micromachines

Review Spin Injection and Transport in Organic Materials

Qipeng Tian 1 and Shijie Xie 2,*

1 School of Physics, Shandong University, Jinan 250100, China 2 School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China * Correspondence: [email protected]; Tel.: +86-531-8837-7031



Received: 12 July 2019; Accepted: 4 September 2019; Published: 10 September 2019


Abstract: This review introduces some important spin phenomena of organic molecules and solids and their devices: Organic spin injection and transport, organic spin valves, organic magnetic field effects, organic excited ferromagnetism, organic spin currents, etc. We summarize the experimental and theoretical progress of organic spintronics in recent years and give prospects.

Keywords: organic spin valves; organic magnetic field effects; organic excited ferromagnetism; organic spin currents; organic spintronics

1. Introduction In the past three decades, there have been two historic breakthroughs in the fields of spintronics: In 1988, Fert and Grunberg independently discovered the giant magnetoresistance (MR) effect in Fe/Cr multilayer films [1,2]; in 1996, Slonczewski and Berger predicted that spin torque transfer [3,4], and will soon be experimentally confirmed [5,6]. In the same year, Wolf first proposed “Spintronics” (namely spin electronics) [7], which included not only the storage of spins, but also the transport of spins. After years of development, spintronics has become an independent emerging discipline, some basic concepts and theories have been established. Spin relaxation time τs is a commonly used microscopic physical quantity to describe spin 1 = 1 + 1 polarization transport and can be given by τs− τ− τ− , where τss0 represents the average time ↑↓ ↓↑ from spin s to s0. It sets the time scale for the loss of spin polarization, and then sets the spatial scale, namely the spin relaxation length ls. The spin relaxation length is defined as the distance of the electron travels in time τss0 . The spin relaxation time of organic semiconductor at room temperature was within 7 5 10 the range of 10− –10− s, which is much larger than 10− s in metals. Compared to conventional inorganic materials, organic materials are easier to process and synthesize. The most important is the “soft” structure that allows it to form good interfacial contact with the electrodes. Organic semiconductors have fairly weak spin-orbital coupling and hyperfine interaction, so the spin diffusion length of electrons can be very long. These properties make organic semiconductors one of the preferred materials for spintronics, which is considered an attractive topic in spintronics. Organic spintronics consists of organic functional materials that intersect with chemistry and spintronics that intersect with physics. It not only broadens our understanding of the organic world, but also has important significance in the applications of spintronics and technology. In 2002, the Dediu group reported on spin injection and transport in organic materials for the first time [8]. In 2004, Xiong et al. prepared a Co/tris-8-hydroxyquinoline aluminum (Alq3)/La1 xSrxMnO3 − (LSMO) device, which measured 40% MR at low temperature and realized the organic spin valve effect [9]. In the same year, Francis et al. applied a small external magnetic field ( 100 mT) to organic ≤ devices without any magnetic elements, indium-tin-oxide (ITO)/poly(3,4-ethylenedioxythiophene) (PEDOT)/polyfluorene/Ca and ITO/PEDOT/sexithienyl (T6)/Ca/Al, they were surprised to find that more than 10% of magnetoresistors could be observed at room temperature and the MR is related

Micromachines 2019, 10, 596; doi:10.3390/mi10090596 www.mdpi.com/journal/micromachines Micromachines 2019, 10, 596 2 of 30 to the thickness of organic layer and external bias [10,11]. Further studies show that not only organic magnetoresistance (OMAR), but also strong magnetic response in photoluminescence (PL), electroluminescence (EL) and the photocurrent (PC) in organic devices were found. Since this phenomenon is difficult to observe in inorganic devices, the organic magnetic field effect has been widely concerned by the fields of physics, chemistry, materials and electronics. Since 2009, people have also revealed the organic multi-iron [12,13], excited ferromagnetic [14–16] and spin current [17,18], showing the infinity of organic materials in terms of functionality. Organic semiconductors have special carriers and a spin-charge relationship. As shown in Table1, there are solitons, polarons, bipolarons, excitons, biexcitons and trions in organic semiconductors. All these carriers are spatial localized due to the strong electron–phonon coupling, which is different from the extended electrons or holes in normal semiconductors.

Table 1. Charge and spin relationship of organic carriers.

Carrier Charge (e) Spin (h¯) Degeneracy Neutral soliton 0 1/2 Degenerate Charged soliton 1 0 Degenerate ± Polaron 1 1/2 Degenerate, Non-degenerate ± Bipolaron 2 0 Non-degenerate ± Singlet exciton 0 0 Non-degenerate Triplet exciton 0 1 Non-degenerate Biexciton 0 0 Non-degenerate Trion 1 1/2 Non-degenerate ±

Organic materials have two special spin related interactions. One is the hyperfine interaction. The spin or magnetic moment of the hydrogen nucleus interacts with the spin of the π-electron [19]: X → H f = an→s n I n, (1) n ·

→ where an represents the hyperfine interaction intensity at lattice points (molecules), and In represents the nuclear spin. Another is the spin-orbit interaction or spin-orbit coupling. From Dirac theory we have the following form [20],

1 1 dV → 1 → Hso = (→s l ) = ξ(r)(→s l ). (2) 4m2c2 r dr · 2 ·

Obviously, the spin-orbit coupling only appears for angular momentum l , 0 of the electron space state. For electrons moving around the nucleus, V = Ze2/r, r Z, one gives ξ Z4, which means ∝ ∝ that heavy atoms have greater spin-orbit coupling strength. In general, organic materials are mainly composed of elements with a lower atomic number, and therefore the spin-orbit coupling of organic materials is generally considered to be weak. Considering the spin-related interactions, the electron spin in a material is generally no longer a good quantum number, and the electron state will be a spin mixed state. In 2010, Tarafder et al. calculated the spin polarization of charged Alq3 with DFT. It is found that a charged Alq3 molecule has a spontaneous magnetization proportionally to the charge quantity [21]. Later study on thiophene ogalimars found a complex relationship between spontaneous magnetization and charge, as shown in Figure1. Magnetization is not only related to the charge quantity, but also to the molecular size, electron–electron interaction, spin-orbit coupling and, especially, the localization of the electronic state. If the doped charges are more than one electronic charge unit, the molecular magnetic moment will decrease. In particular, when a molecule contains two electrons, it is found that the magnetic moment becomes zero [22,23]. Micromachines 2019, 10, x 3 of 31

MicromachinesIn organic2019 semiconductors,, 10, 596 a charge state can be considered as a combination of polaron3 of 30 and bipolaron eigenstate [24],

In organic semiconductors, a chargeψφ=++ stateaaa can be φ considered φ, as a combination of polaron and p↑↑pppbpbp ↓↓ (3) bipolaron eigenstate [24], where φ , φ and φ are the eigenstatesψ = ap φ pof+ theap spinφp + upabp polaron,φbp, spin down polaron and the (3) spin p↑ p↓ bp ↑ ↑ ↓ ↓ where φp , φp and φbp are the eigenstates of the spin up polaron, spin down polaron and the spin zero zero bipolaron.↑ Then↓ the magnetic moment of the charge state is: bipolaron. Then the magnetic moment of the charge state is: 22 22 ma=−() a() a + a . pp↑↓2 2 2 pp ↑↓2 (4) m = ( ap ap )/( ap + ap ). (4) | ↑ | − | ↓ | | ↑ | | ↓ | OrganicOrganic semiconductors semiconductors are are composed composed of of small small mo moleculeslecules or polymers. InIn a a molecular molecular crystal crystal or a polymeror a polymer chain, chain, carrier carrier transport transport can can be beregarded regarded as as band transporttransport to to some some extent. extent. However, However, transporttransport in disordered in disordered organic organic materials materials is is mainly mainly realizedrealized by by hopping. hopping. The The appearance appearance of polarons of polarons and bipolaronsand bipolarons complicates complicates the the transport transport process process in organicorganic materials. materials. These These characteristics characteristics make make the the studystudy of organic of organic spintronics spintronics challenging challenging but but attractive.

FigureFigure 1. Magnetic 1. Magnetic moment moment varies varies with with the the quantity ofof chargescharges injected injected in differentin different thiophene thiophene aggregationaggregation degrees. degrees. TheThe inset inset shows shows the the unit unit structur structuree ofof the the thiophene thiophene molecule. molecule. By HanBy Han et al. et [23 al.] [23] withwith the permission the permission of ofOrganic Organic Electronics. Electronics. 2. Organic Spin Valve 2. Organic Spin Valve 2.1. Organic Spin Valve 2.1. OrganicIn 2002, Spin Dediu Valve first reported spin injection and transport in organic semiconductors [8]. They used semi-metallicIn 2002, Dediu colossal first reported magnetoresistance spin injection (CMR) and material transport LSMO in asorganic a polarized semiconductors electron injector, [8]. They and organic layer used small molecule T to prepare organic device LSMO/T /LSMO. The device used semi-metallic colossal magnetoresistance6 (CMR) material LSMO as a polarized6 electron injector, structure is shown in Figure2. The direction of magnetization of the electrode is disordered before a and organic layer used small molecule T6 to prepare organic device LSMO/T6/LSMO. The device magnetic field is applied, and their magnetization directions become parallel after the magnetic field structureis applied. is shown The negativein Figure MR 2. The in experiment direction (shownof magnetization in Figure3) of indicated the electrode that the is device disordered resistance before a magneticdecreases field after is applied, the magnetic and their field magnetization is applied. With directions the increase become of the thicknessparallel after of the the organic magnetic layer, field is applied.the MR The decays negative to zero, MR from in which experiment they estimated (shown that in the Figure spin relaxation 3) indicated length that in thethe organic device layer resistance is decreasesabout 100–200after the nm. magnetic field is applied. With the increase of the thickness of the organic layer, the MR decays to zero, from which they estimated that the spin relaxation length in the organic layer is about 100–200 nm.

Micromachines 2019, 10, 596 4 of 30 Micromachines 2019, 10, x 4 of 31 Micromachines 2019, 10, x 4 of 31

FigureFigureFigure 2. 2. 2. Structure StructureStructure diagram diagram diagram of of of the the the LSMO/T6/LSMO LSMO/T6/LSMO LSMO/T6/LSMO sandwich sandwich sandwich device. device. device.

Figure 3. Relation between magnetoresistance (MR) and T6 thickness. FigureFigure 3. 3. Relation Relation between between magnetoresista magnetoresistancence (MR) (MR) and and T6 T6 thickness. thickness. In 2004, Xiong et al. prepared LSMO/Alq /Co devices using LSMO and Co with different coercivity In 2004, Xiong et al. prepared LSMO/Alq3 3/Co devices using LSMO and Co with different In 2004, Xiong et al. prepared LSMO/Alq3/Co devices using LSMO and Co with different as electrodes [9]. MR value measured at low temperatures is up to 40%, indicating that the device coercivitycoercivity as as electrodes electrodes [9]. [9]. MR MR va valuelue measured measured at at low low temperatures temperatures is is up up to to 40%, 40%, indicating indicating that that the the has a significant spin valve effect. Majumdar et al. further studied the effects of spin relaxation [25]. devicedevice has has a a significant significant spin spin valve valve effect. effect. Majumdar Majumdar et et al. al. further further studied studied the the effects effects of of spin spin relaxation relaxation It has been found that polymer devices at room temperature still have 1% magnetoresistance, which is [25].[25]. It It has has been been found found that that polymer polymer devices devices at at r roomoom temperature temperature still still have have 1% 1% magnetoresistance, magnetoresistance, hardly observed in small molecule devices. For the device Fe/Alq /Co, the magnetoresistance is 5% at which is hardly observed in small molecule devices. For the device3 Fe/Alq3/Co, the magnetoresistance which is hardly observed in small molecule devices. For the device Fe/Alq3/Co, the magnetoresistance a low temperature of 11K, and when the temperature is raised to 90K, the magnetoresistance is almost isis 5% 5% at at a a low low temperature temperature of of 11K, 11K, and and when when the the te temperaturemperature is is raised raised to to 90K, 90K, the the magnetoresistance magnetoresistance reduced to zero, indicating that the spin relaxation length in the polymer is more long [26]. Pramanik isis almost almost reduced reduced to to zero, zero, indicating indicating that that the the spin spin relaxation relaxation length length in in the the polymer polymer is is more more long long [26]. [26]. prepared Ni/Alq /Co nanowire devices (length 50 nm, intermediate layer thickness 30 nm), they also Pramanik prepared3 Ni/Alq3/Co nanowire devices (length 50 nm, intermediate layer thickness 30 nm), Pramanik prepared Ni/Alq3/Co nanowire devices (length 50 nm, intermediate layer thickness 30 nm), found that after the temperature rise, the device magnetoresistance becomes small [27]. It is worth theythey also also found found that that after after the the temperature temperature rise, rise, the the device device magnetoresistance magnetoresistance becomes becomes small small [27]. [27]. It It is is mentioning that their experiments indirectly measured that the spin relaxation time of the device is worthworth mentioningmentioning thatthat theirtheir experimentsexperiments indirectlyindirectly measuredmeasured thatthat thethe spinspin relaxationrelaxation timetime ofof thethe much longer than that of inorganic materials. To further increase the OMAR, Dediu et al. improved the devicedevice is is much much longer longer than than that that of of inorganic inorganic materials. materials. To To further further increase increase the the OMAR, OMAR, Dediu Dediu et et al. al. improvedexperiment. the They experiment. prepared They LSMO prepared/Alq3/Al LSMO/Alq2O3/Co devices,3/Al2O which3/Co devices, the insulating which Althe2 Oinsulating3 layer prevents Al2O3 improved the experiment. They prepared LSMO/Alq3/Al2O3/Co devices, which the insulating Al2O3 layerinterdi preventsffusion interdiffusion and reaction between and reacti theon electrodesbetween the and electrodes the Alq3 andlayer the so Alq that3 layer the deviceso that hasthe device a clear layer prevents interdiffusion and reaction between the electrodes and the Alq3 layer so that the device interface. Then an apparent room temperature MR is observed [28]. hashas a a clear clear interface. interface. Then Then an an apparent apparent room room temperature temperature MR MR is is observed observed [28]. [28]. As a special organic material, graphene has high carrier mobility, adjustable carrier concentration, AsAs aa specialspecial organicorganic material,material, graphenegraphene hashas highhigh carriercarrier mobility,mobility, adjustableadjustable carriercarrier weak spin-orbital coupling and spin diffusion length over micron at room temperature. Therefore, it is concentration,concentration, weakweak spin-orbitalspin-orbital couplingcoupling andand spinspin diffusiondiffusion lengthlength overover micronmicron atat roomroom one of the alternative materials for long distance spin transport. MR up to 10% and spin diffusion temperature.temperature. Therefore, Therefore, it it is is one one of of the the alternative alternative materials materials for for long long distance distance spin spin transport. transport. MR MR up up length over 100 µm in graphene is observed.μ In 2006, Hill et al. first used a FeNi alloy as a ferromagnetic toto 10% 10% and and spin spin diffusion diffusion length length over over 100 100 μ mm in in graphene graphene is is observed. observed. In In 2006, 2006, Hill Hill et et al. al. first first used used a a electrode to prepare a graphene spin valve [29]. Subsequently, multilayer graphene spin valves with FeNiFeNi alloyalloy asas aa ferromagneticferromagnetic electrodeelectrode toto prepprepareare aa graphenegraphene spinspin valvevalve [29].[29]. Subsequently,Subsequently, multilayerCo and Fe asgraphene electrodes spin and valves graphene with spinCo and valves Fe withas electrodes Al2O3 as and tunneling graphene layers spin were valves also successfullywith Al2O3 multilayer graphene spin valves with Co and Fe as electrodes and graphene spin valves with Al2O3 prepared. Using the magnetic properties of graphene nanoribbon, some novel graphene spin devices asas tunnelingtunneling layerslayers werewere alsoalso successfullysuccessfully prepared.prepared. UsingUsing thethe magneticmagnetic propertiesproperties ofof graphenegraphene have also been proposed. For example, applying a transverse electric field to the zigzag graphene nanoribbon,nanoribbon, somesome novelnovel graphenegraphene spinspin devices devices havehave also also beenbeen proposed.proposed. ForFor example,example, applyingapplying a a nanoribbons (ZGNR) with the anti-ferromagnetic ground state to make the band gap of one spin larger transversetransverse electricelectric fieldfield toto thethe zigzagzigzag graphenegraphene nanoribbonsnanoribbons (ZGNR)(ZGNR) withwith thethe anti-ferromagneticanti-ferromagnetic and the opposite spin band gap smaller, so that ZGNR presents semi-metallic properties to be the spin groundground state state to to make make the the band band gap gap of of one one spin spin larger larger and and the the opposite opposite spin spin ba bandnd gap gap smaller, smaller, so so that that injector or detector. ZGNRZGNR presents presents semi-metallic semi-metallic properties properties to to be be the the spin spin injector injector or or detector. detector. Carbon nanotube is also a special organic material. In 1999, Tsukagoshi et al. prepared the first CarbonCarbon nanotube nanotube is is also also a a special special organic organic material material. .In In 1999, 1999, Tsukagoshi Tsukagoshi et et al. al. prepared prepared the the first first multi-walled carbon nanotube spin device and 9% MR was observed at low temperature 4.2K [30]. multi-walledmulti-walled carbon carbon nanotube nanotube spin spin device device and and 9% 9% MR MR was was observed observed at at low low temperature temperature 4.2K 4.2K [30]. [30]. SelectingSelecting a a higher higher spin-polarized spin-polarized magnetic magnetic electr electrodeode can can further further increase increase the the MR. MR. For For example, example, the the MR of carbon tube devices prepared with La0.7Sr0.3Mn3 can be as high as 61%. MR of carbon tube devices prepared with La0.7Sr0.3Mn3 can be as high as 61%.

