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Effect of spin excited states on electron transport through an organic ferromagnetic device
Organic Electronics 10 (2009) 809–814
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Organic Electronics journal homepage: www.elsevier.com/locate/orgel
Effect of spin excited states on electron transport through an organic ferromagnetic device Hong Jiang a, Guichao Hu c, Ying Guo a, Shijie Xie a,b,* a b c
School of Physics, Shandong University, Jinan 250100, China State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
a r t i c l e
i n f o
Article history: Received 9 December 2008 Received in revised form 10 March 2009 Accepted 3 April 2009 Available online 17 April 2009
PACS: 73.63. b 75.47.m 85.75.d 73.61.Ph Keywords: Spin excited states Organic ferromagnet Organic spintronics
a b s t r a c t Spin excited states in an organic ferromagnet are proposed and investigated on the basis of an extended SSH + Heisenberg (SSH = Su-Schrieffer-Heeger) model. It is found that a spin excited state will form a local distortion of the spin density wave (SDW) of p-electrons while the lattice configuration of main chain has no obvious change. Then the spin-polarized transport properties through an organic ferromagnetic device are investigated with the Landauer-Büttiker formula and Green’s function method. It is obtained that the current will be spin polarized due to the existence of SDW in the ferromagnetic molecule. Both the total current and the spin-polarized current will be modulated when the SDW is excited. The total current through the device is suppressed by the spin excitation of side radicals, through which a conductance switch function may be realized. Compared with ground state, the spin polarization has no obvious change in a low spin excited state and the device still has spin-filter function. Finally, spin excitations induced by temperature is studied and we find that an organic ferromagnetic device can hold a high spin polarization when temperature is not too high. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Recently, two attractive fields have been growing in the minimization of electronic devices: one is molecular electronics aiming at replacing traditional semiconductors with organic materials, such as polymer [1], organic single crystal [2] or even single molecule etc. [3], which opens the way to cheap, low-weight, mechanically flexible, chemically interactive, and bottom-up fabricated electronics; the other is spintronics which manipulates electronic spins as the information carriers while consumes less power than manipulating electronic charge [4]. The combination of the two realms gives birth to a new fascinating field of organic spintronics. In particular, it attracts enormous * Corresponding author. Address: School of Physics, Shandong University, Jinan 250100, China. Tel.: +86 531 8837035 8321. E-mail address: [email protected] (S. Xie). 1566-1199/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.orgel.2009.04.001
interests with its two unique advantages: the very long spin relaxation time due to the weak spin-orbit and hyperfine interactions in an organic material and the easiness to form a good interface between an organic material and a metal electrode. So far, two kinds of organic spintronics devices have been designed: one is to use a nonmagnetic molecule sandwiched between two magnetic electrodes with or without applied magnetic field, such as spin valve and magnetic tunnel junction (MTJ) type devices [5]; the other is to adopt a magnetic molecule as the interlayer [6]. The latter case is to utilize the intrinsic properties of an organic magnet to realize spin functionality. As a combination of ferromagnet and organic materials, organic ferromagnets have been studied in past decades. By far, several organic magnets have been synthesized and tested experimentally, including poly-BIPO [7,8], V[TCNE]x [9,10] and single molecular magnet [3].
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H. Jiang et al. / Organic Electronics 10 (2009) 809–814
Ovchinnikov et al. and Cao et al. have separately synthesized an organic ferromagnet called poly-BIPO, which can be obtained by replacing the H atom of polyacetylene alternately with a heterocycle containing an unpaired electron which we call a side radical, as schematically shown in the central part of Fig. 1. The main zigzag chain consists of carbon atoms with p itinerant electrons. There exists antiferromagnetic coupling between the spin of p-electron along the main chain and the residual spin of the side radical. From an extended SSH + Heisenberg (SSH=Su-Schrieffer-Heeger) model, one obtains that the system will have the lowest energy when the spins of side radical forms a ferromagnetic order [11–13]. Recently, several designs of organic ferromagnetic device have been proposed theoretically and some interesting phenomena such as spin filtering and spin-current rectification are predicted [14–16]. At present, most investigations on an organic polymer ferromagnet are limited to ground state properties of the system. In reality, external stimulations including photoexcitation, magnetic field or temperature etc may drive the magnetic molecule deviate from ground state. Several experiments have revealed the underlying function of spin excited states in electron transport through a magnetic molecule. For example, Petukhov et al. gave an evidence of spin excited states existing in a molecular magnet based on electron paramagnetic resonance (EPR) measurements [17]; Heersche et al. observed a complete current suppression and negative differential conductance in a single Mn12 molecular magnetic device, which is believed to have a relation with the spin excited states of the molecule [6]. For organic ferromagnet poly-BIPO, the spin excited state means that the ferromagnetic order of radical spins is destroyed owning to the spin flipping, which induces the magnetic molecule to a high-energy state. As the radical spins are correlated with the p-electrons in the main chain, it is expected that the spin excited state will affect the pelectron transport along the main chain. In this paper, we construct a metal/organic ferromagnet/metal (M/OF/M) device and then investigate the spin-polarized transport when the organic ferromagnetic molecule is in different spin excited states. The paper is organized as follows: The model and formula are described in Section 2. In Section 3, we give the numerical calculation and the results are analyzed. Finally, in Section 4, a summary is given. 2. Model and method As shown in Fig. 1, an organic ferromagnetic device M/ OF/M is modeled as a quasi-one-dimensional chain. The
