is B1/2 ¼ B0. In organic devices, the PP species play the role of RPs, and the calculated MC (and MEL) response may be expressed in terms of the singlet ФS and triplet ФT PP yields in an external magnetic field B. It is important to note here that finite MC can occur only when the singlet decay rate is different from that of the triplet (Ehrenfreund and Vardeny, 2012). In this section, we show our recent advances in understanding the MFE in OSC two-terminal devices using both experiment and theoretical methods. Specifically, the role of the HFI is readily demonstrated.

12.2.1 Experimental methods and results The MEL and MC measurements in OLEDs have been generally conducted on devices with a typical area of 5 mm2, where the organic spacers are deposited on a hole transport layer: poly(3,4-ethylenedioxythiophene) [PEDOT]-poly(styrene sulfonate) [PSS]. For bipolar devices, we capped the bilayer structure with a transparent anode: indium tin oxide (ITO), and a cathode: calcium (protected by aluminum film). For MEH-PPV, we also fabricated unipolar devices: the hole-unipolar device was in the form of ITO/PEDOT-PSS/MEH-PPV/Au, whereas the electron-unipolar device was Al/LiF (about 2 nm)/MEH-PPV/Ca/Al; these devices did not show EL. The organic diodes were transferred to a cryostat that was placed between the two poles of an electromagnet producing magnetic fields up to about 300 mT. The devices were driven at constant bias V, using a Keithley 236 apparatus; and the current I was measured while sweeping B.

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The MC and MEL responses are defined, respectively, via MCðBÞ ¼ ΔI ðBÞ=I ð0Þ ¼

I ðBÞ  I ðB ¼ 0Þ I ð B ¼ 0Þ

MEL ¼ ΔELðBÞ=ELð0Þ ¼

ELðBÞ  ELðB ¼ 0Þ ELðB ¼ 0Þ

(12.1)

where △ I and △ EL are the field-induced changes in the current and EL intensity, respectively. Fig. 12.3A shows the MEL response of two OLED devices based on H- and D-polymers with the same thickness df, measured at the same bias V; a very similar MC response was measured simultaneously with MEL (Fig. 12.3B). The MEL and MC responses are narrower in the D-polymer device; in fact, the field, B1/2 for the MEL is about twice as large in the H-polymer device than in the D-polymer device. We also found that B1/2 increases with V (Fig. 12.3A, inset) (Wang et al., 2008); actually, B1/2 increases approximately linearly with the device’s electric field, E ¼ (V  Vbi)/df, where Vbi is the built-in potential in the device, which is related to the onset bias voltage where EL and MEL are observed (Bloom et al., 2007, 2009). Importantly, in all cases, we found that B1/2(H) > B1/2(D) for devices having the same value of the electric field, E (Fig. 12.3A, inset).

1.0

H-DOO-PPV

4

0

0

0.5

D-DOO-PPV

D-DOOPPV H-DOOPPV

E (107 V/m) 0

–40

(A)

MC (%)

8

1 mT

MEL (%)

2

1

2

–20

0.0

3

0

20

40

–60

(B)

–40

–20

0 20 B (mT)

40

60

Fig. 12.3 Isotope dependence of MEL (A) and MC (B) responses in OLEDs based on DOOPPV polymers. Room-temperature MEL and MC responses of D- and H-polymers (solid and dashed lines, respectively) measured at bias voltage V ¼ 2.5 V. Inset to (A): the field B1/2, at half the MEL maximum for the two polymers, plotted versus the applied bias voltage, V, which is given in terms of the internal electric field in the polymer layer, E ¼ [V  Vbi]/df, where Vbi is the built-in potential in the device and df is the active layer thickness; the lines are linear fits to “guide the eye.” From Nguyen, T.D., Gautam, B.R., Ehrenfreund, E., Vardeny, Z.V., 2010a. Magnetoconductance response in unipolar and bipolar organic diodes at ultrasmall fields. Phys. Rev. Lett., 105, 166804; Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

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MEL and MC in OLEDs may be considered as an example of a much broader research field that deals with MFE in physics (Groff et al., 1974), chemistry, and biology (Timmel, 1998; Hayashi, 2004). For MFE that results from pairs of radical ions, it was empirically realized (Weller et al., 1983) that B1/2 scales with the HFI constant aHF. In fact, a semiempirical law was advanced (Weller et al., 1983), which for opposite-charge radicals with same aHF reads as B1=2  2aHF ½I ðI + 1Þ1=2 =gμB

(12.2)

where I is the nuclear spin quantum number. In fact, the nuclear spin in the analysis that led to Eq. (12.2) was treated classically (Weller et al., 1983); therefore, it should be considered a crude approximation. Nevertheless, using Eq. (12.2), we get B1/2(H)  aHF(H)√3/gμB for the H-polymer with I ¼ ½, and B1/2(D)  2aHF(D)√2/gμB for the D-polymer with I ¼ 1. Taking aHF(H) and aHF(D) from the fits to the ODMR lines that will be obtained in Section 12.4, we find that B1/2(H)  6 mT for the H-polymer, which is reduced to B1/2(D)  1.5 mT for the D-polymer, compared with the experimental B1/2 values of about 6 mT and about 3 mT, respectively, obtained at small E (Fig. 12.4A, inset). Nonetheless, from the obtained reduction in B1/2, we conclude that the MEL response in OLED of π-CPs is mainly due to the HFI (Sheng et al., 2006; Desai et al., 2007a). Surprisingly, Fig. 12.4A and B show that the MEL and MC has yet another component at low B (that is dubbed “ultra-small-field MEL/MC”; namely, USMEL and USMC), which has an opposite sign as that of the positive MEL (MC) at higher fields. A similar low-field component was also observed in some biochemical reactions (Brocklehurst and McLauchlan, 1996) and anthracene crystals (Belaid et al., 2002),

0.6

D-DOOPPV H-DOOPPV

MC (%)

MEL (%)

1.0

0.5

0.0

0.0 –2

(A)

0.3

–1

0

1

2

–2

(B)

–1

0 B (mT)

1

2

Fig. 12.4 Room-temperature MEL (MC) response of D- and H-polymers (solid and dashed lines, respectively) measured at bias voltage V ¼ 2.5 V, plotted for jB j <3 mT. From Nguyen, T.D., Gautam, B.R., Ehrenfreund, E., Vardeny, Z.V., 2010a. Magnetoconductance response in unipolar and bipolar organic diodes at ultrasmall fields. Phys. Rev. Lett., 105, 166804; Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

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with probably the same underlying mechanism as in OLED devices. The USMEL (USMC) component is also due to the HFI because its width is isotope-dependent; it is indeed seen that the dip in the USMEL response occurs at Bmin  0.7 mT in H-polymer, whereas it is at Bmin ¼ 0.2 mT in the D-polymer. The positive, high-field MEL component was interpreted as being due to less effective ISC between PP spin sublevels at B > 0 (Bergeson et al., 2008; Sheng et al., 2006); therefore, the negative USMEL component should be due to an ISC rate increase between PP spin sublevels at low B. This might happen, for example, if there is a level crossing (LC) between PPS and PPT spin sublevels (Hayashi, 2004). But because the two PPT spin sublevels with Sz ¼ 1 split linearly with B (Bergeson et al., 2008), an isotope-dependent LC in the PP spin sublevels at very low field cannot be easily accounted for with the four basic spin wave functions of PPS and PPT, which are traditionally considered in simple MEL models (Bergeson et al., 2008; Sheng et al., 2006). Therefore, we were led to conclude that additional spin wave functions are needed to explain the USMEL response. The USMFE response is not limited to bipolar devices. In Fig. 12.5A and B, we show MC(B) responses of hole-only and electron-only MEH-PPV diodes; similar responses were measured for DOO-PPV devices (Nguyen et al., 2011a). The high-field MC in unipolar devices is negative (Fig. 12.5A; Wang et al., 2008), and thus the USMFE response here appears as negative-to-positive sign reversal with a maximum at Bm  0.8 mT for the electron-only device and Bm  0.1 mT for the hole-only device

MC/MCmax

0.2 x10

0.0 x2

–0.2 –0.4

(B)

–2

–1

0

1

2

MC (%)

0.0 –0.4

Hole only (x40) Electron only

MEH-PPV

–0.8 –1.2 –30

(A)

–20

–10

0

10

20

30

B (mT)

Fig. 12.5 Normalized MC(B)/USMC(B) response for (A) j B j <30 mT, and (B) j B j < 2 mT in hole- and electron-only unipolar diodes based on MEH-PPV, measured at room temperature and V ¼ 3 and 20 V, respectively. The USMC(B) responses are somewhat shifted in (B) for clarity. From Nguyen, T.D., Gautam, B.R., Ehrenfreund, E., Vardeny, Z.V., 2010a. Magnetoconductance response in unipolar and bipolar organic diodes at ultrasmall fields. Phys. Rev. Lett., 105, 166804, with permission.

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(Fig. 12.5B). Importantly, the HWHM ΔB is smaller in the hole-only device than in the electron-only device; this is consistent with smaller aHF for hole-polaron than for electron-polaron in MEH-PPV, in agreement with recent measurements using transient spin response (McCamey et al., 2010). We therefore conclude that Bm increases with ΔB in unipolar devices similar to bipolar devices (Nguyen et al., 2010a). The USMFE response depends on both bias voltage and temperature; an example is shown in Fig. 12.6 for a D-polymer device. At 10 K, we found that jMCmin j decreases by a factor of 2 as the bias increases from 3.4 to 4.4 V, whereas Bm does not change much. At V ¼ 3.4 V, we found that jMCmin j increases as the temperature increases from 10 to 300 K, whereas Bm is not affected by the temperature. Importantly, the dependence of MCmin on V and T is found to follow the same dependencies as the saturation value, MCmax; so that the ratio, MCmin/MCmax is independent for V and T (Fig. 12.6, insets). This indicates that the USMFE component is correlated with the normal MC response, and thus is also determined by the HFI. We thus conclude that any viable model describing the normal MC(B) response needs to explain the USMFE response component as well.