Micromachines 2019, 10, x 5 of 31 Micromachines 2019, 10, 596 5 of 30 Graphene and carbon tubes are two very special organic materials, and their spintronic properties have been introduced in many special literatures. In this chapter, we mainly focused on Selecting a higher spin-polarized magnetic electrode can further increase the MR. For example, the MR small molecules or polymers. of carbon tube devices prepared with La0.7Sr0.3Mn3 can be as high as 61%. Graphene and carbon tubes are two very special organic materials, and their spintronic properties 2.2. Tunneling Theory of OMAR have been introduced in many special literatures. In this chapter, we mainly focused on small molecules or polymers.Organic spin valve can be simply understood from the tunneling theory. Assuming that spin is conserved during electron tunneling, the probability of tunneling is proportional to the product of 2.2.the state Tunneling densities Theory at ofthe OMAR Fermi surface DF of the electrodes at both ends. Since the conductance is proportionalOrganic to spin the valve probability can be simplyof tunneling, understood the conductance from the tunneling of the magnetization theory. Assuming direction that parallel spin is conservedand antiparallel during between electron the tunneling, left and right the probabilitymagnetic electrodes of tunneling are respectively is proportional expressed to the productas follows, of ↑↑ ↓↓ the state densities at the Fermi surface D∝+F of the electrodes at both ends. Since the conductance is GDDP FLFR() () DD FLFR () (), (5) proportional to the probability of tunneling, the conductance of the magnetization direction parallel and antiparallel between the left and right magnetic electrodes are respectively expressed as follows, ∝+↑↓ ↓↑ GDDDDAP FLFR() () FLFR () (), (6)

GP D↑ D↑ + D↓ D↓ , (5) where the superscripts ↑ and ↓ represent∝ F(L) F (spinR) polarizationF(L) F(R) up and down respectively, the subscripts L and R represent Left and right magnetic electrode respectively. G D↑ D↓ + D↓ D↑ , (6) Since the resistance RG∝ 1 , theAP tunneling∝ F(L) FMR(R) can Fbe(L) calculatedF(R) as follows [9], where the superscripts and represent spin polarization− up and down respectively, the subscripts L ↑ ↓ RRAP P 2 PP12 and R represent Left and right magneticMR electrode== respectively. , (7) RPP1− Since the resistance R 1/G, the tunneling MRp can be calculated12 as follows [9], ∝ where R , R are the device resistance whenRAP theR magnetizP 2P1ationP2 direction of the electrodes at both PAP MR = − = , (7) Rp 1 P1P2 ends is parallel and antiparallel, respectively, and P1 and− P2 are the polarization of the electrodes. In an actual device LSMO/Alq3/Co, Co atoms may penetrate into the organic layer to reduce the effective where RP, RAP are the device resistance when the magnetization direction of the electrodes at both thickness of the organic layer, which can be corrected to the polarization reduction at the Co-end ends is parallel and antiparallel, respectively, and P1 and P2 are the polarization of the electrodes. In an −−()dd /λ ′ = 0 s actualinterface, device PPe22 LSMO/Alq,3 /whereCo, Co datoms is the maythickness penetrate of the into organic the organic layer, layer d0 the to thickness reduce the of e fftheective Co thickness of the organicλ layer, which can be corrected to the polarization reduction at the Co-end permeable layer and s the spin diffusion length of the organic layer. Then the MR can be obtained interface, P = P e (d d0)/λs , where d is the thickness of the organic layer, d the thickness of the Co as follows [9],02 2 − − 0 permeable layer and λs the spin diffusion length of the organic layer. Then the MR can be obtained as −−()dd / λ follows [9], RR− 2 PPe0 s TMR ==AP P 12 (−−d()ddd0)/λ λs. (8) RAP RRPPeP 21P−1P2e− − 0 s TMR = − p = 12 . (8) Rp 1 P P e (d d0)/λs − 1 2 − − PP = 0.32 dnm= 87 λ = 45nm Take P112P2 = 0.32, , d0 = 87 nm andand λss = 45 nm, ,theoretical theoretical curves curves are are in in good good agreement withwith experimental data [[9],9], as shown in Figure4 4..

Figure 4. MR changes with the thickness of the organic layer by Xiong et al. [[9]9] with the permission of Nature.

Micromachines 2019, 10, 596 6 of 30

2.3. Organic Spin Injection and Transport Theory If we considered the transport process within the organic layer, a simple “two-fluid” model could be applied [31]. It is suitable that the spin scattering length is much smaller than the electron scattering length. In organic devices, the injected electrons will form polarons and bipolarons. Since a bipolaron has no spin, we had to generalize the “two-fluid” model to a “three-fluid” one: Spin-up polarons, spin-down polaron and spinless bipolaron. The current spin polarization is usually described as α = (j j )/(j + j ) with the current ↑ − ↓ ↑ ↓ density js with spin s. However, in an organic situation it should be modified as α = (jp jp )/(jp + ↑ − ↓ ↑ jp + jbp), where jp , jp and jbp are the current density contributed by spin up polarons, spin down ↓ ↑ ↓ polarons and spinless bipolarons. From the spin diffusion equation and Ohm’s law, the current spin polarization at the interface can be obtained as follows [32,33]:

  1 σFM 1 1 2 1+ 4 G G (1 β ) σ λFM β0 · λFM − − 0 =   ↓ ↑  α0 γβ0 σ λ λ γ , (9) FM · p · γ σ FM +1 β2+ σ 1 + 1 (1 β2) σFM · λp − 0 4 · λp G G − 0 ↓ ↑ where the polaron ratio is γ = np/(np + nbp). Obviously, when γ = 0, current spin polarization will also be zero as the carriers are all bipolarons without spin. The maximum current polarization occurs at γ = 1, where the carriers are all polarons with spin. In addition, we found that the presence of polarons result in a significant current spin polarization. For example, when the polaron ratio was only 20%, the current spin polarization value was 90% of that when the carriers were all polarons. Therefore, polarons are the effective spin carriers of the spin polarized current. Even if a small number of polarons are present, large current spin polarization can be obtained in organic semiconductors. From Equation (9) we see that the spin polarization is proportional to σ/σFM, so a large spin polarization or injection can be obtained when the conductance of the interlayer matches that of the contact, i.e., σ = σFM. In the actual transport process, polarons and bipolarons do not exist independently. They may transform each other, which can be described by the following set of equations [34].

dn ( )/dt = kn n + bN, (10) ↑ ↓ − ↑ ↓ dN/dt = kn n bN, (11) ↑ ↓ − where n ( ) is the concentration of the spin-up (spin-down) polarons, and N is the concentration of the ↑ ↓ bipolarons. The spin polarization is defined as,

P = (n n )/(n + n ). (12) ↑ − ↓ ↑ ↓ Due to the existence of bipolarons in organic semiconductors, this definition has different meanings compared to that in traditional inorganic semiconductors as bipolarons do not contribute to spin polarization. However, its existence will affect the performance of organic spin devices. Based on Landau-Büttiker theory and quantum dynamics, we could give a microscopic understanding of organic spin injection and transport. In 2002, Zwolak et al. explored the spin-related transport phenomena of ferromagnetic/DNA/ferromagnetic sandwich structures [35]. After calculating the MR of the device by the Green’s function method, it was found that, if Fe and Ni were used as the ferromagnetic layer of the device, the MR effects of 16% and 26% were obtained at room temperature, respectively. Based on the NEGF-DFT theory, the MR of the Ni/octanethiol/Ni tunnel-junction was up to 33%, while that of Ni-octane-Ni was up to more than 100%. Microscopic calculations are mainly for a molecular device and only reflect the nature of macroscopic organic devices to a certain extent. It is difficult to consider the strong electron-lattice interaction effect in organic molecules in the NEGF-DFT Micromachines 2019, 10, 596 7 of 30 theoretical framework. One possible improvement is to combine DFT phonon calculations with appropriate models [36]. Adjusting the spin polarization of the interface can significantly improve the MR. Assuming that the coupling between the ferromagnetic electrode and the organic molecule (or the integral of the interface transition) is related to the spin tσ, the total conductance in the parallel state is GP t t + t t , ∝ ↑ ↑ ↓ ↓ while the total conductance in the anti-parallel is GAP t t + t t . Therefore, MR can be expressed as: ∝ ↑ ↓ ↓ ↑ 2 GP G (1 γ) MR = − AP = − , (13) GAP 2γ where γ = t /t . Although the model is simple, it gives an inspiration on how to obtain high MR. ↓ ↑ Due to the spin dependent scattering, spin of a carrier will no longer be conserved during transport. The reason can be attributed to spin-orbit coupling, hyperfine interactions, electron–electron interactions and other spin-related interactions. The hyperfine interactions in organic molecules are mainly derived from hydrogen nuclear spins. Nguyen et al. replaced the hydrogen atom in poly (2,5-di-octyloxy) p-phenylene ethylene (H-DOO-PPV) with a deuterium atom (D-DOO-PPV), and the experimental results showed that the MR of the spin valve based on them differs by more than one order of magnitude [32]. It indicates that the hyperfine interaction plays an important role in the spin relaxation of organic materials. However, the theoretical calculation of spin relaxation in Alq3 based on the spin-orbital interaction shows that the spin diffusion behavior in Alq3 is completely consistent with that measured by the LE-µSR technique [37], which seems to indicate that the spin-orbital coupling is the main reason for the spin relaxation in organic materials. Therefore, the role of hyperfine interactions and spin-orbit coupling in organic materials remains a problem that needs further study. In 2003, we studied the ground state properties of CMR/organic semiconductor systems [38]. In the calculation, polyacetylene or polythiophene is taken as the organic layer, CMR perovskite material LSMO is taken as the spin injection layer. The tight-binding Hamiltonian is used to describe the interface coupling and electronic transition process of the system, especially as the model contains strong electron–phonon interactions inherent in the organic layer. By adjusting the relative chemical potential of the two materials, electrons can be transferred from the CMR to the organic layer. Micro dynamic studies show that the injected charge forms a wave packet in the organic layer, and each wave packet can contain any value of charge 0–2e and carry a certain spin. Due to the spin dependent interaction, the carrier spin is not in the eigenstate [39]. Figure5 shows the dynamic behavior of the injected charge. After 200 fs of injection, the wave packet has formed and moves in the organic layer driven by the external electric field. The spin polarization exists in the organic layer. However, the spin polarization mainly appears near the interface, and attenuates until it disappears when it penetrates into the organic layer.Micromachines The figure 2019, 10 also, x shows that the injected charge still has obvious spin polarization after 10008 of fs. 31

Figure 5.5. TheThe distributiondistribution of of spin spin up, up, spin spin down down and and net ne spint spin density density in organic in organic layer layer at diff aterent different times, wheretimes, thewhere bias the voltage bias voltage was V = was0.85 V eV = 0.85 and theeV and electric the fieldelectric was fieldE = 0.5was mV E /=nm. 0.5 BymV/nm. Fu et al.By [39Fu] et with al. the[39] permission with the permission of Physical of Review Physical B. Review B.

Applying a voltage in the vertical transport direction can adjust the effective Rashba spin-orbit coupling strength. In the quasi-one-dimensional tight-binding approach, the spin-orbit coupling can be written as follows [20]:

HtCCCCCCCC=−++++ − + − , so so  nn+↑1, , ↓ nn +↓ 1, , ↑ nn , ↓ +↑ 1, nn , ↑ +↓ 1, (14) n + π where tso is the coupling strength and Cns, (Cns, ) is the creation (annihilation) operator of -electrons. When a polaron moves along the molecular chain, its spin will process at the same time, as shown in =−[]ρρ Figure 6a, where the spin at site n is defined as sntz (,)↑↓ (,) nt (,) nt 2 and total spin st()= snt ( ,) zz . At the initial moment, the spin of the polaron is up, and as the polaron moves, its n spin gradually becomes zero and then becomes down. Figure 6b shows the evolution of stz () with the position of the polaron center [33]. It can be clearly seen that during the movement of the polaron, its spin evolves with time due to the spin-orbit coupling.

Figure 6. (a) Spin evolution of polarons, positive values denote spin up, negative values denote spin down and zero denote spinless; and (b) the polaron spin varies with the position of the center. By Lei et al. [33] with the permission of the Journal of Physics: Condensed Matter.

Based on the study of spin valves and spin field effect transistors, we could design a spin diode, which means that the electron spin transport in the external field is asymmetric [40]. We defined =+ charge current as the sum of the currents of the two spin orientations, IIIq ↑↓, and spin current

Micromachines 2019, 10, x 8 of 31

Figure 5. The distribution of spin up, spin down and net spin density in organic layer at different times, where the bias voltage was V = 0.85 eV and the electric field was E = 0.5 mV/nm. By Fu et al. Micromachines[39] with2019 the, 10 permission, 596 of Physical Review B. 8 of 30

Applying a voltage in the vertical transport direction can adjust the effective Rashba spin-orbit couplingApplying strength. a voltage In the in quasi-one-dimensional the vertical transport ti directionght-binding can adjustapproach, the etheffective spin-orbit Rashba coupling spin-orbit can couplingbe written strength. as follows In the[20]: quasi-one-dimensional tight-binding approach, the spin-orbit coupling can be written as follows [20]: HtCCCCCCCC=−++++ − + − , so so  nn+↑1, , ↓ nn +↓ 1, , ↑ nn , ↓ +↑ 1, nn , ↑ +↓ 1, (14) X n + + + + Hso = tso [C + Cn, C + Cn, + C Cn+1, C Cn+1, ], (14) − n 1, ↓ − n 1, ↑ n, ↑ − n, ↓ n ↑ + ↓ ↓ ↑ π where tso is the coupling strength and Cns, (Cns, ) is the creation (annihilation) operator of -electrons. + whereWhen taso polaronis the coupling moves along strength the andmolecularCn,s (C chain,n,s) is theits spin creation will (annihilation)process at the operatorsame time, of asπ-electrons. shown in =−[]ρρ WhenFigure a 6a, polaron where moves the spin along at the site molecular n is defined chain, as its snt spinz (,) will process↑↓ (,) nt at the (,) nt same 2 time,and astotal shown spin ( ) = [ ( ) ( )] inst() Figure= 6 snta, ( where ,) the spin at site n is defined as sz n, t ρ n, t ρ n, t /2 and total spin zzP . At the initial moment, the spin of the polaron is↑ up, and− as↓ the polaron moves, its sz(t) = n sz(n, t). At the initial moment, the spin of the polaron is up, and as the polaron moves, n itsspin spin gradually gradually becomes becomes zero zero and and then then become becomess down. down. Figure Figure 6b6 bsh showsows the the evolution evolution of of stszz()(t) withwith thethe positionposition ofof thethe polaronpolaron centercenter [[3333].]. It can be clearly seen that during the movement of the polaron, itsits spinspin evolvesevolves withwith timetime duedue toto thethe spin-orbitspin-orbit coupling.coupling.

FigureFigure 6.6. ((aa)) Spin Spin evolution evolution of of polarons, polarons, positive positive values values denote denote spin spin up, up,negative negative values values denote denote spin spindown down and zero and zerodenote denote spinless; spinless; and (b and) the (b polaron) the polaron spin varies spin varieswith th withe position the position of the center. of the center.By Lei Byet al. Lei [33] et al. with [33 ]the with permission the permission of the Journal of the Journal of Physics: of Physics: Condensed Condensed Matter. Matter.

BasedBased onon thethe studystudy ofof spinspin valvesvalves andand spinspin fieldfield eeffectffect transistors,transistors, wewe couldcould design a spin diode, whichMicromachineswhich meansmeans 2019 thatthat, 10, x thethe electronelectron spinspin transporttransport inin thethe externalexternal fieldfield isis asymmetricasymmetric [[40].40]. WeWe defineddefined9 of 31 charge current as the sum of the currents of the two spin orientations, Iq = I=++ I , and spin current as charge current as the sum of the currents of the two spin orientations, IIIq ↑↓, and spin current as IeII=−()()/2 . Figure 7 shows three spin current diodes. Figure↑ 7a ↓is a symmetric spin Is =s (}/2e)(I I↑↓). Figure7 shows three spin current diodes. Figure7a is a symmetric spin current, ↑ − ↓ current,Figure7b Figure is a parallel 7b is a spin parallel rectification spin rectification and Figure and7c isFigure an anti-parallel 7c is an anti-parallel spin rectification. spin rectification.

Figure 7. SpinSpin rectification: rectification: ( (aa)) Symmetrical Symmetrical spin spin rectification; rectification; ( (bb)) parallel parallel spin spin rectification rectification and and ( (cc)) anti-parallel spin current rectification.rectification.

A molecular spin diode, such as as thiophene/poly thiophene/poly (1,4-bis(2,2,6,6-tetramethyl-4-piperidyl-1-oxyl)- (1,4-bis(2,2,6,6-tetramethyl-4-piperidyl-1-oxyl)- butadiin (poly-BIPO),(poly-BIPO), is is asymmetrical asymmetrical in in the the spin sp spacein space [41]. [41]. With With spin relatedspin related Landau-Büttiker Landau-Büttiker theory, theory, the current passing through the device and its spin polarization can be calculated [32,42]. It is found that the device exhibits a charge as well as a spin rectification. Currently, most studies on spin transport are carried out with a molecule-based spin valve, which shows a "ferromagnetic/non-magnetic/ferromagnetic" sandwich structure and the non- magnetic interlayer is usually a thin-film molecular layer. In such a device, the spin transport process has been demonstrated to have a close correlation with spin relaxation time and charge carrier τ mobility of π-conjugated molecules. The spin relaxation time s is subsequently computed using the τλ2 ()+ λ 2 D λ relationship s = DDhop ex , where , Dhop and ex , are the spin relaxation length s of molecules, the spin diffusion constants based on the hopping spin transport mode and exchange coupling mode, respectively. When the molecular layer have a high carrier concentration, generally induced via the impurity band [43,44], an exchange coupling model will provide an extra-fast speed compared to hopping transport since the spin transport process can decouple with charge transport. It appears to improve the spin transport distance. In addition, single crystal and organic cocrystals have good application prospects in high performance spin transport due to the ordered stacked aggregation with high mobility and weak spin scattering factors [45–47]. Despite the limitations of technologies and the lack of theoretical models, spintronic devices based on single crystals or cocrystals still attracts people to explore its rich possibilities [48].

