Dynamical Simulations of Polaron Spin-Filtering and Rectification in

Subscriber access provided by Stockholm University Library

C: Surfaces, Interfaces, Porous Materials, and Catalysis

Dynamical Simulations of Polaron Spin Filtering and Rectification in an Organic Magnetic-Nonmagnetic Co-Oligomer: The Interfacial Effect Hui Wang, Hongyan Shi, Jingfen Zhao, Xiaojuan Yuan, Wenjing Wang, Zaifa Yang, Hongxia Bu, Yuanxun Yu, Wenli Guan, Changjian Ji, Kun Gao, Yuan Li, and Desheng Liu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01819 • Publication Date (Web): 23 May 2019 Downloaded from http://pubs.acs.org on May 28, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Dynamical Simulations of Polaron Spin Filtering and Rectification in an Organic Magnetic-Nonmagnetic CoOligomer: The Interfacial Effect Hui Wang1*, Hong-yan Shi1, Jing-fen Zhao1, Xiao-juan Yuan1, Wen-jing Wang1, Zaifa Yang1, Hong-xia Bu1, Yuan-xun Yu1, Wen-li Guan1, Chang-jian Ji1, Kun Gao2, Yuan Li*3, and De-Sheng Liu*2,4 1College

of Physics and Electronic Engineering, Qilu Normal University, Zhangqiu 250200, People’s Republic of China

2

School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China

3

School of Information Science and Engineering, Shandong University, Qingdao 266237, People’s Republic of China 4

Department of Physics, Jining University, Qufu 273155, People’s Republic of China

Abstract The interfacial effect on the dynamical properties of spin-dependent polarons in an organic magnetic/nonmagnetic co-oligomer is investigated by using a tight-binding model coupled with a nonadiabatic dynamics method. It is found that, the dynamical behaviors of spin-up and spin-down polarons are quite different at the interface. In the presence of an external electric field, polarons with a specific spin (up or down) can get trapped near the magnetic/nonmagnetic interface while the motion of polarons with an opposite spin is not affected, which leads to the phenomenon of polaron spin filtering. Interestingly, when the electric field is reversely applied, only polarons with opposite spin can pass through the co-oligomer and spin rectification can be observed. The spin filtering and rectification can be improved by increasing the strength of the spin correlation in the magnetic part of the co-oligomer. And they can also be affected by

* Corresponding

author: [email protected] author: [email protected] * Corresponding author: [email protected] * Corresponding

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 27

the strength of the interfacial electron-lattice coupling and the electronic transfer integral. These findings are useful for the design of organic-based spin logic devices.

1. Introduction Organic ferromagnets (OFMs) have attracted much attention because of the combination of their organic advantages (i.e., flexibility, low-cost, and large-area fabrication) and ferromagnetic properties. The chemical synthesis of OFMs can be traced back to 1980s1, and now several categories of OFMs have been obtained. Some of the OFMs are macromolecule-metal complexes consisted of iron elements (i.e., Mn, Fe, Cr, and V) together with organic radicals2-4. These metal-containing OFMs usually have stable magnetism and the Curie temperature can even reach up to room temperature4-7.

Others

are

purely

organic

ferromagnets

containing

only

organic elements, such as C, H, O, N, and S, and the magnetism can be induced by the spin exchange interactions of electrons in the π-conjugated systems8-9. Recently, ferroelectricity properties has also been observed in this kind of organic ferromagnets10. Rajca et al. reported in 2001 the magnetic properties of an organic magnetic polymer with π-conjugated structure, of which the magnetism exists only at low temperatures11. Some of the purely OFMs can be realized by using organic spin radicals12-15, and roomtemperature magnetic orders have been observed in organic OFMs with similar structure14. The magnetism and electronic structure of this type of OFMs have been investigated theoretically by considering the spin correlation of π-electrons in carbon systems9,

16-17,18-19.