12.2.2 MFE models; HFI, zeeman, and exchange interactions

|MC|min /MC max (%)

In the absence of an external magnetic field, the triplet-singlet zero-field splitting is caused by both the exchange interaction between the unpaired spins of each polaron belonging to the PP excitation, and the HFI between each polaron spin and the

8

0

(A) 8 4 0

2.0 1.0 0.0

3.5

4.0 Bias (V)

4.5

3.4 V 3.8 V 4.4 V

10 K |MC|min /MC max (%)

MC/MCmax (%)

4

3.0

3.0 2.0 1.0 0.0

0

100

200 T (K)

300

10 K 100 K 200 K 300 K

3.4 V

(B)

–0.4

–0.2

0.0 B (mT)

0.2

0.4

Fig. 12.6 Normalized MC(B) response of a bipolar diode based on the D-polymer for jB j <0.5 mT at (A) various bias voltages at T ¼ 10 K, and (B) various temperatures at V ¼ 3.4 V; MCmax is defined in the text above. The insets in (A) and (B) summarize MCmin/MCmax at various voltages at 10 K and various temperatures at 3.4 V, respectively. From Nguyen, T.D., Gautam, B.R., Ehrenfreund, E., Vardeny, Z.V., 2010a. Magnetoconductance response in unipolar and bipolar organic diodes at ultrasmall fields. Phys. Rev. Lett., 105, 166804, with permission.

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adjacent nuclei. For PP excitation in π-CP chains, where the polarons are separated by a distance R > about 1–2 nm, the HFI with protons is expected to be dominant. In deuterated CPs, the strongly coupled protons, 1H (nuclear spin I ¼ ½), are replaced by deuterium, 2H (I ¼ 1), having a considerably smaller HFI constant, aHF(D); thus, the role of the HFI in MC and MEL responses may be readily tested. The PP model for MEL and MC response that we developed is based on the RP models introduced previously to describe the effect of magnetic fields on chemical and biochemical reactions (Timmel, 1998). We take into account the HFI, Zeeman, and exchange interactions. We assume that the PP excitations are immobile, and hence PP diffusion is ignored, but we take into account the overall rate of PP decay (e.g., through exciton recombination and/or dissociation into free polarons that contribute to the device current). The steady-state singlet-dissociated fraction of the PP population (known as the singlet yield, ΦS) is then calculated from the coherent time evolution of PP wave functions subject to the previously discussed interactions multiplied by the singlet decay rate kS. The calculated MC (MEL) response is then expressed as the sum of the singlet (ΦS) and triplet (ΦT) PP yields in an external magnetic field B. In the following discussion, we use the term SP rather than PP in order to include the case of the like-charge spin polaron pair. In the traditional view of organic MEL and MC (dubbed MFE) in OLED, as B increases, the intermixing between the SP singlet/triplet spin configurations decreases due to the increased Zeeman contribution, thereby affecting their respective populations; this leads to a monotonous MFEM(B) response (Bergeson et al., 2008; Wang et al., 2008). However, if the exchange interaction constant, J, is finite, then a new MFELC(B) component emerges at B  BLC ¼ J, where a singlet-triplet LC occurs giving rise to excess spin intermixing between the singlet and triplet SP manifolds. The MFELC(B) component, therefore, has an opposite sign with respect to the regular MFEM(B) response, which results in a strong MFE(B) modulation response at B ¼ BLC (Hayashi, 2004). We show in the following that by explicitly taking into account the HFI between each of the SP constituents and N (1) strongly coupled neighboring nuclei, we can explain the USMFE component response as being due to a LC response at B ¼ 0. Our model is based on the time evolution of the SP spin sublevels in a magnetic field. For bipolar devices, the SP species is the polaron-pair, whereas for unipolar devices the SP species is a π-dimer [i.e., biradical, or bipolaron (Bobbert et al., 2007; Wang et al., 2008)]. The spin Hamiltonian, H, includes exchange interaction (EX), HFI, and Zeeman terms: H ¼ HZ + HHF + Hex, where i P2 PNi h e Si  Aij  Ij is the HFI term, Ae is the hyperfine tensor describing HHF ¼ i¼1

j¼1

the HFI between polaron (i) with spin Si (¼ ½) and Ni neighboring nuclei, each with spin Ij, having isotropic aHF constant; HZ ¼ g1μBBS1z + g2μBBS2z is the electronic Zeeman interaction component; gi is the g-factor of each of the polarons in the SP species (we chose here g1 ¼ g2); μB is the Bohr magneton; Hex ¼ JS1  S2 is the isotropic exchange interaction; and B is along the z-axis. An example of the SP spin sublevels using the Hamiltonian H for N1 ¼ N2 ¼ 1, and I ¼ ½ (namely, overall 16 wave functions) is shown in Fig. 12.7A. Note the multiple LCs that occur at B ¼ 0. Other LCs

E/a

Spintronics and magnetic field effects in organic semiconductors and devices

4

4

2

2

0

0

–2

–2 two-proton PP

–4

0

(A)

1

395

two-deuteron PP

2

gmBB/a

1

2

3

(B)

Fig. 12.7 (A) Energy levels (E) of the 16 spin sublevels of a polaron-pair where each of the two polarons couples to a single proton in the H-polymer (nuclear spin, I ¼ ½), based on the spin Hamiltonian that includes HF (A), exchange (Jex) and Zeeman interactions, as a function of the applied magnetic field, B for the case Jex ≪a. Both E and B are given in units of A. (B) Same as in (A), but for the 36 spin sublevels of a polaron-pair coupled to two 2H nuclei in the D-polymer (I ¼ 1). From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

appear at larger B, but those are between mostly triplet sublevels that hardly change the S-T intermixing rate and related (SP)S and (SP)T populations. The same SP spin sublevels using D for N1 ¼ N2 ¼ 1 and I ¼ 1 is shown in Fig. 12.7B. The steady-state (SP)S and (SP)T populations are determined by the spin-dependent generation rate and “effective recombination rate” that includes dissociation (which contributes to the device current density) and recombination (which contributes to the device EL intensity) rates. The SP spin sublevel populations are also influenced by the S-T intersystem coupling (ISC). Any change of the S-T intermixing rate, such as that produced by B, may perturb the overall relative steady-state spin sublevel populations; and via the SP dissociation mechanism, it may consequently contribute to the MFE(B) response. To obtain sizable MFE, the SP recombination rate needs to be smaller than the S-T intermixing rate by the HFI. The USMFE response in this model results from the competition between the coherent S-T interconversion of nearly degenerate levels at small B (B ≪ aHF) and the SP spin coherence decay rate, k (Timmel, 1998), as explained next. The relevant time evolution of the S-T intermixing that determines the steady-state SPS population is obtained in our model via the time-dependent density matrix, ρ(t). Solving the spin Hamiltonian, H, for the energies En and wave functions Ψ n, we express the time evolution of the singlet population ρS(t) as (Hayashi, 2004; Timmel, 1998)

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  4 XM  S 2 P  cos ωmn t ρS ðtÞ ¼ Tr ρðtÞPS ¼ m,n¼1 mn M

(12.3)

where PSmn are the matrix elements of the (SP)S projection operator, ωmn ¼ (En  Em)/ ℏ, and M is the number of spin configurations included in the SP species (for I¼ ½, M ¼ 2N+2). In the absence of a spin decay mechanism, Eq. (12.3) yields for the (SP)S steady-state population (apart from the rapidly oscillating terms): < ρS(t ¼ ∞) > ¼ 4Σm jPSmm j2/M + 4Σm6¼n jPSmn j2/M, where the summations are restricted to degenerate levels, for which ωmn(B) ¼ 0. Here, the first term contributes to the MFEM(B) response, whereas the second term contributes to the MFELC(B) response that modulates < ρS(t ¼ ∞) > primarily at B ¼ 0, where the S-T degeneracy is relatively high (see Fig. 12.7). The combination of the monotonous MFEM(B) and MFELC(B) components at B  0 explains, in principle, the USMFE response in organic devices. When allowing for SP spin decay, ρS(t) in Eq. (12.3) should then be revised to reflect the disappearance of SP with time. Furthermore, for MFE to occur, the decay rates of singlet and triplet configurations must be different from each other. Thus, in a decaying system, the population of each of the M levels would decay at a different rate, γ n (n ¼ 1,…,M). Under these conditions, Eq. (12.3) for the singlet fraction is given by (Timmel, 1998)   4 XM  S 2 P  cos ðωmn tÞeγ nm t ρS ðtÞ ¼ Tr ρðtÞPS ¼ m,n¼1 mn M

(12.4)

where γ nm ¼ γ n + γ m. Eq. (12.4) expresses the fact the singlet (or triplet) time evolution contains both a coherent character [through the cos(ωmnt) factor] and an exponential decay factor. Then the measured MFE (i.e., MC and MEL) may be calculated using Eq. (12.4). For instance, if the dissociation yields are kSD and kTD for the singlet and triplet configurations, respectively, then the time-dependent dissociated fraction of either the singlet or triplet is kαDρα(t) (α ¼ S,T), and thus the dissociation yield is (Ehrenfreund and Vardeny, 2012) Z

∞

ΦαD ¼ 0

kαD ρα ðtÞdt ¼

4X α kαD γ nm Pn,m σ m,n ð0Þ 2 M n, m γ nm + ω2nm

(12.5)

The total dissociation yield is ΦD ¼ ΦSD + ΦTD, and the MC(B) response is then given by MCðBÞ ¼

ΦD ðBÞ  ΦD ð0Þ ΦD ð0Þ

(12.6)

For a slow decay, such that k ≪ aHF/ℏ, the abrupt MFELC(B) obtained at B ¼ 0 in the absence of the spin decay is spread over a field range of the order of ℏk/gμB, after which ΦS(B) increases again due to the more dominant MFEM(B) component at large B. For the MEL response, the final expression depends on the radiative recombination path of the SE and the detailed relaxation route from PP to the SE. For instance, in

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polymers where the SE-TE gap is relatively large (say, > 10% of the SE energy), a substantial SE-TE intersystem is crossing through the SOC. As a result, PPT (PPS) may transform not only to TE (SE), but also to SE (TE). Let us denote the effective SE (TE) generation rates from the PPα (α ¼ S,T) configuration as kα,SE (kα,TE). Then, similar to MC, we can define the SE generation yield, ΦSE ¼ ΦS, SE + ΦT, SE, where Φα, SE is given by Eq. (12.5), in which kαD is replaced by kα,SE . Because the EL is proportional to the SE density, the MEL response is still given by Eq. (12.6), in which ΦD is replaced by ΦSE. Fig. 12.8 shows the singlet yield and resulting MEL(B) response of the H-polymer OLED. Importantly, the calculated MEL response captures the experimental USMEL response, comprising a negative component with a minimum at Bmin  0.5 mT, that changes sign to positive MEL with an approximate B2/(B20 + B2) shape with B0  4.5 mT. The high field shape, namely B2/(B20 + B2), is the generic feature in this model. For small values of the exchange interaction, B0 is determined mainly by the HFI constant aHF; also, the USMEL response is a strong function of the decay constant k, as shown in Fig. 12.11. The negative component with Bmin appears only for relatively long decay times (e.g., ℏk/aHF 0.1). For Jex/aHF > 1, the characteristic SMEL response is no longer distinguishable. We note that in Fig. 12.8, the MEL HWHM (¼ 4.5 mT) is not exactly equal to aHF/ gμB, presumably because of the contribution of the USMEL component at low B. We also note that high field resolution is needed for observing the USMEL component,

