Magnetic field-modulated exciton generation in organic. semiconductors: an intermolecular quantum correlation effect

What is the name of the process of magnetic field modulated generation of?
What happens to teir scattering?
Spin scattering and spin what?

Transcription

1 Magnetic field-modulated exciton generation in organic semiconductors: an intermolecular quantum correlation effect B. F. Ding*, Y. Yao*, X. Y. Sun, Z. Y. Sun, X. D. Gao, Z. T. Xie, Z. J. Wang, X. M. Ding, Y. Z. Wu, X. F. Jin, C. Q. Wu, and X. Y. Hou Surface Pysics Laboratory, Department of Pysics, Fudan University, Sangai , People s Republic of Cina Magnetoelectroluminescence (MEL)of organic semiconductor as been experimentally tuned by adopting blended emitting layer consisting of bot ole and electron transporting materials. A teoretical model considering intermolecular quantum correlation is proposed to demonstrate two fundamental issues: (1) two mecanisms, spin scattering and spin mixing, dominate te two different steps respectively in te process of te magnetic field modulated generation of exciton; (2) te opping rate of carriers determines te intensity of MEL. Calculation successfully predicts te increase of singlet excitons in low field wit little cange of triplet exciton population. *Tese autors contributed equally to tis work. Electronic mail: cqw@fudan.edu.cn Electronic mail: xyou@fudan.edu.cn 1

2 In te field of organic spintronics [1-13], magnetoelectroluminescence (MEL), i.e., magnetic field-modulated electroluminescence of organic semiconductor devices wit nonmagnetic electrodes as been widely studied [5-13], because it provides a promising way to understand te spin dynamics in organic systems, suc as organic semiconductors and biological systems [14]. Generally, MEL appears to enance rapidly wit magnetic field in te low field region (typically <15mT) but to saturate or even weaken in te ig field region(>30mt)[5,6,10,12]. Unanswered questions in tis area include te reason wy smaller electric field leads to larger MEL[5,6,8,10,12,15], wy insertion of an insulating layer LiF enances MEL [10] and wy minority carriers dominate te magnetic field effect in organic semiconductors [6,15-17]. Tese questions can be reduced to one basic issue, namely wat determines te intensity of MEL in a given magnetic field. Teories of inter-system crossing (ISC)[9,10,16] or triplet-triplet anniilation (TTA) [12,13] ave been proposed by some groups to qualitatively explain MEL. Bot ISC and TTA could be included in a so-called spin mixing (SM) mecanism wic occurs only in spin sub-levels troug spin redistribution [6, 14, 18]. According to ISC or TTA, te increase of singlet excitons sould occur at te expense of triplet excitons. But Reufer et al found tat no cange of singlet triplet balance occurs, especially in low magnetic field [7]. Since MEL correlates directly wit magnetic field-modulated exciton generation, it is critical to consider ow magnetic field influences te process of exciton generation. Generally, exciton generation consists of tree steps[19]: I. carrier injection from electrodes and transport; II. formation of a ole-electron pair at two adjacent molecules; III. formation of an exciton at one molecule by opping. Identifying in wic step SM is active and wic mecanism dominates beyond tis step is te essential question tat must be addressed [6,18].To tis end a quantitative explanation of 2