central organic ferromagnetic molecule is connected with two noninteracting semi-infinite one-dimensional metallic chains. The complete Hamiltonian is written as,
H ¼ HOF þ Hl þ Hr þ Hcoup þ HE
ð1Þ
The first term is the Hamiltonian of organic ferromagnetic molecule [12,13],
HOF ¼
X
½t 0 aðunþ1 un Þðcþn;s cnþ1;s þ cþnþ1;s cn;s Þ
n;s
X K X ðunþ1 un Þ2 þ J f dn;o SnR Sn 2 n n X X þU cþn;" cn;" cþn;# cn;# þ V cþn;s cn;s cþnþ1;s0 cnþ1;s0
þ
ð2Þ
n;s;s0
n
where t0 is the hopping integral of p-electrons along the main chain with a uniform lattice. a stands for the electron-lattice coupling parameter and un the lattice displacement at site n. K is the elastic constant of the lattice atoms, and cþ n;s ðcn;s Þ denotes the creation (annihilation) operator of an electron at site n with spin s. The third term in Eq. (2) describes the correlation between SnR of radical R. spin ~ Sn of p-electron and residual spin ~ It is assumed that the side radicals are connected with the odd sites of the main chain, which is denoted by dn;o . Coupling constant Jf is assumed to be positive (antiferromagnetic coupling). We use mean-field approximation to treat the radical spin ~ SnR as hSznR i, where h i ¼ hGj jGi is the average with respect to the ground state jGi. Then the third term can be written as Jf P z þ þ n dn;o hSnR i cos hnR ðcn;" cn;" cn;# c n;# Þ and hnR the radical 2 spin orientation at site n (angle with -z axis). The last two terms describe the e–e (electron–electron) interactions between p-electrons under the extended Hubbard model. As spin coulomb drag effect may exist between spin-up and spin-down electrons and affect the spinpolarized current during transport [18,19], it is very necessary to take the consideration of the interactions among electrons. So far, may theoretical techniques can deal with e–e interactions, for example, mean-field approximation, perturbation, full coulomb interactions [20,21] and density matrix renormalization group (DMRG) calculation etc [22–24]. As the first step of our investigation, in this paper, we will just adopt the simple mean-field approximation to deal with the Hubbard term. Its validity will be discussed in the later summary. Hl(r) is the Hamiltonian of the left (right) electrode, which is a semi-infinite metal chain,
HlðrÞ ¼
X m;s
elðrÞ aþm;s am;s þ
X
t lðrÞ ðaþm;s amþ1;s þ h:c:Þ
m;s
Fig. 1. Simplified structure of a metal/poly-BIPO/metal nanojunction. The arrows indicate the spin orientation of radical spins.
ð3Þ
H. Jiang et al. / Organic Electronics 10 (2009) 809–814
where el(r) is on-site energy of a metal atom comparing to that of a carbon atom and tl(r) the transfer integral of adjacent sites. aþ m;s ðam;s Þ is the creation (annihilation) operator of an electron in electrodes. The coupling between the electrodes and the molecule is assumed to take place only at the nearest connecting atoms at the interfaces,
Hcoup ¼
X
t IM ðaþ0;s c1;s þ h:c:Þ þ
s
X
trM ðcþN;s aNþ1;s þ h:c:Þ
ð4Þ
s
tl(r)M is the interfacial coupling, which is simplified by neglecting the spin-dependent scattering at the interfaces. N is the total number of the sites in the organic ferromagnetic interlayer. The last term is the contribution of driving field E arising from the bias voltage V between the two electrodes,
X Nþ1 HE ¼ jejE n a þ un cþn;s cn;s 2 n;s X Nþ1 þ jejE n a þ un 2 n
ð5Þ
with e being the electronic charge and a the lattice constant. The first term is the electric potential energy of electrons of all sites and the second term is the electric potential energy of lattice ions. It is assumed that the field is uniform along the whole molecule chain and E = V/ [(N1)a]. This linear treatment is suitable for the case that the bias applied on the molecule is not too large. For the M/OF/M device, the current measured at the right electrode is contributed by both the spin-conserving scattering and spin-flip scattering. As the spin-orbit coupling and hyperfine interaction in an organic material are usually very weak, they will result in a large spin relaxation length [1,25]. In this work, we neglect the spin-flip scattering during the transport. Then the spin-dependent current can be calculated with Landauer-Büttiker formula,
Is ðVÞ ¼
e h
Z
þ1
1
T ss ðE; VÞ½f ðE ll Þ f ðE lr ÞdE
ð6Þ
where f(Ell(r)) = 1/{1+exp[(Ell(r))/kBT]} is the Fermi function and ll(r) = EF ± eV/2 is the chemical potential of the left (right) electrode with Fermi energy EF. The spin-conserving transmission coefficient Tss (E,V) can be obtained from Lattice Green Function through Fish-Lee relation [26] Tss (E,V) = Tr[Cl Gss (E,V) Cr Gþ ss (E,V)], where Gss ðE; VÞ ¼ EHs Hs 1P P with Rl(Rr) being the OF
elec
l
In order to investigate the spin-polarized transport properties of the M/OF/M sandwiched device, we define the spin polarization (SP) of the current as,
P¼
I " I# I " þ I#
ð7Þ
In the calculation, the parameters are chosen as follows [12,15]: For the organic ferromagnet, t0 = 2.5 eV, a = 4.1 eV/Å, K = 21.0 eV/Å2, J = Jf/t0 = 0.8. As the mean-field approximation is only valid in the case of weak e–e interactions, we choose U = 1.0 eV and V = U/3. In ground state, the radical spin is supposed to be hSznR i ¼ 12, hnR = 0. For the electrodes, el(r), tl = tr = 2.5 eV, EF = 1.55 eV. The interfacial coupling is taken as tIM = trM = 1.0 eV. 3. Results and discussion We firstly consider the ground state and spin excited state of an isolated poly-BIPO chain. In ground state, the radical spins form a ferromagnetic order. There exists an antiferromagnetic SDW of p-electrons in the main chain [11]. The SDW is depicted in Fig. 2, where the SDW order parameter is defined as sn ¼ ð1Þnþ1 ðnn" nn# Þ nns ¼ P0 2 l jZ l;n;s j is the electronic charge density of spin s at site n and Zl,n,s the eigenvector obtained by solving Schrödinger equation of Hamiltonian HsOF . A spin excited state means that there is one or several radical spins flipped. For example, if a radical spin at site n0 is excited from hn0 R ¼ 0 to hn0 R ¼ p, we obtain a single-spin excited state. In this case, the SDW of the molecule will be destroyed and a localized spin defect around site n0 appears in the main chain. As shown in Fig. 2, the defect has a width of about 5 7a, which depends on the electron-lattice coupling constant. In the meantime, the appearance of an excited state will result in the change of the electronic states and the energy levels from that of the ground state. It is found that LUMO (lowest unoccupied molecular orbital) of spin-up electrons will departure from the Fermi level and the case is opposite for spin-down ones. Both spin-up and spin-down electronic states near the Fermi level tend to be weakly localized. It is expected that these variations due to spin
