The metal-free magnetism and ferromagnetic narrow gap semiconductor properties in graphene-like carbon nitride

Accepted Manuscript The metal-free magnetism and ferromagnetic narrow gap semiconductor properties in graphene-like carbon nitride Hengshuai Li, Haiquan Hu, Chenglin Bai, Chunjiang Bao, Zhenbao Feng, Feng Guo PII:

S0921-4526(18)30679-3

DOI:

https://doi.org/10.1016/j.physb.2018.11.003

Reference:

PHYSB 311138

To appear in:

Physica B: Physics of Condensed Matter

Received Date: 25 August 2018 Revised Date:

23 October 2018

Accepted Date: 1 November 2018

Please cite this article as: H. Li, H. Hu, C. Bai, C. Bao, Z. Feng, F. Guo, The metal-free magnetism and ferromagnetic narrow gap semiconductor properties in graphene-like carbon nitride, Physica B: Physics of Condensed Matter (2018), doi: https://doi.org/10.1016/j.physb.2018.11.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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The Metal-Free Magnetism and Ferromagnetic Narrow Gap Semiconductor Properties in Graphene-Like Carbon Nitride Hengshuai Lia,b,* Haiquan Huc Chenglin Baic Chunjiang Baoa Feng Guoc

Zhenbao Fengc

a

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School of Mechanical & Automotive Engineering, Liaocheng University, Liaocheng, 252000, China b School of Physics, Shandong University, Jinan, 250100, China c School of Physics Science and Information Technology, Liaocheng University, Liaocheng, 252000, China

Abstract

In spintronics, if a two-dimensional (2D) organic metal-free material has stable magnetism and narrow gap semiconductor properties, it will have a very bright application prospect. A graphene-like carbon nitride (g-C13N13) that we design just

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meets these requirements. As a new structure, firstly the stability of the g-C13N13 has been verified. It has stable electron spin polarization and the magnetic moment of each primitive cell is 1µB. It exhibits ferromagnetic narrow gap semiconductor

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properties through our analysis of energy band structure and charge density. Ferromagnetic ordering between two adjacent primitive cells is stable. The Monte Carlo simulation using the Ising model shows the Curie temperature material is 204K.

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Our research is an inspiration for the applications of this kind of materials in spintronics devices.

Keywords

Metal-free magnetism; Electron spin polarization; Narrow gap semiconductor properties; Ferromagnetic ordering; Monte Carlo simulations

Corresponding author. Tel.: +86 13475895656. E-mail addresses: [email protected] (H. Li)

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1. Introduction There is a long history of research on carbon nitride materials, and nearly two centuries ago, scientists carried out preliminary research [1]. In 1922, the structure of “carbonic nitride” (C3N4) was studied and its synthesis process was analyzed by

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Franklin [2]. Pauling and Sturdivant inferred that a coplanar triazine group is the basic structural unit of this kind of material [3]. Redemann and Lucas suggested the Franklins carbon nitride near to a compact condensation framework with 21 molecules of 2,5,8-triamino-tris-s-triazine, C126H21N175 [4]. However, researches on

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this type of materials had stalled for nearly 50 years due to chemical inertness and low solubility.

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In the 1990s, it was theoretically predicted the compact sp3-bonded C3N4 phase (β-C3N4) may have high bulk modulus and hardness, which has aroused interest in these compounds [5–9]. A great deal of research on β - C3N4 has given people a better understanding of its properties [10–16]. However, because of the low thermodynamic stability of β - C3N4, it is difficult to prepare single phase β - C3N4. After a series of

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studies, it has been shown that g-C3N4 is the most stable allotrope [8, 17–19]. Therefore, a lot of experiments have been made to synthesize g-C3N4 [20-29]. Kroke [30], Antonietti [31], Blinov [32] and Matsumoto [33] make a very detailed analysis

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of these experiments. On the basis of the previous work, the scientific community has synthesized g-C3N4 with many methods and studied its properties in depth

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[21,26,29-30,34-38].

The electron spin polarization of metal-free π conjugated system has attracted the

interest of scientists because of its wide application prospect in organic spin electronic devices. By analyzing many previous studies, it is found the magnetism of many organic materials is caused by vacancy defects [39-43]. The porous structure of g-C3N4 with ordered vacancies reminds us that there may be magnetism. However, theoretical and experimental studies show that there is no spin polarization in g-C3N4. An important task of spintronics is to find electron spin polarization in materials and apply it to logic and storage devices, which will be an information revolution

ACCEPTED MANUSCRIPT [44-46]. In the traditional materials, the metallicity mainly comes from the transition metal. However, transition metal atoms have a large spin coupling effect, which will reduce the performance of spin electronic devices and make transition metals are incompatible with many technical devices. In recent years, two-dimensional graphene,

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due to its excellent electronic properties [47-49], has been widely studied. When graphene is cut into one-dimensional graphene nanoribbons, it produces magnetism at the edge of the zigzag and finite size effect [50-53]. This provides a bright path for the development of the next generation of metal-free spintronics devices.