3 MEL is indispensable. In tis letter, we describe a model formulated by considering te intermolecular correlated effect. Based on te model, te process of magnetic field-modulated step II and step III of exciton generation is quantitatively studied bot experimentally and teoretically. It is found tat SM only dominates magnetic field-modulated step III in ig magnetic field, wile spin scattering (SS), in wic te redistribution of bot spins and carges is involved, controls te modulation of step Ⅱ in low magnetic field. By studying te MEL of te organic ligt emitting diode (OLED) wit a blended emitting layer, it is found tat opping rate of carriers influences bot SS and SM. Tis proves tat intermolecular quantum correlated effect plays an essential role in organic MEL and suggests tat te magnetic field effect in oter relevant systems[3,14,16] sould be reconsidered. In present work, a special structure of OLED was designed to reveal te effect of intermolecular correlation on exciton generation. Te OLED was fabricated wit a blended layer of tris-(8-ydroxyquinoline) aluminum (Alq 3 ) and N,N -bis(l-naptyl)-n,n -dipenyl-1,l - bipentl-4,4 -diamine (NPB), acting as te fluorescent emitting layer, as sown in Fig. 1(a). Te device area is approximately 4 4 mm 2. Besides, 40nm NPB and 50nm Alq 3 form te ole-transporting and electron-transporting layers respectively. Because of its wide band gap[20], BCP (batocuproine) is used as an exciton-blocking layer to prevent exciton diffusion from te blended layer to te 50nm-tick Alq 3 layer. Te anode and composite catode are ITO and LiF/Al respectively. Figure 1(b) sows te MEL of six representative devices wit different blending volume ratios of NPB to Alq 3 as function of external magnetic field under constant driving current of 150µA. Te MEL is expressed by EL / EL = [( EL( B) EL(0)]/ EL(0), were EL(B) and 3

4 EL (0) are te electroluminescence wit and witout external magnetic field B respectively. Similar to te reported results[6], eac curve is caracterized by fast enancement in te low field region followed by saturation in te ig field region. Te intensity of MEL under a given field depends strongly on te blending ratio. To confirm te relation between MEL and blending ratio, Fig. 1(c) sows EL / EL at 50mT under tree different driving conditions constant driving current of 500µA, constant driving voltage of 7V, and constant initial brigtness of 20cd/m 2. Wit te ratio increasing from 0% to 30%, under te condition of constant initial brigtness of 20cd/m 2, EL / EL increases from 3% to 7%. However, furter increase of te ratio from 30% to 80% causes EL / EL to decrease from 7% to 2%. MEL under te oter two driving conditions sows similar beavior. Experiments reveal an intrinsic relation between MEL and blending ratio. Liu et al reported previously tat electrical conductivity, wic is determined by carrier mobility, reaces a minimum around te blending ratio of 30% in a blended layer of NPB and Alq3[21]. Te ratio of 30% agrees well wit te ratio in te present experiments in wic MEL reaces its maximum. Quantum mecanically, mobility of carriers is dominated by teir opping rate. Te opping rate is one of te key factors tat affect te interaction among intermolecular carriers, and is intrinsically a result of correlated effect. All of te above experimental results demonstrate tat a correlated effect is likely to determine te intensity of MEL. Based on te results sown in Fig. 1, it is proposed tat te Hubbard model, a typical model for correlated systems, can be used to describe suc a correlated effect [22]. Te Hamiltonian, including bot te intermolecular transportation of electrons/oles and te interaction between electrons/oles and nuclear spins, reads H = H 1 + H 2, (1) 4

5 Te first part of (1) includes opping and Coulomb interaction of carriers. H e e e ( ti, i' di, σ di', σ + t j, j' c j, σc j', +. c.) + U ( n n + n n ) + V, (2) i i j j 1 = σ i, j, σ i, j were d i,σ ( d i, σ ) and c j,σ ( c j, σ ) create (anniilate) a ole and an electron wit spin σ up ( ) or down ( ) in te i- and j-t molecule, i and j denote te neigbors of te i- and j-t molecule, t i i', and e t j, j' are te opping rates (in unit of µev by te uncertainty principle E t ħ/2) of ole and electron. U is te Coulomb repulsive energy between two oles or two electrons wit different spins at te same molecule, ni, σ ( d i,σ d i, σ ) and e n j, σ ( c j,σ c ) j, σ te corresponding ole and electron number operators, and V te attractive interaction between ole and electron at te same molecule. Te second part of (1) sows te effect of an external magnetic field and yperfine interactions, e H 2 = gµ B ( B ext + B yp, i ) S i + ( B ext + B yp, j ) S j, (3) i, j were g=2.0 for organic materials[7], µ B is Bor magneton, ext is te external magnetic field cosen along te z-direction, and yp, i( j) is te effective nuclear magnetic field of i-t (j-t) molecule tat will be treated classically. For example, for oles, B yp, i S i = B yp, i cos θi ( d d d d ) + B, sin ( +,,,, yp i θi d d d d i i i i i, i, i, i, ), (4) were θ i is te angle between B yp, i and ole spin. In tis work, we focus on te intrinsic features of te organic semiconductor. Te model is a two-step one including only step II and step III of exciton generation mentioned above. Because step II and step III are different, tey are treated separately. Generally, opping rates t i i', t and e j, j' vary from molecule to molecule due to te disorder of organic materials. t and t e are estimated to be between 1µeV and 100µeV[23], depending on te blending ratio. U is taken as 0.1eV[24], wic is large enoug to prevent double occupancy of te same polarity of carriers at one molecule, yet spin excange between two molecules still operates wen many excitons interacting 5

