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Article

Spin Dependent Transport and Optical Properties of Transparent Half Metallic g-CN Films 4

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Arqum Hashmi, M. Umar Farooq, Tao Hu, and Jisang Hong J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp510179p • Publication Date (Web): 05 Dec 2014 Downloaded from http://pubs.acs.org on December 7, 2014

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The Journal of Physical Chemistry C 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.

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The Journal of Physical Chemistry

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Spin dependent transport and optical properties of

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transparent half-metallic g-C4N3 films

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Arqum Hashmi, M. Umar Farooq, Tao Hu, and Jisang Hong

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Department of Physics, Pukyong National University, Busan 608-737, Korea

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ABSTRACT

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Half-metallic materials play an essential role in the spin dependent transport study and so far it is

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believed that the 3d transitional metal elements are necessary to obtain ferromagnetic state.

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Herein, we demonstrate that the metal free two-dimensional graphitic carbon nitride (g-C4N3)

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film show half metallic state and this is independent of the film thickness and stacking order. We

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find that the half-metallicity results in a very large magnetoresistance even at finite bias.

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Moreover, we have also investigated various optical properties. The g-C4N3 thin films have a

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very high refractive index for parallel polarization and extremely weak reflectivity for

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perpendicular polarization. Additionally, the g-C4N3 thin films are optically transparent because

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of very weak absorption coefficients. Overall, our findings suggest that the transparent half-

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metallic g-C4N3 thin films can be used for both spintronics and optical applications because of

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potential multifunctionality.

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ACS Paragon Plus Environment

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INTRODUCTION

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Spintronics is one of the most promising fields in condensed matter physics because the spin

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degree of freedom can provoke various applications of innovative technologies. Regarding the

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spintronics, half-metallic materials have many advantages because one spin channel is

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conductive, but the other spin channel is insulating.1,2 This will result in a giant

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magnetoresistance which is an essential quantity for spintronics. Various types of materials show

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half-metallic state, but most of them are based on the conventional 3d transition metal

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elements.3–8

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In general, 2p electron systems show a non-magnetic behavior in a bulk state. Of course, several

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studies proposed defect induced magnetic state in two-dimensional geometry.9–11 However, those

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studies were about local magnetic state, not ferromagnetism arising from long range ordering. In

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the spin dependent transport study, a long spin relaxation time is an important factor for spin

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information delivery. By virtue of the fact that the spin relaxation time is inversely proportional

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to the strength of spin-orbit coupling, the half-metallicity in 2p electron system will bring an

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interesting issue in the spin dependent transport property. Nonetheless, it is rare to find such

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reports on the half-metallicity from pure 2p electronic materials.12,13

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Interestingly, the graphitic carbon nitride, namely g-C4N3, was synthesized and showed a half-

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metallic state in free standing monolayer.14,15 After then, many other works were reported on

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free standing structure.16–20 Recently, the influence of Li adsorption and the mechanism of stable

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adsorption of hybridized system with BN layer were presented as well.21,22 However,


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manipulating a single layer structure will require highly precise experimental technique and also

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complex fabrication process for device applications. It will be more practical, realistic, and easier

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to treat thicker layers than free standing monolayer. So far, no studies on this issue have been

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performed. In this respect, our objective is to propose that the g-C4N3 film can maintain half-

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metallic state even in multilayer structure and this half-metallicity can be applied for spintronics.

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We will prove this by calculating the spin dependent current and magnetoresistance at finite bias.

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Along with these magnetic properties, if the multilayer g-C4N3 system can be utilized for optical

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device applications, it will be a remarkable finding and attract great research interests in diverse

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fields in condensed matter physics because of potential multifunctionality. Thus, we will study

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the frequency dependent optical properties such as dielectric functions, refractive index,

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reflectivity, and absorption coefficients.