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A new type of graphene-like carbon nitride (g-C13N13) that we design will be an ideal metal-free spintronics material. In this paper, we for the first time predicted that

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the g-C13N13 exhibits metal-free magnetism and ferromagnetic narrow gap semiconductor properties. The stability of the g-C13N13 has been analysed. The magnetic moment of each primitive cell is 1µB. The variation of its magnetism with temperature was studied. Through calculation and analysis, we obtain the results that the g-C13N13 is an inspiration for the applications of this kind of materials in

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2. methods

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spintronics devices.

The calculations are performed within first-principles using the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) [54], which is

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in the Vienna Ab-initio Simulation Package (VASP) [55,56]. The electron–ion interactions are described within the projector-augmented-wave (PAW) potentials. [57,58]. A plane-wave basis set with the maximum plane-wave energy of 600 eV is used for the valence electron wave functions. All parameters in the calculation are chosen to converge the total energy to 0.01 eV. A vacuum region of 15 Å is employed along the z direction to avoid interaction between images. The Brillouin zone (BZ) integration was sampled on a grid of 9×9×1 kpoints for structural optimizations of the unit cells and a 5×5×1 grid for the large 2×2×1 supercell.

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3. Results and discussion

Fig. 1. (a) is the atomic structure diagram of g-C13N13 in a top view, where the yellow

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area represents unit cell. (b) is the atomic structure diagram in a side view. (c) is the phonon spectral dispersion diagram.

The structure of g-C13N13 has s-tri-azine and carbon-rich tri-s-triazine (C7N6) as

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building structures which are jointed together directly by C-C bonds，as shown in Fig. 1(a) and Fig. 1(b). The planar configuration and six-fold symmetry were maintained in optimized structure, which should be due to the conjugated p orbital of the structure.

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The chemical formula of per primitive cell is C13N13 in the structure. The equilibrium lattice constants of the g-C13N13 is 11.71‐Å. Around the center of the C7N6, the

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lengths of the C-C band are 1.50 Å, shorter than that bridging building blocks (i.e.1.42 Å). The C-N bonds lengths are 1.34 Å.‐These data are very close to the g-C3N4 that has been synthesized experimentally for a long time [20, 21, 23, 29]. Although g-C13N13 has not been synthesized up to now, many similar synthesized

materials have made us believe that it can be synthesized [59-63]. To further verify that it can be synthesized, we analyze its structure stability. Firstly, we check the kinetic stability through the phonon spectral dispersion diagram. Fig. 1(c) is the phonon spectral dispersion relations with the force-constant theory. Obviously, the phonon spectral dispersion relations are free from imaginary frequencies, indicating the structure framework is kinetically stable. Secondly, we test the dynamic stability

ACCEPTED MANUSCRIPT with molecular dynamics (MD) simulations. At 300 K, the large (2×2) supercell containing 104 atoms is simulated with a Nose–Hoover thermostat. It is found that the structure maintains well after 3 ps, which shows the stability of g-C13N13 at room temperature. With the change of time, the geometric shape of g-C13N13 remains

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unchanged except for the slight change of temperature and total energy. The data of

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molecular dynamics simulation is in the Supporting Information.

Fig. 2. The spin up and spin down electron density of states (DOS) (a), and energy band structure distributions by PBE method (b) of g-C13N13. The energy band gap by the HSE06 hybrid function method is in (c). The amplification diagram of degenerate band near Fermi energy level is also drawn, and Fermi energy is set to zero.

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Next, we analyze the electronic structures of the g-C13N13 lattice. The density of states and the energy band structure distributions are given in Fig. 2(a) and Fig. 2(b). By analyzing the electronic structure, we can conclude that the structure is magnetic,

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magnetic moment of each primitive cell is 1µB. In the spin up orbit, it has no energy band near the Fermi energy level, but in the spin down orbit, it has two bands near the Fermi energy. Because the band gap between the two bands near the Fermi energy level is very small, we believe that it is a ferromagnetic narrow gap semiconductor.

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As well known, PBE functional is usually underestimate the energy gap in DFT calculations, and a hybrid functional such as HSE06 [64] is expected to perform well

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in predicting the accurate gap. Therefore, we calculated the energy band gap by the HSE06 hybrid function method. The more accurate band gap is shown in Figure 2(c). It is found that the gap in the spin down orbit is tiny enough to claim a ferromagnetic narrow gap semiconductor.

The same conclusion can be obtained by analyzing the distribution of charge

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density. Fig. 3(a) is the charge density distribution of the band under the Fermi level, Fig. 3(b) is the charge density distribution of the band above Fermi energy level. In comparison with Fig. 3(a) and Fig. 3(a), it is found that many of the charge density

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distributions overlap, which indicates that electrons are easy to transition, and they are easy to return to the original band and recombine with the holes. From the above analysis, it can be concluded that the g-C13N13 has the properties of a ferromagnetic

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narrow gap semiconductor and can be applied to spin electronics devices.

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Fig. 3. (a) is the charge density distribution of the band under the Fermi energy level,

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(b) is the charge density distribution of the band above the Fermi energy level of g-C13N13. The Fermi energy is set to zero.