r
self-energy operators due to the coupling with left (right) electrode. HsOF and Hselec correspond to the electron Hamiltonian with spin s in Eqs. (2) and (5). Cr(l) denotes the broadening matrix which is related to self energy with P P CrðlÞ ¼ i½ rðlÞ þrðlÞ . The calculation is performed as follows: we firstly solve the electronic eigenequation of an isolated poly-BIPO molecule. By minimizing the total energy, the lattice and the electronic structures of an isolated poly-BIPO molecule can be obtained self-consistently. Then we use Green’s function formula to calculate the transmission probability of spin s, and the spin-dependent current is obtained from Eq. (6).
811
Fig. 2. SDW in the ground state and a single-spin excited state.
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H. Jiang et al. / Organic Electronics 10 (2009) 809–814
excitations will seriously affect the conductance and current polarization of such a spin device. If two or more radical spins are excited, it is found that they will attract each other to form a coupled spin excitation, which will be lower in energy than separated ones. With the increasing of the number of excited radical spins, the system will lay in a high spin excited state in energy. We define the excited energy as,
DEðmÞ ¼ EðmÞ E0
ð8Þ
Here E(m) denotes the total energy of system when there are m radical spins being excited, and E0 the ground state. Fig. 3 shows the dependence of DE(m) on the number of the excited radical spins. It is found that spin excitation energy increases with the number of excited spins. We note that when m > m0 = 8, the excitation energy keeps nearly unchanged. The reason is that the ferromagnetic molecule is degenerate with hSznR i ¼ 1=2. When m > m0, the excited zone of the system forms a stable domain and excitation energy only exists in the domain walls. In the following, we investigate the electron transport properties of a poly-BIPO device in different spin excited states. Firstly, we consider the effect of spin excitations on total current through the device. The result is shown in Fig. 4. We see that, at a fixed bias voltage V = 0.5 V, the total current decreases apparently with the number of excited spins. This current suppression effect on the transport of high spin state has been found in single molecular magnets experimentally [6]. It is predicated that such an organic ferromagnetic device can realize a controllable charge transport. In present parameters, a current suppression ratio c = (IexIg)/Ig = 34% is obtained for only one single-spin excitation. Especially, if the molecule lay in a high-energy excited state, it is found that the current may disappear, which means that the device may have a function of a conductance switch. It has been found that the ferromagnetic molecule has spin-filter function in ground state. Now we consider the spin-polarized transport property through the device when the molecule is excited. A spin excitation may appear either at the interface of M/OF/M or in the interior of the molecule, which has a little difference of about 0.025 eV
Fig. 3. Dependence of spin excitation energy DE on the number of excited radical spins.
Fig. 4. Dependence of total current on the number of excited radical spins at V = 0.5 V.
in energy for a single-spin excitation. Here, we only consider the case of low spin excited states, i.e. there is a single-spin excitation or a double-spin excitation. The results are shown in Fig. 5 for the dependence of SP on the external bias. It is found that the SP has a little decrease whether the spin excitation is at the interface or in the interior. There is no much difference for the case of a double-spin and a single-spin excitation. To understand the effect of spin excitations on SP, we fix bias V = 0.5 V and calculate the dependence of SP on the number of exited radical spins. The result is shown in Fig. 6. It is found that, if the number of excited spins is less (m 6 3 in present case), the decreasing of SP is m not apparent. In this case, the device can serve as a spin function with a high spin polarization. However, if the number of the excited spins is close to half of the total radical spins, it is found that the SP will decrease to near zero, which means that the spin-up electrons and the spin-down
Fig. 5. Calculated spin polarization as the function of bias voltage. (a) Single-spin excitation. (b) Double-spin excitation.
H. Jiang et al. / Organic Electronics 10 (2009) 809–814
Fig. 6. Current spin polarization as a function of the number of excited radical spins at V = 0.5 V.
electrons have the same probability to tunnel through the molecule. Of course, such a spin excitation needs a high energy as indicated in Fig. 3. Therefore, an M/OF/M device is stable to serve a spin filter. To give the explanation of total current suppression in Fig. 4 and SP modulation effect in Fig. 6, we depict the spin-dependent transmission coefficient at a fixed bias V = 0.5 V with the number of excited radical spins from m = 0 to m = 5. The results are shown in Fig. 7. When there is no spin excitation in the system, it is found that only the transmission peak of spin-up LUMO lies in the conducting region [0.25 V, +0.25 V]. In this case, the current is contributed mainly by spin-up electrons and so the SP through the device is nearly 100%. With the exciting of the radical spins, the peak corresponding to the spin-up LUMO is moving away from conducting region gradually. As no (or not apparent) any other transmission enter the conducting region all the time, so the conductance decreases. At a high
Fig. 7. Spin-dependent transmission coefficient at V = 0.5 V in different spin excited states.