3. Organic Magnetic Field Effect

3.1. Organic Magnetic Field Effect Experiment For an organic device with no any magnetic elements included, at room temperature, the optoelectronic properties will respond significantly to very small magnetic fields (on the order of mT) 222+ [10,49,50]. For most of the organic devices, the MR follows empirical Lorentz B /(BB0 ) or non- []+ 2 Lorentz BBB/(0 ) [11,51]. Figure 8 shows some experimental results and fitting curves. n 24+ 24+ Individual devices may follow power-law distributions such as B , f12//BfBor dB12 dB [52,53].

Micromachines 2019, 10, 596 9 of 30

the current passing through the device and its spin polarization can be calculated [32,42]. It is found that the device exhibits a charge as well as a spin rectification. Currently, most studies on spin transport are carried out with a molecule-based spin valve, which shows a “ferromagnetic/non-magnetic/ferromagnetic” sandwich structure and the non-magnetic interlayer is usually a thin-film molecular layer. In such a device, the spin transport process has been demonstrated to have a close correlation with spin relaxation time and charge carrier mobility of π-conjugated molecules. The spin relaxation time τs is subsequently computed using the relationship 2 2 τs = λ /(Dhop + Dex), where λ , Dhop and Dex, are the spin relaxation length λs of molecules, the spin diffusion constants based on the hopping spin transport mode and exchange coupling mode, respectively. When the molecular layer have a high carrier concentration, generally induced via the impurity band [43,44], an exchange coupling model will provide an extra-fast speed compared to hopping transport since the spin transport process can decouple with charge transport. It appears to improve the spin transport distance. In addition, single crystal and organic cocrystals have good application prospects in high performance spin transport due to the ordered stacked aggregation with high mobility and weak spin scattering factors [45–47]. Despite the limitations of technologies and the lack of theoretical models, spintronic devices based on single crystals or cocrystals still attracts people to explore its rich possibilities [48].

3. Organic Magnetic Field Effect

3.1. Organic Magnetic Field Effect Experiment For an organic device with no any magnetic elements included, at room temperature, the optoelectronic properties will respond significantly to very small magnetic fields (on the order of mT) [10,49,50]. 2 ( 2 + 2) For most of the organic devices, the MR follows empirical Lorentz B / B B0 or non-Lorentz 2 [B/( B + B0)] [11,51]. Figure8 shows some experimental results and fitting curves. Individual devices | | n 2 4 2 4 Micromachinesmay follow 2019 power-law, 10, x distributions such as B , f1/B + f2/B or d1B + d2B [52,53]. 10 of 31

FigureFigure 8. The 8. The fitting fitting curve curve of of the the MR MR of didifferentfferent organic organi materialsc materials with with the change the change of magnetic of magnetic field by field Mermer et al. [11] with the permission of Physical Review B. by Mermer et al. [11] with the permission of Physical Review B. Figure9 shows a typical device for experimentally studying the magnetic field e ffect. The metal electrodesFigure 9 shows on both a sides typical and device the intermediate for experimentally organic layer studying form a sandwich the magnetic structure. field After effect. an electric The metal electrodesvoltage on is applied both sides between and the the two intermediate electrodes, carriers organic are injectedlayer form from a the sandwich electrodes structure. into the organic After an electriclayer voltage and they is transportapplied between into the organic the two layer. electrod Thenes, a magnetic carriers fieldare isinjected applied from to study the theelectrodes effect of into the organicthe magnetic layer field and onthey the transport transport. into the organic layer. Then a magnetic field is applied to study the effect of the magnetic field on the transport.

Figure 9. Schematic diagram of the experimental device corresponding to the magnetic field effect of organic devices by Mermer et al. [11] with the permission of Physical Review B.

In 1996, Frankevich et al. experimentally found that the photocurrent in the polymer poly(2,5- diheptyloxy-p-phenylene vinylene) (HO-PPV) device increases after applying a magnetic field [54]. In 2003, Kalinowski et al. studied light-emitting device of small molecules Alq3, and they found that the light emitting efficiency of the device is increased by 5% as the magnetic field from 0 to 300mT [55]. Subsequently, Mermer et al. discovered MR in polymer poly(9,9-dioctylfluorenyl-2,7-diyl) (PFO) devices. At room temperature, the MR of the device reaches 10% at 100mT [31,56]. Figure 10 shows the MR curve in the ITO/PFO (≈ 60 nm)/Ca device at 200 K, and it found that the MR was negative at low voltage, but it becomes a positive value at high voltage.

Micromachines 2019, 10, x 10 of 31

Figure 8. The fitting curve of the MR of different organic materials with the change of magnetic field by Mermer et al. [11] with the permission of Physical Review B.

Figure 9 shows a typical device for experimentally studying the magnetic field effect. The metal electrodes on both sides and the intermediate organic layer form a sandwich structure. After an electric voltage is applied between the two electrodes, carriers are injected from the electrodes into the organic layer and they transport into the organic layer. Then a magnetic field is applied to study Micromachines 2019, 10, 596 10 of 30 the effect of the magnetic field on the transport.

FigureFigure 9. Schematic 9. Schematic diagram diagram of ofthe the experimental experimental device device correspondingcorresponding to to the the magnetic magnetic field field effect effect of of organicorganic devices devices by byMermer Mermer et etal. al. [11] [11 ]with with the the permission of of Physical Physical Review Review B. B.

In 1996,In 1996, Frankevich Frankevich et etal. al. experimentally experimentally found found that thethe photocurrentphotocurrent in in the the polymer polymer poly(2,5- poly(2,5- diheptyloxy-p-phenylene vinylene) (HO-PPV) device increases after applying a magnetic field [54]. diheptyloxy-p-phenylene vinylene) (HO-PPV) device increases after applying a magnetic field [54]. In 2003, Kalinowski et al. studied light-emitting device of small molecules Alq3, and they found that In 2003, Kalinowski et al. studied light-emitting device of small molecules Alq3, and they found that the light emitting efficiency of the device is increased by 5% as the magnetic field from 0 to 300mT [55]. the lightSubsequently, emitting Mermerefficiency et of al. the discovered device is MR incr ineased polymer by 5% poly(9,9-dioctylfluorenyl-2,7-diyl) as the magnetic field from 0 (PFO)to 300mT [55]. devices.Subsequently, At room Mermer temperature, et al. discovered the MR of the MR device in polymer reaches poly(9,9-dioctylfluorenyl-2,7-diyl) 10% at 100mT [31,56]. Figure 10 shows (PFO) devices.the MRAt curveroom intemperature, the ITO/PFO the ( 60 MR nm) of/Ca the device device at 200reaches K, and 10% it found at 100mT that the [31,56]. MR was Figure negative 10 shows at ≈ Micromachinesthe MRlow curve voltage, 2019 in, 10 butthe, x itITO/PFO becomes ( a≈ positive 60 nm)/Ca value device at high at voltage. 200 K, and it found that the MR was negative11 of 31at low voltage, but it becomes a positive value at high voltage.

FigureFigure 10. MR 10. MRversus versus magnetic magnetic field field in in ITO/PFO ITO/PFO ( (≈ 6060 nm)/Ca nm)/Cadevices. devices. The The inset inset shows shows the the variation variation ≈ of deviceof device resistance resistance with with voltage voltage by by Mermer Mermer et et al. al. [11] [11] withwith thethe permission permission of of Physical Physical Review Review B. B.

In 2009,In 2009, Hu Huet etal. al. explored explored the the photoluminescencephotoluminescence effi efficiencyciency of organic of organic light diodeslight diodes (OLEDs) (OLEDs) and and foundfound thatthat pure pure organic organic N,N’-diphenyl-N,N’-bis(3-methylphenyl)-[1,1’-biphenyl]-4,4’-diamine N,N’-diphenyl-N,N’-bis(3-methylphenyl)-[1,1’-biphenyl]-4,4’-diamine (TPD) (TPD)and and 2,5-bis(5-tert-butyl-2-benzoxazolyl)-thiophene 2,5-bis(5-tert-butyl-2-benzoxazolyl)-thiop (BBOT)hene (BBOT) have no have magnetic no magnetic field effect, field as shown effect, as in Figure 11. However, the photoluminescence efficiency of the hybrid device (doped with different shown in Figure 11. However, the photoluminescence efficiency of the hybrid device (doped with ratios of poly(methyl methacrylate) (PMMA)) is improved, and the magnetic field effects produced by different ratios of poly(methyl methacrylate) (PMMA)) is improved, and the magnetic field effects the different ratios of the mixture devices are also different [49]. produced by the different ratios of the mixture devices are also different [49].

Figure 11. Photoluminescence efficiency of organic mixtures with different ratios varies with the magnetic field by Shao et al. [49] with the permission of Advanced Materials.

Nguyen et al. compared the magnetic field effect of an OLED composed of a π-conjugated polymer poly(dioctyloxy)phenylenevinylene (DOOPPV) with hydrogen and deuterium (the latter having a weak hyperfine interaction) [32]. They found that devices composed of deuterated polymers showed significant narrowing of the electroluminescence magnetic field effect, as shown in Figure 12, which indicates that hyperfine interaction is one of the important factors of the organic magnetic field effect.

Micromachines 2019, 10, x 11 of 31

Figure 10. MR versus magnetic field in ITO/PFO (≈ 60 nm)/Ca devices. The inset shows the variation of device resistance with voltage by Mermer et al. [11] with the permission of Physical Review B.

In 2009, Hu et al. explored the photoluminescence efficiency of organic light diodes (OLEDs) and found that pure organic N,N’-diphenyl-N,N’-bis(3-methylphenyl)-[1,1’-biphenyl]-4,4’-diamine (TPD) and 2,5-bis(5-tert-butyl-2-benzoxazolyl)-thiophene (BBOT) have no magnetic field effect, as shown in Figure 11. However, the photoluminescence efficiency of the hybrid device (doped with different ratios of poly(methyl methacrylate) (PMMA)) is improved, and the magnetic field effects Micromachines 2019, 10, 596 11 of 30 produced by the different ratios of the mixture devices are also different [49].

Figure 11. PhotoluminescencePhotoluminescence efficiency efficiency of of organic organic mixtur mixtureses with with different different ratios varies with the magnetic field field by Shao et al. [[49]49] with the permission of Advanced Materials.

Nguyen et al. compared compared the the magnetic magnetic field field effect effect of of an an OLED composed of a π-conjugated polymer poly(dioctyloxy)phenylenevinylene (DOOPPV (DOOPPV)) with with hydrogen hydrogen and deuterium (the latter having a weak hyperfine hyperfine interactio interaction)n) [[32].32]. They found that devices devices composed composed of deuterated deuterated polymers showed significantsignificant narrowingnarrowing ofof the the electroluminescence electroluminescence magnetic magnetic field field eff effect,ect, as as shown shown in Figurein Figure 12, which12, which indicates indicates that that hyperfine hyperfine interaction interaction is is one one of of the the important important factors factors ofof thethe organicorganic magnetic Micromachines 2019, 10, x 12 of 31 fieldfield eeffect.ffect.

FigureFigure 12. 12.E ffEffectect of of isotope isotope e ffeffectect on on magnetoluminescence magnetoluminescenc effi efficiencyciency in in organic organic light light diodes diodes (OLEDs) (OLEDs) byby Nguyen Nguyen et et al. al. [32 [32]] with with the the permission permission of of Nature Nature Materials. Materials. 3.2. Organic Magnetic Field Effect Theory 3.2. Organic Magnetic Field Effect Theory Based on the basic current density formula, current density J depends not only on the carrier Based on the basic current density formula, current density J depends not only on the carrier concentration n but also on the carrier mobility or velocity v through J = nev. For a magnetic concentration n but also on the carrier mobility or velocity v through J = nev . For a magnetic conductance (inverse of MR) that is not very large, we have: conductance (inverse of MR) that is not very large, we have:

n(B) nnB(()0) −− n (0)v(B) vB ()v(0) v (0) MC  −≅+=++ − = MC(n, B) + MC(v, B), (15) MCMCnBMCvB( ) ( ) (, ) (, ), (15) n 0 nv(0)v 0 (0) wherewhereMC M(CnBn(,, B) )and andMC M(CvBv,(,B) are ) are the the responses responses of of concentration concentration and and mobility mobility to to the the magnetic magnetic field, respectively [34]. Experimentally, it seems to reveal that both the carrier concentration and field, respectively [34]. Experimentally, it seems to reveal that both the carrier concentration and mobility respond to the magnetic field. For example, Nguyen et al. measured the dependence mobility respond to the magnetic field. For example, Nguyen et al. measured the dependence of the of the concentration of singlet excitons, triplet excitons and polarons on the magnetic field by concentration of singlet excitons, triplet excitons and polarons on the magnetic field by using using electroluminescence spectroscopy and charge-induced absorption spectroscopy techniques [57]. electroluminescence spectroscopy and charge-induced absorption spectroscopy techniques [57]. They found that all concentrations increase with the field. However, Veeraraghavan et al. measured They found that all concentrations increase with the field. However, Veeraraghavan et al. measured MR in PFO, and found the magnetic field effect is related to the carrier mobility instead of the MR in PFO, and found the magnetic field effect is related to the carrier mobility instead of the carrier carrier concentration [58]. In addition, Ding et al. studied OLEDs mixed by N, N’-bis(l-naphthyl)-N, concentration [58]. In addition, Ding et al. studied OLEDs mixed by N, N’-bis(l-naphthyl)-N, N’- diphenyl-1,1’-biphentl-4,4’-diamine (NPB):Alq3 and found that the electroluminescence magnetic field effect has a close relationship with carrier mobility [59]. The process of understanding the effects of organic magnetic fields is multi-view and gradually deepened, and many mechanisms or models are proposed. Since the magnetic field has an effect on either the spin or the orbit of π-electrons, there are spin magnetic resistance (spin-MR) and orbital magnetic resistance (orbital-MR). The following are some of the main OMAR mechanisms. Polaron pairing mechanism: In a bipolar device, holes injected from the anode and electrons injected from the cathode form positive and negative polarons in the organic layer, respectively. They are bound together by coulomb attraction to form a pair of polarons or excitons, which can be classified into a singlet and triplet depending on the spin configuration. The change of the singlet/triplet ratio due to the magnetic field in the polaron pairs will change the radiation or current [60]. Figure 13 shows the structural changes of the single and triplet levels with different distances. S denotes a singlet exciton, T denotes a triplet exciton and PP1 is a single-state polaron pair, PP3 is a triplet polaron pair. For the polaron pairs, since the distance between the positive and negative polaron is large, there is a small spin exchange interaction energy between them, and the energy level between the triplet polaron pairs are degenerate. However, for excitons, the difference between singlet and triplet energy levels is large. When the magnetic field B = 0, as shown in Figure 13a, the energy level of PP3 is a triple degeneracy state, so that the singlet and the triplet are most easily converted into each other. When the magnetic field is not zero, PP3 appears to be Zeeman splitting, and thereby the triply degenerate is released, so in this case the interconversion only occurs in PP1 3 and PP0 [61], as shown in Figure 13b. In a word, the mutual transformation of the single and triplet

Micromachines 2019, 10, 596 12 of 30

N’-diphenyl-1,1’-biphentl-4,4’-diamine (NPB):Alq3 and found that the electroluminescence magnetic field effect has a close relationship with carrier mobility [59]. The process of understanding the effects of organic magnetic fields is multi-view and gradually deepened, and many mechanisms or models are proposed. Since the magnetic field has an effect on either the spin or the orbit of π-electrons, there are spin magnetic resistance (spin-MR) and orbital magnetic resistance (orbital-MR). The following are some of the main OMAR mechanisms. Polaron pairing mechanism: In a bipolar device, holes injected from the anode and electrons injected from the cathode form positive and negative polarons in the organic layer, respectively. They are bound together by coulomb attraction to form a pair of polarons or excitons, which can be classified into a singlet and triplet depending on the spin configuration. The change of the singlet/triplet ratio due to the magnetic field in the polaron pairs will change the radiation or current [60]. Figure 13 shows the structural changes of the single and triplet levels with different distances. S denotes a singlet exciton, T denotes a triplet exciton and PP1 is a single-state polaron pair, PP3 is a triplet polaron pair. For the polaron pairs, since the distance between the positive and negative polaron is large, there is a small spin exchange interaction energy between them, and the energy level between the triplet polaron pairs are degenerate. However, for excitons, the difference between singlet and triplet energy levels is large. When the magnetic field B = 0, as shown in Figure 13a, the energy level of PP3 is a triple degeneracy state, so that the singlet and the triplet are most easily converted into each other. When the magnetic field is not zero, PP3 appears to be Zeeman splitting, and thereby the triply degenerate is Micromachines 2019, 10, x 1 3 13 of 31 released, so in this case the interconversion only occurs in PP and PP0 [61], as shown in Figure 13b. In a word, the mutual transformation of the single and triplet state changes with the external magnetic statefield, changes and thewith ratio the ofexternal the singlet magnetic polaron field, pairs and changes, the ratio so the of etheffects singlet of the polaron magnetic pairs field changes, on the so the effectscurrent of and the the magnetic like are revealed. field on the current and the like are revealed.

FigureFigure 13. Structure 13. Structure change change of ofsingle single and and triplet triplet energy levelslevels with with di differentfferent distances. distances. The The insets insets are are schematicschematic diagrams diagrams of ofthe the mutual mutual transformation transformation betweenbetween singlet singlet and and triplet triplet polaron polaron pairs pairs when when (a) (a) B = 0mboxemphB and (b) B ≠ =0.0 By and Prigodin (b) B , 0. et By al. Prigodin [61] with et al.the [ 61permission] with the permission of Synthetic of SyntheticMetals. Metals.