FS

0.7 0.6 0.5

MEL (%)

(A)

–16

–8

0

8

16

–16

–8

0 B (mT)

8

16

0.8 0.4 0.0

(B)

Fig. 12.8 Calculated magnetic field response of the singlet yield (A) and magneto-conductance (B) for a two-proton PP, where g1 ¼ g2 ¼ g 2, a1 ¼ a2 ¼ a, with a/gμB ¼ 3.5 mT, J ¼ 0, δTS ¼ 0.96, and ℏk/a ¼ 2 103. The resulting MEL response HWHM is about 4.5 mT, and Bmin is about 0.5 mT. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

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and this might be the main reason why this component has not been observed thus far in organic magneto-transport. The calculated MEL response for various decay rate constant, k is shown in Fig. 12.9, in which Bmin is strongly dependent on k. Moreover, the model calculation obtained using ℏk/aHF  0.002 also nicely reproduces the USMEL effect (Fig. 12.10), where the calculated Bmin occurs at about 0.7 and 0.3 mT in the H- and D-polymer, respectively; in excellent agreement with the experiment (Fig. 12.4A). Fig. 12.11 shows the calculated MC(B) response, together with its energy sublevels for an axially symmetric anisotropic HFI with N1 ¼ N2 ¼ 1 (I ¼ ½; M ¼ 16), where aHF(electron)/gμB ¼ 3aHF(hole)/gμB ¼ 3 mT, these parameters extracted from the unipolar MEH-PPV MC(B) response, J ¼ 0, δTS ¼ 0.96, and an exponential SP decay ħk/ aHF ¼ 0.001. The calculated MC(B) response captures the experimental USMC response comprising a negative component having its minimum at Bm  aHF/6gμB ¼ 0.5 mT, with an approximate positive B2/(B20 + B2) shape at large B, and B0  4.5 mT. The excellent agreement between theory and experiment, including both Bm, and the USMC intricate response and relative amplitude, validates the model used.

12.2.3 Conclusions In the research investigations described in this section, we elucidated the role of HFIs in the MFE response of conductivity and EL in various OLEDs based on DOO-PPV isotopes that have different hyperfine coupling constants. We showed that both MEL

0.2 k/a = 0.2 0.4

0.1

0.0

0.3

0.04 0.02

–0.2

0.2 0.1

0.002

k/a

0.0 0.00

0.0002

0.0

gmBBmin/a

MEL (%)

0.4

0.5

0.05

1.0

0.10

1.5

gmBB/a

Fig. 12.9 Calculated MEL response for the two-polaron, two-proton model, for various decay rate constants k (given here in units of a). The inset shows the calculated dependence of Bmin on k; it approximately follows the functional dependence, Bmin/a  (ℏk/a)0.28. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

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2

Model

0 MEL (%)

(A) –30

–20

–10

0

10

20

30

1

2

3

2 Protons Deutrons

0

(B) –3

–2

–1

0 B (mT)

Fig. 12.10 Simulations of the MEL response in the two polymers, which reproduces the response data in Figs. 12.3 and 12.4 based on the described model (Timmel, 1998) using the calculated spin sublevels given in Fig. 12.7. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

and MC are strongly dependent on the HFI constant of the materials; the stronger the HFI constant, the broader is the MFE response. Our findings may be useful for material scientists for designing the novel materials for MFE applications. Furthermore, we analyzed the novel USMFE response at B << aHF/gμB found in many bipolar and unipolar organic devices, which demonstrates that MEL(B) and MC(B) responses are much richer than previously anticipated. The USMFE component scales with the normal MC(B) response and thus is also due to the HFI of the SP pair with B. Our simple model to simulate the MFE explicitly includes in the SP Hamiltonian the most strongly interacting nuclear spins, and it is capable of reproducing the entire MFE(B) response, including the USMFE component. Our findings show that via the USMFE component, relatively small B is capable of substantially altering both the electrical and optoelectronic responses in organic diodes, as well as chemical and biological reactions discussed elsewhere (Hayashi, 2004). Therefore, it should be seriously considered. In fact, a chemical USMFE has been proposed to be at the heart of the “avian magnetic compass” in migratory birds (Maeda et al., 2008). In this respect, our work shows that the USMFE component appears in the MFE response of many more organic compounds that have been considered before.

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E/gmB (mT)

6 0 –6 –6

MC (%)

(A)

–3

0

3

6

–3

0 B (mT)

3

6

0.5 a 1 = 3 mT a 2 = 1 mT

0.0 –6

(B)

Fig. 12.11 (A) Example of calculated spin energy levels versus B using the Hamiltonian H in the text for a spin pair with isotropic HFI; a1 ¼ 3a2 ¼ 3 mT, and J ¼ 0. Note the multiple LC at B ¼ 0. (B) Calculated MC(B) response for an SP with axially symmetric HFI averaged over all magnetic field directions. The isotropic HFI is the same as in (A), whereas the anisotropic HFI component is azz ¼ 0.15ai for the respective spin-half species. From Nguyen, T.D., Gautam, B.R., Ehrenfreund, E., Vardeny, Z.V., 2010a. Magnetoconductance response in unipolar and bipolar organic diodes at ultrasmall fields. Phys. Rev. Lett., 105, 166804, with permission.

12.3

Organic spin valves (OSVs)

The electronic spin sense was basically ignored in charge-based electronics until a few decades ago. The technology of spintronics, where the electron spin is used as the information carrier in addition to the charge, offers opportunities for a new generation of electronic devices combining standard microelectronics with spin-dependent effects from the interaction between the carrier spin and externally applied magnetic fields. Adding the spin degree of freedom to conventional semiconductor chargebased electronics substantially increases the functionality and performance of electronic products. The advantages of these new devices are increased data-processing speed, decreased electric-power consumption, and increased integration densities compared to conventional semiconductor electronic devices, that are nearly at their physical limits nowadays. The discovery of the GMR effect in 1988 is considered as the beginning of the new generation of spin-based electronics (Baibich et al., 1988); this discovery led to the Nobel Prize in Physics in 2008. Since then, the role of the electron spin in solid-state devices and possible technology that specifically exploits spin rather than charge properties has been studied extensively (Prinz, 1998). A good example of the rapid transition from discovery to commercialization for spintronics is the application of GMR and tunneling magneto-resistance (TMR) (Miyazaki and Tezuka, 1995; Moodera et al., 1995) in magnetic information storage.

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Since the first laboratory demonstration of GMR in 1988, the first GMR device as a magnetic field sensor was commercialized in 1994; and the release of “read-heads” for magnetic hard disk drives was announced in 1997 by IBM. Major challenges in the field of spintronics are the optimization of electron spin lifetimes, the detection of spin coherence in nanoscale structures, the transport of spin-polarized carriers across relevant length scales and heterointerfaces, and the manipulation of both electron and nuclear spins on sufficiently fast time scales (Zutic et al., 2004). The success of these ventures depends on a deeper understanding of fundamental spin interactions in solid-state materials, as well as the roles of dimensionality, defects, and semiconductor band structure in modifying the spin properties. With proper understanding and control of the spin degrees of freedom in semiconductors and heterostructures, the potential for realization of high-performance spintronic devices are excellent. The research in this field so far has led to the understanding that the future of spintronics relies mainly on successful spin injection into multilayer devices and optimization of spin lifetimes in these structures. Hence, for obtaining multifunctional spintronic devices operating at room temperature, the materials suitable for efficient spin injection and spin transport have to be studied thoroughly. In recent years, spintronics has benefited from the class of emerging materials, mainly semiconductors. The III-V and II-VI systems, as well as magnetic atom-doped III-V and II-VI systems (dilute magnetic semiconductors), have been studied extensively as either promising spin-transport materials or spin-injecting electrodes (Zutic et al., 2004; Tang and Al, 2002). Little attention has been paid so far to the use of OSCs such as small molecules or π-conjugated polymers (PCPs) as spin-transporting materials. The conducting properties of PCPs was discovered in the late 1970s, and later the semiconducting properties of OSCs and PCPs have given birth to a completely new field of electronics—namely, “Organic, or Plastic Electronics.” OSCs and PCPs are mainly composed of light atoms such as carbon and hydrogen, which leads to a large spin correlation length due to weak spin-orbit coupling. This makes the small molecules and PCPs more promising materials for spin transport than their inorganic counterparts (Ruden and Smith, 2004; Rocha et al., 2005). The ability to manipulate the electron spin in organic molecules offers an alternative route to spintronics. Key requirements for success in engineering spintronics devices using spin injection via FM electrodes in a two-terminal device such as a diode (or junction) include the following processes (Zutic et al., 2004; Yunus et al., 2008): (1) efficient injection of spin-polarized charge carriers through one device terminal (i.e., FM electrode) into the semiconductor interlayer; (2) efficient transport and sufficiently long spin relaxation time within the semiconductor spacer; (3) effective control and manipulation of the spin-polarized carriers in the structure; and (4) effective detection of the spinpolarized carriers at a second device terminal (i.e., another FM electrode). Usually, FM metals have been used as injectors of spin-polarized charge carriers into semiconductors, and they can serve to detect a spin-polarized current. However, more recently, magnetic semiconductors have been sought to serve as spin-injectors because of the conductivity mismatch between the metallic FM and the semiconductor interlayer (as discussed next). The conductivity mismatch was thought to be less severe using OSC as the medium in which spin-aligned carriers are injected from the FM electrodes