813
spin excited state, for example m = 5, the transmission becomes nearly zero in the conducting region, so there is no current in this case. From Fig. 7 we also note that the transmission strengths become weaker and weaker with the number of excited radical spins. It is because the electronic states near the Fermi level tend to be weakly localized with the appearance of excited spin defect. As stated above, spin excitations can affect the conductance and the current polarization of an M/OF/M device. However, the investigation also shows that a low-energy excitation could not destroy the SP and the device can serve a SP function. To give a further understanding, we consider the effect of temperature on the SP as thermal fluctuation may make the radical spins to deviate from the ferromagnetic ground state. It is supposed that the anSnR is randomly valued and gle hnR 2 [0,h0] of radical spin ~ obeys a uniform distribution. Here h0 means the strength of thermal perturbation, which is related to temperature through a simple Boltzman relation De kBT/2, where De denotes the energy difference per site freedom between states at a distribution {hnR} and the ground state of the system. We firstly calculate the order parameter hsn i of the molecule. It is found that the order parameter will decrease with temperature. In present work, the order parameter will decrease to nearly zero when temperature is higher than the critical value T = Tc 360 K, which is close to the experimental value [7]. It means that the magnetism of the molecule will vanish beyond the critical point. Then we investigate the behavior of SP in different temperature. The results are shown in Fig. 8, where the inset gives the dependence of SP on temperature at a fixed bias V = 0.5 V. From it we see that, although there is a decreasing of the SP with the temperature, the current through the device is still apparently spin polarized if temperature is not too high. In present parameters, the current can keep a high spin polarization when temperature is less than 280 K. However, when temperature approaches the critical point, the SP drops rapidly and becomes very small when temperature is beyond the critical point.
Fig. 8. Current spin polarization as a function of bias voltage in different temperatures. The inset is the dependence of current spin polarization on temperature at V = 0.5 V.
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H. Jiang et al. / Organic Electronics 10 (2009) 809–814
4. Summary
Acknowledgements
In summary, spin excited states in organic ferromagnet poly-BIPO are investigated to study the spin transport in an organic metal/poly-BIPO/metal device under a finite temperature. The picture of spin excited state is elucidated by calculating the SDW along the molecular chain and the spin excited energy. A localized defect of SDW appears when a spin excited state forms. The spin excited energy increases with the number of excited spins and keeps nearly unchanged when the number of excited spins is over a certain value. Then the spin-dependent transport through a metal/poly-BIPO/metal device is investigated. It is found that a suppression of the total current may take place when the magnetic molecule is in a spin excited state, which predicts a conductance switch function of the device. It is also found that a low spin excited state has little effect on SP and the device may still function as a spin filter. The intrinsic mechanism is explained by calculating the spin-dependent transmission in different spin excited states. The temperature effect on the spin-polarized transport is studied. The current can keep a high spin polarization when temperature is not too high. The result indicates that the device may serve as a stable spin filter. Finally, it should be mentioned about the validity of the e–e interactions adopted in present work. Usually Hubbard model is considered to be the simplest one to treat e–e interactions, although it is only valid in a narrow-band system. In organic semiconductors, Hubbard model is widely adopted, and the strength of Hubbard U is considered to be widely distributed from 1.0 to 11.0 eV [27]. A strong e–e interaction will seriously affect the electronic structure of the system and so the spin current polarization. For example, a spin-polarized ground state may be obtained in the case of large U. As the first step to understand the spin current polarization in an organic device, in present work, we only considered the case of a weak Hubbard interaction. The effect of e–e interactions was mainly reflected in the structure of the electronic energy levels of the system, which will affect the transmission probability of spin-up and spin-down electrons to some extent. In the further work, we will try to consider the effect of e–e interactions on the ferromagnetic ground state and the spin drag effect with a more effective technique beyond the mean-field approximation.