As an example, let us consider a pair of polarons with state , 1 , 2. , means the nuclei As an example, let us consider a pair of polarons with state|↑ ↑⇑,,i |↑ ↑⇓i |↑. ⇓↑,i means the nuclei spin up and the polaron spin down. The first polaron is in eigenstate and12 the second one will evolve spinwith up and time. the Considering polaron spin the edown.ffects of The external first polaro magneticn is fields in eigenstate and hyperfine and fields,the second one will evolve with time. Considering the effects of external magnetic fields and hyperfine fields, a → H = ω0sz + →s I . (16) } a ·  H =+⋅ω ssI . (16) The first term represents the Zeeman energy produced0 z by the external magnetic field, ω0 = gµBB/},  where µB is the Bohr magneton and g is the Landau factor. The second term represents the interaction The first term represents the Zeemanˆ energy produced by the external magnetic field, of spin with the hydrogen nuclear spin →I (assumed to be }/2), and a is the interaction strength. We can ωμ= gB/ μ 0 get theB expected , where value ofB theis the total Bohr spin, magneton and g is the Landau factor. The second term ˆ represents the interaction of spin with the hydrogen nuclear spin I (assumed to be /2), and a ω2 ω2 q  1+2 1 0 0 2 2  1 1 is the interaction strength.sz (t) = We1 can+ get the+ expectedcos valueω of+ thea t total= +spin,(p P pAP), (17) 2 2 + 2 2 + 2 0  2 2 − ω0 a ω0 a ωω22 12+ 111 2 2 s ()tatpp=+ 100 + cos ω + =+−(), (17) z ωω22++ 22 0 PAP 22200aa where p and p respectively indicates the probability that the pair of polarons are in parallel P AP and anti-parallel states. The above formula shows that the total spin of a pair of positive and negative polarons oscillates with time. The experiment found that the oscillation frequency is much higher than the recombination rate of their formation (bound state), so we take the average and get the recombination rate,

1 ωω22 γγ=+ γ =+00 γ + γ ppP PAPAP P AP, (18) 22()ωω22++aa 2() 22 00 γ γ where P and AP respectively indicate the rate of recombination for parallel and antiparallel pairs. Therefore,

Δ−=γγ()BB γ ( 0) ω 2 ==β 0 , (19) γγ=+ ω22 (0)Ba0 γγ− where the parameter β = PAP. The above formula represents the Lorentz type MR found γγ+ PAP experimentally. Bipolaron mechanism: In a unipolar device, there is only one kind of charge (electron or hole) injected. In this case, a bipolaron model is proposed, which is based on the transformation between the polaron and the bipolaron. Using diffusion theory we write the transformation equation as [34]:

Micromachines 2019, 10, 596 13 of 30

where pP and pAP respectively indicates the probability that the pair of polarons are in parallel and anti-parallel states. The above formula shows that the total spin of a pair of positive and negative polarons oscillates with time. The experiment found that the oscillation frequency is much higher than the recombination rate of their formation (bound state), so we take the average and get the recombination rate,

 2  2 1 ω  ω γ = p γ + p γ =  + 0 γ + 0 γ , (18) P P AP AP 2 ( 2 + 2)  P ( 2 + 2) AP 2 ω0 a 2 ω0 a where γP and γAP respectively indicate the rate of recombination for parallel and antiparallel pairs. Therefore, ∆γ γ(B) γ(B = 0) ω2 = − = β 0 , (19) γ γ(B = 0) 2 + 2 ω0 a γ γ where the parameter β = P− AP . The above formula represents the Lorentz type MR found experimentally. γP+γAP Bipolaron mechanism: In a unipolar device, there is only one kind of charge (electron or hole) injected. In this case, a bipolaron model is proposed, which is based on the transformation between the polaron and the bipolaron. Using diffusion theory we write the transformation equation as [34]:

 dnpp  = γapnpp + γ0 nap  dt − ap  dn  ap = n n + kn bn , (20)  dt γap pp γ0ap ap bp ap  − −  dnbp  = kn + bnap dt − bp where npp(nap) is the concentration of spin-parallel (anti-parallel) polaron pairs and nbp is the concentration of the bipolarons. γapnpp( γ nap) means the reduction of the spin-parallel polaron − − 0ap pairs (bipolarons) due to the external magnetic field and the hyperfine field. Parameter b represents the recombination rate of polaron pair to form bipolaron. k represents the dissociation rate of bipolaron;

γap represents the conversion rate of spin parallel polaron pair to spin antiparallel polaron pair and γ0ap is the opposite process above. Under the external magnetic field and the hyperfine effect, the above conversion rate can be obtained as follows,

1 ω4 γap = [1 ]γ0, (21) 2 − 8(ω2 + α2)2

1 ω4 γap0 = [1 + ]γ0, (22) 2 8(ω2 + α2)2 where γ0 is a constant. Combining current density:

J(B) = 2e[npp(B) + nap(B)]νp + 2enbp(B)νbp, (23) the magnetic conductance is given as:

ω4 MC = MC , (24) ∞ ω4 + 2βa2ω2 + βa4

2(1 α)k/b where MC = − is the value of the saturated MC. α = vbp/vp is the rate ratio of ∞ (α+2k/b)(7+16k/b) = + 1 bipolarons and polarons, and β 1 16k/b+7 . Since β 1, when the external magnetic field is ≈ 2 2 much larger than the hyperfine equivalent field B B (ω a), MC MC ω = MC B hf ω2+2βa2 B2+B2   ≈ ∞ ∞ hf and this form is the empirical formula of Lorentz form. When the external magnetic field is small, i.e., B < Bhf, the MC curve deviates from the Lorentz curve, as shown in the inset in Figure 14. Micromachines 2019, 10, 596 14 of 30

In organic semiconductors, the concentration of polarons is usually greater than that of bipolarons, so a positive MC is obtained. With the appropriate parameters, a calculation result equivalent to 2% of the experimental value can be obtained [34]. It is worth noting that the calculated MC saturation value has no relationship with the hyperfine equivalent field, as shown in Figure 14. These calculation resultsMicromachines are completely 2019, 10, x consistent with the experimental measurement [36]. 15 of 31

Micromachines 2019, 10, x 15 of 31

FigureFigure 14. 14.MC MC curve curve with with the the magnetic magnetic field field in thein the case case ofdi offf differenterent hyperfine hyperfine equivalent equivalent fields, fields,Bhf B=hf 3.5= , 5.5 and3.5,Figure 5.5 7.5 and mT.14. MC Symbol7.5 mT.curve Symbol withis the the experimental× magneticis the experimental field value in the at casevalueB = of100 differentat mT.B = By100 hyperfine Qin mT. et By al. equivalentQin [34] et with al. fields, the[34] permission with Bhf = the × of Appliedpermission3.5, 5.5 Physicsand of 7.5 Applied Letters.mT. Symbol Physics × Letters.is the experimental value at B = 100 mT. By Qin et al. [34] with the permission of Applied Physics Letters. ExcitonExciton quenching quenching model: model: The The long long lifetime lifetime of a of triplet a triplet exciton exciton makes makes it easy it easy for a for polaron a polaron to collide to withcollide it, whichExciton with leads it, quenching which to two leads consequences:model: to two The consequences: long One lifetime is to Oneof obstruct a istriplet to obstruct the exciton movement the makes movement it of easy the polaron;forof thea polaron polaron; the otherto the is collide with it, which leads to two consequences: One is to obstruct the movement of the polaron; the to reactother to is eachto react other. to each One other. of the One reaction of the reaction channels channels is to form is to a form short-lived a short-lived singlet singlet exciton exciton [62], [62], other is to react to each other. One of the reaction channels is to form a short-lived singlet exciton [62],

σ −σσσσσσ σ 0 0 P− +P−σσσσT+→+TPSP + S 0 . (25) +→+ex exex ex . (25) P TPSex→ ex . (25) TwoTwo triplet triplet excitons excitons also also annihilate annihilate into into singlet singlet excitons excitons [[63],63], Two triplet excitons also annihilate into singlet excitons [63], σσ σ σ 0 T +σσT −− σ σ S 0 ex σσex+→− −−− σ σ ex0. (26) TTex+→ ex→ S ex . (26) TTex ex S ex . (26) A magnetic field will change the collision probability, which affects the mobility of polarons, A magnetic field will change the collision probability, which affects the mobility of polarons, so so that theA magnetic current offield the will device change is the changed collision by probabil the magneticity, which field. affects Through the mobility non-adiabatic of polarons, so kinetic thatthat the the current current ofof thethe devicedevice isis changed byby thethe magneticmagnetic field. field. Through Through non-adiabatic non-adiabatic kinetic kinetic evolution methods, Sun et al. studied the scattering process between a negative polaron and a triplet evolutionevolution methods, methods, Sun Sun et et al.al. studiedstudied the scatteringscattering process process between between a negativea negative polaron polaron and and a triplet a triplet exciton on the polyacetylene molecular chain, as shown in Figure 15[ 64]. The figure shows that the excitonexciton on on the the polyacetylene polyacetylene molecularmolecular chain, asas sh shownown in in Figure Figure 15 15 [64]. [64]. The The figure figure shows shows that that the the transporttransporttransport of aof of polaron a apolaron polaron is indeedis is indeed indeed hindered hinderedhindered by byby a aatriplet triplet triplet exciton. exciton.

FigureFigure 15. The 15. The evolution evolution of of polaron polaron and and triplet triplet excitonexciton la latticettice configuration configuration under under electric electric field fieldwith with timeFigure bytime Su by 15. et Su The al. et [ 64al.evolution ][64] with with the of the permissionpolaron permission and of tripletof Journal Journal exciton of Chemical Chemical lattice configuration Physics. Physics. under electric field with time by Su et al. [64] with the permission of Journal of Chemical Physics. The OMAR can also be understood based on the spin blocking effect. Using the tight-binding modelThe of OMAR organic can small also molecule be understood crystals, basedthe Hamiltonian on the spin of theblocking system effect. is [65]: Using the tight-binding model of organic small molecule crystals, the Hamiltonian of the system is [65]:

Micromachines 2019, 10, x 16 of 31 Micromachines 2019, 10, 596 15 of 30

11 H =−+−[(ταuuCCCC )](++ + ) + MuKuu22 + ( − ), The OMARTO can also be understood n++11,,,1, n based n s ns on the ns spin n + s blocking enffect. Using n + 1 the n tight-binding(27) ns, nn22 model of organic small molecule crystals, the Hamiltonian of the system is [65]: τ where un is the deviation of the nth molecule from the equidistant molecular arrangement, is the X + + X 1 . 2 X 1 2 electronH =transfer[ τintegral+ α(u +beforeun)]( theC molecularCn,s + C deviationC + ) +and α M isu an+ electron–phononK(u + un) coupling, (27) TO − n 1 − n+1,s n,s n 1,s 2 n 2 n 1 − constant. Mn,s is the molecular mass and K is the intermolecularn elasticn coupling constant. The external magnetic field and hyperfine interaction are given by equation (16). where un is the deviation of the nth molecule from the equidistant molecular arrangement, τ is the Driven by an external electric field, the evolution of the electronic state is given by the time- electron transfer integral before the molecular deviation and α is an electron–phonon coupling constant. dependent Schrödinger equation, M is the molecular mass and K is the intermolecular elastic coupling constant. The external magnetic field and hyperfine interaction are given by equation (16). ∂ Driven by an external electric=−τα field, − the − evolution of −the τα −electronic − state is given by the time- iZt μσ,nnnnnnn ,() [ ( uuZ−− 1 )] μ , 1, σ () t [ ( uuZt + 1 )] μ , + 1, σ () dependent Schrödinger∂t equation, . (28) ++gBBZteEnauZtμσ()() −+ ( ) () ∂ Bhypnn,,,μσ nn μσ ,, i} Zµ,n,σ(t) = [τ α(un un 1)]Zµ,n 1,σ(t) [τ α(un+1 un)]Zµ,n+1,σ(t) ∂t − − − − − − − − (28) At the same time, the+ atomicgµBσ( Bnucl+ Bei (or) CHZµ,n units),σ(t) willeE(na evaluate+ un)Z µwith,n,σ( tthe) electronic states, which hyp,n − are determined by the classical Newtonian equation of motion: At the same time, the atomic nuclei (or CH units) will evaluate with the electronic states, which are determined by the classical Newtonian equation of motion: =+−+αρ − ρ − ρ − mun() t K ( u n+−11 u n 2 u n ) 2 [ nn ,11, + () t n − n ()] t eE [ nn , () t 1], (29) .. mun(t) = K(un+1 + un 1 2un) + 2α[ρn,n+1(t) ρn 1,n(t)] eE[ρn,n(t) 1], (29) where the electronic state and the density− − matrix, respectively,− are:− − − where the electronic state and the density matrix, respectively, are: Z n ϕ P μ ,,n ↑  μ!↑ n Zµ,n, n ψ ==ϕµ  = μ =  n ↑ | i , (30) ψµ ϕ↑ P Z n , (30) ϕµ μ ↓ Zµμ,n,,n, ↓ n  ↓ nn ↓ | i X * ρm,nρ= = Z∗ ZfZfµZµ,n,σ.. (31) mn,,,,, µ,mμ,σ mσ μμ nσ (31) µ μ

Equations (28) (28) and and (29) (29) can can be be solved solved by bythe the Runge–Kutta Runge–Kutta method method with with 8-order 8-order controllable controllable step size.step size.At the At beginning, the beginning, supposing supposing there is there a polaron is a polaron in the insystem, the system, its velocity its velocity is solved is solved by the byabove the equations,above equations, which is which dependen is dependentt upon the upon magnetic the magnetic field B, thus field givingB, thus the giving MR of the the MR velocity of the response. velocity Asresponse. shown Asin shownFigure in16, Figure MR decreases16, MR decreases rapidly rapidlywith the with decrease the decrease of hyperfine of hyperfine field intensity. field intensity. For example,For example, the fixed the fixed external external magnetic magnetic field field B = B80= mT,80 mT,when when the thehyperfine hyperfine field field decreased decreased from from 4.6 mT4.6 mTto 2.4 to 2.4mT, mT, MR MR decreased decreased from from 1.78% 1.78% to to 0.88%. 0.88%. The The OMAR OMAR effect effect disappears disappears if if there there is is no hyperfinehyperfine field.field.

0.0 C 0.0mT 60 2.4mT PCBM 4.1mT Alq3-d18 -0.5 4.6mT Alq3

-1.0 MR (%)

-1.5

-2.0 -80 -60 -40 -20 0 20 40 60 80 B (mT) Figure 16. DependenceDependence of of MR MR with with the the magnetic magnetic fi fieldeld under under a a different different hyperfine hyperfine field. field. ▼H represents the experimental data [[66,67].66,67]. The The curves curves represent represent the theoretical results [[65].65].

Micromachines 2019, 10, x 17 of 31

Micromachines 2019, 10, 596 16 of 30 For most OLEDs, the organic layers are amorphous, the coherent transport mechanism described before is not suitable. In this case, polarons move from one molecule to another by a For most OLEDs, the organic layers are amorphous, the coherent transport mechanism described hoppingbefore manner. is not It suitable. involves In this spin-conserved case, polarons move hopping from one as molecule well as to anotherspin-reversed by a hopping one, manner. as shown in Figure 17.It involves spin-conserved hopping as well as spin-reversed one, as shown in Figure 17.

Figure 17.Figure Schematic 17. Schematic diagram diagram of the of the polaron polaron transition: transition: ( a()a A) A transition transition without without a spin a state spin and state (b) aand (b) a transitiontransition containing containing a spin a spinstate. state.

To describe the hopping process, we assumed that the spin and charge hopping rates were To describe the hopping process, we assumed that the spin and charge hopping rates were independent, Wis,js = αss ωij, where ωij is the normal charge hopping given by the Marcus formula: = αω0 0 ω independent, Wis,' js′ ss ij , where ij is the normal charge hopping given by the Marcus formula: t2  2  ij π 1  (λ + εj εi)  2  −  ωij = [ ] exp , (32) } kBTλ − 4kBTλ  22 t π 1 ()λε+− ε ω =[ij ]exp2 − j i , where tij = t0 exp( 2γRij) is theij transition integral between the molecules i and j. Rij = Rj Ri is (32) − kTλλ4 kT | − | the distance between the two molecules, BBγ is the local factor of the wave function, which reflects the localization of the polaron and εi is the on-site energy. After applying a driving electric field, the where ttexponential=−exp( factor 2γ R )in is the the equation transition (32) should integral add an between energy contribution the molecules of the electrici and fieldj. R eER=−RR is ij0 ij −ijij,x j i the distance(e is the between charge value the oftwo the molecules, carriers). λ is theγ molecularis the local reforming factor energy of the that wave reflects function, the properties which of reflects organic materials. α reflects the spin hopping rate. When we consider the hopping between molecule ss ε the localizationi and j, its of spin the will polaron be affected and by thei isexternal the on-site magnetic energy. field and After the hyperfine applying field. a driving Hamiltonian electric is field, written as: ˆ ˆ the exponential factor in the equation (32) should→ add→ an energy→ contribution of the electric field Hˆ ij = gµB→s B + ai→s I i + aj→s I j. (33) − · λ · · eERij, x (e is the charge value of the carriers). is the molecular reforming energy that reflects the Considering all possible spin configurations and taking the statistical average of these configurations, the spin hoppingα rate is obtained as [68]: properties of organic materials. ss reflects the spin hopping rate. When we consider the hopping  between molecule i and j , its spin will be affectedB2+7a2 /4 by the external magnetic field and the hyperfine  H (s = s )  B2+9a2 /4 0  H field. Hamiltonian is written as: αss = . (34) 0  a2 /2  H (s s )  2+ 2 , 0 B 9aH/4 ˆ =⋅+⋅+⋅μ ˆˆ   In order to calculate the magneticH ij conductancegsBasIasI B ini an i organic j device, j . the master equation is (33) employed by including a spin index as [68], Considering all possible spin configurations and taking the statistical average of these dP X configurations, the spin hoppingis = rate is[ WobtainedP (1 asP [68]:) + W P (1 P )], (35) dt − is,js0 is − js0 js0,is js0 − is j,i,s0

22 where Pis is the number of occupied polarons Ba+ of7/4 spin s of lattice i. The mobility of the system is H (s = s′ ) expressed as:  Ba22+ 9/4 α =  H ss′  . (34) a 2 /2  H (s ≠ s′ )  22+  Ba9/4H In order to calculate the magnetic conductance in an organic device, the master equation is employed by including a spin index as [68],

dPis =−[(1)(1)]WP′′′′ −+ P WP − P,  is,, js is js js is js is (35) dt jis≠ , ′

Micromachines 2019, 10, x 18 of 31

where Pis is the number of occupied polarons of spin s of lattice i. The mobility of the system is expressed as:

1 Micromachines 2019, 10, 596 17 of 30 μ =−WP′′(1 PR ) .  is,, js is js ij x (36) PE is, js′

Then the magnetic conductance of the1 X system is given by [34], µ = W P (1 P )R . (36) PE is,js0 is − js0 ij,x is,js0 μμ(B )− (0) Then the magnetic conductance of theMC system= is given by [34. ], (37) μ (0) µ(B) µ(0) MC = − . (37) With proper parameters, the calculated mobilityµ(0) in the absence of external magnetic field is −−−5211 μ ()02.5410cmVs=×With proper parameters, referring the to calculated that of mobilityAlq3. When in the an absence external of externalmagnet magneticic field was field applied, is it 5 2 1 1 µ(0) = 2.54 10 cm V− s referring to that of Alq . When an external magnetic field was applied, × − − 3 was foundit was that found the thatmobility the mobility was wassignificantly significantly chan changed,ged, andand a a magnetic magnetic conductance conductance value ofvalue up to of up to 75% was75% obtained. was obtained. Figure Figure 18 shows 18 shows the the change change of thethe magnetic magnetic conductance conductance with awith magnetic a magnetic field field calculatedcalculated at a different at a different polaron polaron density. density.