Furthermore, the static properties of polarons in organic

ferromagnets have been reported20-22 and the phenomena of spin-charge disparity of polarons were found, as revealed by Hu et al.22. In addition to the study of materials themselves, OFMs have also been widely studied for potential applications in spintronic devices. Epstein et al. investigated the spin-dependent transport properties of V[TCNE]x-based organic spin valves, and a room-temperature magnetoresistance was observed experimentally23-25. It is noted that the functionality of the device improved when V[TCNE]x/Rubrene and V[TCNE]x/Alq3 2


Page 3 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


interface occur26-27. Sugawara et al. first observed field-effect-transistor characteristics of organic magnetic molecule devices28. They also investigated the spin-dependent transport properties of organic ferromagnetic devices based on spin-polarized wire molecules (ESBN)ClO4 connected to gold nanoparticles, and a magnetoresistance of up to about 5% was obtained and charge rectification was observed29-30. Furthermore, theoretical models for organic ferromagnet-based functional devices have also been developed on the basis of the tunneling theory. Wang31, Hu32, and Yao33et al. respectively designed spin filters based on organic ferromagnets, and according to their calculations, nearly completely spin polarized currents were obtained. Yao investigated the spin filtering and rectification properties of devices based on biradical/triradical organic magnetic molecular junctions34. Hu et al. reported the phenomena of charge and spin rectification through an organic magnetic/nonmagnetic heterojunction, and the rectification properties can be regulated by the gate voltage and the proportion and chain length of the co-oligomer35-36. It is noted that, although the organic magnetic/nonmagnetic interface plays a very important role on device functionality24,25. The effect of such interface is still unclear. To better understand the charge and spin transport properties of such devices, the understanding of the dynamical properties of spin-dependent polarons in organic heterojunctions with magnetic/nonmagnetic interface is highly required. In this paper, we present a dynamical simulation of spin-dependent polarons in an organic magnetic/nonmagnetic co-oligomer; the interfacial properties are investigated as a function of the magnitude of the interfacial electronic transfer integral and electronlattice coupling. Interestingly, spin filtering and rectification are obtained in this system, which has potential application in organic spintronic devices.

2. Model and method:

3



Page 4 of 27

Figure 1. Schematic diagram of an organic magnetic-nonmagnetic co-oligomer chain.

We consider in our simulation a co-oligomer chain with the left half an organic ferromagnetic polymer and the right half a nonmagnetic one, which are covalently bonded at the interface, as shown schematically in Figure 1. Specifically, the cooligomer is modeled as an organic polymer chain with side radicals, such as poly-BIP, connected to only the left part of the chain. The Hamiltonian of the system can be described by the extended Su-Schrieffer-Heeger (SSH) model. For the ferromagnetic part, a Heisenberg-like Hamiltonian is used to describe the spin correlation between the backbone of the molecule and the side radicals. Thus, the total Hamiltonian of the system is written as:

H  H e  H R-s  H L  H E .

(1)

H e represents the Hamiltonian of the π -electrons in the molecule with the form of:37

H e   t0    un 1  un    cn, s cn 1, s  cn1, s cn , s . ,

(2)

n,s

where t0 denotes the average electronic transfer integral,  the electron-lattice  coupling parameter, and un the lattice displacement of the nth site. cn , s and cn , s

respectively describe the creation and annihilation operator of π electrons at the nth site with spin s. For poly-BIPO-like organic ferromagnetic polymers, the ferromagnetic properties were inferred from the π electrons on the backbone and the nonbonding electrons of the oxygen atoms on the side radicals16-18,

22.The

second term in Eq. (1) denotes the

correlation between the spin of electrons on the backbone and that on the side radicals (see Figure 1), 4


Page 5 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


𝐻R - s = 𝐽𝑓∑𝑛𝛿𝑛,𝑖𝑆𝑛𝑅 ⋅ 𝑆𝑧.

(3)

Here, J f denotes the strength of the spin correlation, and a positive value of J f is chosen in our simulation to describe the antiferromagnetic correlation that widely exists in poly-BIPO-like organic ferromagnetic polymers. 𝑆represents the spin operator on the corresponding sites,  n ,i a delta function, and the subscript i the sequence number of the site to which the side radical is connected. In our simulation, the radical spin 𝑆𝑛𝑅 is treated to

z use mean-field approximation. Where S nR

… = G… G

average with respect to the ground state G . The radical spin is set to be

is the

z S nR =

1 in 2

our calculation. The third term in Eq. (1) denotes the lattice part of the Hamiltonian for acoustic vibrations:

[𝐾

1

]

𝐻𝐿 = ∑𝑛 2 (𝑢𝑛 + 1 ― 𝑢𝑛)2 + 2𝑀𝑢2𝑛 .