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because carriers are injected into the OSC, mainly by tunneling, and the tunnel barrier may depend upon the magnetic field, which defuses the conductivity mismatch (Yunus et al., 2008). Spin-relaxation lifetimes in conventional, inorganic semiconductors are primarily limited by the spin-orbit interaction (Wolf et al., 2001; Zutic et al., 2004). However, OSCs are composed of light elements such as carbon and hydrogen, which have weak spin-orbit interactions for the relevant electronic states that participate in the electrical conductance process. Consequently, they are thought to possess long spin-relaxation times (Dediu et al., 2002; Sanvito and Rocha, 2006). Therefore, OSCs appear to offer significant potential applications for spintronic devices (Naber et al., 2007; Sanvito and Rocha, 2006). Fig. 12.12A schematically shows the canonical example of a spintronic device, the spin valve (Xiong et al., 2004; Jonker, 2003). Two FM electrodes [in this example, La2/3Sr1/3MnO3 (LSMO) and Co, respectively (Xiong et al., 2004)], used as a spin injector and a spin detector, respectively, are separated by a nonmagnetic spacer (which in OSVs is an OSC layer). By engineering the two FM electrodes so that they have different coercive fields (Hc), their relative magnetization directions may switch from parallel to antiparallel alignment (and vice versa) upon sweeping the external magnetic field, H. The FM electrode capability for injecting spin-polarized carriers depends on its interfacial spin-polarization value, P, which is defined in terms of the density, n, of carriers close to the FM metal Fermi level with spin up, n " and spin down, n# ; and is given by the relation: P ¼ [n" n#]/[n " + n #]. The spacer decouples the FM electrodes, while allowing spin transport from one contact to the other. The device’s electrical resistance depends on the relative orientation of the magnetization in the two FM-injecting electrodes; this has been dubbed magnetoresistance (MR). The electrical resistance is usually higher for the AP magnetization orientation, an effect referred to as GMR (Wolf et al., 2001), which is due to spin injection and transport through the spacer interlayer. The spacer usually consists of a nonmagnetic metal, semiconductor, or a thin insulating layer (in the case of a magnetic tunnel junction). The MR effect in the latter case is referred to as TMR, and it does not necessarily show spin injection into the spacer interlayer as in the case of GMR

OSEC LSMO SrTiO

Current (µA)

Al

1.2

0.5

6K 100 K 200 K 240 K

Current (µA)

1.6 Co

0.8 0.4

(A)

0.4 0.3

10 K 80 K 140 K 180 K

0.2 0.1

H-polymer

D-polymer 0.0 0.0

(B)

0.1 0.2 Voltage (V)

0.3

0.0 0.0

(C)

0.1

0.2 0.3 Votlage (V)

0.4

Fig. 12.12 Typical OSV structure (A) and I–V characteristic response of (B) D-polymer, and (C) H-polymer OSV devices at various temperatures. From Pramanik, S. 2007. Observation of extremely long spin relaxation times in an organic nanowire spin valve. Nat. Nanotech. 2, 216–219, with permission.

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response, but rather the spin-polarized carriers are injected through the nonmagnetic overlayer. Semiconductor spintronics is very promising because it allows electrical control of spin dynamics; and due to the relatively long spin relaxation time, multiple operations on the spins can be performed when they are out of equilibrium (i.e., transport via spinpolarized carriers occurs; Awschalom and Flatte, 2007). This type of spin valve [e.g., based on GaAs as a spacer (Lou et al., 2007)] may have other interesting optical properties, such as circular polarized emissions that may be controlled by an external magnetic field (Sanvito, 2007). Significant spin injection from FM metals into nonmagnetic semiconductors is challenging, though, because in thermal equilibrium conditions, the carrier density with spin-up and spin-down are equal, and no spin polarization exists in the semiconductor layer. Therefore, to achieve spin-polarized carriers, the semiconductor needs to be driven far out of equilibrium and into a situation characterized by different quasi-Fermi levels for spin-up and spin-down charge carriers. Early calculations of spin injection from a FM metal into a semiconductor showed that the large difference in conductivity of the two materials inhibits the creation of such nonequilibrium situations, which makes efficient spin injection from metallic FM into semiconductors difficult (Sanvito, 2007; Smith and Silver, 2001; Albrecht and Smith, 2002); this has been known in the literature as the “conductivity mismatch” hurdle. However, a tunnel barrier contact between the FM metal and the semiconductor may effectively achieve significant spin injection (Wang et al., 2005). The tunnel barrier contact can be formed by adding a thin insulating layer between the FM metal and the semiconductor (Dediu et al., 2008). Tunneling through a potential barrier from a FM contact is spin selective because the barrier transmission probability, which dominates the carrier injection process into the semiconductor spacer, depends on the wave functions of the tunneling electron in the contact regions (Yunus et al., 2008). In FM materials, the wave functions are different for spin-up and spin-down electrons at the Fermi surface, which are referred to as majority and minority carriers, respectively; and this contributes to their spin injection capability through a tunneling barrier layer. OSCs are composed of light element building blocks, such as carbon and hydrogen atoms, that have a weak spin-orbit interaction; consequently, they are supposed to possess long spin relaxation times, making them ideal materials for spin transport (Ruden and Smith, 2004; Pramanik, 2007; McCamey, 2008). Indeed, GMR has been measured in OSV devices based on small organic molecule and polymer spacers, both as thick films and thin tunnel junctions (Xiong et al., 2004; Pramanik, 2007; Majumdar, 2006; Wang et al., 2005; Hueso, 2007; Tombros, 2007; Dediu et al., 2008; Vinzelberg, 2008; Drew, 2009; Santos, 2007). The role of HFI has been theoretically studied on organic magneto-transport (Bobbert et al., 2009). It is noteworthy that if the HFI determines the spin lattice relaxation time, TSL of the injected carriers, and consequently also their spin diffusion length in OSVs, then the device performance may be enhanced simply by manipulating the nuclear spins of the organic spacer atoms. Moreover the HFI also plays an important role in other organic magneto-electronic devices such as two-terminal devices (see Section 12.2), and other spin response processes such as ODMR in OSC films (see Section 12.4).

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In this section, we summarize our studies of the HFI role in polymer OSV devices and films by replacing various atoms in the organic interlayer composed of a π-CP poly(dioctyloxy) phenyl vinylene (DOO-PPV) by different isotopes. First, we replaced all strongly coupled hydrogen atoms (1H, nuclear spin I ¼ ½; dubbed here H-polymers), with deuterium atoms (2H, I ¼ 1) [hereafter called D-polymers; see Fig. 12.1] with much smaller HFI constants, aHF [namely, aHF(D) ¼ aHF(H)/6.5 (Carrington and McLachlan, 1967)]. We also replaced some of the 12C atoms (I ¼ 0) in the polymer chains by 13C (I ¼ ½; hereafter called C13-rich polymers; see Fig 12.2). We studied the influence of the isotope exchange on the GMR in OSVs, where the spin transport in the device determines its performance (Xiong et al., 2004). We also report GMR in OSV devices fabricated with C60 spacer that has very small HFI and thus show exceptional MR response properties.

12.3.1 Experimental methods The OSVs were fabricated using the DOOPPV polymers and C60 molecules as spacers between two FM electrodes (Xiong et al., 2004); these were LSMO (bottom electrode, FM1), and cobalt (Co; top electrode, FM2). The LSMO films with thickness of about 200 nm and area of 5 5 mm2, were grown epitaxially on <100 > oriented SrTiO3 substrates at 735°C using a dc magnetron sputtering technique, with Ar and O2 flux in the ratio of 1:1. The films were subsequently annealed at 800°C for about 10 h before slow cooling to room temperature. The LSMO films were subsequently patterned using standard photolithography and chemical etching techniques. Contrary to cobalt, the LSMO films are already stable against oxidation; consequently, the LSMO films can be cleaned and reused multiple times as substrates without serious degradation. Following the LSMO substrate cleaning using chloroform, we deposited the DOOPPV polymer layer by spin casting from a 6 mg/mL 1,2-dichlorobenzene solution. Subsequently, the hybrid organic/inorganic junction was introduced into an evaporation chamber with a base pressure of 5 107 torr, where we deposited a thin (10–15 nm) Co film capped by an aluminium (Al) film using a shadow mask. The obtained active device area was typically about 0.2 0.4 mm2. We fabricated several OSV devices having various DOOPPV layer thickness, with df controlled by the spin angular speed, and calibrated against measurements using thickness profilometry methods (KLA Tencor). Films with df > 80 nm appeared segregated and were subsequently discarded, whereas films having 20 < df < 80 nm were smooth. D- and H-polymer-based OSV with various values of df were measured and compared at several bias voltage, V, and temperature, T. For the df dependence of the MR, we used the same LSMO substrate and device structure in which df was physically reduced using a doctor blade and subsequently measured using the profilometer. The I–V characteristics of the OSV devices were nonlinear with weak temperature dependence (see Fig. 12.12). Typical device resistance was in the range of 100–500 kΩ and depended on df. Most devices showed a “metallic” behavior, where R increases with T; however, some devices showed mixed behavior (Fig 12.12). The OSV MR was measured in a closed-cycle refrigerator with T in the range from 10–300 K, using the “four-probe” method, while varying an external in-plane

Spintronics and magnetic field effects in organic semiconductors and devices

1.0

1.0

10 K 0.5

0.5 M/Ms

M/Ms

405

0.0 –0.5

0.0 80 K

–0.5

240 K

–1.0

–300 –200 –100

(A)

–1.0

Co on D-polymer Co on H-polymer

0 100 B (G)

200

300

LSMO Film

–9

(B)

–6

–3

0 3 B (mT)

6

9

Fig. 12.13 Magneto-optic Kerr effect of (A) Co on H- and D-polymer and (B) LSMO. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

magnetic field. The magnetization properties of the FM electrodes were measured by the magneto-optic Kerr effect (MOKE; Fig. 12.13); from these measurements, we determined typical low-temperature coercive fields for the electrodes alone as Bc1  4 mT and Bc2  10 mT, for the LSMO and Co films, respectively.