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NUMERICAL METHOD

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We employed the Vienna ab initio simulation package (VASP) using a plane wave basis

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set.23,24 The core electron interactions were described using the projector augmented wave

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(PAW) method. For layer structured materials, it is of necessity to include van der Waals

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interaction. Thus, in this report, we explore the structural, adsorption, electronic and magnetic

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properties of multilayer g-C4N3 using non-empirical vdW-DF method proposed by Dion et al.25

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as implemented in the VASP code. We used most recently developed less repulsive optB88-like

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exchange functional method

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interlayer distances were achieved.25,27,28 A vacuum distance of 15 Å was imposed and we

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carried the self-consistent calculations with 9x9x1 k-mesh. All results have been obtained with

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very high plane-wave energy cut-off of 700 eV. The structure optimization has been performed

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because significant improvements in binding energies and


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until the residual forces on individual atoms were smaller than 0.01 eVÅ-1. The convergence

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criterion for energy was set to 0.1 meV. It is worth noting that the g-C4N3 is known to have a

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(2x2) reconstructed surface geometry. Thus, the ground state lattice constant of g-C4N3 is 9.68 Å

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and entire calculations were performed with this lattice constant. In addition, ferromagnetic

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(FM), antiferromagnetic (AFM) and non-magnetic (NM) spin configurations were considered to

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find out the magnetic ground state. The thickness varies from bilayer to 4 monolayers (MLs). In

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this type of layer structured material, it is necessary to find the stacking order. Thus, three

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different stacking orders, so called, AA, AB and AC for bilayer system and ABA, ABB and

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ABC stacking orders for the trilayer film were examined. Using the result of trilayer structure,

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we adopted the stacking order of ABAB for 4 ML film. For the transport calculations, we

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employ the non-equilibrium Green's function (NEGF) method based on density functional

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theory. All of the electron transport calculations were performed using the density functional

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theory code OpenMX, which is based on localized pseudoatomic orbitals (PAOs) and norm-

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conserving pseudopotentials.29,30 Two primitive orbitals (s and p orbitals) generated by a

78

confinement scheme with cutoff of 5 Bohr radius are employed.31,32 The Perdew-Burke-

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Ernzerhof (PBE) exchange-correlation functional, which is derived within the generalized

80

gradient approximation (GGA) is used.33 To obtain bias dependent current, we have divided the

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sheet of g-C4N3 into three parts; two leads and scattering part.34 The central sheet sandwiched

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between two g-C4N3 leads is used for the NEGF calculations. For spin dependent transport study,

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we changed the relative spin direction in the two leads and the bias dependent current in both

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parallel and antiparallel configurations is obtained

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NUMERICAL RESULTS

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The g-C4N3 bilayer structure can have three different configurations such as AA, AB, and AC

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stacking as shown in Figure 1 (a) - (c). For clarification, we also present the (1x1) cell of free

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standing g-C4N3 layer in Figure 1(d). The C and N atoms located on the hexagonal ring are

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referred as C1 and N1, respectively, whereas C atom located outside the ring is denoted as C2. In

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AA stacking, carbon and nitrogen atoms of two layers have the same lateral positions. In AB

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stacking, C1 and N1 atoms are on the hexagonal rings of the other layer while C2 atoms have no

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direct coupling. In AC stacking, carbon and nitrogen atoms of both layers are on the bridge sites

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of each other. Figure 1 (e) – (g) shows three different stacking orders for the trilayer film. Here,

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we considered ABA, ABB, and ABC stacking. Since the AB stacking was the most stable

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configuration in bilayer system, we constructed trilayer structure by adding one more layer to the

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AB stacked bilayer g-C4N3. Table 1, the ABA stacking became the most stable structure. Thus,

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this suggests that the multilayer film may display ABAB stacking with increase of the film

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thickness. So, we only considered ABAB stacking in 4 ML film.

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Table I presents the total energy differences among FM, AFM and NM spin arrangements and

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magnetic moment per (1x1) cell. Here, it should be remarked that we have calculated the total

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energy with (2x2) cell and the same spin configurations are considered as Du et al. did.15 In

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bilayer and trilayer systems, the total energy of AB and ABA stacking in FM state was set to

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zero, respectively as a reference energy.