(4)

where K denotes the elastic constant and M the mass of a CH group. A driving electric field E is applied to drive the spin polaron:

H E  e E   na  un cn, s cn , s  e E   na  un  , n,s

(5)

n

where e is the electronic charge and a the lattice constant. Based on the Hamiltonian of Eq. (1), we simulate the dynamics of the system by using a nonadiabatic mixed quantum-classical method. In our calculations, the electronic wave function is expanded on the spin-dependent Wannier basis

    Z  ,n , s n, s , where  describes the  th energy level and Z  ,n , s the n,s

probability amplitude of the state  

at the nth site with spin s. In such representation,

the electronic Hamiltonian is a 2N by 2N matrix, for which 2N energy levels can be obtained. The polaron energy levels are not spin degeneracy due to the spin correlation of electrons on the main chain and the side radical. The initial polaron states can be obtained by solving the eigen equation of electron

5



Page 6 of 27

1 z  t0    un 1  un   Z  ,n 1, s  t0    un  un 1   Z  ,n 1, s  J f  n ,i S nR Z  ,n,s    Z  ,n,s 2 (6) self-consistently with the balance equation of lattice



 1 N  un 1  un     n ,n 1, s   n ,n 1, s  ,  K s  N  1 n 1 

(7)

occ

* where  n ,n, s =  Z  ,n , s Z  ,n, s denotes the charge density matrix. When a spin-down n 1

polaron is considered, the first N+1 energy levels are set to be singly occupied. When a spin-up polaron is considered, the first N energy levels and the N+2th energy level are set to be singly occupied. The occupation number of these energy levels remains unchanged throughout the self-consistent calculations. The evolution of the electronic states is obtained by solving the time-dependent Schrӧdinger equation:

ih

 1 z Z  ,n , s  t   tn ,n 1Z  ,n 1, s  t   tn ,n 1Z  ,n 1, s  t    J f  s   ni S nR Z  ,n,s  t  t 2 + e E  na  un  Z  ,n , s  t 

(8)

while the evolution of the lattice coordinates is described by the classical Newtonian equation of motion: 𝑀𝑢(𝑡) = 𝐾(𝑢𝑛 + 1(𝑡) + 𝑢𝑛 ― 1(𝑡) ― 2𝑢𝑛(𝑡)) + 𝛼∑𝑠(𝜌𝑛,𝑛 + 1,𝑠 ― 𝜌𝑛 ― 1,𝑛,𝑠) + |𝑒|𝐸(∑𝑠𝜌𝑛,𝑛,𝑠 ― 1) (9

.

) Fixed boundary conditions are used in the calculation. The charge distribution of a polaron on the nth site at time t can be calculated by occ



2

2



 nc  t    Z  ,n ,  t   Z  ,n ,  t   1  1

(10) .

To better describe the movement of the polaron, we use a parameter pc to describe the center of the motional polaron:  N / 2  pc   N     / 2   N  2    / 2

if cos  n  0 and sin  n  0 if cos  n  0 otherwise

(11) .

6


Page 7 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


sin  n   Z N 1,n , s sin 2 n / N , 2

Here, N is the number of lattice sites,

n,s

cos  n   Z N 1,n , s cos 2 n / N , and   arctan 2

n,s

sin  n cos n

. The polaron velocity at

time t is given by v(t )   pc (t  t )  pc (t )  / t . The values of parameters in the simulations are chosen as follows:

t0l  t0r  2.5 eV ,  l   r  41 eV/nm , K l  K r  2100 eV/nm 2 ,

and

M l  M r  1349.14 eV  fs 2 / A 2 , which are relevant to poly-BIPO and polyacetylene32.

The superscript l and r denote the left and right part of the co-oligomer, respectively. In our simulations, t

inter 0



1  t0l  t0r  2

and 

int er



 2  l   r  2

are used to describe

the interfacial electronic transfer integral and the electron-lattice coupling strength of the co-oligomer, respectively, where 1 and  2 are the binding parameters denoting the coupling strength. The number of lattice sites is chosen as N l  N r  80 . While the model parameters are chosen to specifically describe poly-BIPO and polyacetylene, the conclusions obtained in our study are expected to be qualitatively applicable to other organic magnetic-nonmagnetic co-oligomers with similar structures.