12.3.2 Results and discussion 12.3.2.1 Giant magneto-resistance (GMR) in organic spin valves (OSVs); isotope dependence For the spin injection and transport investigations comparing the three polymer isotopes, we used OSV devices where the polymer film was sandwiched between two FM electrodes having different coercive fields, Bc. In our design, these were LSMO and Co thin films, with low temperature Bc1  4 mT and Bc2  15 mT, respectively (Xiong et al., 2004; Nguyen et al., 2010b), which depend on the LSMO and Co film thicknesses; and nominal spin injection polarization degree P1  95% and P2, which depend on the environment (Santos, 2007; Dediu et al., 2008; Vinzelberg, 2008; Barraud et al., 2010). Because Bc1 6¼ Bc2, then it is possible to switch the relative magnetization directions of the FM electrodes between parallel (P) and antiparallel (AP) alignments, upon sweeping the external magnetic field, B (Fig. 12.14), where the device resistance, R is dependent on the relative magnetization orientations. When R(AP) > R(P), the maximum MR value, [ΔR/R]max (or MRSV), is given by the ratio [R(AP)-R(P)]/R(P). According to a modified Jullie`re formula ( Jullie`re, 1975), MRSV is related to the polarization degree of the FM electrodes P1 and P2 by (Xiong et al., 2004) ½ΔR=Rmax ¼ 2P1 P2 D=ð1  P1 P2 DÞ

(12.7)

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MR (%)

25 20 15 D-DOO-PPV 10 5 0 (A) 3 –60 –40

–20

0

20

40

60

–20

0

20

40

60

2 1 0 3

H-DOO-PPV

(B) –60

–40

2 13

C-DOO-PPV

1 0

(C)

–40

–20

0 B (mT)

20

40

Fig. 12.14 Magnetoresistance loop of an OSV device with the configuration of LSMO (200 nm)/DOO-PPV (about 30 nm)/Co (15 nm) spin-valve devices measured at T ¼ 10 K and V ¼ 20 mV, based on (A) D-polymers, (B) H-polymers, and (C) C13-rich polymers. The circle (square) curve denotes MR measurements made upon increasing (decreasing) B. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

In Eq. (12.7), D ¼ exp[(df)/λs], where λs is the carrier spin diffusion length in the organic interlayer (Xiong et al., 2004). We measured the MR hysteresis loop to obtain the MRSV value in OSVs based on the three polymer isotopes at various bias voltage, V, and temperature, T, using the same LSMO substrate but different devices. In most cases, we fitted the MR response using the equation (Bobbert et al., 2009):   MRðBÞ ¼ ½MRmax ½1  m1 ðBÞm2 ðBÞexp df =ls ðBÞ

(12.8)

where MRmax is the MR when neglecting spin relaxation, and ls(B) is a fielddependent spin diffusion length parameter given by the relation ls(B) ¼ ls(0)[1 + (B/B0)2]3/8, where B0 is a characteristic field related to aHF/gμB. The functions m1,2(B) in Eq. (12.8) stand for the normalized magnetizations of the FM electrodes, which are used here as free parameters; for simplicity, we used for m(B) the “error function” centered at the respective “turn-on” and “turn-off” fields (Bobbert et al., 2009). Fig. 12.14 shows representative MR hysteresis loops for three similar OSVs (df  25 nm) based on D-, H- and C13-rich polymers measured at T ¼ 10 K and V ¼ 10 mV. The following points are worth emphasizing:

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(i) When using freshly prepared LSMO substrates, we obtained positive MR, where R(AP) > R(P), in agreement with results on another polymer OSV (Majumdar, 2006). Because P1 > 0, the positive MR may be readily explained using Eq. (12.7) only if P2 > 0 for the Co electrode, in agreement with recent measurements using organic magnetic tunnel junctions (Santos, 2007). (ii) Importantly, all devices based on the D-polymer have much larger MRSV values than those based on the H- and C13-polymers. This holds true for similar devices at all V, T, and df. The improved magnetic properties of OSVs based on the D-polymer may be explained using Eq. (12.7) by a larger λs. Indeed, the major difference between the injected spin-half carriers in D-polymer and the other two polymer isotopes (namely, H- and C13-rich polymers) is their spin relaxation time TSL, which was shown to be much longer in the D-polymer (Nguyen et al., 2010b; Nguyen et al., 2011b). To examine this assumption, we studied the MR response of OSVs from D- and H-polymers at various values of df, but otherwise the same LSMO substrate, which were measured at the same temperature and applied voltage (Fig. 12.15; Nguyen et al., 2010b). From the obtained exponential MRmax(df) dependence, we got λs(D) ¼ 49 nm, whereas λs(H) ¼ 16 nm; this was in agreement with the increase in TSL of the D-polymer measured using ODMR. The larger obtained λs(D) is also reflected in the fitting parameters to the MR(B) response when using Eq. (12.7); we indeed found (Nguyen et al., 2010b) that ls(0) is about 3 times larger in the D-polymer than in the H-polymer, whereas B0, which is related to aHF (Nguyen et al., 2010b), is about 2.5 times smaller. Based on our results, we therefore conclude that the improved spin transport in the organic layer is the main advantage of the D-polymers that allows them to form more efficient OSVs. (iii) The MR(V) dependence of the three polymer OSVs (Fig. 12.16) shows a power law dependence MRSV(V)∝ V p, where the exponent p < 1. It was suggested (Zhang and White, 1998) that there are two tunneling processes from the FM electrode; a direct tunneling that conserves spin and a two-step tunneling (involving hopping) that does not. Because the

MR (%)

10

D lD = 49 nm

1

lH = 16 nm

0

H

20

40 d (nm)

Fig. 12.15 The maximum MR values (MRSV) of D- and H-polymer OSVs having various interlayer thicknesses, df measured at T ¼ 10 K and V ¼ 80 mV. The lines are fit to the data points, where MRSV(df) ¼ 6.7% exp( df/λs), with spin diffusion lengths λs(D) ¼ 49 nm and λs(H) ¼ 16 nm, respectively. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

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100

|V |–0.65 |V |–0.44 D

10 13 C

–0.37

|V |

V >0

1

V <0 1

10 |V | (mV)

H 100

Fig. 12.16 The maximum MR value (MRSV) of three isotope OSV devices having df ¼ 35  5 nm, as a function of the applied bias voltage, V, measured at T ¼ 10 K. Note that data are plotted on a log-log scale showing a power law behavior, Vp with the isotope-dependent exponent p. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2011b. The hyperfine interaction role in the spin response of π-conjugated polymer films and spin valve devices. Synth. Met. 161, 598–603, with permission. latter process has a less steep voltage dependence, it dominates at large bias voltage. This may explain the MR(V) decrease at large V because the device MR is mainly determined by the two-step, nonspin conserving tunneling process. Inelastic tunneling via “magnetic impurities” accompanied by phonon emissions gives rise to a power law dependence (Sheng et al., 2006), MRSV(V)∝ V p. The exponent p was predicted to be isotopedependent (Sheng et al., 2004)—namely, p  M3/2, where M is the effective isotope mass that determines the phonon spectrum that participate in the hopping process. In Fig. 12.16, we plot MRSV(V) for the three isotopes in double logarithmic scale; it is indeed seen that MRSV(V) obeys a power law decay with V, having p < 1 that is isotope-dependent. We obtained a larger p for the deuterated device, as predicted by the model (Sheng et al., 2004); we found that the ratio p(D)/p(H)  1.7. This ratio is larger than the mass ratio [M(CD)/M(CH)]3/2  1.1, which is expected from the simple model. However, for the C13-rich polymer, we found p(C13)/p(C12)  1.18, which has very good agreement with the predicted ratio [M(C13H)/M(C12H)]3/2  1.12. (iv) We also note that MRSV strongly decreases at high T for all OSV devices, regardless of the MRSV value at low T (Fig. 12.17); thus, it is mainly caused by the spin injection properties of the LSMO electrode into the organic layer (Wang et al., 2007; Dediu et al., 2009), rather than by the organic interlayer. We therefore conclude that different spin injectors need be found to achieve a significant advance in organic spintronics. In this regard, the use of deuterated OSCs as the device interlayer, both as evaporated small molecules or spin-cast polymers, should substantially improve the OSV device performance.

12.3.2.2 Giant magneto-resistance (GMR) of C60-based organic spin valves (OSVs) Because the GMR response of D-polymer OSVs shows an improved response that is mainly caused by the small HFI of this polymer isotope, it is tempting to fabricate OSV devices made of a C60 film interlayer. The C60 molecule is composed of

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6 D H

MR (%)

4

13

C

2

0 0

100

200

300

T (K)

Fig. 12.17 Normalized MRSV of three isotope OSVs similar to those shown in Fig. 12.16, but as a function of temperature, T (in K), measured at V ¼ 80 mV. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2011b. The hyperfine interaction role in the spin response of π-conjugated polymer films and spin valve devices. Synth. Met. 161, 598–603, with permission.

60 carbon atoms that include two isotopes: 99% 12C with nuclear spin I ¼ 0, and 1% 13 C with I ¼ ½ (Abragam, 1961; see Fig. 12.1 for the chemical structure). From these values, we can estimate the average effective HFI per C60 molecule to be about a(13C)/ 60 < 0.1 mT. It should be beneficial, therefore, to fabricate C60-based OSV devices (Wang, 2009). Fig. 12.18 shows the GMR response of a LSMO/C60/Co/Al OSV device measured at 120 K and 60-mV bias, where the C60 interlayer was thermally evaporated with a 6

|DR/R(AP)| (%)

5 4 3 120 K 2

60 mV

1 0 –1,500 –1,000 –500 0 500 Magnetic field (Oe)

1,000 1,500

Fig. 12.18 MR(V) loop of an LSMO (200 nm)/C60 (40 nm)/Co (5 nm) spin-valve device measured at T ¼ 120 K and V ¼ 60 mV. The circle (square) curve denotes MR measurements made upon increasing (decreasing) B. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2011b. The hyperfine interaction role in the spin response of π-conjugated polymer films and spin valve devices. Synth. Met. 161, 598–603, with permission.

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measured thickness, df ¼ 40 nm. At this relatively large thickness, we do not expect tunneling MR to dominate the OSV MR response. It is seen that the MR(B) response is very sharp and maintains a large value even at these relatively high temperatures and bias voltages. The GMR is still reversed [namely, R(antiparallel) < R(parallel)], showing that one of the P’s in Eq. (12.7) is negative (Xiong et al., 2004; Barraud et al., 2010). Also, the sharp response shows that the ratio df/ls(B) when using Eq. (12.8) to fit the MR(B) response is rather small (Bobbert et al., 2009). Because df ¼ 40 nm, we may conclude that the spin diffusion length in C60 film is indeed large. It is also noteworthy that the turn-off coercive field due to the Co electrode on the C60 spacer is much larger than the Co coercive fields obtained in the polymer-based OSV devices (Fig. 12.14); this shows that the Co coercive field is extremely sensitive to the environment (Schultz et al., 2010). The large and sharp GMR response is very encouraging, as it emphasizes the important role that C60 might play in the field of organic spintronics, even at room temperature (Wang, 2009; Nguyen et al., 2013; Gautam et al., 2013). We thus conclude that the fullerenes are ideal for studying OSV devices.