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TABLE 1: Stacking order dependent total energy difference (in meV/cell) and energy

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difference per atom (in meV) shown in parentheses. The magnetic moment (in µB) per (1x1)

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unit cell . FM

AFM

NM

µB / cell

AB

0

365 (6.5)

357 (6.3)

1.000

AC

29 (0.5)

340 (6.1)

342 (6.1)

0.968

AA

42 (0.8)

328 (5.8)

328 (5.8)

0.921

ABA

0

518 (6.2)

552 (6.6)

1.000

ABB

62 (0.7)

532 (6.3)

534 (6.3)

0.935

ABC

71 (0.8)

563 (6.7)

568 (6.8)

0.969

0

700 (6.3)

735 (6.6)

1.000

Stacking 2ML

3ML

4ML ABAB 110 111

The most stable bilayer structure is found in the AB stacking. FM ground state was still

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preserved in the bilayer structure and the magnetic ground state is independent of the stacking

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order. The calculated total magnetic moment of the bilayer g-C4N3 film in 2x2 supercell is 8.00

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µB , 7.75 µB and 7.37 µB in AB, AC and AA stacking respectively. Note that the magnetic

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moment of pristine free standing g-C4N3 monolayer is 1.0 µB per (1x1) unit cell.15,19,22 In bilayer

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system, we found an integer magnetic moment in AB stacking. This implies that the most stable

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AB stacking film has a half-metallic state. On the other hand, we find the same behavior even in

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3 and 4 ML films. This result tells that the g-C4N3 displays half-metallic state in multilayer

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films. From Table I, we find that the order of spin polarization in bilayer is AB>AC>AA while it

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becomes ABA>ABC>ABB in trilayer structures. There is an interesting relationship between


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spin polarization and stacking order. First of all, the AB stacking order produces the largest spin

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polarization and the smallest spin polarization is obtained in identical stacking (AA order) in

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bilayer system. If we add one more layer on AB bilayer structure to form a trilayer film, the ABB

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stacking will have the least spin polarization because of the identical BB stacking. In addition,

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the BC arrangement in ABC stacking is like an AC bilayer stacking if we start from the layer B.

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On the other hand, BA arrangement in ABA stacking is equivalent to AB bilayer stacking with

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respect to the B layer. Thus, we find the order of spin polarization such as ABA>ABC>ABB.

128 129

It is noteworthy that the stability of FM state seems increasing as the film thickness increases.

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However, in reality, the energy difference per atom remains almost the same as shown in

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parentheses of Table 1. Hence, the ferromagnetic stability shows no significant thickness

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dependency. Indeed, we have checked another AFM configuration. In this case, the AFM

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interaction between different layers of g-C4N3 is considered. The FM state is still stable spin

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configuration and the calculated energy difference was almost 20 meV as compared with AFM

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state. In addition, this value is also thickness and stacking order independent. We now show the

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geometric feature and adsorption energy,

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Ntot represent the total energy of the fully optimized N layer g-C4N3 film, the energy of free

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standing single layer g-C4N3, the number of layers and the total number of atoms in the supercell,

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respectively. The optimized interlayer distances and adsorption energies are presented in Table 2.

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TABLE 2: Optimized interlayer distances (in Å) and adsorption energies (Ea in meV/atom) 2ML AB stacking AC stacking AA stacking

=

( ( × )

where EN, , N and

Interlayer Distance

3.27

3.30

3.32

Ea

-0.032

-0.031

-0.031


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3ML

ABA stacking

ABB stacking

ABC stacking

Interlayer Distance

(AB) 3.27

(AB) 3.30

(AB) 3.30

(BA) 3.27

(BB) 3.31

(BC) 3.31

Ea

-0.044

-0.043

-0.043

4ML

ABAB stacking

_

_

Interlayer Distance

3.27

_

_

Ea

-0.051

_

_

141 142

We have observed that the multilayer films still maintain corrugated layer structure as found in

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free standing single layer g-C4N3 structure.15,21 From the calculated adsorption energy, one can

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understand that the g-C4N3 multilayer is a weakly bounded system. This suggests that the main

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interaction among layers should be described by the van der Waals interaction because the

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adsorption energy per atom is very small as compared with that of bilayer graphene.35

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Figure 2 and 3 shows the band structures and density of states (DOS) for bilayer and trilayer

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respectively. Indeed, the band structures and DOS in 4ML films were almost the same as those

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of bilayer and trilayer systems, thus we here only presented the results of bilayer and trilayer