Results and discussions In our dynamical simulations, the external electric field is added smoothly to the system in terms of E (t )  E0  t / tc for 0  t  tc and E (t )  E0 for t  tc , where the critical time is chosen as tc  75 fs . The side radicals are connected with the odd sites of the molecule and the spin of side radical electrons is set to spin up.

7



Page 8 of 27

Figure 2. Time evolution of the charge distribution of a polaron in the presence of electric fields with different strength. The driven electric field is E0=1.0×10-2 V/nm for (a) and (c), and E0=1.3× 10-2 V/nm for (b) and (d). The value of the binding parameter is

1 = 2 =1.0 , and the spin coupling

parameter is chosen as Jf= 0.5 eV.

The results of the charge distribution of spin-dependent polarons in the presence of a leftward electric field are shown in Figure 2. The polarons are initially located in the magnetic part of the chain, and the polaron center is on the 40th site. When an electric field with strength of E0=1.0×10-2 V/nm is applied, both spin-up and spindown polarons are driven to move along the co-oligomer chain with a velocity of about 0.026nm/fs. Interestingly, when approaching the mangnetic/nonmagnetic interface (the red dashed line in Figure 2), the spin-down polarons get trapped and no longer pass through the co-oligomer molecule unless the strength of the driven electric field is larger than 1.3×10-2 V/nm as shown in Figure 2 (a) and (b). In contrast, the spin-up polaron can smoothly pass through the mangnetic/nonmagnetic interface. Indeed, according to our calculations, the spin-up polarons can easily pass through the mangnetic/nonmagnetic interface even if the driven electric field is one hundred times weaker. Since the critical electric field for spin-down polarons is about 8


Page 9 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Ecd =1.25 102 V / nm , a low-bias polaron spin filtering effect can be observed in such magnetic-nonmagnetic co-oligomer.

Figure 3. Time evolution of the charge distribution of a polaron in the presence of electric fields with different strength. The driven electric field is E0=1.0×10-2 V/nm for (a) and (c), and E0=-1.0 × 10-2 V/nm for (b) and (d). The value of the binding parameter is

1 = 2 =1.0 , and the spin

coupling parameter is chosen as Jf= 0.5 eV.

We also investigate the spin rectification in the magnetic-nonmagnetic structure, by considering both leftward and rightward electric field, and the results have been shown in Figure 3. As mentioned above, when a leftward electric field is applied, the spin-up polaron can easily pass through the magnetic-nonmagnetic co-oligomer molecule, while the spin-down polaron remains trapped at the interface in the presence of a weak electric field. As shown in Figure 3 (a) and (c), only the spin-up polaron can transport along the co-oligomer molecule when the strength of the electric field is

E0 =1.0 102 V / nm . In contrast, when a rightward electric field with a certain strength is applied, the spin-up polaron is blocked at the interface while the spin-down polaron 9



Page 10 of 27

can easily pass through the co-oligomer. The critical electric field is found to be about

Ecu =1.25 102 V / nm for spin-up polarons, which is the same as the results of spindown polarons in the case of leftward electric field. The results that only spin-up/down polarons can pass through the co-oligomer with leftward/rightward electric field point to a phenomenon of spin rectification in the system.

Figure 4. Energy of the polaron levels in both organic magnetic and nonmagnetic polymers. The value of the binding parameter is 1 = 2 =1.0 , and the spin coupling parameter is chosen as Jf= 0.5 eV.

To further understand the spin filtering and spin rectification, we calculated the energy of polaron levels in both organic magnetic and nonmagnetic polymers, and the results have been shown in Figure 4. In the case of magnetic co-oligomer, when the spin correlation between the backbone and the side radicals is taken into account, the energy levels of the spin-up and spin-down polarons are not spin degenerate, with a spin splitting of about 0.075 eV (see the left part of Figure 4). The lower LUMO level is occupied by a spin-down electron while the higher LUMO level is occupied by a spin-up electron. However, in the case of nonmagnetic co-oligomer, the polaron energy levels remain spin degenerate. As a result, the spin-up/down polaron level in the magnetic part is higher/lower in energy (about 0.038 eV) than that in the nonmagnetic 10


Page 11 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


part of the co-oligomer. When a leftward/rightward electric field is applied, the spindown/up polaron will get stuck at the interface as a result of the level offset of the LUMO, and the spin-up/down polaron will not be affected. This represents the reason responsible for the phenomena of spin filtering and spin rectification in such a magnetic/nonmagnetic structure.