Figure 18.Figure Dependence 18. Dependence of the of themagnetic magnetic conductance conductance onon the the magnetic magnetic field field at di ffaterent different polaron polaron concentrationsconcentrations by Yang by Yang et al. et al.[68] [68 with] with the permissionpermission of the of Journalthe Journal of Chemical of Chemical Physics. Triangles Physics. and Triangles dots are experimental data [69]. and dots are experimental data [69]. Considering the Lorentz effect of the magnetic field on moving polarons, orbital MR is addressed [70]. ConsideringThis effect maythe Lorentz be significant effect in of organic the magnetic layers with field asymmetric on moving molecules polarons, or configurations. orbital MR In is the addressed [70]. Thispresence effect may of a magneticbe significant field, due in organic to the charge layers Lorentz with effect, asymmetric the transition molecules integral or between configurations. two In the presencemolecules of a canmagnetic be modified field, to, due to the charge Lorentz effect, the transition integral between two 2 Z molecules can be modified to, } ∂ψ2 ∂ψ1∗ 2i t = [(ψ1∗ ψ2) Axψ1∗ ψ2] x=d/2dydz, (38) m ∂x − ∂x − φ0 |

2 * where A is the x component of the magnetic∂∂ψψ vector potential,2i φ = c /e is the magnetic flux quantum x =−− ψψψψ**21 0 } t[( ) A ] = dydz , (38) number, ψ1 and ψ2 are electronicmxx states12122 on∂∂ two molecules, andφ theyxxd are usually local states of polarons. The integral range is the entire plane of x = d/2, located between0 the two molecules. If two molecules are not symmetric with respect to y = 0 or z = 0, the imaginary part of this integral will be obvious. A φ = where x Consideringis the x component the transport of process the magnetic of a positive vector polaron potential, and a negative 0 polaronce injectedis the intomagnetic the flux organic layer. They meet and collide with each other. One of the yields of the collision is an exciton. quantum number, ψ and ψ are electronic states on two molecules, and they are usually local The Lorentz effect1 generated2 by the magnetic field will affect the polaron motion, and then change states ofthe polarons. yield of excitons. The integral The calculated range magnetic is the conductanceentire plane is shownof x = ind Figure2 , located 19, which between is in good the two agreement with the experimental data. A further study also finds that the magnetic conductivity molecules. If two molecules are not symmetric with respect to y = 0 or z = 0 , the imaginary part is sensitive to the structural symmetry and electron-lattice coupling strength of organic molecules, of this integralwhich also will explains be obvious. why the organic magnetic field effect (OMFE) is more significant than that in Consideringinorganic materials the transport [71]. process of a positive polaron and a negative polaron injected into the organic layer. They meet and collide with each other. One of the yields of the collision is an exciton. The Lorentz effect generated by the magnetic field will affect the polaron motion, and then change the yield of excitons. The calculated magnetic conductance is shown in Figure 19, which is in good agreement with the experimental data. A further study also finds that the magnetic conductivity is sensitive to the structural symmetry and electron-lattice coupling strength of organic molecules,

Micromachines 2019, 10, x 19 of 31 which also explains why the organic magnetic field effect (OMFE) is more significant than that in Micromachines 2019, 10, 596 18 of 30 inorganic materials [71].

Figure 19.Figure Change 19. Change of magnetic of magnetic conductance conductance under under differe differentnt electron phonon phonon coupling. coupling. Lines Lines are are the theoreticalthe theoreticalresults by results Li et by al. Li [71] et al. with [71] with the the perm permissionission ofof OrganicOrganic Electronics. Electronics. Data forData the for block the block symbols are for PtOEP [72], and triangle symbols for Ir(ppy)3 [73]. symbols are for PtOEP [72], and triangle symbols for Ir(ppy)3 [73]. 4. Organic Excited Ferromagnetism 4. Organic ExcitedMultiferroic Ferromagnetism materials refer to having two or more kinds of properties of ferromagnetic, ferroelectric and ferroelastic. However, due to the weak magnetoelectric coupling strength, research in this field Multiferroic materials refer to having two or more kinds of properties of ferromagnetic, has been slow. Since the discovery of multiferroic material BiMnO3 [74] and BiFeO3 [75] in 2003, ferroelectricmultiferroic and ferroelastic. materials have However, rapidly become due a to research the weak hotspot magnetoelectric in the field of physics coupling and material strength, science research in this fielddue tohas their been rich slow. physical Since properties the discovery and potential of multiferroic applications in material functional BiMnO devices.3 In[74] multiferroic and BiFeO3 [75] in 2003, materials,multiferroic the charge,materials spin, have orbital rapidly and phonons become in thea research lattice are hotspot strongly coupledin the field to each of other,physics and materialmaking science the due multiferroic to their rich material physical rich in properties physical properties, and potential facilitating applications the rapid development in functional of devices. condensed matter physics and materials science. In addition to inorganic materials, the discovery of In multiferroic materials, the charge, spin, orbital and phonons in the lattice are strongly coupled to organic multiferroic materials has begun to attract more and more attention, providing a new idea each other,for the making application the ofmultiferro magnetoelectricic material coupling rich multiferroic in physical devices properties, [76,77]. The characteristicsfacilitating ofthe rapid developmentroom temperature of condensed ferroelectric, matter ferromagnetic physics and and material magnetoelectrics science. coupling In addition were found to inorganic in the organic materials, the discoverycharge transferof organic complex. multiferroic The supramolecular materials design has technique begun canto assembleattract themore electron and donor more and attention, providingacceptor a new molecules idea for intothe anapplication ordered charge of magnetoelectric transfer network to coupling realize ferroelectricity. multiferroic devices [76,77]. The characteristicsAccording of room to Landau’stemperature theory, ferroelectric, the free energy ferromagnetic of multiferroic materials and magnetoelectric can be written as: coupling were found in the organic charge transferf (→E, H→) complex. = f P E TheM supramolecularH 1 ε E E 1 µ designH H technique can assemble the 0 − 0i i − 0i i − 2 ij i j − 2 ij i j (39) electron donor and acceptor molecules into1 an ordered1 charge transfer network to realize αijEiHj 2 βijkEiHjHk 2 γijkHiEjEk ... ferroelectricity. − − − − Accordingwhere Ei andto Landau'sHi are electric theory, field component the free andenergy magnetic of multiferroic field component, materialsP0i and M can0i are be spontaneous written as: electric polarization intensity and spontaneous magnetization intensity and εij and µij are dielectric constant and permeability of materials. βijk and γijk are the second-order magneto-electric coupling 11 coefficients. Therefore, the expressions=− of the polarization − − strengthεμ − and the magnetization are: fEH(, ) f00 PEii MH 0 i i iji EE j iji HH j 22, (39) → → ∂ f 1 Pi(E, H) = = P0i +11εijEj + αijHj + βijkHjHk + ..., (40) −∂−−Eαβi EH EH H −2 γ HEE −... ij i j22 ijk i j k ijk i j k

→ → ∂ f 1 where E and H are electricMi(E, Hfield) = component= M0i + µandijHj +magneticαjiEj + γ ijkfieldEjEk component,+ .... P and (41) M are i i −∂Hi 2 0 i 0i

According to Equations (40) and (41), αij is the first-order linear response of the electric polarizationε μ spontaneous electric polarization intensity and spontaneous magnetization intensity and ij and ij intensity (or magnetization intensity) to the magnetic field (or electric field), while βjik and γijk are the β γ are dielectricsecond-order constant responses. and permeability of materials. ijk and ijk are the second-order magneto- electric coupling coefficients. Therefore, the expressions of the polarization strength and the magnetization are:

 ∂f 1 PEH( , )=− = P +εα E + H + β HH + ..., i∂ 0 i ij j ij j ijk j k (40) Ei 2

Micromachines 2019, 10, x 20 of 31

 ∂f 1 MEH(, )=− = M +μα H + E + γ EE + .... i∂ 0 i ij j ji j ijk j k (41) Hi 2 α According to Equations (40) and (41), ij is the first-order linear response of the electric β polarization intensity (or magnetization intensity) to the magnetic field (or electric field), while jik γ and ijk are the second-order responses. In 2009, Giovannetti et al. used the DFT binding model method to predict the multiferroic of organic molecular crystal TTF-CA (tetrathiafulvalene-p-chloranyl) [12]. The two molecules are alternately arranged TTF-CA-TTF-CA forming a D–A array. TTF-CA shows a neutral-ionic transition at 81K, but there is small charge transfer (~0.3 e) even above the transition temperature. The entire array will undergo dimerization as shown in Figure 20a. At this time, the symmetry of the system is reduced, and the electric dipole moment appears as a whole. The electric polarization is approximately 3.5 µC∙cm−2. It was also found that the ground state of this system is antiferromagneticallyMicromachines 2019 coupled., 10, 596 Subsequently, Kagawa et al. studied the one-dimensional19 of 30 organic charge transfer system TTF-BA (tetrathiafulvalene-p-bromanil) and predicted that TTF-BA is almost ionic in a wholeIn temperature 2009, Giovannetti region et al. and used undergoes the DFT binding a spin-Peierls model method transition to predict theat 53K. multiferroic It does not show ferromagnetismof organic but molecular shows ferroelectricity crystal TTF-CA (tetrathiafulvalene-p-chloranyl) [13]. [12]. The two molecules are alternately arranged TTF-CA-TTF-CA forming a D–A array. TTF-CA shows a neutral-ionic transition TTF-CAat 81K,is a butcharge there istransfer small charge salt, transfer TTF as (~0.3 an e) electron even above donor the transition and CA temperature. as an electron The entire acceptor. It is found that arrayelectrons will undergo on TTF dimerization spontaneously as shown intransi Figuretion 20a. Atto thisCA time, and the the symmetry ferroelectric of the system phenomena is and complete hysteresisreduced, and theloops electric were dipole observed moment appears in asmany a whole. charge The electric transfer polarization salt is approximatelysystems. Spin-thermal 3.5 µC cm 2. It was also found that the ground state of this system is antiferromagnetically coupled. electronics in organic· − materials are also quietly emerging, and this effect focuses on the interaction of Subsequently, Kagawa et al. studied the one-dimensional organic charge transfer system TTF-BA spin and heat(tetrathiafulvalene-p-bromanil) flow [78]. The thermoelectric and predicted thatan TTF-BAd thermomagnetic is almost ionic in effect a whole has temperature been applied to thermometers,region generators and undergoes and a spin-Peierls coolers. transition These at st 53K.udies It does include not show thermal ferromagnetism conductivity but shows and spin- dependent ferroelectricitySeebeck/Peltier [13]. coefficients, thermal spin transfer torque and spin anomalous TTF-CA is a charge transfer salt, TTF as an electron donor and CA as an electron acceptor. It is thermoelectricfound Hall that effects. electrons on TTF spontaneously transition to CA and the ferroelectric phenomena and In additioncomplete to hysteresis the study loops of were the observed charge in manytransfer charge salt transfer system, salt systems. interesting Spin-thermal phenomena electronics have been in organic materials are also quietly emerging, and this effect focuses on the interaction of spin and found in the study of photoexcitation of organic compounds. In 2012, Ren et al. doped C60 in organic heat flow [78]. The thermoelectric and thermomagnetic effect has been applied to thermometers, semiconductinggenerators single and coolers.crystal These poly-3(hexylthioph studies include thermalene) conductivity nanowires and spin-dependent (nw-P3HT) Seebeck[14]. By/Peltier measuring the hysteresis loopcoeffi cients,of the thermal sample, spin it transfer is found torque that and the spin anomalousmaximum thermoelectric magnetic Hallsusceptibility effects. of the sample is about 10 emu·Incm addition−3 without to the studylight. of At the charge615 nm transfer and salt 20 system, mW interestingof red light, phenomena the maximum have been magnetic found in the study of photoexcitation of organic compounds. In 2012, Ren et al. doped C in organic susceptibility is raised to about 30 emu·cm−3 (as shown in Figure 21a). The experiment60 also found that semiconducting single crystal poly-3(hexylthiophene) nanowires (nw-P3HT) [14]. By measuring the both the electrichysteresis field loop and of the the sample, stress it is can found regulate that the maximum the magnetic magnetic susceptibility susceptibility of the (as sample shown is about in Figure 21b), 3 10 emu cm without light. At 615 nm and 20 mW of red light, the maximum magnetic susceptibility is60 and no magnetic· susceptibility− was detected in both the nw-P3HT single crystal and the C elemental. raised to about 30 emu cm 3 (as shown in Figure 21a). The experiment also found that both the electric It indicates that the charge ·transfer− caused by illumination is the source of the system’s magnetic field and the stress can regulate the magnetic susceptibility (as shown in Figure 21b), and no magnetic properties. This photoexcited ferromagnetism can also be regulated by an electric field, indicating susceptibility was detected in both the nw-P3HT single crystal and the C60 elemental. It indicates that the materialthat the chargehas transferthe characteristics caused by illumination of magnetoelectric is the source of the coupling. system’s magnetic After properties. that, photoexcited This photoexcited ferromagnetism can also be regulated by an electric field, indicating that the material ferromagnetism was also observed in single-walled carbon nanotubes/ C60 system and nw-P3HT/Au has the characteristics of magnetoelectric coupling. After that, photoexcited ferromagnetism was also system [15,16]. observed in single-walled carbon nanotubes/ C60 system and nw-P3HT/Au system [15,16].

Figure 20. (a) Schematic diagram of the TTF-CA molecular crystal. The figure above shows the Figure 20. molecular(a) Schematic arrangement diagram diagram of when the the TTF-CA distribution molecu is uniform,lar crystal. and the electrical The figure polarization above of shows the molecular arrangementthe system is zero. diagram The middle when diagram the isdistribution the molecular is arrangement uniform, diagram and the after electrical dimerization, polarization of and the system is electrically polarized. The figure below shows the system antiferromagnetic coupling and the (b) phase diagram of the system magnetism varying with electron–phonon coupling and electron–electron interaction. By Giovannetti et al. [12] with the permission of Physical Review Letters. Micromachines 2019, 10, x 21 of 31

the system is zero. The middle diagram is the molecular arrangement diagram after dimerization, and the system is electrically polarized. The figure below shows the system antiferromagnetic coupling and the (b) phase diagram of the system magnetism varying with electron–phonon coupling and electron–electronMicromachines interaction.2019, 10, 596 By Giovannetti et al. [12] with the permission of Physical 20Review of 30 Letters.