The authors would like to acknowledge the financial support from the National Basic Research Program of China (Grant No. 2009CB929204) and the National Natural Science Foundation of the People’s Republic of China (Grant Nos. 10874100, 10747143, and 10847151). References [1] V. Dediu, M. Murgia, F.C. Matacotta, C. Taliani, S. Barbanera, Solid State Commun. 122 (2002) 181. [2] V. Podzorov, E. Menard, A. Borissov, V. Kiryukhin, J.A. Rogers, M.E. Gershenson, Phys. Rev. Lett. 93 (2004) 086602. [3] M.P.S. Wenjie Liang, Marc Bockrath, Jeffrey R. Long, H. Park, Nature 417 (2002) 725. [4] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Molnar, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488. [5] Z.H. Xiong, D. Wu, Z. Valy Vardeny, J. Shi, Nature 427 (2004) 821. [6] H.B. Heersche, Z. De Groot, J.A. Folk, H.S.J. Van der Zant, Phys. Rev. Lett. 96 (2006) 206801. [7] Y.V. Korshak, T.V. Medvedeva, A.A. Ovchinnikov, V.N. Spector, Nature 326 (1987) 370. [8] Y. Cao, P. Wang, Z. Hu, S. Li, L. Zhang, J. Zhao, Synth. Met. 27 (1988) 625. [9] J.M. Manriquez, G.T. Yee, R.S. McLean, A.J. Epstein, J.S. Miller, Science 252 (1991) 1415. [10] N.P. Raju, T. Savrin, V.N. Prigodin, K.I. Pokhodnya, J.S. Miller, A.J. Epstein, J. Appl. Phys. 93 (2003) 6799. [11] Z. Fang, Z.L. Liu, K.L. Yao, Phys. Rev. B 49 (1994) 3916. [12] Z. Fang, Z.L. Liu, K.L. Yao, Z.G. Li, Phys. Rev. B 51 (1995) 1304. [13] S.J. Xie, J.Q. Zhao, J.H. Wei, S.G. Wang, L.M. Mei, S.H. Han, Europhys. Lett. 50 (2000) 635. [14] W.Z. Wang, Phys. Rev. B 73 (2006) 235325. [15] G.C. Hu, Y. Guo, J.H. Wei, S.J. Xie, Phys. Rev. B 75 (2007) 165321. [16] G.C. Hu, K.L. He, A. Saxena, S.J. Xie, J. Chem. Phys. 129 (2008) 234708. [17] K. Petukhov, S. Hill, N.E. Chakov, K.A. Abboud, G. Christou, Phys. Rev. B 70 (2004) 054426. [18] I. D’Amico, G. Vignale, Phys. Rev. B 62 (2000) 4853. [19] G. Vignale, Phys. Rev. B 71 (2005) 125103. [20] C.Q. Wu, X. Sun, Phys. Rev. Lett. 59 (1987) 831. [21] S.J. Xie, L.M. Mei, Phys. Rev. B 10 (1992) 6169. [22] M.B. Lepetit, G.M. Pastor, Phys. Rev. B 56 (1997) 4447. [23] Z.G. Yu, A. Saxena, A.R. Bishop, Phys. Rev. B 56 (1997) 3697. [24] Z. Shuai, J.L. Brédas, Phys. Rev. B 58 (1998) 15329. [25] S. Pramanik, C.G. Stefanita, S. Patibandla, S. Bandyopadhyay, K. Garre, N. Harth, M. Cahay, Nat. Nanotechnol. 2 (2007) 216. [26] Z.M. Zeng, J.F. Feng, Y. Wang, X.F. Han, W.S. Zhan, X.G. Zhang, Z. Zhang, Phys. Rev. Lett. 97 (2006) 106605. [27] W. Barford, R.J. Bursill, Richard W. Smith, Phys. Rev. B 66 (2002) 115205.
Contents lists available at ScienceDirect
Organic Electronics journal homepage: www.elsevier.com/locate/orgel
Effect of spin excited states on electron transport through an organic ferromagnetic device Hong Jiang a, Guichao Hu c, Ying Guo a, Shijie Xie a,b,* a b c
School of Physics, Shandong University, Jinan 250100, China State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China College of Physics and Electronics, Shandong Normal University, Jinan 250014, China
a r t i c l e
i n f o
Article history: Received 9 December 2008 Received in revised form 10 March 2009 Accepted 3 April 2009 Available online 17 April 2009
PACS: 73.63. b 75.47.m 85.75.d 73.61.Ph Keywords: Spin excited states Organic ferromagnet Organic spintronics
a b s t r a c t Spin excited states in an organic ferromagnet are proposed and investigated on the basis of an extended SSH + Heisenberg (SSH = Su-Schrieffer-Heeger) model. It is found that a spin excited state will form a local distortion of the spin density wave (SDW) of p-electrons while the lattice configuration of main chain has no obvious change. Then the spin-polarized transport properties through an organic ferromagnetic device are investigated with the Landauer-Büttiker formula and Green’s function method. It is obtained that the current will be spin polarized due to the existence of SDW in the ferromagnetic molecule. Both the total current and the spin-polarized current will be modulated when the SDW is excited. The total current through the device is suppressed by the spin excitation of side radicals, through which a conductance switch function may be realized. Compared with ground state, the spin polarization has no obvious change in a low spin excited state and the device still has spin-filter function. Finally, spin excitations induced by temperature is studied and we find that an organic ferromagnetic device can hold a high spin polarization when temperature is not too high. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Recently, two attractive fields have been growing in the minimization of electronic devices: one is molecular electronics aiming at replacing traditional semiconductors with organic materials, such as polymer [1], organic single crystal [2] or even single molecule etc. [3], which opens the way to cheap, low-weight, mechanically flexible, chemically interactive, and bottom-up fabricated electronics; the other is spintronics which manipulates electronic spins as the information carriers while consumes less power than manipulating electronic charge [4]. The combination of the two realms gives birth to a new fascinating field of organic spintronics. In particular, it attracts enormous * Corresponding author. Address: School of Physics, Shandong University, Jinan 250100, China. Tel.: +86 531 8837035 8321. E-mail address: [email protected] (S. Xie). 1566-1199/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.orgel.2009.04.001
interests with its two unique advantages: the very long spin relaxation time due to the weak spin-orbit and hyperfine interactions in an organic material and the easiness to form a good interface between an organic material and a metal electrode. So far, two kinds of organic spintronics devices have been designed: one is to use a nonmagnetic molecule sandwiched between two magnetic electrodes with or without applied magnetic field, such as spin valve and magnetic tunnel junction (MTJ) type devices [5]; the other is to adopt a magnetic molecule as the interlayer [6]. The latter case is to utilize the intrinsic properties of an organic magnet to realize spin functionality. As a combination of ferromagnet and organic materials, organic ferromagnets have been studied in past decades. By far, several organic magnets have been synthesized and tested experimentally, including poly-BIPO [7,8], V[TCNE]x [9,10] and single molecular magnet [3].