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To analyse the magnetic coupling between two adjacent primitive cells, we calculated the distribution of magnetic charge density of the large supercell. From the different initial spin coupling, calculations finally obtained two stable magnetic

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coupling states: ferromagnetic (FM) coupling state and anti-ferromagnetic (AFM) coupling state in Fig. 4. Comparing the energy of the two coupling states, the antiferromagnetic coupling state is 57.5 meV higher than the ferromagnetic coupling state, which reveals the ferromagnetic coupling state is more prior. In the ferromagnetic coupling state, the magnetic moment is 4 µB.

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Fig. 4. The spatial distribution of the spin-polarized electron density of g-C13N13 in (a)

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ferromagnetic (FM) and (b) anti-ferromagnetic (AFM) coupling states. The isosurface value is set to 0.003 Å-3.

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In order to realize its application in spin electronics, it is necessary to understand the variation of its magnetism with temperature. When there is no external field, the

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Hamiltonian of the Ising model can be expressed as  = − ∑ , J  m H · m

(1)

Where m and m are the magnetic moment at sites i and j, and J is the exchange parameter. The value of J is obtained by the energy difference between different magnetic coupling states. For the g-C13N13, the value of J was obtained by following formula: J = ∆E/16m

(2)

In the above formula, ∆E is the energy difference between FM and AFM coupling |. After calculation, we can get the J is 0.23 state in a 2×2 supercell, and m = |m

ACCEPTED MANUSCRIPT meV. The value is very close to that in previous literature [65]. According to all possible spin configurations, the partition function was calculated. Then we can calculate the Curie temperature Tc through determining the bifurcation critical point of ensemble average magnetic moment m . The partition

Z=



!",#,$"

= 2 cosh

 〈〉 e 

*+ 〈,〉 -. /

+ 2 cosh

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function can be derived from the following formula

1*+ 〈,〉 -. /

(3)

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Where the possible values of 2 are 1 and -1, because the magnetic moment of a primitive cell in the g-C13N13 is 1µB. So the average spin of each magnet is "

Let's assume a parameter p, *+

8=-

./

*+ 〈,〉

+ 6 sinh

1*+ 〈,〉

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〈2〉 = 42 sinh 3

-. /

-. /

7

(4)

(5)

So the equation (4) can be rewritten as

9 :;<=〈,〉>?1 9 :;<1=〈,〉>

〈2〉 =

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@A9;<=〈,〉>?@A9;<1=〈,〉>

(6)

On the basis of the above formula, it can be concluded that the static solution m changes with the change of the parameter p, and the critical point is *+

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8B = -

. /C

"

=D

(7)

This critical point between the ferromagnetic state and the paramagnetic state is the

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Curie temperature TC. Finally, the calculated Curie temperature TC is 255 K. The above calculation is based on the mean-field theory, which may be

overestimated. In order to obtain more accurate TC value, we performed Monte Carlo simulation. A 100×100 supercell including 104 µB was used for simulation, which is for 1×109 loops. In every loop, every spin is changed correspondingly. Monte Carlo Simulation of g-C13N13 using Ising Model can obtain Fig. 5 (a) the change rule of magnetism per primitive cell. From the figure we can see that the magnetic moment per primitive cell becomes 0 µB when the temperature is higher than 206 K, which is 20% lower than the estimated value of the mean-field theory mentioned above. The

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and quantum fluctuations.

Fig. 5. Monte Carlo Simulation of g-C13N13 using Ising Model can obtain (a) the

change of temperature.

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change rule of magnetism per primitive cell, and (b) the heat capacities with the

To understand the ferromagnetic–paramagnetic transition of g-C13N13, the heat capacity (C) is represented by the following formula: ∆HI →# ∆

(8)

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C = lim∆

Where ∆E is the increment of the total energy of g-C13N13 from T to T+∆T. Fig. 5(b) shows the value of the heat capacities with the change of temperature. It can be seen

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that the Curie temperature (Tc) is about 204 K. The Tc is slightly higher than that studied in the Mn phthalocyanine framework [65]. The similar half-metallicity and

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thermal stability of ferromagnetic coupling state below 204 K are quite practical for applications of g-C13N13 in spintronic devices.

4. Conclusions

We have designed a new grapheme-like carbon nitride, which is a planar hexagonal symmetric structure. The stability of the structure is verified. From the electron spin-polarization of 2D g-C13N13, it can be concluded that the g-C13N13 has the properties of ferromagnetic narrow gap semiconductor and can be applied to spin electronics devices. To analyse the magnetic coupling between two adjacent primitive

ACCEPTED MANUSCRIPT cells, we calculated the distribution of magnetic charge density of the large (2×2) supercell. The ferromagnetic coupling state is more stable. In order to realize its application in spin electronics, the variation of its magnetism with temperature was studied. Monte Carlo simulations using Ising model obtain the Curie temperature Tc is

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204 K. Our results are very important for potential applications in spintronics.

Acknowledgements

This study is supported by the National Natural Science Foundation of China (No.

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11504153, 11504386), Science and Technology Planning Project of higher School in Shandong Province (No. J18KA243) and Liaocheng University High-level Talents &

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Ph. D. Research Start-up Foundation (No. 318051619).

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