Figure 21. (a)Figure In the 21. ( a)nw-P3HT/C In the nw-P3HT/60C 60device,device, the the hysteresis hysteresis loop of the deviceloopbefore of the and afterdevice illumination before and after and (b) the magnetization of the nw-P3HT/C60 device with the bias voltage, indicating that the device illumination andhas magnetoelectric(b) the magnetization coupling nature. of By the Ren nw-P3HT/C et al. [14] with the60 permissiondevice with of Advanced the bias Materials. voltage, indicating that the device has magnetoelectric coupling nature. By Ren et al. [14] with the permission of An organic composite chain composed of electron donor and acceptor can be described with Advanced HamiltonianMaterials. [79],

An organic composite chain composedH = ofHD electr+ HA +onHDA donor. and acceptor can be (42) described with Hamiltonian [79], In organic semiconductors, excitons are generated by photoexcitation of electrons from HOMO to LUMO. The probability of electronic transition is determined by the interband transition matrix element

ψ H ψ , where H represents the photo-electrical interaction. In the non-relativistic LUMO| 0 | HOMO 0 approximation, the photo-electrical interaction=++ mainly affects the spatial component of electrons. H HHHD ADA. (42) The spin remains conserved during the transition, and the photo-excited products of interband In organictransition semiconductors, are mainly spin excitons singlet excitons are generate (SE). Consideringd by photoexcitation the transition prohibition, of electrons the output from HOMO of triplet excitons (TE) is negligible. However, if H0 contains spin-related interactions, such as to LUMO. Thespin-flip probability effects, theof electronic yield of triplet transition excitons will is increase determined significantly. by the If the interband electron is intransition a matrix element ψψspin-mixedH ′ , state,where there H is′ no represents pure state transition, the photo-electrical and the SE and TEinteraction. transitions evolve In the into non-relativistic LUMOEX1 and HOMO EX2 transitions (as shown in Figure 22b). For example, for excited EX1, the transition approximation,matrix the photo-electrical element contains both interaction spin conserved mainly transitions affects and the spin sp flipatial transitions, component written of as electrons. The D E D E ψLUMO H0 ψHOMO = ψLUMO,s H0 ψHOMO,s + ψLUMO,s H0 ψHOMO, s . In organic charge transfer spin remains conserved| | during the transition,| | and the photo-excited| | − products of interband transition complexes, photoexcitation may occur within the molecules (donor or acceptor molecules) to form are mainly spinintramolecular singlet excitons excitons; it (SE). may also Considering occur between molecules,the transition where charge prohibition, transfer occurs the to formoutput of triplet excitons (TE) isintermolecular negligible. excitons, However, also known if H as′ charge contains transfer spin-related state. Based on interactio the above model,ns, such a calculation as spin-flip effects, result is shown in Figure 23. For intramolecular excitons, the spin density distribution of the two the yield of tripletexcited excitons states is shownwill increa in Figurese 23 significantly.a,c. It can be found If that the EX1 electron had a local is spinin a density spin-mixed distribution state, there is no pure state transition,with total and net spinthe magneticSE and moment TE transition 1.98 µB, wheres evolveµB is theinto Bohr EX1 magneton. and EX2 EX2 transitions had no spin. (as shown in Figure 22b). ForThe example, spin density for distributions excited ofEX1, the intermolecular the transition excitons matrix EX1 and element EX2 are shown contai in Figurens both 23b,d, spin conserved respectively. For EX1, the calculation shows that the net magnetic moment on the electron donor was transitions and spin flip transitions, written as ψψψψψψHH''=+ H '. In organic 0.91 µB and the net magnetic moment on the acceptorLUMO was 0.96 HOMOµB. Consider LUMO,,,, s the same HOMO s spin LUMO polarization, s HOMO− s charge transferthe complexes, total net magnetic photoexcitation moment was 1.87 µ Bmay. For EX2,occur net magneticwithin moment the molecules on the electron (donor donor or acceptor was 0.85 µ and the net magnetic moment on the acceptor was 0.93 µ . Consider the opposite spin − B B molecules) to polarizationform intramolecular direction, the total excitons; net magnetic it moment may wasalso 0.08 occurµB. between molecules, where charge transfer occurs to form intermolecular excitons, also known as charge transfer state. Based on the above model, a calculation result is shown in Figure 23. For intramolecular excitons, the spin density distribution of the two excited states is shown in Figure 23a,c. It can be found that EX1 had a local spin density distribution with total net spin magnetic moment 1.98 µB, where µB is the Bohr magneton. EX2 had no spin. The spin density distributions of the intermolecular excitons EX1 and EX2 are shown in Figure 23b,d, respectively. For EX1, the calculation shows that the net magnetic moment on the electron donor was 0.91 µB and the net magnetic moment on the acceptor was 0.96 𝜇B. Consider the same spin polarization, the total net magnetic moment was 1.87 µB. For EX2, net magnetic moment on the electron donor was −0.85 µB and the net magnetic moment on the acceptor was 0.93 µB. Consider the opposite spin polarization direction, the total net magnetic moment was 0.08 µB.

MicromachinesMicromachines 2019, 10,2019 x , 10, 596 21 of 30 22 of 31 Micromachines 2019, 10, x 22 of 31

Figure 22. (a) Schematic diagram of the nw-P3HT/C60 charge transfer complex device and Figure 22. (a) Schematic diagram of the nw-P3HT/C charge transfer complex device and corresponding Figurecorresponding 22. (a) theoreticalSchematic modeling diagram and of (bthe) transitions nw-P3HT/C60 of photoexcited60 charge transfer electrons complex between device HOMOand and correspondingtheoretical theoretical modeling modeling and (b) transitions and (b of) transitions photoexcited of electrons photoexcited between electrons HOMOand between LUMO before HOMOand LUMO beforeand after and spin after mixing. spin mixing. LUMO before and after spin mixing.

Figure 23.Figure Intramolecular 23. Intramolecular (a,c) (aand,c) and intermolecular intermolecular ((bb,d,d)) exciton exciton spin spin density density distribution. distribution. (a,b) For (a,b) For Figureexciton 23.EX1exciton Intramolecular and EX1 (c, andd) for (c,d exciton) for(a,c exciton) and EX2. EX2.intermolecular (b,d) exciton spin density distribution. (a,b) For exciton EX1 and (c,d) for exciton EX2. The spontaneous magnetization observed in the excited state is critical to understand the excited Theferromagnetism spontaneous magnetization in organic composites. observ Consideringed in the excited the spin-dependent state is critical interactions, to understand the excited the excited The spontaneous magnetization observed in the excited state is critical to understand the excited ferromagnetismstates of thein systemorganic are composites. intermolecular Considerin EX1 and EX2g statesthe spin-dependent with spin mixing. Dueinteractions, to the intrinsic the excited ferromagnetismstates of strongthe system electron–phonon in organic are intermolecular composites. interaction of EX1Considerin organic and materials,EXg2 thestates theyspin-dependent with are spatiallyspin mixing. localized,interactions, Due similar to thethe to intrinsic excited states of spin-quasiparticles,the system are intermolecular with local spin → sEX1and and→s respectively.EX2 states with As shown spin inmixing. Figure 24Due, →s to, the→s ,intrinsic strong electron–phonon interaction of organic1 material2 s, they are spatially localized,| 1similar| | 2| to spin- strong electron–phononregardless of whether interaction→s 1 and →s 2 ofexhibit organic ferromagnetic material couplings, they are or anti-ferromagneticspatially localized, coupling,≠ similar the to spin- quasiparticles, with local spin s1 and s2 respectively. As shown in Figure 24, s12s , regardless quasiparticles,system with always local has aspin net magnetics and moment.s respectively. Experiments As haveshown also in shown Figure that, 24, in nw-P3HTs≠ s /,C regardless60,   1 2 12 of whetherthe couplings1 and configurations2 exhibit offerromagnetic the two molecules coupling has a certain or anti-ferromagnetic effect on the ferromagnetic coupling, intensity. the system of whether s and s exhibit ferromagnetic coupling or anti-ferromagnetic coupling, the system If the1 coupling2 configuration is similar to that shown in Figure 24, the system is likely to exhibit always has a net magnetic moment. Experiments have also shown that, in nw-P3HT/C60, the coupling excited ferromagnetism. In fact, the configuration of Figure 24b is similar to the model of the organic alwaysconfiguration has a net of magneticthe two molecules moment. hasExperime a certainnts effehavect alsoon the shown ferromagnetic that, in nw-P3HT/C intensity. 60If, the coupling ferromagnetic molecule poly-BIPO [80–82], and the spin coupling between EX1 and EX2 is described configuration ofis the similar two molecules to that shownhas a certain in Figure effect on24, thethe ferromagnetic system is likely intensity. to exhibit If the coupling excited by the Heisenberg model HH = J →s →s . The coupling strength is related to the overlap integral or configuration is similar to that −shown12 1 · in2 Figure 24, the system is likely to exhibit excited ferromagnetism.exciton density In fact, of the the exciton configuration state. of Figure 24b is similar to the model of the organic ferromagnetism.ferromagnetic molecule In fact, poly-BIPO the configuration [80–82], and of Figuthe spinre 24b coupling is similar between to the EX1 model and EX2 of isthe described organic ferromagnetic molecule poly-BIPO=− [80–82], ⋅ and the spin coupling between EX1 and EX2 is described by the Heisenberg model H H Js12 1 s 2 . The coupling strength is related to the overlap integral or by the Heisenberg model H =−Js ⋅ s. The coupling strength is related to the overlap integral or exciton density of the excitonH state. 12 1 2 exciton density of the exciton state.

Micromachines 2019, 10, 596 22 of 30 Micromachines 2019, 10, x 23 of 31 Micromachines 2019, 10, x 23 of 31

FigureFigure 24. Schematic 24. Schematic diagrams diagram of (a )of only exciton triplet coupling or EX1 configuration excitons in parallel of organic configuration, compounds. and (b) alternativeFigure EX1 24. and Schematic EX2 configuration. diagram of exciton coupling configuration of organic compounds. We noticed that one type of room-temperature chiral charge transfer magnet nw-P3HT/C60 was reportedWe noticed [83]. Compared that that one one totype type the of achiral, of room-temperature room-temperature it has not only chiral good chiral charge thermal charge transfer stability transfer magnet but magnet also nw-P3HT/C good nw-P3HT tunability60 /wasC60 wasreportedon both reported saturation[83]. Compared [83]. Comparedmagnetizatio to the achiral, ton the and achiral, it magnetoelectric has not it hasonly not good onlycoupling thermal good e stabilityffect thermal under but stability circularlyalso good but alsotunabilitypolarized good tunabilityonlight. both Yang saturation on et bothal. have saturationmagnetizatio found that magnetizationn organic and magnetoelectric charge and transfer magnetoelectric coupling complex epyrene-F4TCNQ couplingffect under eff ectcircularly under (pyrene-2,3,5,6- circularlypolarized polarizedlight.tetrafluoro-7,7,8,8-tetracyanoquinodimethane) Yang light. et al. have Yang found et al. that have organic found charge that can organic transfer display charge complex anisotropic transfer pyrene-F4TCNQ magnetoelectric complex pyrene-F4TCNQ (pyrene-2,3,5,6- coupling and (pyrene-2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane)tetrafluoro-7,7,8,8-tetracyanoquinodimethane)changing the fluorine content in complexes, macangnetoelectric display anisotropic can coupling display magnetoelectric anisotropicand magnetization magnetoelectric coupling can and be couplingchangingtuned [84]. andthe In changingparticular,fluorine thecontent observation fluorine in complexes, content of the in Cotton– complexes, magnetoelectricMouton magnetoelectric effect coupling in the complex couplingand magnetization provided and magnetization a feasiblecan be cantunedpath be for [84]. tuned the In design [particular,84]. In of particular, organic observation magnetoelectric observation of the Cotton– of devices. the Cotton–MoutonMouton effect in etheffect complex in the complex provided provided a feasible a feasiblepath for paththe design for the of design organic of organicmagnetoelectric magnetoelectric devices. devices. 5. Organic Spin Current 5. Organic Spin Current In a spin valve, the polarization current is injected into the organic layer from the ferromagnetic electrodeIn a spinby driving valve, the voltage. polarization In 2013, current Ando isof injectedinjeTohokucted into University the organic and layerWatanabe from theof the ferromagnetic Cambridge electrodeUniversity by discovered driving voltage. the existenc In In 2013, e of Ando pure ofspin Tohoku current University in organi and c semiconductors Watanabe of the [17, CambridgeCambridge 18]. They University discovered the existence of pure spin current in organic semiconductors [17,18]. Universityprepared discovereddevice Ni 80theFe 20existenc/PBTTTe of( poly(2,5-bis(3-alkylthiophen-2-yl)thieno[3,2-b]thiophenepure spin current in organic semiconductors [17, 18]. They)/Pt. They prepared device Ni Fe /PBTTT (poly(2,5-bis(3-alkylthiophen-2-yl)thieno[3,2-b]thiophene)/Pt. preparedStructure ofdevice the device Ni 80isFe80 shown20/PBTTT20 in Figure (poly(2,5-bis(3-alkylthiophen-2-yl)thieno[3,2-b]thiophene 25. )/Pt. Structure of the device is shown inin FigureFigure 2525..

Figure 25. Schematic diagram of an organic pure spin current device by Watanabe et al. [18] with the Figurepermission 25. Schematic of Nature diagram Physics. of The an middle organic layer pure is spin an organiccurre currentnt polymerdevice by film. Watanabe et al. [[18]18] with the permission of Nature Physics.Physics. The middle layer is an organic polymer film.film. By microwave excitation, spin is pumped to the organic polymer layer PBTTT. The spin current is convertedBy microwave into a excitation,currentexcitation, detected spinspin isis atpumped pumped the metal to tothe Ptthe end organic organic (inverse polymer polyme spinr layer Halllayer PBTTT.effect, PBTTT. ISHE) The The spin spindue current tocurrent spin- is convertedisorbit converted coupling, into into a which current a current demonstrates detected detected at theat the the metal existence metal Ptend Pt ofend (inverse the (inverse pure spin spin spin Hall current. Hall effect, effect, ISHE)In this ISHE) due experiment, todue spin-orbit to spin- no coupling,orbitexternal coupling, electric which whichfield demonstrates was demonstrates applied, the existencethus the there existence of was the no pureof directionalthe spin pure current. spin movement current. In this of experiment, In carriers this experiment, in nothe externalorganic no electricexternallayer. The fieldelectric Hall was bias field applied, measured was applied, thus in there the thus Pt was thereelectrode no was directional isno proportional directional movement movement to the of spin carriers of current carriers in the that in organic thereaches organic layer. the Thelayer.electrode Hall The bias through Hall measured bias the measured organic in the Ptlayer. in electrode the The Pt electrode measurement is proportional is proportional of toHall the voltage spin to currentthe varies spin that withcurrent reaches the thatthickness the reaches electrode of the −d /λ electrode through the organic layer. TheVde measurement()∝ s ofλ Hall=± voltage varies with the thickness of the organic layer is the exponential form, ISHE , s 153 32 nm characterizes the spin decay −d /λ Vde()∝ s λ =± organic layer is the exponential form, ISHE , s 153 32 nm characterizes the spin decay

Micromachines 2019, 10, 596 23 of 30 through the organic layer. The measurement of Hall voltage varies with the thickness of the organic d/λ layer is the exponential form, V (d) e s , λs = 153 32 nm characterizes the spin decay length ISHE ∝ − ± in the organic layer. The exponential behavior further demonstrates that the bias is generated by the ISHE in the non-magnetic Pt electrode. At the same time, the exponential behavior also indicates that the spin current in the organic layer is likely to be transported in some way. This study shows that pure spin currents can be achieved in organic semiconductors and are transported by spin polarons. Meanwhile, Ando et al. directly measured the spin-charge conversion effects of PSS (poly (4-styrenesulphonate)) doped with the PEDOT (poly (3,4-ethylenedioxythiophene)) molecule [17]. They injected the spin current from the magnetic insulator Y3Fe5O12 vertically into the PEDOT: PSS by spin pumping. The conversion voltage measured in the gold electrodes on both sides is 600 nanovolts, which is two orders of magnitude smaller than the conversion voltage of metal Pt and close to the inorganic semiconductor silicon switching voltage (microvolt order of magnitude) [85]. The experimenter further found that, although the conversion bias is low, the organic spin-charge conversion efficiency is almost comparable to that of metal Pt. They believe that although the spin-orbit coupling in organic materials is much weaker than that of metal Pt, its longer spin relaxation time and conductivity anisotropy are conductive to improve the spin-charge conversion efficiency. Pulse-ferromagnetic resonance technique was used to inject spin current from ferromagnetic metal NiFe into organic semiconductors with different spin-orbit coupling strengths. The spin-charge conversion phenomena were also observed by the measurements of conversion bias and conversion efficiency [86]. Similarly, the spin-charge conversion phenomena in single-layer graphene have also been observed in spin-pumped experiments [87]. Yu proposed a polaron coupling model in organic semiconductors [88]. The Hamiltonian can be written as H = H0 + Hh + He, where: X + + → H0 = εi(a ai + a ai ) gµB→s i B, (43) i ↑ i ↓ − · i ↑ ↓ X = ( + + + ) Hh Vij ais ajs ajs ais , (44) ij s h i X He = J →s →s , (45) ij i · j ij + where ais indicates that a polaron with spin s is generated on molecule i. εi is the positional energy of P the polaron. Spin of the polaron can be written as →s = ( /2) a+→σ a . V is the polaron transition i } iσ σσ0 iσ0 ij σσ0 integral, and Jij is the exchange integral between polarons. If we considered the incoherent transport, polaron hopping between molecules is described by the master equation, and the spin polarization at molecule i follows the kinetic equation,

dM→ X X i = M→ →ω w (1 f )(M→ M→ ) f η (M→ M→ ), (46) dt i × − ij − j i − j − j ij i − j j j

→ e → where ω = 2m B, fj is the probability of a polaron at molecule j and determined by the master equation,

d fj X = [w f (1 f ) w f (1 f )], (47) dt − ji j − i − ij i − j i where wij indicates the hopping rate of the polaron from molecule i to j per unit time, which can be given P 2 = √ 2 2 = 2 ( + ) by the Marcus transition formula. ηij πJij/ωe, ωe 8JijS S 1 /3 12J . Polaron hopping j ' occurs between occupied and unoccupied molecules, as described by the second term on the right side Micromachines 2019, 10, x 25 of 31

where wij indicates the hopping rate of the polaron from molecule i to j per unit time, which can be given by the Marcus transition formula. η = πωJ 2 , ω 22=+8(1)312J SS J 2. Polaron ij ij e eij  j hopping occurs between occupied and unoccupied molecules, as described by the second term on the right side of Equation (46); spin exchange of polaron occurs between occupied molecules and is given by the third item on the right of Equation (46), which contributes to the spin distribution. When the spin polarization changes slowly in space, the kinetic equation can be reduced to the continuous equation: Micromachines 2019, 10, 596 24 of 30  dM 2  =+∇+×()DD MMω , (48) of Equation (46); spin exchange of polarondt occurshe between occupied molecules and is given by the third item on the right of Equation (46), which contributes to the spin distribution. = 2 =≡ηπ22 whereWhen Dh thewa spin and polarization DRe changes12 slowly JR are in space, hopping-induced the kinetic equation and exchange-induced can be reduced to spin the continuous equation: η η diffusion (SD) constants respectively. w() is the ensemble average of wij() ij , and aR() is the → dM 2 → → average spacing of molecules (polarons).= (SinceD + DDe) = 0M, +theM diffusion→ω, constant of charge and spin (48) is dt h e ∇ × the same in inorganic materials. D =0 in magnetic insulators, so spin transport is mainly generated 2 2 h 2 where D = wa and De = ηR √π/12J R are hopping-induced and exchange-induced spin by exchange.h The spin-exchange coupling≡ between polarons is determined by their interaction and w( ) w ( ) a(R) diffusion (SD) constants respectively. η is the ensemble average of ij −ηij ξ, and is the average φ r / spacingthe overlap of molecules of wave functions. (polarons). Sinc Sincee theD epolaron= 0, the is di aff localizedusion constant state of~ chargee , andthe exchange spin is the coupling same in inorganichas the following materials. form:Dh = 0 in magnetic insulators, so spin transport is mainly generated by exchange. The spin-exchange coupling between polarons is determined by their interaction and the overlap 5/2 r/ξ of wave functions. Since the polaron is a localized2 state φ e− , the exchange coupling has the eR −2/R ξ Je= 0.821 ∼ , (49) following form: εξ ξ 2 !5/2 e R 2R/ξ J = 0.821 e− , (49) where ε is the dielectric constant and ξ isεξ theξ local length of the polaron state. The average

−1/3 Rn= nfV= 3 wheredistanceε is of the the dielectric polarons constantis related and to itsξ is concentration, the local length of the, polaron state.i . For The the average Alq molecule, distance 1/3 P i of the polarons is related to its concentration, R = n− , n = fi/V. For the Alq3 molecule, ε = 2, ε = ξ = 1 i 2 , and fixed D h . Figure 26 gives the relationship between exchange-induced spin ξ = 1 and fixed Dh. Figure 26 gives the relationship between exchange-induced spin diffusion and diffusion and polaron concentration. It can be seen that when the polaron concentration n 17exceeds3 polaron concentration. It can be seen that when the polaron concentration n exceeds 10 cm− , 1017 cm−3, the exchange-induced spin diffusion begins to become apparent and quickly dominates. the exchange-induced spin diffusion begins to become apparent and quickly dominates.