6 wit eac oter in step III[22] are considered. Because of te random orientation of molecular yp, it is necessary to calculate te statistical average for te angle of nuclear spinsθ ( (0, π )). Hyperfine interaction gµ B B yp, i( j) is set to 0.5µeV[24,25]. Tus an external magnetic field about five times iger tan te yperfine interaction (>25mT) can be considered as a ig field. Ten, given an initial state tat electron and ole reside on different molecules, te average generation probability of bot singlet and triplet excitons can be calculated over te time range 0 to 10ns, covering te mean lifetime of excitons. Figure 2 sows results of te present simulation, compared to te corresponding experimental measurements. Witout loss of generality, all calculations ave been normalized wit te result of pure Alq 3 structure. Eac curve contains two parts corresponding to magnetic field-modulated step II and step III respectively, as marked in te figure. Calculated EL / EL, sown as solid lines, is consistent wit te experimental data. It is seen tat for step II te calculated EL / EL increases quickly in low magnetic field, sowing close agreement wit te experimental results. For step III, te calculated EL / EL saturates and reproduces te experimental data above 25mT. Two insets in Fig. 2 sow te opping rate parameters for magnetic field-modulated step II and magnetic field-modulated step III. Hopping rates in step II are taken to be one order smaller tan tose used in step III, since in step III te stronger Coulomb interaction between electron and ole increases te opping rates[27]. It is found tat te calculated EL / EL increases monotonically wit decreasing opping rate in bot steps, beaving in te same way as experimentally observed. It sould be empasized tat present work only focuses on two regions of MEL, te low and te ig field region. Te transition region will be considered in future. Tese results confirm tat te correlated effect, wic is controlled by te intermolecular opping 6

7 rate, is essential for MEL and tat lowering te opping rate can enance te MEL. To understand te pysics of te two-step model, a possible illustration is given in Fig. 3, sowing scematically ow step Ⅱ and III are influenced in different magnetic field regions. Magnetic field-modulated step II is sown in Fig. 3(a) and Fig 3(b), demonstrating ow a low external magnetic field influences te SS, and tus increases te generation probability of ole-electron pairs. If no external magnetic field ext exists,te intensity value of, te effective nuclear magnetic field of a molecule, is identical for eac molecule, as sown by black yp arrows in Fig. 3(a). Tis means tat te intensity distribution of Byp is uniform in space. However, yp for a given low ext, te total tot of ext and is not identical due to te random orientation of yp, resulting in non-uniform intensity distribution of Btot, as sown by red arrows in Fig. 3(a). If B ext >> B yp, all tot are almost te same as ext and te intensity distribution of tot sould be uniform. Te non-uniform tot acts like disorder in energy distribution for te carrier spins, strengtening teir scattering and resulting in enancement of te formation probability of ole-electron pairs. Te dependence of spin scattering on Bext is very similar to tat in te case of dilute magnetic semiconductors, were te spin scattering between carrier and magnetic atom is proportional to x(1-x), were x is te density of magnetic atoms[28]. In Fig. 3(b), te carrier capture cross section is used to describe te spin scattering. Witout, ext te intensity distribution of yp is uniform. Te carrier capture cross section for a molecule is small, as sown in te left part of Fig. 3(b). Low ext will cause non-uniform intensity distribution of tot, and tus enlarge te carrier capture cross section, as sown in te rigt part of Fig. 3(b). Wen Bext >> B yp, te intensity distribution of tot is uniform again and te carrier capture cross section will decrease to te value in te case of Bext =0. Magnetic 7