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films. Band structure and DOS of AB and ABA stacking of bilayer and trilayer show the half

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metallic behavior as shown in Figure 2(a) and 3(a), respectively. One can clearly find that the

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majority spin electrons are fully occupied below the Fermi level, whereas the minority spin

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bands cross the Fermi level. In AA and AC configurations for bilayer and ABB and ABC

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configurations for trilayer, we find a similar trend although the majority spin bands barely cross

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the Fermi level. Nonetheless, the minority spin bands maintain the same features as found in AB

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and ABA stacking. This can be confirmed by the spectral shape of DOS. This half-metallic


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characteristic in thin film geometry will bring an interesting issue in the spin dependent transport

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phenomenon because a giant magnetoresistance can be achieved.

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We now discuss the spin dependent transport properties at finite bias. In Figure 4 (a) and (b), the

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schematic illustration for two leads and scattering part for both parallel and antiparallel

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configurations is displayed, respectively. We apply the bias voltages along the negative x-axis,

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so the electrons move to the positive x-axis. The periodic boundary condition is used along the y-

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axis and the vacuum distance of 12 Å is applied along the perpendicular to the film surface. We

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performed the NEGF calculation by taking 150 numbers of poles along the x-direction and 9 k-

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points along the y direction and the convergence criterion is kept 10-8 Hartree. It is obvious that

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the electronic band structure controls the transport property of a material. As we discussed

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already, the most stable configuration of multilayer g-C4N3 shows the half-metallic state and no

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substantial changes in their ground state band structures were found. Thus, we expect that the

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essential transport properties for multilayer g-C4N3 will be the same. Hence, we only calculated

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the transport properties of single layer g-C4N3. In Figure 4 (c), we present the spin dependent I-V

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curve originated from each spin component as a function of external bias. In parallel spin

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configuration, the majority spin current is completely suppressed and this is a straightforward

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result because the majority spin band has a gap as shown in Figure. 2 and only the minority spin

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electrons contribute to the current. In antiparallel spin configuration, the current is significantly

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suppressed because of the reversed spin direction in the opposite lead. From these I-V curves of

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each spin component, we calculate bias dependent magnetoresistance (MR) ratio defined by

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MR(%) = (Ip-Iap)/Ip where the Ip(ap) represents the total current of parallel (antiparallel) spin

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configuration. Then, the maximum MR ratio is 100 % in the theoretical point of view when the


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total current in an antiparallel configuration is zero at any bias voltage. However, in general, the

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Iap can be measured at finite bias, so the 100 % MR ratio is hardly achievable at finite bias. In

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our system, we find that the MR ratio is still large enough even at bias voltage of 0.5 eV and this

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giant MR ratio suggests that the g-C4N3 film can be an ideal candidate for spintronics.

185 186

To explore the optical properties, the most important quantity is the frequency dependent

187

dielectric function () = () + () because various optical properties such as

188

refractive index, reflectivity, and absorption function can be extracted from this value. Here, we

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have considered both parallel (E‫ )׀׀‬and perpendicular (E⊥) electric field polarization to the film

190

surface. From the calculated electronic band structures, one can easily understand that the

191

contribution to the dielectric function due to the intraband transition is negligible if the photon

192

energy is larger than approximately 0.6 eV. Thus, the interband transition plays an essential role

193

in a wide range of photon energy for the frequency dependent dielectric function. Additionally,

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we expect very weak interband optical transition in the visible range because of the band

195

characteristic. This implies that the g-C4N3 films will be optically transparent. Thus, the g-C4N3

196

films can be utilized for both spintronics and optical application purposes.