Figure 5. Values of the critical electric field for spin-down polarons as a function of Jf. The value of the binding parameter is 1 = 2 =1.0 .

We further studied the effects of the spin-correlation strength in the magnetic part of the co-oligomer on the polaron spin filtering and rectification properties. Figure 5 plots the values of the critical electric field for spin-down polarons as a function of Jf, and the polaron spin filtering and spin rectification can be obtained if the electric field is weaker than the critical value. It is found that the values of the critical electric field for the spin-down polarons increase almost linearly as a function of Jf. As seen from Figure 5, the values of the critical electric field for spin-down polarons increases from 0.67×10-2 V/nm to 1.93×10-2 V/nm when Jf increases from 0.3 eV to 0.7 eV. The spin splitting of the polaron energy levels in the magnetic part of the co-oligomer becomes more evident when the strength of the spin correlation increases. These results 11



Page 12 of 27

suggest that it is easier to observe polaron spin filtering and spin rectification in cooligomers with stronger spin correlation in the magnetic part.

Figure 6. (a) Values of the critical electric field for both spin-up and spin-down polarons and (b) the spin-filtering range of the electric field as a function of

1 . The value of the spin coupling

parameter is Jf= 0.5 eV.

We also studied how the magnetic/nonmagnetic interface impacts the polaron spin filtering and rectification. The effects of the interfacial electronic transfer integral are investigated by changing the value of the binding parameter 1 , and the results are shown in Figure 6. Here we only plot the results in the case of leftward electric field, and those in the case of rightward electric field are similar. The difference E =Ecd  Ecu is defined to describe the range of the electric field for spin filtering and rectification. It is found that the values of the critical electric field for the spin-down polarons first decrease and then increase almost linearly as a function of 1 ; the critical electric field for

the

spin-down

polarons

decreases

to

the

smallest

value

of

about

Ecd =1.15 102 V / nm when 1 increases to 0.99, as seen from Figure 6(a). However, 12


Page 13 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the values of the critical electric field for the spin-up polarons first decrease with 1 and, when the value of

1 increases to almost 0.99, it decreases to zero and remains

unchanged. As a result, the range of the electric field for spin filtering and rectification also decreases first and then increases as a function of 1 . Differently, however, the range of the electric field for spin filtering and rectification decreases to the smallest value when 1 increases to only 0.97, as shown in Figure 6 (b). Despite of the value of 1 , the range of the electric field for spin filtering and rectification is larger than E =1.01 102 V / nm . These results suggest that magnetic/nonmagnetic co-oligomers

with large and small interfacial electronic transfer integrals are both conducive to the creation of polaron spin filtering and rectification.

Figure 7. (a) Values of the critical electric field for both spin-up and spin-down polarons and (b) the spin-filtering range of the electric field as a function of

 2 . The value of the spin coupling

parameter is Jf= 0.5 eV

We finally discuss how the strength of the magnetic/nonmagnetic interfacial 13



Page 14 of 27

electron-lattice coupling impacts the polaron spin filtering and rectification. The results of the critical electric field for both spin-up and spin-down polarons and the spinfiltering range of the electric field as a function of the binding parameter  2 have been shown in Figure 7. It is seen that the values of the critical electric field for spin-down polarons first increase almost exponentially and then increase with  2 . For instance, the value of the critical electric field for spin-down polarons decreases from 1.45×102

V/nm to about 1.24×10-2 V/nm as a function of increasing  2 from 0.8 to 1.05, and

then it increases from 1.26×10-2 V/nm to about 1.39×10-2 V/nm when  2 increases from 1.1 to 1.3, as shown in Figure 7 (a). Differently, the value of the critical electric field for the spin-up polarons first keeps independent of  2 ; when the value of  2 is larger than 1.05, it increases rapidly as a function of  2 . The value of the critical electric field for the spin-up polaron increases from zero to about 0.28 × 10-2 V/nm when  2 increases from 1.05 to 1.3. It can be seen from Figure 7 (a) that the value of the critical electric field for spin-up polarons increases faster than that for the spin-down polarons. As a result, the range of the electric field for polaron spin filtering and rectification decreases as a function of the strength of the magnetic/nonmagnetic electron-lattice coupling, as shown in Figure 7 (b). These results indicate that the polaron spin filtering and rectification can be improved when reducing the strength of the magnetic/nonmagnetic electron-lattice coupling.