8 field-modulated step III is sown in Fig. 3(c) and Fig. 3(d), demonstrating ow a ig external magnetic field suppresses te spin flip, and tus increases te ratio of singlet to triplet excitons. In te case of B ext =0, as sown in te left part of Fig. 3(d), a ole and an electron are located at two adjacent molecules to form a singlet ole-electron pair. Wen te electron ops to te adjacent molecule were te ole resides, te electron spin will be modulated by bot and of te two molecules were ole and electron reside respectively. Due to teir random orientation, yp e yp and point to different directions. In suc case, provides te transversal component to yp e yp yp e yp. It is well known tat te transversal component makes spin flip feasible during electron opping[28]. Terefore te singlet ole-electron pair can undergo transition to a triplet exciton, as sown in te left part of Fig 3(d). Tis is indeed te mecanism of SM caused by random nuclear field[29]. However, a ig Bext can align B tot towards B ext, terefore B tot would no longer be random as B yp, as sown by red arrows in Fig. 3(c). Te rigt part of Fig. 3(d) sows wen B ext >> B yp, compared to te large longitudinal component of tot te transversal component becomes insignificant. In tis case spin flip will ardly occur. Terefore te inibition of SM effectively increases te number of singlet excitons. MEL in different ranges of magnetic field is dominated by different mecanisms - SS and SM. Tey dominate te magnetic field-modulated step II and step III respectively. From te two-step model, te intrinsic property of te mecanism of SS is tat increase of singlet excitons is not obtained solely at te expense of triplet excitons. Fig. 4(a) sows te teoretical result concerning te variation of singlet and triplet excitons wit low magnetic field. It can be seen tat te influence of magnetic field on singlet excitons is muc stronger tan tat on triplet excitons. Experimentally, Reufer et al ave examined weter an external magnetic field 8

9 could cange te singlet/triplet ratio by using a posporescent ydrocarbon polymer wit simultaneous emission of fluorescence and posporescence, but te metod could ardly prevent te internal energy transfer between singlet and triplet excitons[7,18]. In order to eliminate te internal energy transfer, a special structure of OLED, as scematically sown in Fig. 4(b), was adopted, wic was similar to te structure reported before for studying te posporescence of posporescent dye 2,3,7,8,12,13,17,18-octaetyl-21H,23H-porpine platinum(Ⅱ) (PtOEP)[30]. In Fig. 4(b), C6 stands for Coumarine 540. Since C6 (PtOEP) is a fluorescent (posprescent) dye wit efficient Förster (Dexter) energy transfer from singlet (triplet) exciton of Alq 3 to singlet (triplet) exciton of C6 (PtOEP), C6 (PtOEP) doped Alq 3 layer wit volume doping ratio of 1.0% (4.0%) acts as te singlet (triplet) exciton recombination zone. Te singlet exciton recombination zone and te triplet exciton recombination zone are separated by a 20nm Alq 3 layer. 20nm is sufficiently tick to avoid internal energy transfer between te two recombination zones[30]. Tus te variation of singlet and triplet excitons in magnetic field sould be observed simultaneously. Fig. 4(c) sows te MEL of te device under a field of 6mT. Te peaks of 510nm and 652nm are emitted from te singlet exciton recombination zone and te triplet exciton recombination zone respectively. Te spectra adjacent to te two peaks are amplified and sown in te left and rigt insets. Wit field of 6mT, EL / EL around 510nm is calculated to be about 2.5%, wile EL / EL around 652nm is almost zero. Fig. 4(d) sows te experimental results of EL / EL for singlet excitons and triplet excitons in te low field range. Increasing te field from 1mT to 6mT, EL / EL for singlet excitons increases from 0.2% to 2.5%, wile EL / EL for triplet excitons is nearly zero over tis range. Similar to te results sown in Fig. 4(a) tese experimental results also indicate tat te influence of te low magnetic field on singlet excitons is muc 9