197 198

Figure 5 shows the real and imaginary part of frequency dependent dielectric functions for both

199

bilayer and trilayer by changing the stacking order. At a zero frequency, the static dielectric

200

functions (ε1(0)) are subject to the thickness and polarization. In bilayer, the ε1(0) is in the range

201

from 13 to 25 for parallel polarization while it is about 4 for perpendicular polarization. In

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trilayer, the ε1(0) is in the range from 35 to 50 for parallel polarization while it is about 6 for

203

perpendicular polarization. As the photon energy increases, the thickness and stacking order


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204

dependence of the dielectric function disappear, but only the electric field polarization

205

dependence remained. One can see noticeable asymmetric behavior in the imaginary part of the

206

dielectric function. This may indicate an anisotropic optical behavior with respect to the electric

207

polarization. In Figure 6 (a) and (b), the calculated refractive index is presented for bilayer and

208

trilayer films, respectively. The real part of the refractive index of parallel electric polarization

209

was larger than that of perpendicular polarization and the refractive index of perpendicular

210

polarization is frequency dependent, but it is almost constant of 1.2 in the visible range for

211

parallel polarization. Interestingly, we find very large refractive index of 2.6 near the blue light

212

for parallel polarization. This large value of refractive index can have potential application for

213

optical device. The reflectivity value is also an important quantity for reflecting and anti-

214

reflecting applications. For instance, it is highly desirable to obtain zero reflectivity for anti-

215

reflection coating purposes. As shown in Figure 6(c) and (d), the perpendicular polarization

216

component has very weak reflectivity. On the other hand, we can find high reflectivity in the

217

ultraviolet region for parallel polarization. In Figure 6(e) and (f), we present the frequency

218

dependent absorption coefficients. We also find an anisotropic behavior in the frequency

219

dependent functions. As displayed, the absorption coefficient for perpendicular polarization is

220

quite small compared with that of parallel polarization. Since the intensity of propagating light

221

decays exponentially as a function of length, the calculated absorption coefficients indicate that

222

the g-C4N3 films can be optically transparent even in much thicker films.

223 224

CONCLUSION

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In summary, we investigated the structural, magnetic, optical and spin dependent transport

226

properties of g-C4N3 films. The most stable structure was found in AB type stacking order. The


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adsorption energy calculations indicated that the interlayer interaction should be described by the

228

van der Waals interaction. We found metal free half metallic behavior and the essential

229

electronic structure was insensitive to the film thickness and stacking order. Due to the half-

230

metallic behavior, the minority spin electrons contribute to the spin dependent current at finite

231

bias in parallel spin configuration whereas the current is strongly suppressed in an antiparallel

232

configuration. Consequently, we find very large magnetoresistance up to the bias voltage of 0.5

233

eV. Along with these magnetic properties, we also explored the optical properties. In general,

234

the optical properties are insensitive to the film thickness and stacking order, but they are

235

strongly subjective to the electric polarization. For instance, the refractive index for

236

perpendicular polarization seems frequency independent in the visible range. Interestingly, a

237

large refractive index of 2.6 was found in parallel polarization, whereas an extremely low

238

reflectivity was obtained in perpendicular polarization. In addition, the multilayer g-C4N3 films

239

are optically transparent. Overall, we propose that the metal free transparent half metallic g-C4N3

240

films can be utilized for spintronics and optical device applications.

241


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242

AUTHOR INFORMATION

243

Corresponding Author

244

*E-mail: [email protected]

245

Notes

246

The authors declare no competing financial interest.

247

ACKNOWLEDGMENT

248

This research was supported by Basic Science Research Program through the National

249

Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and

250

Technology (No. 2013R1A1A2006071) and by the Supercomputing Center/Korea Institute of

251

Science and Technology Information with supercomputing resources including technical support

252

(KSC-2014-C3-015)


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Kim, D.; Hashmi, A.; Hwang, C.; Hong, J. Magnetization Reversal and Spintronics of

Ni/Graphene/Co Induced by Doped Graphene. Appl. Phys. Lett. 2013, 102, 112403. (10) Yang, J.; Kim, D.; Hong, J.; Qian, X. Magnetism in Boron Nitride Monolayer: Adatom and Vacancy Defect. Surf. Sci. 2010, 604, 1603–1607. (11) Si, M. S.; Xue, D. S. Magnetic Properties of Vacancies in a Graphitic Boron Nitride Sheet by First-Principles Pseudopotential Calculations. Phys. Rev. B 2007, 75, 193409. (12) Li, Y.; Zhou, Z.; Shen, P.; Chen, Z. Spin Gapless Semiconductor−Metal−Half-Metal Properties in Nitrogen-Doped Zigzag Graphene Nanoribbons. ACS Nano 2009, 3, 1952–1958.