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Ovchinnikov et al. and Cao et al. have separately synthesized an organic ferromagnet called poly-BIPO, which can be obtained by replacing the H atom of polyacetylene alternately with a heterocycle containing an unpaired electron which we call a side radical, as schematically shown in the central part of Fig. 1. The main zigzag chain consists of carbon atoms with p itinerant electrons. There exists antiferromagnetic coupling between the spin of p-electron along the main chain and the residual spin of the side radical. From an extended SSH + Heisenberg (SSH=Su-Schrieffer-Heeger) model, one obtains that the system will have the lowest energy when the spins of side radical forms a ferromagnetic order [11–13]. Recently, several designs of organic ferromagnetic device have been proposed theoretically and some interesting phenomena such as spin filtering and spin-current rectification are predicted [14–16]. At present, most investigations on an organic polymer ferromagnet are limited to ground state properties of the system. In reality, external stimulations including photoexcitation, magnetic field or temperature etc may drive the magnetic molecule deviate from ground state. Several experiments have revealed the underlying function of spin excited states in electron transport through a magnetic molecule. For example, Petukhov et al. gave an evidence of spin excited states existing in a molecular magnet based on electron paramagnetic resonance (EPR) measurements [17]; Heersche et al. observed a complete current suppression and negative differential conductance in a single Mn12 molecular magnetic device, which is believed to have a relation with the spin excited states of the molecule [6]. For organic ferromagnet poly-BIPO, the spin excited state means that the ferromagnetic order of radical spins is destroyed owning to the spin flipping, which induces the magnetic molecule to a high-energy state. As the radical spins are correlated with the p-electrons in the main chain, it is expected that the spin excited state will affect the pelectron transport along the main chain. In this paper, we construct a metal/organic ferromagnet/metal (M/OF/M) device and then investigate the spin-polarized transport when the organic ferromagnetic molecule is in different spin excited states. The paper is organized as follows: The model and formula are described in Section 2. In Section 3, we give the numerical calculation and the results are analyzed. Finally, in Section 4, a summary is given. 2. Model and method As shown in Fig. 1, an organic ferromagnetic device M/ OF/M is modeled as a quasi-one-dimensional chain. The
central organic ferromagnetic molecule is connected with two noninteracting semi-infinite one-dimensional metallic chains. The complete Hamiltonian is written as,
H ¼ HOF þ Hl þ Hr þ Hcoup þ HE
ð1Þ
The first term is the Hamiltonian of organic ferromagnetic molecule [12,13],
HOF ¼
X
½t 0 aðunþ1 un Þðcþn;s cnþ1;s þ cþnþ1;s cn;s Þ
n;s
X K X ðunþ1 un Þ2 þ J f dn;o SnR Sn 2 n n X X þU cþn;" cn;" cþn;# cn;# þ V cþn;s cn;s cþnþ1;s0 cnþ1;s0
þ
ð2Þ
n;s;s0
n
where t0 is the hopping integral of p-electrons along the main chain with a uniform lattice. a stands for the electron-lattice coupling parameter and un the lattice displacement at site n. K is the elastic constant of the lattice atoms, and cþ n;s ðcn;s Þ denotes the creation (annihilation) operator of an electron at site n with spin s. The third term in Eq. (2) describes the correlation between SnR of radical R. spin ~ Sn of p-electron and residual spin ~ It is assumed that the side radicals are connected with the odd sites of the main chain, which is denoted by dn;o . Coupling constant Jf is assumed to be positive (antiferromagnetic coupling). We use mean-field approximation to treat the radical spin ~ SnR as hSznR i, where h i ¼ hGj jGi is the average with respect to the ground state jGi. Then the third term can be written as Jf P z þ þ n dn;o hSnR i cos hnR ðcn;" cn;" cn;# c n;# Þ and hnR the radical 2 spin orientation at site n (angle with -z axis). The last two terms describe the e–e (electron–electron) interactions between p-electrons under the extended Hubbard model. As spin coulomb drag effect may exist between spin-up and spin-down electrons and affect the spinpolarized current during transport [18,19], it is very necessary to take the consideration of the interactions among electrons. So far, may theoretical techniques can deal with e–e interactions, for example, mean-field approximation, perturbation, full coulomb interactions [20,21] and density matrix renormalization group (DMRG) calculation etc [22–24]. As the first step of our investigation, in this paper, we will just adopt the simple mean-field approximation to deal with the Hubbard term. Its validity will be discussed in the later summary. Hl(r) is the Hamiltonian of the left (right) electrode, which is a semi-infinite metal chain,
HlðrÞ ¼
X m;s
elðrÞ aþm;s am;s þ
X
t lðrÞ ðaþm;s amþ1;s þ h:c:Þ
m;s
Fig. 1. Simplified structure of a metal/poly-BIPO/metal nanojunction. The arrows indicate the spin orientation of radical spins.