10 stronger tan tat on triplet excitons. Some difference exists between te teoretical result sown in Fig. 4(a) and te experimental result sown in Fig. 4(d) for te triplet excitons. It indicates more pysical processes sould be taken into consideration in te model. Furtermore, it must be mentioned tat te structure sown in Fig. 4(b) can not be used experimentally to observe te beavior of triplet excitons in ig magnetic field, since ig field influences many unclear effects in PtOEP, suc as spin-orbit interaction and spin-spin interaction, wic in turn influence te experimental result. In conclusion, we report tat MEL strongly depends on te blending ratio of NPB to Alq 3.Te maximum MEL occurs at te blending ratio of 30%, wic corresponds to te minimum conduction of blended layer. Compared to te teoretical result, we confirm tat te intermolecular correlations play te essential role in MEL. In addition, to confirm te result as predicted by te proposed model, we adopt te special structure of OLED to avoid internal energy transfer between singlet and triplet exciton,so as to observe tem simultaneously and individually. Te increase of singlet excitons in low field wit little cange of triplet exciton population exceeds all experimental and teoretical results reported before. 10

11 Acknowledgements Tis work is supported by te National Natural Science Foundation of Cina (Grant No ) and Sangai Science and Tecnology Commission (Grant No 08JC ) and te MST of Cina (Grant No. 2009CB929200). YY and CQW are also supported by te EC Project of OFSPIN (Grant No. NMP3-CT ). We would like to tank Edward Obbard for is assistance in proofreading te manuscript. 11

12 References [1] V. Dediu, M. Murgia, F. C. Matacotta, C. Taliani, and S. Barbanera, Solid State Commun. 122, (2002). [2] V. Dediu, L. E. Hueso, I. Bergenti, and C. Taliani, Nature Mater 8, (2009). [3] Z. H. Xiong, D. Wu, Z. V. Vardeny, and J. Si, Nature 427, (2004). [4] B. F. Ding et al., Appl. Pys. Lett. 93, (2008). [5] J. Kalinowski, M. Cocci, D. Virgili, P. Di Marco, and V. Fattori, Cem. Pys. Lett. 380, (2003). [6] F. J. Wang, H. Bässler, and V. Z. Vardeny, Pys. Rev. Lett. 101, (2008). [7] M. Reufer et al., Nature Mater. 4, (2005). [8] Y. Wu, Z. H. Xu, B. Hu, and J. Howe, Pys. Rev. B 75, (2007). [9] J. Kalinowski, M. Cocci, D. Virgili, V. Fattori, and P. D. Marco, Pys. Rev. B 70, (2004). [10] H. Odaka et al., Appl. Pys. Lett. 88, (2006). [11] J. Wilkinson, A. H. Davis, K. Bussman, and J. P. Long, Appl. Pys. Lett. 86, (2005). [12] R. Liu, Y. Zang, T. L. Lei, P. Cen, and Z. H. Xiong, J. Appl. Pys. 105, (2009). [13] B. Hu, L. Yan, and M. Sao, Adv. Mater. 21, (2009). [14] K. Maeda et al., Nature 453, (2009). [15] T. D. Nguyen, Y. Seng, J. Rybicki, and M. Wolgenannt, Pys. Rev. B 77, (2008). [16] B. Hu and Y. Wu, Nature Mater. 6, (2007). [17] F. L. Bloom, W. Wagmans, L. Kemerink, and B. Koopmans, Pys. Rev. Lett. 99, (2008). [18] J. M. Lupton and C. Boeme, Nature Mater. 7, (2008). [19] M. Segal et al., Nature Mater. 6, (2007). [20] I. G. Hill and A. Kan, J. Appl. Pys. 86, (1999). [21] S. W. Liu, J. H. Lee, C. C. Lee, C. T. Cen, and J. K. Wang, Appl. Pys. Lett. 91, (2007). [22] A. Auerbac, Interacting Electrons and Quantum Magnetism (Springer, New York, 1998). [23] A. J. Drew et al., Pys. Rev. Lett. 100, (2008). [24] P. A. Bobbert, T. D. Nguyen, F. W. A. van Oost, B. Koopmans, and M. Wolgenannt, Pys. Rev. Lett. 99, (2007). [25] Y. Seng et al., Pys. Rev. B 74, (2006). [26] R. P. Groff, R. E. Merrifield, A. Suna, and P. Avakian, Pys. Rev. Lett. 29, (1972). [27] M. Kuwata-Gonokaml et al., Nature 367, (1994). [28] M. Foygel, J. Niggemann, and A. G. Petukov, IEEE Trans. Magn. 43, (2007). [29] W. Barford and E. E. Moore, Pysics/ (2004). [30] M. A. Baldo et al., Nature 395, (1998). 12