Conclusion In summary, we have simulated the dynamical properties of spin-dependent polarons in an organic magnetic/nonmagnetic co-oligomer by focusing on the effect of the organic magnetic/nonmagnetic interface. It is found that, the phenomena of both polaron spin-filtering and rectification can be realized in such system. The values of the critical electric field for both spin-filtering and rectification are found to be markedly influenced by the strength of the spin correlation in the magnetic part of the co-oligomer. 14


Page 15 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Furthermore, the spin-filtering and rectification properties are not qualitatively affected by the interfacial electronic transfer integral but by the interfacial electron-lattice coupling. Our findings are expected to be useful for guiding the design of organic-based spin filter devices.

Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 11747132, 11574118, 21473102, 11674195, 11604170), the Fundamental Research Funds of Shandong University, Scientific Research in Universities of Shandong Province (No. J16LJ06), the Natural Science Foundation of Shandong Province (No. ZR2014AQ018), the Higher Educational Science and Technology Program of Shandong Province (No. J18KB104) and the Foundation of Qilu Normal University (Nos. BS2017002, BS2017005, 2017L0603, 2017L0604).

Reference 1.

Miller, J. S.; Krusic, P. J.; Epstein, A. J.; Reiff, W. M.; Hua Zhang, J., Linear Chain

Ferromagnetic Compounds – Recent Progress. Mol. Cryst. Liquid Cryst. 1985, 120, 2734. 2.

Inoue, K.; Hayamizu, T.; Iwamura, H.; Hashizume, D.; Ohashi, Y., Assemblage

and Alignment of the Spins of the Organic Trinitroxide Radical with a Quartet Ground State by Means of Complexation with Magnetic Metal Ions. A Molecule-Based Magnet with Three-Dimensional Structure and High Tc of 46 K. J. Am. Chem. Soc 1996, 118, 1803-1804. 3.

Kaul, B. B.; Yee, G. T., A Charge-Transfer Salt Magnet Based on a Non-

Cyanocarbon

Acceptor,

1,4,9,10-Anthracenetetrone

and

Decamethylferrocene.

Polyhedron 2001, 20, 1757-1759. 4.

Manriquez, J. M.; Gordon, T. Y.; McLean, R. S.; Epstein, A. J.; Miller, J. S., A

Room-Temperature Molecular/Organic-Based Magnet. Science 1991, 252, 1415-1417. 5.

Ferlay, S.; Mallah, T.; Ouahes, R.; Veillet, P.; Verdaguer, M., A Room15



Page 16 of 27

Temperature Organometallic Magnet Based on Prussian Blue. Nature 1995, 378, 701703. 6.

Haskel, D.; Islam, Z.; Lang, J.; Kmety, C.; Srajer, G.; Pokhodnya, K. I.; Epstein,

A. J.; Miller, J. S., Local Structural Order in the Disordered Vanadium Tetracyanoethylene Room-Temperature Molecule-Based Magnet. Phys. Rev. B 2004, 70, 054422. 7.

Chilton, N. F.; Goodwin, C. A. P.; Mills, D. P.; Winpenny, R. E. P., The First near-

Linear Bis(Amide) F-Block Complex: A Blueprint for a High Temperature Single Molecule Magnet. Chem. Commun. 2015, 51, 101-103. 8.

Mataga, N., Possible “Ferromagnetic States” of Some Hypothetical Hydrocarbons.

Theor. Chim. Acta 1968, 10, 372-376. 9.

Ovchinnikov, A. A.; Spector, V. N., Organic Ferromagnets. New Results. Synth.