ð3Þ
H. Jiang et al. / Organic Electronics 10 (2009) 809–814
where el(r) is on-site energy of a metal atom comparing to that of a carbon atom and tl(r) the transfer integral of adjacent sites. aþ m;s ðam;s Þ is the creation (annihilation) operator of an electron in electrodes. The coupling between the electrodes and the molecule is assumed to take place only at the nearest connecting atoms at the interfaces,
Hcoup ¼
X
t IM ðaþ0;s c1;s þ h:c:Þ þ
s
X
trM ðcþN;s aNþ1;s þ h:c:Þ
ð4Þ
s
tl(r)M is the interfacial coupling, which is simplified by neglecting the spin-dependent scattering at the interfaces. N is the total number of the sites in the organic ferromagnetic interlayer. The last term is the contribution of driving field E arising from the bias voltage V between the two electrodes,
X Nþ1 HE ¼ jejE n a þ un cþn;s cn;s 2 n;s X Nþ1 þ jejE n a þ un 2 n
ð5Þ
with e being the electronic charge and a the lattice constant. The first term is the electric potential energy of electrons of all sites and the second term is the electric potential energy of lattice ions. It is assumed that the field is uniform along the whole molecule chain and E = V/ [(N1)a]. This linear treatment is suitable for the case that the bias applied on the molecule is not too large. For the M/OF/M device, the current measured at the right electrode is contributed by both the spin-conserving scattering and spin-flip scattering. As the spin-orbit coupling and hyperfine interaction in an organic material are usually very weak, they will result in a large spin relaxation length [1,25]. In this work, we neglect the spin-flip scattering during the transport. Then the spin-dependent current can be calculated with Landauer-Büttiker formula,
Is ðVÞ ¼
e h
Z
þ1
1
T ss ðE; VÞ½f ðE ll Þ f ðE lr ÞdE
ð6Þ
where f(Ell(r)) = 1/{1+exp[(Ell(r))/kBT]} is the Fermi function and ll(r) = EF ± eV/2 is the chemical potential of the left (right) electrode with Fermi energy EF. The spin-conserving transmission coefficient Tss (E,V) can be obtained from Lattice Green Function through Fish-Lee relation [26] Tss (E,V) = Tr[Cl Gss (E,V) Cr Gþ ss (E,V)], where Gss ðE; VÞ ¼ EHs Hs 1P P with Rl(Rr) being the OF
elec
l
In order to investigate the spin-polarized transport properties of the M/OF/M sandwiched device, we define the spin polarization (SP) of the current as,
P¼
I " I# I " þ I#
ð7Þ
In the calculation, the parameters are chosen as follows [12,15]: For the organic ferromagnet, t0 = 2.5 eV, a = 4.1 eV/Å, K = 21.0 eV/Å2, J = Jf/t0 = 0.8. As the mean-field approximation is only valid in the case of weak e–e interactions, we choose U = 1.0 eV and V = U/3. In ground state, the radical spin is supposed to be hSznR i ¼ 12, hnR = 0. For the electrodes, el(r), tl = tr = 2.5 eV, EF = 1.55 eV. The interfacial coupling is taken as tIM = trM = 1.0 eV. 3. Results and discussion We firstly consider the ground state and spin excited state of an isolated poly-BIPO chain. In ground state, the radical spins form a ferromagnetic order. There exists an antiferromagnetic SDW of p-electrons in the main chain [11]. The SDW is depicted in Fig. 2, where the SDW order parameter is defined as sn ¼ ð1Þnþ1 ðnn" nn# Þ nns ¼ P0 2 l jZ l;n;s j is the electronic charge density of spin s at site n and Zl,n,s the eigenvector obtained by solving Schrödinger equation of Hamiltonian HsOF . A spin excited state means that there is one or several radical spins flipped. For example, if a radical spin at site n0 is excited from hn0 R ¼ 0 to hn0 R ¼ p, we obtain a single-spin excited state. In this case, the SDW of the molecule will be destroyed and a localized spin defect around site n0 appears in the main chain. As shown in Fig. 2, the defect has a width of about 5 7a, which depends on the electron-lattice coupling constant. In the meantime, the appearance of an excited state will result in the change of the electronic states and the energy levels from that of the ground state. It is found that LUMO (lowest unoccupied molecular orbital) of spin-up electrons will departure from the Fermi level and the case is opposite for spin-down ones. Both spin-up and spin-down electronic states near the Fermi level tend to be weakly localized. It is expected that these variations due to spin
r
self-energy operators due to the coupling with left (right) electrode. HsOF and Hselec correspond to the electron Hamiltonian with spin s in Eqs. (2) and (5). Cr(l) denotes the broadening matrix which is related to self energy with P P CrðlÞ ¼ i½ rðlÞ þrðlÞ . The calculation is performed as follows: we firstly solve the electronic eigenequation of an isolated poly-BIPO molecule. By minimizing the total energy, the lattice and the electronic structures of an isolated poly-BIPO molecule can be obtained self-consistently. Then we use Green’s function formula to calculate the transmission probability of spin s, and the spin-dependent current is obtained from Eq. (6).
811
Fig. 2. SDW in the ground state and a single-spin excited state.
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excitations will seriously affect the conductance and current polarization of such a spin device. If two or more radical spins are excited, it is found that they will attract each other to form a coupled spin excitation, which will be lower in energy than separated ones. With the increasing of the number of excited radical spins, the system will lay in a high spin excited state in energy. We define the excited energy as,
DEðmÞ ¼ EðmÞ E0
ð8Þ
Here E(m) denotes the total energy of system when there are m radical spins being excited, and E0 the ground state. Fig. 3 shows the dependence of DE(m) on the number of the excited radical spins. It is found that spin excitation energy increases with the number of excited spins. We note that when m > m0 = 8, the excitation energy keeps nearly unchanged. The reason is that the ferromagnetic molecule is degenerate with hSznR i ¼ 1=2. When m > m0, the excited zone of the system forms a stable domain and excitation energy only exists in the domain walls. In the following, we investigate the electron transport properties of a poly-BIPO device in different spin excited states. Firstly, we consider the effect of spin excitations on total current through the device. The result is shown in Fig. 4. We see that, at a fixed bias voltage V = 0.5 V, the total current decreases apparently with the number of excited spins. This current suppression effect on the transport of high spin state has been found in single molecular magnets experimentally [6]. It is predicated that such an organic ferromagnetic device can realize a controllable charge transport. In present parameters, a current suppression ratio c = (IexIg)/Ig = 34% is obtained for only one single-spin excitation. Especially, if the molecule lay in a high-energy excited state, it is found that the current may disappear, which means that the device may have a function of a conductance switch. It has been found that the ferromagnetic molecule has spin-filter function in ground state. Now we consider the spin-polarized transport property through the device when the molecule is excited. A spin excitation may appear either at the interface of M/OF/M or in the interior of the molecule, which has a little difference of about 0.025 eV
Fig. 3. Dependence of spin excitation energy DE on the number of excited radical spins.