13 Figure legends FIG. 1 MEL versus magnetic field and blending ratios of NPB to Alq3 of blending layer. (a) Scematic structure of blending-layer-based OLED. (b) MEL of six devices versus external magnetic field. For all of te devices, te measurement is under constant current driving of 150µA. (c) MEL in field of 50mT versus blending ratios for tree different driving conditions (black squares: constant current of 500µA; red circles: constant voltage of 7V; blue triangles: constant initial brigtness of 13

14 20cd/m 2 ). FIG. 2 Results of calculation. Dots are experimental data wit five representative blending ratios, wile te solid lines sow te relative results of te present two-step model calculation. Two sets of solid lines in low field and ig field are results of calculation for te magnetic-field-modulated step II and step III of te exciton generation. Hopping rate parameters are sown in te insets: t II and e t II ( t III and step II (step III). e t III ) are opping rate of ole and electron respectively for magnetic-field-modulated 14

15 FIG. 3 Scematic diagram of te influence of external magnetic field in different ranges on te exciton generation. Blue arrow/black arrow represents external magnetic field ext /effective nuclear magnetic field yp, and red arrow stands for tot (te resultant field of ext and yp ). (a) Low ext canges te uniform distribution of intensity of yp into non-uniform distribution. (b) Left part indicates tat witout ext carrier capture cross section is small. Rigt part indicates tat te non-uniform distribution caused by low ext increases carrier capture cross section, and tus increases te formation probability of ole-electron pairs. (c) Hig ext can align random orientation of yp towards te same orientation. (d) Left part sows ow singlet ole-electron pair transits to triplet exciton troug spin flip witout ext. Rigt part sows wen >> yp, te spin flip is ineffective, and te singlet ole-electron pair can only transit to singlet exciton. ext 15

16 FIG. 4 Beaviors of singlet and triplet excitons in te range of low magnetic field were spin scattering dominates. (a) Teoretical calculation of te beavior of singlet and triplet excitons: singlet excitons are more sensitive to magnetic field tan triplet excitons. Solid black and red lines are for singlet and triplet excitons respectively. (b) Scematic arcitecture of devices consisting of a layer doped wit fluorescent dye C6 for detecting and removing singlet excitons and anoter layer doped wit a posporescent dye for detecting triplet excitons. (c) Spectra obtained from te device wit structure sown in (b): blue spectrum is measured witout external field; red spectrum is measured under 6mT field. Left and rigt insets sow amplified curves around two peaks. (d) Experimental results for beaviors of singlet and triplet excitons in low magnetic field. 16