Met. 1988, 27, 615-624. 10. Kagawa, F.; Horiuchi, S.; Tokunaga, M.; Fujioka, J.; Tokura, Y., Ferroelectricity in a One-Dimensional Organic Quantum Magnet. Nat. Phys. 2010, 6, 169-172. 11. Rajca, A.; Wongsriratanakul, J.; Rajca, S., Magnetic Ordering in an Organic Polymer. Science 2001, 294, 1503-1505. 12. Korshak, Y. V.; Medvedeva, T. V.; Ovchinnikov, A. A.; Spector, V. N., Organic Polymer Ferromagnet. Nature 1987, 326, 370-372. 13. Cao, Y.; Wang, P.; Hu, Z.; Li, S.; Zhang, L.; Zhao, J., Chemical and Magnetic Characterization of Organic Ferromagnet- Poly-Bipo. Synth. Met. 1988, 27, 625-630. 14. Zaidi, N. A.; Giblin, S. R.; Terry, I.; Monkman, A. P., Room Temperature Magnetic Order in an Organic Magnet Derived from Polyaniline. Polymer 2004, 45, 5683-5689. 15. Sugano, T.; Blundell, S. J.; Lancaster, T.; Pratt, F. L.; Mori, H., Magnetic Order in the Purely Organic Quasi-One-Dimensional Ferromagnet 2-Benzimidazolyl Nitronyl Nitroxide. Phys. Rev. B 2010, 82, 180401. 16. Fang, Z.; Liu, Z. L.; Yao, K. L., Theoretical Model and Numerical Calculations for a Quasi-One-Dimensional Organic Ferromagnet. Phys. Rev. B 1994, 49, 3916-3919. 17. Fang, Z.; Liu, Z. L.; Yao, K. L.; Li, Z. G., Spin Configurations of Π Electrons in 16


Page 17 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Quasi-One-Dimensional Organic Ferromagnets. Phys. Rev. B 1995, 51, 1304-1307. 18. 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. EPLEurophys. Lett. 2000, 50, 635. 19. Wang, W. Z.; Yao, K. L.; Lin, H. Q., Boundary Conditions, Solitons, and Spin Configuration in Interchain Coupled Organic Ferromagnetic Polymers. J. Chem. Phys. 2000, 112, 487. 20. Miao, Y.; Qiu, S.; Zhang, G.; Ren, J.; Wang, C.; Hu, G., Ground-State Properties of Metal/Organic-Ferromagnet Heterojunctions. Phys. Rev. B 2018, 98, 235415. 21. Miao, Y.; Qiu, S.; Zhang, G.; Ren, J.; Wang, C.; Hu, G., Polarons in Organic Ferromagnets. Org. Electron. 2018, 55, 133-139. 22. Hu, G. C.; Wang, H.; Ren, J. F.; Xie, S. J.; Timm, C., Spin-Charge Disparity of Polarons in Organic Ferromagnets. Org. Electron. 2014, 15, 118-125. 23. Prigodin, V. N.; Raju, N. P.; Pokhodnya, K. I.; Miller, J. S.; Epstein, A. J., SpinDriven Resistance in Organic-Based Magnetic Semiconductor V[Tcne]X. Adv. Mater. 2002, 14, 1230-1233. 24. Yoo, J.-W.; Edelstein, R. S.; Lincoln, D. M.; Raju, N. P.; Xia, C.; Pokhodnya, K. I.; Miller, J. S.; Epstein, A. J., Multiple Photonic Responses in Films of Organic-Based Magnetic Semiconductorv(Tcne)X,X∼2. Phys. Rev. Lett. 2006, 97. 25. Konstantin, P.; Michael, B.; Vladimir, P.; Arthur, J. E.; Joel, S. M., Carrier Transport in the V[Tcne] X (Tcne = Tetracyanoethylene; X ∼ 2) Organic-Based Magnet. J. Phys.-Condes. Matter 2013, 25, 196001. 26. Yoo, J.-W.; Chen, C.-Y.; Jang, H. W.; Bark, C. W.; Prigodin, V. N.; Eom, C. B.; Epstein, A. J., Spin Injection/Detection Using an Organic-Based Magnetic Semiconductor. Nat. Mater. 2010, 9, 638-642. 27. Li, B.; Zhou, M.; Lu, Y.; Kao, C.-Y.; Yoo, J.-W.; Prigodin, V. N.; Epstein, A. J., Effect of Organic Spacer in an Organic Spin Valve Using Organic Magnetic Semiconductor. Org. Electron. 2012, 13, 1261-1265. 28. Minamoto, M.; Matsushita, M. M.; Sugawara, T., Construction of a Network Structure Composed of Gold Nanoparticles and Spin-Polarized Molecular Wires and 17