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(13) Dutta, S.; Pati, S. K. Half-Metallicity in Undoped and Boron Doped Graphene

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Nanoribbons in the Presence of Semilocal Exchange-Correlation Interactions. J. Phys. Chem. B

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2008, 112, 1333–1335.

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(14) Lee, J. S.; Wang, X.; Luo, H.; Dai, S. Fluidic Carbon Precursors for Formation of

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Functional Carbon under Ambient Pressure Based on Ionic Liquids. Adv. Mater. 2010, 22, 1004–

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1007.

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(15) Du, A.; Sanvito, S.; Smith, S. C. First-Principles Prediction of Metal-Free Magnetism and Intrinsic Half-Metallicity in Graphitic Carbon Nitride. Phys. Rev. Lett. 2012, 108, 197207. (16) Sun, S.-J. Interior Edges Induced Half-Metallic Ferromagnetism in Graphitic Carbon Nitride Structures. J. Magn. Magn. Mater. 2013, 344, 39–43. (17) Li, Y.; Sanvito, S.; Hou, S. Origin of the Half-Metallic Properties of Graphitic Carbon Nitride in Bulk and Confined Forms. J. Mater. Chem. C 2013, 1, 3655–3660.


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(18) Li, X.; Zhou, J.; Wang, Q.; Kawazoe, Y.; Jena, P. Patterning Graphitic C–N Sheets into a Kagome Lattice for Magnetic Materials. J. Phys. Chem. Lett. 2013, 4, 259–263. (19) Li, X.; Zhang, S.; Wang, Q. Stability and Physical Properties of a Tri-Ring Based Porous G-C4N3 Sheet. Phys. Chem. Chem. Phys. 2013, 15, 7142–7146. (20) Wu, M.; Wang, Q.; Sun, Q.; Jena, P. Functionalized Graphitic Carbon Nitride for Efficient Energy Storage. J. Phys. Chem. C 2013, 117, 6055–6059. (21) Hashmi, A.; Hu, T.; Hong, J. Transition from Half Metal to Semiconductor in Li Doped G-C4N3. J. Appl. Phys. 2014, 115, 124312. (22) Hashmi, A.; Hong, J. Metal Free Half Metallicity in 2D System: Structural and Magnetic Properties of G-C4N3 on BN. Sci. Rep. 2014, 4. (23) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15–50. (24) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169–11186. (25) Dion, M.; Rydberg, H.; Schröder, E.; Langreth, D. C.; Lundqvist, B. I. Van Der Waals Density Functional for General Geometries. Phys. Rev. Lett. 2004, 92, 246401. (26) Klimeš, J.; Bowler, D. R.; Michaelides, A. Chemical Accuracy for the van Der Waals Density Functional. J. Phys. Condens. Matter 2010, 22, 022201.


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(27) Graziano, G.; Klimeš, J.; Fernandez-Alonso, F.; Michaelides, A. Improved Description of

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Soft Layered Materials with van Der Waals Density Functional Theory. J. Phys. Condens.

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Matter 2012, 24, 424216.

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(28) Liu, W.; Carrasco, J.; Santra, B.; Michaelides, A.; Scheffler, M.; Tkatchenko, A. Benzene

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Adsorbed on Metals: Concerted Effect of Covalency and van Der Waals Bonding. Phys. Rev. B

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2012, 86, 245405.

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(29) The Code, OpenMX, Pseudo-Atomic Basis Functions and Pseudopotentials Are Available on Web Site (http://www.openmx-Square). (30) Troullier, N.; Martins, J. L. Efficient Pseudopotentials for Plane-Wave Calculations. Phys. Rev. B 1991, 43, 1993–2006. (31) Ozaki, T. Variationally Optimized Atomic Orbitals for Large-Scale Electronic Structures. Phys. Rev. B 2003, 67, 155108. (32) Ozaki, T.; Kino, H. Numerical Atomic Basis Orbitals from H to Kr. Phys. Rev. B 2004, 69, 195113. (33) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (34) Ozaki, T.; Nishio, K.; Kino, H. Efficient Implementation of the Nonequilibrium Green Function Method for Electronic Transport Calculations. Phys. Rev. B 2010, 81, 035116. (35) Birowska, M.; Milowska, K.; Majewski, J. A. Van Der Waals Density Functionals for Graphene Layers and Graphite Acta Physica Polonica A 2011, 845.