FigureFigure 26.26. Relationship between the spin didiffusionffusion (SD) constantconstant and polaron density by Yu etet al.al. [[88]88] with the permission of Physical Review Letters. Black and red (gray) lines are De and D/Dh respectively, with the permission of Physical Review Letters. Black and red (gray) lines are D e and DDh D = k T e = 6cm2 s where h νh B / and νh 10− / . The inset illustrates−62 hopping-induced and exchange-induced respectively, where DkTe= ν and ν = 10 cm s . The inset illustrates hopping-induced and solid (open) circles representhhB occupied (vacant)h sites. and exchange-induced and solid (open) circles represent occupied (vacant) sites. 6. Organic Spin Device Outlook 6. OrganicSince theSpin 1980s, Device the Outlook major progress or breakthrough comes about every decade. In the 1980s, the focus of research was on the conductivity of organic materials, which is throughout the research of organic semiconductors; in the 1990s, organic light-emitting achieved a major breakthrough. At present, the organic display has gone to market, and optimized research is still going on. Organic spintronics has been the focus of research for the past decade. New phenomena such as organic spin valves, organic strong magnetic effects, organic multiferroics and organic spin currents are emerging one after another. Organic semiconductors have abundant properties in electromagnetism and optics, which can be used to prepare various electronic devices, such as OLEDs, organic transistors and organic solar cells. Monochromatic and multi-color displays based on OLEDs have entered the commercial application Micromachines 2019, 10, 596 25 of 30 stage. As new phenomena continue to be revealed, some novel organic devices may be fabricated. For example, OLED luminescence is mainly based on spin singlet excitons, which can be controlled by a magnetic electrode or the external magnetic field to realize the magnetic regulation of luminescence. Some studies indicated that considerable spin-orbit coupling strength of organic materials could be achieved in some cases. First, some molecules contain heavy atoms in their own components. For example, the current Alq3 molecule wildly studied contains the Al element, and the CuPc molecule contains the Cu element. When the molecule contains S or an atom with a larger atomic number, its spin-orbit coupling can have a significant effect on spin relaxation. Theoretical calculation shows the dependence of organic spin diffusion length on temperature and electric field, indicating that the Elliott–Yafet mechanism caused by spin-orbit coupling plays an important role in organic spin relaxation [89]. This also makes the introduction of heavy elements an organic one of the effective ways to artificially design organic materials with strong spin-orbit coupling. For example, Liu et al, from the University of Utah, have theoretically designed a two-dimensional organometallic mesh by introducing heavy metal elements (Mn, In, Ti, etc.) into the triphenyl molecules, and the first-principles calculation shows that this structure can realize a topological insulator, quantum anomalous hall effect and other phenomena [90]. On the other hand, studies have shown that changes of organic molecular structure and orbital hybridization can also result in enhancement of spin-orbit coupling strength even without heavy elements. Such as Shuai et al. DFT study shows that the distortion between carbon ball substituents or benzene rings changes the spin-orbit coupling, and then changes the intersystem transition [91]; according to the theoretical calculations, Yu pointed that when the two biphenyl rings of biphenyl molecules are perpendicular to each other rather than coplanar structures, spin-orbit coupling strength of the system can be increased by nearly four orders of magnitude [92]. It is worth mentioning that when the orbital hybridization of individual carbon atoms changes from sp2 to sp3 by introducing structural defects to a single-layer graphene containing only carbon atoms, the spin-orbit coupling is improved by nearly three orders of magnitude [93]. In terms of order of magnitude of spin-orbit couplings strength, bending carbon nanotubes is comparable to GaAs semiconductors, which results from variation of sp2 hybrid state caused by the curved structure. The peculiar phenomenon has aroused great research interest in the past few years. Structural diversity of organic molecules and abnormally abundant methods of structural modulation, such as changing the torsion angle, side group substitution, tensile compression, etc., provide many feasible paths to enhance spin-orbit coupling in pure organic materials. In 2006, the Naaman group, in Israel, adsorbed a double-stranded DNA monolayer on the Au substrate. It is found that its photoelectron transmission spectrum has a spin polarization phenomenon, which is called CISS (chiral-induced spin selectivity) [94]. The effect does not seem to exist in a single helix DNA molecule [95]. However, spin polarization of transmitted electrons in bacteriorhodopsin (a single α-helix bacterial rhodopsin) was found by Mishra et al. in 2013 and Einati et al. in 2015, respectively [96,97]. Therefore, the CISS effect should be a general feature of chiral molecules or chiral nanostructured materials. Spiral or axial chirality is an important type of chiral structure. DNA and proteins have a helical chiral structure, and carbon nanotubes can also form chiral structures. Chiral molecules can self- assemble into nanostructures, superstructures and even macrostructures, and their unique structural spin-orbit coupling can produce many novel spin-charge correlation phenomena. “Chiral Electronics” or “Chiral Spintronics” has quietly appeared [98–104]. Researches on organic chiral spin-related phenomena not only promote the development of organic spintronics, promote the intersection of physics and chemistry and micro-nano electronics and develop the application of organic chiral molecules and fibers in functions such as electromagnetism optics and others; but also contribute to understand the information storage and transmission of biological macromolecules, provide a physical perspective of the complex life and design more organic (spin) electronics that are stretchable, wearable or implantable. Micromachines 2019, 10, 596 26 of 30

Over the past few years, more and more functional properties of organic materials have been exploited, including electrical, magnetic and optical properties. We believed that all-organic devices would appear in the future. They have functions of display, sensing and recognition, and have features such as low energy consumption, low cost and foldability. This chapter reviews the recent developments in organic spintronics, including the theoretical work of our group related to the chapter. Organic materials are soft, resourceful and inexpensive. Compared to inorganic materials, organic functional materials have advantages in the application fields of future electronic and spintronic devices. All these properties motivate people to develop organic functional devices. The development of this field is not so smooth, such as the instability of experimental data, the diversity of theoretical models and so on. Nevertheless, research on organic spintronics has only just begun, people’s enthusiasm for organic spintronics is growing. We believed that persistent research on organic functional materials and organic devices will contribute to understanding the relevant effect mechanisms that are not yet clear and explore better application potential.

Author Contributions: Writing—original draft preparation, Q.T.; writing—review and editing, Q.T. and S.X. Funding: This review is supported by the National Natural Science Foundation of China (No.11574180, No.11974212) and the 111 Project of State Administration of Foreign Experts Affairs P. R. China (B13029). Acknowledgments: We are grateful to Liu Yang who provided rich theoretical results, and to Fujiang Yang who collected and organized a great deal of work. Conflicts of Interest: The authors declare no conflicts of interest.

References

1. Baibich, M.N.; Broto, J.M.; Fert, A.; Nguyen Van Dau, F.; Petroff, F.; Etienne, P.; Creuzet, G.; Friederich, A.; Chazelas, J. Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices. Phys. Rev. Lett. 1988, 61, 2472–2475. [CrossRef][PubMed] 2. Binasch, G.; Grunberg, P.; Saurenbach, F.; Zinn, W. Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange. Phys. Rev. B Condens. Matter 1989, 39, 4828–4830. [CrossRef][PubMed] 3. Slonczewski, J.C. Current-driven excitation of magnetic multilayers. J. Magn. Magn. Mater. 1996, 159, L1–L7. [CrossRef] 4. Berger, L. Emission of spin waves by a magnetic multilayer traversed by a current. Phys. Rev. B 1996, 54, 9353–9358. [CrossRef][PubMed] 5. Tsoi, M.; Jansen, A.G.M.; Bass, J.; Chiang, W.C.; Seck, M.; Tsoi, V.; Wyder, P. Excitation of a Magnetic Multilayer by an Electric Current. Phys. Rev. Lett. 1998, 80, 4281–4284. [CrossRef] 6. Myers, E.B.; Ralph, D.C.; Katine, J.A.; Louie, R.N.; Buhrman, R.A. Current-Induced Switching of Domains in Magnetic Multilayer Devices. Science 1999, 285, 867. [CrossRef][PubMed] 7. Wolf, S.A.; Awschalom, D.D.; Buhrman, R.A.; Daughton, J.M.; von Molnár, S.; Roukes, M.L.; Chtchelkanova, A.Y.; Treger, D.M. Spintronics: A Spin-Based Electronics Vision for the Future. Science 2001, 294, 1488. [CrossRef] [PubMed] 8. Dediu, V.; Murgia, M.; Matacotta, F.C.; Taliani, C.; Barbanera, S. Room temperature spin polarized injection in organic semiconductor. Solid State Commun. 2002, 122, 181–184. [CrossRef] 9. Xiong, Z.H.; Wu, D.; Valy Vardeny, Z.; Shi, J. Giant magnetoresistance in organic spin-valves. Nature 2004, 427, 821–824. [CrossRef][PubMed] 10. Francis, T.L.; Mermer, Ö.; Veeraraghavan, G.; Wohlgenannt, M. Large magnetoresistance at room temperature in semiconducting polymer sandwich devices. New J. Phys. 2004, 6, 185. [CrossRef] 11. Mermer, Ö.; Veeraraghavan, G.; Francis, T.L.; Sheng, Y.; Nguyen, D.T.; Wohlgenannt, M.; Köhler, A.; Al-Suti, M.K.; Khan, M.S. Large magnetoresistance in nonmagneticπ-conjugated semiconductor thin film devices. Phys. Rev. B 2005, 72, 205202. [CrossRef] 12. Giovannetti, G.; Kumar, S.; Stroppa, A.; van den Brink, J.; Picozzi, S. Multiferroicity in TTF-CA organic molecular crystals predicted through ab initio calculations. Phys. Rev. Lett. 2009, 103, 266401. [CrossRef] [PubMed] Micromachines 2019, 10, 596 27 of 30

13. Kagawa, F.; Horiuchi, S.; Tokunaga, M.; Fujioka, J.; Tokura, Y. Ferroelectricity in a one-dimensional organic quantum magnet. Nat. Phys. 2010, 6, 169–172. [CrossRef] 14. Ren, S.; Wuttig, M. Organic exciton multiferroics. Adv. Mater. 2012, 24, 724–727. [CrossRef][PubMed] 15. Qin, W.; Gong, M.; Chen, X.; Shastry, T.A.; Sakidja, R.; Yuan, G.; Hersam, M.C.; Wuttig, M.; Ren, S. Multiferroicity of carbon-based charge-transfer magnets. Adv. Mater. 2015, 27, 734–739. [CrossRef] 16. Qin, W.; Chen, X.; Li, H.; Gong, M.; Yuan, G.; Grossman, J.C.; Wuttig, M.; Ren, S. Room Temperature Multiferroicity of Charge Transfer Crystals. ACS Nano 2015, 9, 9373–9379. [CrossRef] 17. Ando, K.; Watanabe, S.; Mooser, S.; Saitoh, E.; Sirringhaus, H. Solution-processed organic spin-charge converter. Nat. Mater. 2013, 12, 622–627. [CrossRef] 18. Watanabe, S.; Ando, K.; Kang, K.; Mooser, S.; Vaynzof, Y.; Kurebayashi, H.; Saitoh, E.; Sirringhaus, H. Polaron spin current transport in organic semiconductors. Nat. Phys. 2014, 10, 308–313. [CrossRef] 19. Anderson, P.W. Antiferromagnetism. Theory of Superexchange Interaction. Phys. Rev. 1950, 79, 350–356. [CrossRef] 20. Sun, Q.-F.; Wang, J.; Guo, H. Quantum transport theory for nanostructures with Rashba spin-orbital interaction. Phys. Rev. B 2005, 71, 165310. [CrossRef] 21. Tarafder, K.; Sanyal, B.; Oppeneer, P.M. Charge-induced spin polarization in nonmagnetic organic moleculeAlq3. Phys. Rev. B 2010, 82, 060413. [CrossRef] 22. Hou, D.; Qiu, J.; Xie, S.; Saxena, A. Charge-induced spin polarization in thiophene oligomers. New J. Phys. 2013, 15, 073044. [CrossRef] 23. Han, S.; Jiang, H.; Li, X.; Xie, S. Spontaneous spin polarization in organic thiophene oligomers. Org. Electron. 2014, 15, 240–244. [CrossRef] 24. Sakurai, J.J.; Napolitano, J. Modern Quantum Mechanics, 2nd ed.; Cambridge University Press: Cambridge, UK, 2018. 25. Majumdar, S.; Majumdar, H.S.; Laiho, R.; Österbacka, R. Comparing small molecules and polymer for future organic spin-valves. J. Alloy. Compd. 2006, 423, 169–171. [CrossRef] 26. Wang, F.J.; Xiong, Z.H.; Wu, D.; Shi, J.; Vardeny, Z.V. Organic spintronics: The case of Fe/Alq3/Co spin-valve devices. Synth. Met. 2005, 155, 172–175. [CrossRef] 27. Pramanik, S.; Stefanita, C.G.; Patibandla, S.; Bandyopadhyay, S.; Garre, K.; Harth, N.; Cahay, M. Observation of extremely long spin relaxation times in an organic nanowire spin valve. Nat. Nanotechnol. 2007, 2, 216–219. [CrossRef] 28. Dediu, V.; Hueso, L.E.; Bergenti, I.; Riminucci, A.; Borgatti, F.; Graziosi, P.; Newby, C.; Casoli, F.; De Jong, M.P.; Taliani, C.; et al. Room-temperature spintronic effects inAlq3-based hybrid devices. Phys. Rev. B 2008, 78, 115203. [CrossRef] 29. Hill, E.W.; Geim, A.K.; Novoselov, K.; Schedin, F.; Blake, P. Graphene Spin Valve Devices. IEEE Trans. Magn. 2006, 42, 2694–2696. [CrossRef] 30. Tsukagoshi, K.; Alphenaar, B.W.; Ago, H. Coherent transport of electron spin in a ferromagnetically contacted carbon nanotube. Nature 1999, 401, 572–574. [CrossRef] 31. Julliere, M. Tunneling between ferromagnetic films. Phys. Lett. A 1975, 54, 225–226. [CrossRef] 32. Nguyen, T.D.; Hukic-Markosian, G.; Wang, F.; Wojcik, L.; Li, X.G.; Ehrenfreund, E.; Vardeny, Z.V. Isotope effect in spin response of pi-conjugated polymer films and devices. Nat. Mater. 2010, 9, 345–352. [CrossRef][PubMed] 33. Lei, J.; Li, H.; Yin, S.; Xie, S.-J. Spin precession of a polaron induced by a gate voltage in one-dimensional organic polymers. J. Phys. Condens. Matter 2008, 20, 095201. [CrossRef] 34. Qin, W.; Yin, S.; Gao, K.; Xie, S.J. Investigation on organic magnetoconductance based on polaron-bipolaron transition. Appl. Phys. Lett. 2012, 100, 124. [CrossRef] 35. Zwolak, M.; Di Ventra, M. DNA spintronics. Appl. Phys. Lett. 2002, 81, 925–927. [CrossRef] 36. Li, K.-S.; Chang, Y.-M.; Agilan, S.; Hong, J.-Y.; Tai, J.-C.; Chiang, W.-C.; Fukutani, K.; Dowben, P.A.; Lin, M.-T. Organic spin valves with inelastic tunneling characteristics. Phys. Rev. B 2011, 83, 172404. [CrossRef] 37. Yu, Z.G. Spin-orbit coupling, spin relaxation, and spin diffusion in organic solids. Phys. Rev. Lett. 2011, 106, 106602. [CrossRef][PubMed] 38. Xie, S.J.; Ahn, K.H.; Smith, D.L.; Bishop, A.R.; Saxena, A. Ground-state properties of ferromagnetic metal/conjugated polymer interfaces. Phys. Rev. B 2003, 67, 125202. [CrossRef] 39. Fu, J.-Y.; Ren, J.-F.; Liu, X.-J.; Liu, D.-S.; Xie, S.-J. Dynamics of charge injection into an open conjugated polymer: A nonadiabatic approach. Phys. Rev. B 2006, 73, 195401. [CrossRef] Micromachines 2019, 10, 596 28 of 30