Page 18 of 27

Its Conducting and Magnetic Properties. Polyhedron 2005, 24, 2263-2268. 29. Sugawara, T.; Minamoto, M.; Matsushita, M. M.; Nickels, P.; Komiyama, S., Cotunneling Current Affected by Spin-Polarized Wire Molecules in Networked Gold Nanoparticles. Phys. Rev. B 2008, 77. 30. Nickels, P.; Matsushita, M. M.; Minamoto, M.; Komiyama, S.; Sugawara, T., Controlling Co-Tunneling Currents in Nanoparticle Networks Using Spin-Polarized Wire Molecules. Small 2008, 4, 471-5. 31. Wang, W. Z., Model of a Gate-Controlled Spin Filter Based on a Polymer Coupled to a Quantum Wire. Phys. Rev. B 2006, 73. 32. Hu, G.; Guo, Y.; Wei, J.; Xie, S., Spin Filtering through a Metal/OrganicFerromagnet/Metal Structure. Phys. Rev. B 2007, 75. 33. Zhu, L.; Yao, K. L.; Liu, Z. L., Molecular Spin Valve and Spin Filter Composed of Single-Molecule Magnets. Appl. Phys. Lett. 2010, 96, 082115. 34. Zhu, L.; Yao, K. L.; Liu, Z. L., Biradical and Triradical Organic Magnetic Molecules as Spin Filters and Rectifiers. Chem. Phys. 2012, 397, 1-8. 35. Hu, G.; He, K.; Xie, S.; Saxena, A., Spin-Current Rectification in an Organic Magnetic/Nonmagnetic Device. J. Chem. Phys. 2008, 129, 234708. 36. Hu, G. C.; Zhang, Z.; Zhang, G. P.; Ren, J. F.; Wang, C. K., Inversion of SpinCurrent Rectification in Magnetic Co-Oligomer Diodes. Org. Electron. 2016, 37, 485490. 37. Li, Y.; Liu, X.-j.; Fu, J.-y.; Liu, D.-s.; Xie, S.-j.; Mei, L.-m., Bloch Oscillations in a One-Dimensional Organic Lattice. Phys. Rev. B 2006, 74.

Table of Contents Graphic 18


Page 19 of 27


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 19



Figure 1. Schematic diagram of an organic magnetic-nonmagnetic co-oligomer chain.


Page 20 of 27

Page 21 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. Time evolution of the charge distribution of a polaron in the presence of electric fields with different strength. The driven electric field is E0=1.0×10-2 V/nm for (a) and (c), and E0=1.3×10-2 V/nm for (b) and (d). The value of the binding parameter is β1=β2=1.0, and the spin coupling parameter is chosen as Jf= 0.5 eV. 286x201mm (300 x 300 DPI)



Figure 3. Time evolution of the charge distribution of a polaron in the presence of electric fields with different strength. The driven electric field is E0=1.0×10-2 V/nm for (a) and (c), and E0=-1.0×10-2 V/nm for (b) and (d). The value of the binding parameter is β1=β2=1.0, and the spin coupling parameter is chosen as Jf= 0.5 eV. 286x201mm (300 x 300 DPI)


Page 22 of 27

Page 23 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Energy of the polaron levels in both organic magnetic and nonmagnetic polymers. The value of the binding parameter is β1=β2=1.0, and the spin coupling parameter is chosen as Jf= 0.5 eV. 286x201mm (300 x 300 DPI)



Figure 5. Values of the critical electric field for spin-down polarons as a function of Jf. The value of the binding parameter is β1=β2=1.0. 287x201mm (300 x 300 DPI)


Page 24 of 27

Page 25 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 6. (a) Values of the critical electric field for both spin-up and spin-down polarons and (b) the spinfiltering range of the electric field as a function of β1. The value of the spin coupling parameter is Jf= 0.5 eV. 286x201mm (300 x 300 DPI)



Figure 7. (a) Values of the critical electric field for both spin-up and spin-down polarons and (b) the spinfiltering range of the electric field as a function of β2. The value of the spin coupling parameter is Jf= 0.5 eV 286x201mm (300 x 300 DPI)


Page 26 of 27

Page 27 of 27 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


84x47mm (300 x 300 DPI)


Dynamical Simulations of Polaron Spin-Filtering and Rectification in

Recommend Documents