12.3.3 Conclusions and future outlook In this section, we reviewed some of the latest achievements in OSV research at the University of Utah and Technion, related to the important role of the HFI in determining the spin response. By replacing the building block atoms in the polymer chains such as carbon and hydrogen, with different isotopes, it is then possible to tune the HFI, and thus study in detail its influence in the material spin response. We showed elsewhere (Nguyen et al., 2010b, 2011b) that the HFI plays a crucial role in determining the spin-half ODMR line-width and saturation properties, from which we inferred that the HFI governs the spin-half relaxation rate in semiconducting polymers. This led us to fabricate OSV devices based on polymers having different isotopes, with the anticipation that tuning the HFI also would lead to better control over the spin diffusion length in the organic interlayer (Nguyen et al., 2010b). We found that this is indeed the case for OSV based on the three DOO-PPV isotopes, where the D-polymer showed the best GMR performance and obtained longer diffusion lengths. Surprisingly, we also found that the GMR voltage dependence in OSV is isotopedependent, where lighter isotopes show steeper voltage dependence. We proposed a model to explain this phenomenon based on the tunneling properties of spinpolarized carriers at the organic/FM interface. However, our model is by no means conclusive; much more experimental and theoretical work needs to be done before a more definitive understanding of the GMR(V) response in OSV devices is achieved. The organic spintronics field is in its infancy; much more work has to be accomplished before the field will mature. At the present time, controversies regarding the exact operation of OSV still exist, especially the MR signs in these devices (Barraud et al., 2010; Schultz et al., 2010). Recently, spin-polarized carrier injection into an OSC has been directly observed using low-energy muon spin rotation (Drew, 2009), so the doubts raised at the beginning of the organic spintronics field (Xu et al., 2007; Jiang et al., 2008) can be defused. In general, spin injection achieved in OSV is of the same magnitude as in spin valves fabricated using inorganic

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semiconductor spacers. In particular, both organic and inorganic semiconductor interlayers suffer from the same conductivity mismatch problem (Schmidt, 2005), and show only little MR at room temperature. A noticeable difference, however, is the ability to change the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) levels of the organic interlayer in OSVs by depositing a thin insulator layer, such as LiF or SiOx, prior to the deposition of the FM electrode (Dediu et al., 2008; Schultz et al., 2010; Yunus et al., 2010). This may lead to a variety of magneto-transport effects that cannot be achieved with inorganic spin valves.

12.4

Optically detected magnetic resonance in DOO-PPV isotopes

Resonant absorption resulting from the application of MW radiation with a frequency matching the energy difference of the Zeeman split levels of a spin system under magnetic field is the basis for various related magnetic resonance techniques. In conventional electron spin resonance (ESR), the resonant absorption of the MW is directly detected, thus measuring properties of the ground electronic state in thermal equilibrium (Carrington and McLachlan, 1967). ODMR techniques are extensions of the more common ESR techniques (Cavenet, 1981). ODMR measures changes in optical absorption [photo-induced, absorption-detected magnetic resonance (PADMR) and/ or emission [photoluminescence-detected magnetic resonance (PLDMR)] that occur as a result of electron spin transitions. Because the ground state of CPs is almost always spin singlet, only spin-bearing electronic excited states are studied. When applied to π-conjugated semiconductor films, ODMR techniques can be used for assigning the correct spin quantum number to the optical absorption bands of longlived photoexcitations and/or for studying spin-dependent reactions that may occur between these photoexcitations (Vardeny and Wei, 1997). One major advantage of ODMR over ESR is a much higher sensitivity in the detection of resonant processes because the energy range of the detected photons in ODMR is much higher (order of 1–3 electron-volts) than the MW energies that monitor ESR (tens of micron-electronvolts). Much better detectors with higher detectivity exist for photons in the eV-range than in the μeV-range. A significant increase in the sensitivity of ODMR when compared to ESR also results from differences in the spin polarization; in ODMR experiments on π-CPs, the typically obtained spin polarizations exceed the thermal equilibrium polarization by at least one order of magnitude (Vardeny and Wei, 1997).

12.4.1 Experimental methods As an illustrative example, we show in Fig. 12.19 the basic experimental setup for PADMR in OSC thin films. The sample is mounted in an MW cavity equipped with windows for optical transmission, and between the poles of a superconducting dc magnet. The cavity is a liquid helium-cooled cryostat. As in photomodulation, the sample is illuminated by both pump and probe beams. The pump beam produces photoexcitations in the sample film. After being modulated, the moderately strong MW

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Handbook of Organic Materials for Electronic and Photonic Devices Mirror Power supply

Mirror

Monochromator Laser Magnet

Detector Magnet controller

Sample Light source

Cryostat Preamplifier

Mirror MW modulator Mirror

MW source

Function generator

Lock-in amplifier

Fig. 12.19 ODMR experimental setup.

at fMW ¼ 3 GHz is introduced into the cavity through a waveguide. Then the changes ΔT in transmission (T) of the probe associated with the MW-induced changes in the photoexcitation recombination kinetics in the dc magnetic field are detected with a lock-in amplifier using a phase-sensitive technique. For the PLDMR measurement, the photoluminescence changes induced by MW transitions from the film are detected without using the probe beam. This technique is complementary to the PADMR.

12.4.1.1 Discussion ODMR in organics is in fact an MFE that occurs under resonance conditions with MW radiation that induces spin-sublevel mixing among the polaron pair (PP) spin sublevels (Vardeny and Wei, 1997). It is thus not surprising that models similar to those used to explain the MFE without MW radiation have been advanced to explain spinhalf ODMR in the organics. In the following analysis, we assume that the ODMR response dynamics occurs exclusively when all spin levels actively participate in determining the measured MFE physical quantity (Yang et al., 2007). When the PPS decay rate (γ S) is effectively faster than the PPT decay rate (γ T), then at steady state, when MW is off, nS,off < nT,off , where nS,off (nT,off) is the PPS (PPT) density when the MW is off (Vardeny and Wei, 1997). Under resonant MW radiation (MW with the frequency fMW being on), a net transfer from PPT to PPS takes place (via the mT ¼ 0 spin sublevel in the PPT

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manifold), bringing the system to a new quasiequilibrium state in which the total PP density, nPP ¼ nS + nT , is reduced (i.e., nPP,on < nPP,off). Under square wave MW modulation at frequency f, both ΔnS(f ) ¼ nS,on  nS,off and nT(f ) ¼ nT,on  nT,off responses decrease with increasing f (e.g., in the form of Lorentzians in f, if their time decays are exponentials; see McCamey, 2008). To quantify the Δn(f ) response, we use the fact that the two triplet spin sublevels (ms ¼ 1) should have common dynamics. We also take the limit of strong singlet to ms ¼ 0 triplet mixing (Yang et al., 2007), thus reducing the coupled set of four rate equations to a coupled set of two rate equations for the PP in the triplet and singlet/ triplet states, respectively. These equations are written for the experimental conditions T ≫ hfMW/kB  0.14 K as follows (Yang et al., 2007): dnS γ ¼ GS  γ S nS  SL ðnS  nT Þ  PðnS  nT Þ dt 2 dnT γ ¼ GT  γ T nT  SL ðnT  nS Þ  PðnT  nS Þ dt 2

(12.9)

where nS denotes the coupled mS ¼ 0 sublevels of PPT and PPS and nT denotes the mS ¼ 1 in PPT, γ SL is spin-lattice relaxation rate, P is the MW spin flip rate (assumed to be proportional to the MW power, PMW), and G is the generation rate. The steady-state solution of Eq. (12.9)—i.e., dnS/dt ¼ dnT/dt ¼ 0)—show typical magnetic resonance saturation behavior: nS,T ∝

P Γ eff + P

(12.10)

with an effective rate constant Γ eff ¼

γ SL 1 + 1 1 2 γS + γT

Thus, Γ eff can be directly obtained by measuring the ODMR as a function of MW power, PMW.

12.4.2 ODMRs of DOOPPV isotopes: Role of the HFI For the ODMR investigations described here, we used an S-band resonance system at about 3 GHz and 10 K, where the MW power, PMW, was modulated at about 200 Hz (Yang et al., 2007). The PL intensity increases due to enhancement of the photogenerated PP recombination in the polymer film upon MW absorption at resonance; therefore, the ODMR signal appears at B  100 mT, which corresponds to spinhalf species with g  2. Fig. 12.20A and B show the spin-half ODMR of polaron-pairs in H- and D-polymer films, respectively. Importantly, the resonance in D-polymer is narrower than that in

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ODMR (arb. units)

1.0

1.0 Data, D Model

Data, H Model

0.5

0.5

0.0

0.0 –3.0

–1.5

(A)

0.0 1.5 B-B0 (mT)

–3.0

3.0

(B)

–1.5

0.0 1.5 B-B0 (mT)

3.0

Fig. 12.20 Isotope dependence of spin-half ODMR response in DOO-PPV polymers. (A) and (B) show the normalized spin-half ODMR response in the H- and D-polymers; the lines though the data points are based on a model fit that takes into account the HFI splitting and the polaron spin density spread on the polymer chain, as well as inhomogeneous and natural line-broadening contributions to the resonance width. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

H-polymer; at small PMW, the resonance full width at half maximum (FWHM) is δBD  0.7 mT in the D-polymer, as opposed to δBH  1.2 mT in the H-polymer (Fig. 12.20). Because the HFI constant aHF(D) ¼ aHF(H)/6.5 (Carrington and McLachlan, 1967), we expect to obtain a much narrower δBD; however, δB is also determined by the wave-function extent of the polaron on the polymer chain, which determines its spin density spread on the number of hydrogen nuclei, N, of the polymer chain (Weinberger, 1980). Thus, aHF and N together determine an “intrinsic” HFI line width, δBHF. The spin-half density of the polaron excitation in π-CP chains is usually spread over several repeat units, which may consist of about N ¼ 10 CH building blocks (Fesser et al., 1983). Consequently, the polaron spin-half ODMR (and -ESR) line shapes in resonance conditions are susceptible to interactions with N protons in the immediate vicinity of the backbone intrachain carbon atoms. Having nuclear spin-half, each coupled proton splits the two electron-polaron spin levels (ms ¼ ½) into two electron-polaron/proton levels via the HFI; and these lines are further split by the other N  1 coupled protons (Carrington and McLachlan, 1967). Therefore, the energy levels of the ensemble system containing one electronpolaron and N protons depends on the HFI constant aHF and field B, which is given by the spin Hamiltonian: H ¼ HHFI + HZ