Fig. 4. Dependence of total current on the number of excited radical spins at V = 0.5 V.
in energy for a single-spin excitation. Here, we only consider the case of low spin excited states, i.e. there is a single-spin excitation or a double-spin excitation. The results are shown in Fig. 5 for the dependence of SP on the external bias. It is found that the SP has a little decrease whether the spin excitation is at the interface or in the interior. There is no much difference for the case of a double-spin and a single-spin excitation. To understand the effect of spin excitations on SP, we fix bias V = 0.5 V and calculate the dependence of SP on the number of exited radical spins. The result is shown in Fig. 6. It is found that, if the number of excited spins is less (m 6 3 in present case), the decreasing of SP is m not apparent. In this case, the device can serve as a spin function with a high spin polarization. However, if the number of the excited spins is close to half of the total radical spins, it is found that the SP will decrease to near zero, which means that the spin-up electrons and the spin-down
Fig. 5. Calculated spin polarization as the function of bias voltage. (a) Single-spin excitation. (b) Double-spin excitation.
H. Jiang et al. / Organic Electronics 10 (2009) 809–814
Fig. 6. Current spin polarization as a function of the number of excited radical spins at V = 0.5 V.
electrons have the same probability to tunnel through the molecule. Of course, such a spin excitation needs a high energy as indicated in Fig. 3. Therefore, an M/OF/M device is stable to serve a spin filter. To give the explanation of total current suppression in Fig. 4 and SP modulation effect in Fig. 6, we depict the spin-dependent transmission coefficient at a fixed bias V = 0.5 V with the number of excited radical spins from m = 0 to m = 5. The results are shown in Fig. 7. When there is no spin excitation in the system, it is found that only the transmission peak of spin-up LUMO lies in the conducting region [0.25 V, +0.25 V]. In this case, the current is contributed mainly by spin-up electrons and so the SP through the device is nearly 100%. With the exciting of the radical spins, the peak corresponding to the spin-up LUMO is moving away from conducting region gradually. As no (or not apparent) any other transmission enter the conducting region all the time, so the conductance decreases. At a high
Fig. 7. Spin-dependent transmission coefficient at V = 0.5 V in different spin excited states.
813
spin excited state, for example m = 5, the transmission becomes nearly zero in the conducting region, so there is no current in this case. From Fig. 7 we also note that the transmission strengths become weaker and weaker with the number of excited radical spins. It is because the electronic states near the Fermi level tend to be weakly localized with the appearance of excited spin defect. As stated above, spin excitations can affect the conductance and the current polarization of an M/OF/M device. However, the investigation also shows that a low-energy excitation could not destroy the SP and the device can serve a SP function. To give a further understanding, we consider the effect of temperature on the SP as thermal fluctuation may make the radical spins to deviate from the ferromagnetic ground state. It is supposed that the anSnR is randomly valued and gle hnR 2 [0,h0] of radical spin ~ obeys a uniform distribution. Here h0 means the strength of thermal perturbation, which is related to temperature through a simple Boltzman relation De kBT/2, where De denotes the energy difference per site freedom between states at a distribution {hnR} and the ground state of the system. We firstly calculate the order parameter hsn i of the molecule. It is found that the order parameter will decrease with temperature. In present work, the order parameter will decrease to nearly zero when temperature is higher than the critical value T = Tc 360 K, which is close to the experimental value [7]. It means that the magnetism of the molecule will vanish beyond the critical point. Then we investigate the behavior of SP in different temperature. The results are shown in Fig. 8, where the inset gives the dependence of SP on temperature at a fixed bias V = 0.5 V. From it we see that, although there is a decreasing of the SP with the temperature, the current through the device is still apparently spin polarized if temperature is not too high. In present parameters, the current can keep a high spin polarization when temperature is less than 280 K. However, when temperature approaches the critical point, the SP drops rapidly and becomes very small when temperature is beyond the critical point.
Fig. 8. Current spin polarization as a function of bias voltage in different temperatures. The inset is the dependence of current spin polarization on temperature at V = 0.5 V.
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4. Summary
Acknowledgements
In summary, spin excited states in organic ferromagnet poly-BIPO are investigated to study the spin transport in an organic metal/poly-BIPO/metal device under a finite temperature. The picture of spin excited state is elucidated by calculating the SDW along the molecular chain and the spin excited energy. A localized defect of SDW appears when a spin excited state forms. The spin excited energy increases with the number of excited spins and keeps nearly unchanged when the number of excited spins is over a certain value. Then the spin-dependent transport through a metal/poly-BIPO/metal device is investigated. It is found that a suppression of the total current may take place when the magnetic molecule is in a spin excited state, which predicts a conductance switch function of the device. It is also found that a low spin excited state has little effect on SP and the device may still function as a spin filter. The intrinsic mechanism is explained by calculating the spin-dependent transmission in different spin excited states. The temperature effect on the spin-polarized transport is studied. The current can keep a high spin polarization when temperature is not too high. The result indicates that the device may serve as a stable spin filter. Finally, it should be mentioned about the validity of the e–e interactions adopted in present work. Usually Hubbard model is considered to be the simplest one to treat e–e interactions, although it is only valid in a narrow-band system. In organic semiconductors, Hubbard model is widely adopted, and the strength of Hubbard U is considered to be widely distributed from 1.0 to 11.0 eV [27]. A strong e–e interaction will seriously affect the electronic structure of the system and so the spin current polarization. For example, a spin-polarized ground state may be obtained in the case of large U. As the first step to understand the spin current polarization in an organic device, in present work, we only considered the case of a weak Hubbard interaction. The effect of e–e interactions was mainly reflected in the structure of the electronic energy levels of the system, which will affect the transmission probability of spin-up and spin-down electrons to some extent. In the further work, we will try to consider the effect of e–e interactions on the ferromagnetic ground state and the spin drag effect with a more effective technique beyond the mean-field approximation.
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