40. Dalgleish, H.; Kirczenow, G. Spin-current rectification in molecular wires. Phys. Rev. B 2006, 73, 235436. [CrossRef] 41. Gallagher, N.M.; Olankitwanit, A.; Rajca, A. High-spin organic molecules. J. Org. Chem. 2015, 80, 1291–1298. [CrossRef] 42. Ruden, P.P.; Smith, D.L. Theory of spin injection into conjugated organic semiconductors. J. Appl. Phys. 2004, 95, 4898–4904. [CrossRef] 43. Bergenti, I.; Borgatti, F.; Calbucci, M.; Riminucci, A.; Cecchini, R.; Graziosi, P.; MacLaren, D.A.; Giglia, A.; Rueff, J.P.; Céolin, D.; et al. Oxygen Impurities Link Bistability and Magnetoresistance in Organic Spin Valves. ACS Appl. Mater. Interfaces 2018, 10, 8132–8140. [CrossRef][PubMed] 44. Riminucci, A.; Yu, Z.-G.; Prezioso, M.; Cecchini, R.; Bergenti, I.; Graziosi, P.; Dediu, V.A. Controlling Magnetoresistance by Oxygen Impurities in Mq3-Based Molecular Spin Valves. ACS Appl. Mater. Interfaces 2019, 11, 8319–8326. [CrossRef][PubMed] 45. Tsurumi, J.; Matsui, H.; Kubo, T.; Häusermann, R.; Mitsui, C.; Okamoto, T.; Watanabe, S.; Takeya, J. Coexistence of ultra-long spin relaxation time and coherent charge transport in organic single-crystal semiconductors. Nat. Phys. 2017, 13, 994. [CrossRef] 46. Wang, C.; Dong, H.; Jiang, L.; Hu, W. Organic semiconductor crystals. Chem. Soc. Rev. 2018, 47, 422–500. [CrossRef][PubMed] 47. Zhang, X.; Dong, H.; Hu, W. Organic Semiconductor Single Crystals for Electronics and Photonics. Adv. Mater. 2018, 30, 1801048. [CrossRef][PubMed] 48. Guo, L.; Qin, Y.; Gu, X.; Zhu, X.; Zhou, Q.; Sun, X. Spin Transport in Organic Molecules. Front. Chem. 2019, 7, 428. [CrossRef][PubMed] 49. Hu, B.; Yan, L.; Shao, M. Magnetic-Field Effects in Organic Semiconducting Materials and Devices. Adv. Mater. 2009, 21, 1500–1516. [CrossRef] 50. Davis, A.H.; Bussmann, K. Large magnetic field effects in organic light emitting diodes based

on tris(8-hydroxyquinoline aluminum) (Alq3)/N,N0-Di(naphthalen-1-yl)-N,N0diphenyl-benzidine (NPB) bilayers. J. Vac. Sci. Technol. A 2004, 22, 1885–1891. [CrossRef] 51. Shakya, P.; Desai, P.; Somerton, M.; Gannaway, G.; Kreouzis, T.; Gillin, W.P. The magnetic field effect on the transport and efficiency of group III tris(8-hydroxyquinoline) organic light emitting diodes. J. Appl. Phys. 2008, 103, 103715. [CrossRef] 52. Martin, J.L.; Bergeson, J.D.; Prigodin, V.N.; Epstein, A.J. Magnetoresistance for organic semiconductors: Small molecule, oligomer, conjugated polymer, and non-conjugated polymer. Synth. Met. 2010, 160, 291–296. [CrossRef] 53. Kang, H.; Park, C.H.; Lim, J.; Lee, C.; Kang, W.; Yoon, C.S. Power law behavior of magnetoresistance in tris(8-hydroxyquinolinato)aluminum-based organic light-emitting diodes. Org. Electron. 2012, 13, 1012–1017. [CrossRef] 54. Frankevich, E.; Zakhidov, A.; Yoshino, K.; Maruyama, Y.; Yakushi, K. Photoconductivity of poly(2,5-diheptyloxy-p-phenylene vinylene) in the air atmosphere: Magnetic-field effect and mechanism of generation and recombination of charge carriers. Phys. Rev. B 1996, 53, 4498–4508. [CrossRef][PubMed] 55. Kalinowski, J.; Cocchi, M.; Virgili, D.; Di Marco, P.; Fattori, V. Magnetic field effects on emission and current in Alq3-based electroluminescent diodes. Chem. Phys. Lett. 2003, 380, 710–715. [CrossRef] 56. Zhang, Y.; Ren, J.; Lei, J.; Xie, S. Effect of Co permeation on spin polarized transport in a Co/organic semiconductor (OSC) structure. Org. Electron. 2009, 10, 568–572. [CrossRef] 57. Nguyen, T.D.; Sheng, Y.; Rybicki, J.; Veeraraghavan, G.; Wohlgenannt, M. Device-spectroscopy of magnetic field effects in several different polymer organic light-emitting diodes. Synth. Met. 2010, 160, 320–324. [CrossRef] 58. Veeraraghavan, G.; Nguyen, T.D.; Sheng, Y.; Mermer, O.; Wohlgenannt, M. Magnetic field effects on current, electroluminescence and photocurrent in organic light-emitting diodes. J. Phys. Condens. Matter 2007, 19, 036209. [CrossRef] 59. Ding, B.F.; Yao, Y.; Sun, Z.Y.; Wu, C.Q.; Gao, X.D.; Wang, Z.J.; Ding, X.M.; Choy, W.C.H.; Hou, X.Y. Magnetic field effects on the electroluminescence of organic light emitting devices: A tool to indicate the carrier mobility. Appl. Phys. Lett. 2010, 97, 228. [CrossRef] 60. Majumdar, S.; Majumdar, H.S.; Aarnio, H.; Vanderzande, D.; Laiho, R.; Österbacka, R. Role of electron-hole pair formation in organic magnetoresistance. Phys. Rev. B 2009, 79, 201202. [CrossRef] Micromachines 2019, 10, 596 29 of 30

61. Prigodin, V.N.; Bergeson, J.D.; Lincoln, D.M.; Epstein, A.J. Anomalous room temperature magnetoresistance in organic semiconductors. Synth. Met. 2006, 156, 757–761. [CrossRef] 62. Obolda, A.; Peng, Q.; He, C.; Zhang, T.; Ren, J.; Ma, H.; Shuai, Z.; Li, F. Triplet-Polaron-Interaction-Induced Upconversion from Triplet to Singlet: A Possible Way to Obtain Highly Efficient OLEDs. Adv. Mater. 2016, 28, 4740–4746. [CrossRef][PubMed] 63. Wallikewitz, B.H.; Kabra, D.; Gélinas, S.; Friend, R.H. Triplet dynamics in fluorescent polymer light-emitting diodes. Phys. Rev. B 2012, 85, 045209. [CrossRef] 64. Sun, Z.; Liu, D.; Stafstrom, S.; An, Z. Scattering process between polaron and exciton in conjugated polymers. J. Chem. Phys. 2011, 134, 044906. [CrossRef][PubMed] 65. Troisi, A.; Orlandi, G. Charge-transport regime of crystalline organic semiconductors: Diffusion limited by thermal off-diagonal electronic disorder. Phys. Rev. Lett. 2006, 96, 086601. [CrossRef][PubMed] 66. Nguyen, T.D.; Sheng, Y.; Wohlgenannt, M.; Anthopoulos, T.D. On the role of hydrogen in organic magnetoresistance: A study of C60 devices. Synth. Met. 2007, 157, 930–934. [CrossRef] 67. Rolfe, N.J.; Heeney, M.; Wyatt, P.B.; Drew, A.J.; Kreouzis, T.; Gillin, W.P. Elucidating the role of hyperfine interactions on organic magnetoresistance using deuterated aluminium tris(8-hydroxyquinoline). Phys. Rev. B 2009, 80, 241201. [CrossRef] 68. Yang, F.J.; Qin, W.; Xie, S.J. Investigation of giant magnetoconductance in organic devices based on hopping mechanism. J. Chem. Phys. 2014, 140, 144110. [CrossRef] 69. Desai, P.; Shakya, P.; Kreouzis, T.; Gillin, W.P. Magnetoresistance in organic light-emitting diode structures under illumination. Phys. Rev. B 2007, 76, 235202. [CrossRef] 70. Wang, X.R.; Xie, S.J. A theory for magnetic-field effects of nonmagnetic organic semiconducting materials. EPL (Europhys. Lett.) 2010, 92, 57031. [CrossRef] 71. Li, S.; Dong, X.; Yi, D.; Xie, S. Theoretical investigation on magnetic field effect in organic devices with asymmetrical molecules. Org. Electron. 2013, 14, 2216–2222. [CrossRef] 72. Nguyen, T.D.; Sheng, Y.; Rybicki, J.; Veeraraghavan, G.; Wohlgenannt, M. Magnetoresistance in π-conjugated organic sandwich devices with varying hyperfine and spin–orbit coupling strengths, and varying dopant concentrations. J. Mater. Chem. 2007, 17, 1995–2001. [CrossRef] 73. Sheng, Y.; Nguyen, T.D.; Veeraraghavan, G.; Mermer, Ö.; Wohlgenannt, M. Effect of spin-orbit coupling on magnetoresistance in organic semiconductors. Phys. Rev. B 2007, 75, 035202. [CrossRef] 74. Kimura, T.; Goto, T.; Shintani, H.; Ishizaka, K.; Arima, T.; Tokura, Y. Magnetic control of ferroelectric polarization. Nature 2003, 426, 55–58. [CrossRef][PubMed] 75. Wang, J.; Neaton, J.B.; Zheng, H.; Nagarajan, V.; Ogale, S.B.; Liu, B.; Viehland, D.; Vaithyanathan, V.;

Schlom, D.G.; Waghmare, U.V.; et al. Epitaxial BiFeO3 Multiferroic Thin Film Heterostructures. Science 2003, 299, 1719. [CrossRef][PubMed] 76. Ishihara, S. Electronic ferroelectricity in molecular organic crystals. J. Phys. Condens. Matter 2014, 26, 493201. [CrossRef][PubMed] 77. Qin, W.; Xu, B.; Ren, S. An organic approach for nanostructured multiferroics. Nanoscale 2015, 7, 9122–9132. [CrossRef][PubMed] 78. Bauer, G.E.; Saitoh, E.; van Wees, B.J. Spin caloritronics. Nat. Mater. 2012, 11, 391–399. [CrossRef] 79. Han, S.; Yang, L.; Gao, K.; Xie, S.; Qin, W.; Ren, S. Spin polarization of excitons in organic multiferroic composites. Sci. Rep. 2016, 6, 28656. [CrossRef] 80. Fang, Z.; Liu, Z.L.; Yao, K.L.; Li, Z.G. Spin configurations of pi electrons in quasi-one-dimensional organic ferromagnets. Phys. Rev. B Condens. Matter 1995, 51, 1304–1307. [CrossRef] 81. Xie, S.J.; Zhao, J.Q.; Wei, J.H.; Wang, S.G.; Mei, L.M.; Han, S.H. Effect of boundary conditions on SDW and CDW in organic ferromagnetic chains. Europhys. Lett. (EPL) 2000, 50, 635–641. [CrossRef] 82. Hu, G.; Guo, Y.; Wei, J.; Xie, S. Spin filtering through a metal/organic-ferromagnet/metal structure. Phys. Rev. B 2007, 75, 165321. [CrossRef] 83. Wang, Z.; Gao, M.; Wei, M.; Ren, S.; Hao, X.-T.; Qin, W. Organic Chiral Charge Transfer Magnets. ACS Nano 2019, 13, 4705–4711. [CrossRef][PubMed] 84. Yang, Y.; Liu, G.; Liu, J.; Wei, M.; Wang, Z.; Hao, X.; Maheswar Repaka, D.V.; Ramanujan, R.V.; Tao, X.; Qin, W.; et al. Anisotropic Magnetoelectric Coupling and Cotton–Mouton Effects in the Organic Magnetic Charge-Transfer Complex Pyrene–F4TCNQ. ACS Appl. Mater. Interfaces 2018, 10, 44654–44659. [CrossRef] [PubMed] Micromachines 2019, 10, 596 30 of 30

85. Ando, K.; Saitoh, E. Observation of the inverse spin Hall effect in silicon. Nat. Commun. 2012, 3, 629. [CrossRef][PubMed] 86. Sun, D.; van Schooten, K.J.; Kavand, M.; Malissa, H.; Zhang, C.; Groesbeck, M.; Boehme, C.; Valy Vardeny, Z. Inverse spin Hall effect from pulsed spin current in organic semiconductors with tunable spin-orbit coupling. Nat. Mater. 2016, 15, 863–869. [CrossRef][PubMed] 87. Ohshima, R.; Sakai, A.; Ando, Y.; Shinjo, T.; Kawahara, K.; Ago, H.; Shiraishi, M. Observation of spin-charge conversion in chemical-vapor-deposition-grown single-layer graphene. Appl. Phys. Lett. 2014, 105, 162410. [CrossRef] 88. Yu, Z.G. Suppression of the Hanle effect in organic spintronic devices. Phys. Rev. Lett. 2013, 111, 016601. [CrossRef] 89. Bandyopadhyay, S. Dominant spin relaxation mechanism in compound organic semiconductors. Phys. Rev. B 2010, 81, 153202. [CrossRef] 90. Liu, Z.; Wang, Z.F.; Mei, J.W.; Wu, Y.S.; Liu, F. Flat Chern band in a two-dimensional organometallic framework. Phys. Rev. Lett. 2013, 110, 106804. [CrossRef] 91. Beljonne, D.; Shuai, Z.; Pourtois, G.; Bredas, J.L. Spin Orbit Coupling and Intersystem Crossing in Conjugated − Polymers: A Configuration Interaction Description. J. Phys. Chem. A 2001, 105, 3899–3907. [CrossRef] 92. Yu, Z.-G. Spin relaxation and diffusion in disordered organic solids. J. Photonics Energy 2018, 8, 032213. [CrossRef] 93. Castro Neto, A.H.; Guinea, F. Impurity-Induced Spin-Orbit Coupling in Graphene. Phys. Rev. Lett. 2009, 103, 026804. [CrossRef][PubMed] 94. Ray, S.G.; Daube, S.S.; Leitus, G.; Vager, Z.; Naaman, R. Chirality-induced spin-selective properties of self-assembled monolayers of DNA on gold. Phys. Rev. Lett. 2006, 96, 036101. [CrossRef][PubMed] 95. Göhler, B.; Hamelbeck, V.; Markus, T.Z.; Kettner, M.; Hanne, G.F.; Vager, Z.; Naaman, R.; Zacharias, H. Spin Selectivity in Electron Transmission Through Self-Assembled Monolayers of Double-Stranded DNA. Science 2011, 331, 894. [CrossRef][PubMed] 96. Eremko, A.A.; Loktev, V.M. Spin sensitive electron transmission through helical potentials. Phys. Rev. B 2013, 88, 165409. [CrossRef] 97. Einati, H.; Mishra, D.; Friedman, N.; Sheves, M.; Naaman, R. Light-controlled spin filtering in bacteriorhodopsin. Nano Lett. 2015, 15, 1052–1056. [CrossRef][PubMed] 98. Di Nuzzo, D.; Kulkarni, C.; Zhao, B.; Smolinsky, E.; Tassinari, F.; Meskers, S.C.J.; Naaman, R.; Meijer, E.W.; Friend, R.H. High Circular Polarization of Electroluminescence Achieved via Self-Assembly of a Light-Emitting Chiral Conjugated Polymer into Multidomain Cholesteric Films. ACS Nano 2017, 11, 12713–12722. [CrossRef][PubMed] 99. Naaman, R.; Paltiel, Y.; Waldeck, D.H. Chirality and Spin: A Different Perspective on Enantioselective Interactions. Chimia (Aarau) 2018, 72, 394–398. [CrossRef][PubMed] 100. Tassinari, F.; Jayarathna, D.R.; Kantor-Uriel, N.; Davis, K.L.; Varade, V.; Achim, C.; Naaman, R. Chirality Dependent Charge Transfer Rate in Oligopeptides. Adv. Mater. 2018, 30, e1706423. [CrossRef] 101. Varade, V.;Markus, T.; Vankayala, K.; Friedman, N.; Sheves, M.; Waldeck, D.H.; Naaman, R. Bacteriorhodopsin based non-magnetic spin filters for biomolecular spintronics. Phys. Chem. Chem. Phys. 2018, 20, 1091–1097. [CrossRef] 102. Naaman, R.; Waldeck, D.H. The Chiral Induced Spin Selectivity (CISS) Effect. In World Scientific Reference on Spin in Organics; World Scientific: Singpore, 2018; pp. 235–270. [CrossRef] 103. Al-Bustami, H.; Koplovitz, G.; Primc, D.; Yochelis, S.; Capua, E.; Porath, D.; Naaman, R.; Paltiel, Y. Single Nanoparticle Magnetic Spin Memristor. Small 2018, 14, e1801249. [CrossRef][PubMed] 104. Koplovitz, G.; Leitus, G.; Ghosh, S.; Bloom, B.P.; Yochelis, S.; Rotem, D.; Vischio, F.; Striccoli, M.; Fanizza, E.; Naaman, R.; et al. Single Domain 10 nm Ferromagnetism Imprinted on Superparamagnetic Nanoparticles Using Chiral Molecules. Small 2019, 15, e1804557. [CrossRef][PubMed]

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).