(12.11)

where HZ ¼ gμBBSz is the electronic Zeeman component (we ignore the nuclear Zeeman interaction), and HHFI (¼ ΣnaHFn SIn) is the isotropic HFI term. Here, aHFn, In (In ¼ ½) are the HFI constant and nuclear spin operator of the nth nucleus (n ¼ 1,…, N)

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and S (S ¼ ½) is the electron-polaron spin operator. Solving the Schr€odinger equation with the Hamiltonian in the form of Eq. (12.11) in the high field limit (μBB ≫ aHF), we find that each of the ms ¼ ½ electron-polaron energy levels splits into 2N levels (for I ¼ ½). As a result, there are 2N ms ¼ ½ to ms ¼ ½ allowed optical transitions in the GHz range (hereafter referred to as satellite lines) that leave the nuclear spins unchanged. In general, the satellite lines do not have equal spacing because the values of aHFn in Eq. (12.11) are not equal to each other in the most general case. The satellite lines form a distribution in B, of which width, ΔHF, can be conveniently calculated from the square root of the second moment (Carrington and McLachlan, 1967): h i1=2 ΔHF ¼ 2 Σn ðBn  B0 Þ2 =2N

(12.12)

where B0 is the resonance field in the absence of HFI, and Bn are the resonance fields for the satellite lines. For a uniform spin distribution, we take aHFn ¼ aHF/N; and consequently, there are N + 1 nondegenerate electron/proton energy levels which, when using Eq. (12.12), give ΔHF  aHF/√ N. Under this condition, we find for the polaron excitation in DOO-PPV polymer chains with N ¼10, ΔHF  0.3aHF. In addition, the inhomogeneous broadening causes an “extrinsic” line width, δBinh. When δBinh < δBHF, the resonance line width, δB, can be approximately written as δB  δBHF + δBinh + δB0

(12.13)

where δB0 (<δBHF) is the homogeneous line width (about 1/T2, the dephasing rate). The spin-density distribution among N CH units decreases the effective HFI, aHFeff of each nucleus; a uniform polaron spin distribution leads to aHFeff ¼ aHF/N (Weinberger, 1980). For the H-polymer, HFI with one spin-half nucleus splits the resonant line into two separate lines, with ΔB ¼ aHF/gμB (Abragam, 1961). With electronic spin distribution on N nuclei, the two lines are further split into (N + 1) satellite lines with unequal intensities that are separated by ΔBeff ¼ aHFeff/gμB and can be readily calculated. The solid line in Fig. 12.20A for the H-polymer is a model calculation for the spin-half resonance, assuming N ¼ 10, where a(H) ¼ 3.5 mT and δBinh + δB0 ¼ 0.65 mT (Eq. 12.13); it is in excellent agreement with the data. For the D-polymer with spin 1 nucleus, each resonant line is split into three lines, which are further split into (2N + 1) satellite lines for N CH units, The solid line in Fig. 12.20B for the D-polymer was similarly calculated using N ¼ 10 and δBinh + δB0 ¼ 0.65 mT, but with a(D)/gμB ¼ a(H)/6.5gμB ¼ 0.54 mT. The excellent agreement with the data using the known a(D)/a(H) ratio indicates that the model calculation captures the main effect of the hydrogen isotope exchange on the g  2 ODMR line in the polymer. In Fig. 12.21, we show the dependence of the g  2 ODMR line intensity, δPL, on PMW for both H- and D-polymers. The ODMR intensity shows a saturation behavior (Yang et al., 2007)—namely, δPL  PMW/(PMW + PS), where PS ¼ αΓ eff, α is an experimentally determined constant, and Γ eff is given by the following relation (Yang et al., 2008): Γ eff ¼ γ + ½γ SL

(12.14)

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ODMR

0.9

0.6

0.3 D H 0

25

50 PMW (mW)

75

100

Fig. 12.21 The microwave power (PMW) dependence of the integrated ODMR signal intensity for the two polymers; the lines through the data points are a model fit using a saturation equation. From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

where γ is an average PP recombination rate and γ SL ¼ T1 SL . Because the PP recombination process at B  0.1 Tesla is not expected to depend on the isotope exchange, variation in PS upon deuteration reflects changes in γ SL via Eq. (12.14). Fig. 12.21 shows that PS is smaller for the D-polymer; in fact, from the data fit, we obtain the ratio PS(H)/PS(D) ¼ 1.4; and using Eq. (12.14), we conclude that γ SL is smaller in the D-polymer due to the weaker HFI. In the following discussion, we determine the ratio, η, of the γ SL rates for the polarons in the two isotope polymers more precisely, using a complementary ODMR method. In Fig. 12.22, we show that the ODMR line width, δB, nonlinearly increases with PMW in both polymers, and also that the increase is steeper for the H-polymer. The increase in δB may be related to the magnetic field strength, B1, of the MW electromagnetic radiation, which influences the homogeneous line width δB0 through the following relation (Abragam, 1961): δB0 ðPMW Þ ¼ δB0 ð0Þ ½1 + ðβ=γ SL ÞPMW 1=2

(12.15)

where β ¼ (T2δB0(0)α)1 and PMW ¼ α(B1)2. Because δB0(0) and β are independent on the hydrogen isotope, from the excellent fit to the data in Fig. 12.22 using Eq. (12.15), we determine the ratio η to be η  γ SL(H)/γ SL(D)  4. This indicates that the spin relaxation time of polarons in the D-polymer is substantially longer than in the H-polymer; and this should increase the spin diffusion length of spin-polarized carriers in OSV devices based on this polymer (as discussed earlier in this chapter, in Section 12.3).

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FWHM (mT)

1.5

1.0

0.5

0

D H 25

50 PMW (mW)

75

100

Fig. 12.22 The microwave power dependence of the ODMR line width for the two polymers; the lines through the data points are model fits based on Eq. (12.15). From Nguyen, T.D., Hukic-Markosian, G., Wang, F., Wojcik, L., Li, X.-G., Ehrenfreund, E., Vardeny, Z.V. 2010b. Isotope effect in spin response of [Pi]-conjugated polymer films and devices. Nat. Mater., 9, 345–352, with permission.

12.5

Time-resolved magneto (M)-photoinduced absorption (PA) in donor-acceptor (DA) copolymers

Donor-acceptor (DA) copolymers contain two organic moieties with different electron affinities that play the role of electron donor (D) and electron acceptor (A; Zuo et al., 2006, Blouin et al., 2007, Tautz et al., 2012, Kularatne et al., 2012, Liang et al., 2010). The small optical band gap, Eg (1.4–1.6 eV), in the DA copolymers that are used in the most efficient solar cells, may lead to a resonant coupling between a singlet exciton (SE) and a triplet-triplet (TT) pair, known as SE-TT resonant coupling. It is known that the energy difference ΔST between SE and triplet exciton (TE) energies in polymers (Monkman et al., 2001) is about 0.7 eV. Then, in DA copolymers, the TE energy is ET ¼ Eg  ΔST  1.5–0.7  0.8 eV. This would lead to nearresonant conditions between the lowest SE (at ES ¼ Eg  1.5 eV) and the intrachain TT-pair state at energy 2ET  1.6 eV. This resonant SE-TT coupling may have strong influence on the photophysics of the DA copolymers. For investigating a possible SE-TT resonant interaction in DA copolymers having Es  2ET, the technique of time-resolved magneto (M)-photoinduced absorption (PA; Huynh et al., 2017), transient magneto-PA (t-MPA)(t,B,λ)  PA(t,B,λ)/PA(t,0,λ)  1, was used in the time domain from 0.2 picoseconds to milliseconds, where λ designates the wavelength at which the transient PA (t-PA)  PA(t,B,λ) is measured. Because PA(t) is proportional to the specific excited state transient population [e.g., SE (at λ ¼ λSE) or TT (at λTT)], and these populations are field-dependent, it generates time and field-dependent t-MPA(t,B). Spin entanglement between the SE- and TT-states in the copolymer chains has been measured, resulting in a unique magnetic field response. Furthermore, spin coherence is conserved upon TT decomposition into two geminate intrachain

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TEs, and consequently, their spin entanglement is maintained up to microseconds, the copolymer spin-lattice relaxation time. We discuss the ps transient spectroscopy of PDTP-DFBT by first examining the mid-IR ps t-PA spectrum of a traditional π-CP, which is a soluble derivative of the polymer poly-(p-phenylene-vinylene) [namely, DOO-PPV (Fig. 12.23A)]. The t-PA spectrum of DOO-PPV film contains a single PA band (PASE) due to the photogenerated SE that peaks at 0.95 eV (Frolov et al., 2000). This PA band is correlated with the stimulated emission band of DOO-PPV and decays with a time constant, 10

3 DOO-PPV 1.0 MPA %

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Fig. 12.23 Room-temperature, ps-transient PA spectroscopy of pristine PDTP-DFBT embedded in a polystyrene matrix, where the copolymer chains are isolated. (A) The t-PA spectrum of DOO-PPV polymer film in the mid-infrared (mid-IR) measured at t ¼ 0 excited at 3.1 eV is shown here for comparison with the t-PA in PDTP-DFBT. The inset shows the lack of t-MPA(B) response at 100 ps. (B) The time evolution of the t-PA spectrum in isolated chains of PDTP-DFBT measured at several delay times, t, following the pump excitation at 1.55 eV. PA1 and PA2 bands are assigned. (C) The normalized SE (black), TT (red), and TE (blue) PA bands extracted from the t-PA spectrum in (B) using the GA method. (D) The PA band dynamics as calculated by the GA method plotted in logarithmical scale for t, which shows that early decay of the PASE and PATT leads to build-up of PATE within about 50 ps.