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Page 18 of 25

332

Figure 1. Schematic illustrations of (a) AA stacking (b) AB stacking (c) AC stacking in bilayer

333

film (d) 1x1 unit cell of g-C4N3 (e) ABA stacking (f) ABB stacking (g) ABC stacking in trilayer

334

film.

335

Figure 2. Calculated Band structures of (a) AB stacking (b) AC stacking (c) AA stacking and

336

DOS of (d) AB stacking (e) AC stacking (f) AA stacking.

337

Figure 3. Calculated Band structures of (a) ABA stacking (b) ABB stacking (c) ABCstacking

338

and DOS of (d) ABA stacking (e) ABB stacking (f) ABC stacking.

339

Figure 4. Schematic illustrations of device components for transport calculations with two leads

340

and scattering part (central region). The arrow indicates the direction of electron flow in (a)

341

parallel spin configuration (b) antiparallel spin configurations. (c) I-V curve and

342

magnetoresistance (MR) with the applied voltage. The left and right scales are for current and

343

MR ratio, respectively.

344

Figure 5. Real part of the frequency dependent dielectric function of (a) bilayer (b) trialyer

345

and imaginary part of the frequency dependent dielectric function of (c) bilayer (d) trilayer.

346

Figure 6. Frequency and polarization dependent (a) - (b) refractive index (c) - (d) reflectivity (e)

347

–(f) absorption coefficient for bilayer and trilayer, respectively.

348 349 350 351


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Page 19 of 25

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Table of Contents (TOC)

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Page 20 of 25

Page 21 of 25 3

3

2

2

2

E n e r g y (e V )

(a )

(b )

(c )

1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

G

-3

K

G

M

G

-3

4 0

M

G

-2 0

-2

0

E n e r g y (e V )

2

G

M

(f)

2 0

2 0

0

0

-2 0

-2 0

-4 0 4

K

4 0

0

-4

G

(e )

2 0

-4 0

K

-3

4 0

(d )

D O S ( S t a t e s /e V .a t o m .s p in )

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

The Journal of Physical Chemistry 3

-4

-2 0 2 ACS ParagonE Plus Environment n e r g y (e V )

-4 0 4

-4

-2

0

E n e r g y (e V )

2

4

The Journal of Physical Chemistry 3

3

3

2

2

2

E n e r g y (e V )

(a )

(b )

(c )

1

1

1

0

0

0

-1

-1

-1

-2

-2

-2

G

-3

4 0

D O S ( S t a t e s /e V .a t o m .s p in )

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

Page 22 of 25

K

G

M

G

-3

4 0

(d )

K

M

G

G

-3

4 0

(e )

2 0

2 0

0

0

0

-2 0

-2 0

-2 0

-4 0

-4 0

-4 0

-2

0

E n e r g y (e V )

2

4

-4

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4

G

M

(f)

2 0

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-2

0

E n e r g y (e V )

2

4

Page 23 of 25

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




5 0

E

(a )

5 0

//

A A -s ta c k in g A B -s ta c k in g A C -s ta c k in g

4 0

E

//

A B A -s ta c k in g A B B -s ta c k in g A B C -s ta c k in g E

⊥

3 0


2 0

E

(b )

4 0

⊥

3 0

ε1(ω)

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

Page 24 of 25

A B A -s ta c k in g A B B -s ta c k in g A B C -s ta c k in g

1 0

2 0

1 0

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1

2

3

4

5

3 0

0

1

2

3

4

5

3 0

E

//

(c )

A A -s ta c k in g A B -s ta c k in g A C -s ta c k in g E

2 0

⊥

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//

(d )

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4

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Page 25 of 25


8

R e f r e a c t i v e I n d e x N ( ω)

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4

5

3

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⊥

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0 .2

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0 .0

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3

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5

0

8

A b s o rp tio n c o e ffic ie n t / 1 0 5 (c m -1 )

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

8 R e a l

1

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3


4

5

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1

2


Spin-Dependent Transport and Optical Properties ... - ACS Publications

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