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τ, of about 200 ps, in agreement with the PL quantum efficiency of this polymer [τ/1 (ns)  20%; Samuel et al., 1995)]. In contrast, as seen in Fig. 12.23B. there are two PA bands at t ¼ 0 in the copolymer film. The two PA bands completely decay within 300 ps; at that time, the t-PA spectrum is dominated by a different PA band that peaks at 0.94 eV; its spectrum is enlarged in Fig. 12.23C. This PA band is exactly the same as PAT in the steady state-PA spectrum, which is due to triplet excitons that are photogenerated in the ps time domain. Because the spin-orbit coupling of this copolymer is relatively weak due to lack of heavy atoms, intersystem crossing rate should be small and cannot explain the fast TE generation. We therefore conclude that the fast TEs are generated via decomposition of the TT excitations, generated by resonant photoexcitation, singlet fission, or both. It is important to know whether the fast PAT is photogenerated immediately or is a by-product of the PASE and PATT decays. To study the PAT fast dynamics, we have employed a generic algorithm (GA) as a numerical method to decompose the overlapping PA bands in the t-PA spectrum (Rao et al., 2013; Gelinas et al., 2014). Fig. 12.23C shows three decomposed bands for SE, TT, and TE, and their associated dynamics are shown in Fig. 12.23D. We see that SE and TT are instantaneously photogenerated within a 300-fs resolution and decay together. Importantly, some PAT is also generated within 300 fs; however, the decay of SE and TT continues to generate TE. We thus conclude that PAT is in fact a by-product of PATT, which is correlated with PASE. The following t-MPA studies further characterize the curious interrelation of these primary photoexcitation species. Fig. 12.24A shows the transient magnetic field response, t-MPA(B) of PASE and PATT bands at a fixed time, t ¼ 200 ps, whereas Fig. 12.24B depicts the t-MPA time evolution at a fixed field of B ¼ 300 mT. It is clearly seen that PATT increases with B, whereas PASE decreases with B, having the same t-MPA(B) response. Also, the two t-MPA responses have the same dynamics (namely, t-MPATT increases with time in the same way that t-MPASE decreases with time). The t-MPA experiment was also attempted on the PASE band in the DOO-PPV polymer; however, null response was found at any delay time (see Fig. 12.23A, inset); this “control experiment” shows that PASE in DOO-PPV is due to pure SE and thus is not susceptible to relatively small magnetic fields. We thus conclude that the t-MPA obtained in PDTP-DFBT is a unique feature of the primary photoexcitations of this compound. Although SE species in the copolymer have a predominantly spin singlet character (because they are instantaneously photogenerated), they nevertheless possess a unique spin character whose different components may have nonzero spin. Importantly, the t-MPA(B) response seen in Fig. 12.24A cannot be understood using the Merrifield model spin-Hamiltonian of the TT-pair (Merrifield, 1971), which well describes the intermolecular singlet fission and triplet-triplet annihilation processes in various organic compounds (Burdett and Bardeen, 2012); this is because this model does not fit the experimental t-MPA(B) response here. Also, the t-MPA(B) response does not originate from an isolated TE with larger zero-field splitting parameters either because such a species would not show two PA bands (Drori et al., 2010; Frolov et al., 2000). We thus conclude that the obtained t-MPA originates from

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Handbook of Organic Materials for Electronic and Photonic Devices 1.0 MPATT

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Fig. 12.24 The t-MPA response of pristine PDTP-DFBT film in the picosecond-tomicrosecond time domains. (A) The t-MPA(B) response of PASE (blue line) and PATT (red line) measured at t ¼ 200 ps up to B ¼ 300 mT. The lines through the data are fit using a 10

10 model Hamiltonian. (B) The evolution of the t-MPA at B ¼ 300 mT for PASE (black triangles) and PATT (black stars) up to t ¼ 200 ps. The red symbols are calculated based on the 10 10 model Hamiltonian (Huynh et al., 2017). (C) The PA decays in the μs time domain measured at 0.9 eV and 40 K, at magnetic field B ¼ 0 (black line) and B ¼ 180 mT (red line), respectively up to t ¼ 40 μs. The inset shows the t-MPA at B ¼ 180 mT up to 40 μs calculated from the PA decays dependence on B. (D) The t-MPA(B) response up to B ¼ 180 mT measured at different times t as indicated.

photoexcitations that have more elaborate properties compared to simple SE or TT, and thus the magnetic field response needs be described by a spin-Hamiltonian that has not been used before in the field of organic magnetic field effect (Gautam et al., 2012; Merrifield, 1971; Burdett and Bardeen, 2012; Zimmerman et al., 2010). To explain the correlated opposite-sign t-MPA(B) response for PASE and PATT bands and its transient dynamics, we use the SE-TT coupling model described by Huynh et al. (2017), assuming that SE and TT are nearly in resonance. Identifying PASE with optical transition from the lowest SE and PATT with transitions from the triplet spin configuration shown in Fig. 12.24A, the calculated response was overlain on the measured t-MPA(B) response of these two PA bands. For our calculations,

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we used a powder-pattern angular average over the B-direction with respect to the TE axes in the TT pair. The following best-fitting parameters were used to obtain the fit shown in Fig. 12.24A: The zero-field splitting parameters of the two parallel TE in the TT state are D ¼ 5.8 μeV, E ¼ 2.1 μeV; the exchange interaction, X, between the two TEs is X ¼ 0.8 μeV; the resonance coupling parameters between SE and the TT pair spin states are SE-S, SE-T, and SE-Q ¼ 1.8, 1.8, and 0 μeV, respectively; the average system decay time is about 1 ns; and the spin-dependent decay rate ratios are SE:S:T:Q ¼1.07:1:0.8:1. The good agreement between the experimental and calculated t-MPA(B) response validates this approach. Obviously, at t ¼ 0+ (i.e., immediately following pulse photoexcitation), no decay has occurred yet, and thus t-MPA(t ¼ 0+,B) ¼ 0 for both PASE and PATT. As time progresses, the imbalance of spin densities increases, leading to a growing t-MPA(t,B) response, as observed experimentally. Fig. 12.24B shows the calculated transient response of t-MPA(t,B ¼ 300 mT) for PATT (positive) and PASE (negative), along with the respective experimental responses. Our model nicely reproduces the increasing t-MPA value with the delay time for both PA bands. It is interesting to study the t-MPA response at longer times using transient nanosecond-to-millisecond PA spectroscopy. The optical setup for these measurements was the same as the cw PA apparatus, except that the pump excitation was a pulsed laser (Quanta-ray) having 10-ns pulse durations at 10-Hz repetition rates, operated at 680 nm. For monitoring ΔT(t), a probe beam from a laser diode at 1300 nm was used. Fig. 12.24C and D show the t-PA decay and t-MPA evolution of PAT in the μs time domain at 40 K. Fig. 12.24C shows that PAT decay measured at 0.9 eV is strongly dependent on the magnetic field. From the change ΔPA(t) in t-PA with B, we obtain the t-MPA(B,t) response and study its time evolution. Fig. 12.24C (inset) shows that the t-MPA at B ¼ 180 mT changes polarity at t  4 μs. This is reflected in the t-MPA(B) response (Fig. 12.24D), which dramatically changes in the interval 1 < t < 10 μs. In fact, the t-MPA(B) response changes from an early time response that is similar to that obtained for PATT in the ps time domain (Fig. 12.24A) to a longer time response similar to that of individual, uncorrelated TE in the ss-MPA. We therefore interpret this interesting t-MPA(B) evolution as spin-decoherence, when the spins of the two geminate TEs that were born from the same TT photoexcitation lose their initial spin-entanglement. This experimental result is strong evidence for the existence of initially photogenerated, intrachain TT-pairs, which subsequently decompose into two geminate TEs at t < 200 ps. The surprising finding here is that even though TT decays into geminate TEs in the ps time domain, their spin entanglement is still preserved into the μs time domain.

12.6

Conclusions

In this chapter, we reviewed the latest achievements in organic spintronics research at the University of Utah and the Technion, related to the important role of the HFI, resonant SE-TT coupling in optically pumped OSCs, and exchange interaction in

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determining the spin response. By replacing the building block atoms in the polymer chains such as carbon and hydrogen, with different isotopes, it was then possible to tune the HFI and thus study in detail its influence on the material spin response. We showed compelling evidence that the HFI plays a crucial role in determining the magnetic response of three spin-dependent processes in OSCs—namely, magnetic field effect in OLEDs, GMR in OSV devices, and electron resonance response in thin films. In particular, we showed that both MEL(B) and MC(B) responses in OLEDs are strongly dependent on the HFI constant of the materials; the stronger the HFI constant, the broader the magnetic-field response. Furthermore, we found a novel, ultrasmall response at B ≪ aHF/gμB in many bipolar and unipolar organic devices. This MFE response component scales with the normal MC(B) response, and thus it is also due to the HFI of the spin pairs with B. We introduced a simple model to simulate the MFE response that explicitly includes in the spin pair Hamiltonian the most strongly interacting nuclear spins and is capable of reproducing the entire MFE(B) response, including the ultra-small component. We also demonstrated that the HFI plays an important role in determining the polaron spin-half resonance line-width and saturation properties, and that the HFI determines the spin diffusion length of the injected spin-polarized electrons; the weaker the HFI, the longer the spin diffusion length, and the larger the GMR in the device. In addition to magnetic field effects in devices, studies of time-resolved magnetophotoinduced absorption in films of OSCs have been described. Our review includes both time-dependent and steady-state investigations. We have used simplified theoretical models in which the spin degree of freedom is solely responsible for the magnetic field effects, and we also showed that most of the experimental results can be accounted for by these models. In particular, these models can explain the magnetic field response in the steady-state, intermediate (microsecond-to-nanosecond) and fast (1–100-ps) transient regimes. Our findings may be useful to material scientists for designing novel materials for organic spintronics applications. For example, the ideal OSCs for OSV applications should have a miniature HFI for supporting electron-polarized-spin transport. Among the existing materials such as the fullerenes, C60 might be an excellent candidate for spin-polarized transport because it naturally contains 99% 12C with nuclear spin I ¼ 0, and only 1% 13C with I ¼ ½, and thus some small HFI. At the present time, the application of MFE in OLEDs as an Earth-magnetic sensor is still pending. One of the reasons is that substantial MFE response only occurs at a few mT, which is still too large for MFE-based magnetic sensor applications. Our findings pave the way to reducing the necessary field for the MFE simply by exchanging isotopes to lower the HFI in the active material. However, if the HFI is too small, as in the case of C60, then the MFE response is very weak because the HFI is also the origin of the MFE response itself. An alternative solution to improve the MFE-based sensor is to use the USMFE. In fact, a chemical USMFE has been proposed to be at the heart of the avian magnetic compass in migratory birds. In this respect, our work shows that the USMFE component appears in the MFE responses of many more organic compounds that had previously been thought.

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Acknowledgments We thank L. Wojcik for the synthesis of the DOO-PPV polymers with different isotopes. We also thank Professor X.-G. Li for the LSMO films that he supplied for the OSV studies. In addition, we thank Drs. F. Wang and G. Hukic for the ODMR work, and the graduate students in Vardeny’s research group for many useful discussions. This work was supported by NSF Grant No. DMR-1701427 (Spin-valves and MFE) and AFOSR Grant FA9550-16-1-0207 (Time resolved PA); and the Israel Science Foundation (ISF 598/14; E.E.).

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