Induction of an atomically thin ferromagnetic semiconductor in 1T′ phase ReS2 by doping with transition metals

Physics Letters A 383 (2019) 125883

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Physics Letters A www.elsevier.com/locate/pla

Discussion

Induction of an atomically thin ferromagnetic semiconductor in 1T phase ReS2 by doping with transition metals Jing Pan, Xiaoyu Zhou, Jiansheng Zhong, Jingguo Hu ∗ College of Physics Science and Technology, Yangzhou University, Yangzhou, 225002, China

a r t i c l e

i n f o

Article history: Received 10 April 2019 Received in revised form 4 July 2019 Accepted 5 August 2019 Available online 8 August 2019 Communicated by R. Wu

a b s t r a c t Two-dimensional 1T phase ReS2 , a transition metal dichalcogenide, has a unique structure and electronic properties that are independent of thickness. The pure phase is a nonmagnetic semiconductor. Using density functional theory calculations, we show that ReS2 can be tuned to a magnetic semiconductor by doping with transition metal atoms. The magnetism mainly comes from the dopant transition metal and neighboring Re and S atoms as a result of competition between exchange splitting and crystal field splitting. ReS2 doped with Co can be considered as a promising diluted magnetic semiconductor owing to its strong ferromagnetism with long-range ferromagnetic interaction, high Curie temperature (above room temperature) and good stability. These findings may stimulate experimental validation and facilitate the development of new atomically thin diluted magnetic semiconductors based on transition metal dichalcogenides. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Two-dimensional semiconducting transition metal dichalcogenides (TMCDs) have received a lot of attention in recent years as a result of their distinctive chemical and physical properties [1–7]. Modifying the carrier type and density of these semiconductor materials can change their electronic structure and extend their applications in nanodevices. Doping with transition metal (TM) atoms is an effective method of engineering the band structure of two-dimensional semiconductors—for example, substitutional doping with Nb can change MoS2 into a stable p-type semiconductor. Joonki et al. [8] designed van der Waals p–n homojunctions based on vertically stacked MoS2 and achieved gate-tunable current rectification. Wang et al. [9] found that the efficiency of MoS2 -based catalysts in the hydrogen evolution reaction was greatly improved by substituting Mo with isovalent W, giving an onset potential of −37 mV and an over-potential of 138 mV for 10 mA cm−2 . Cheng et al. [10] reported that doping MoS2 with Mn, Fe, Co and Zn results in promising diluted magnetic semiconductors (DMSs). DMSs show excellent magnetic, magneto-optical and magnetoelectric properties due to the possibility of controlling both the spin and charge of electrons. They are widely used in high-density memory devices, optical isolators, low-power spin field-effect tran-

*

Corresponding author. E-mail address: [email protected] (J. Hu).

https://doi.org/10.1016/j.physleta.2019.125883 0375-9601/© 2019 Elsevier B.V. All rights reserved.

sistors and many other applications [11–15]. Although spintronic devices can be designed by the substitutional doping of TMCDs, low temperatures limit their operation and practical applications. The development of room temperature DMSs remains a challenge in the rapid development of TMDCs-based spintronic devices. ReS2 has attracted interest as a new member of the TMDC family due to its unique structure and electro-optical and chemical properties [16–28]. Unlike other, more common, TMDCs, ReS2 exhibits a distorted 1T phase, denoted as 1T , with the Re atoms clustering in a diamond shape and interlinking together to form diamond-shaped chains, which gives rise to in-plane anisotropy [24,26]. The interlayer decoupling effect means that the bulk material is an electronically and vibrationally decoupled monolayer. Bulk ReS2 is therefore a direct band gap (∼1.5 eV) semiconductor with electronic properties that are almost independent of thickness [16,21,22]. These distinctive properties mean that ReS2 displays unique optical and electrical behavior in nanodevices, although spintronic applications based on ReS2 have rarely been reported. Doping with TMs is an effective method by which to manipulate the magnetism of TMDCs. We doped ReS2 with 3d Cr, Mn and Co to form p-type, isovalent and n-type doped semiconductors. Our density functional theory calculation has shown that ReS2 can be tuned from a nonmagnetic semiconductor to a magnetic semiconductor by doping with TMs. The magnetism concentrates on the TM and the neighboring Re and S atoms as a result of competition between exchange splitting and crystal field splitting. Importantly, Co-doped ReS2 shows a strong ferromagnetic character with

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Fig. 1. (a) Atomic model for the 2×2 supercell of 1T -ReS2 with a doping concentration of 6.25% and (b) band structure and atom partial density of states of monolayer ReS2 , where the blue, yellow and white balls mean Re, S and the dopant TM atoms, respectively. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

a Curie temperature (T C ) above room temperature, long-range ferromagnetic coupling and a good stability. The findings may open the application of 1T -ReS2 based DMSs in nanodevices and spintronics.

Table 1 Binding energy (E b ), total magnetic moment (M tot ), magnetic moment of TM dopant atom, Re and S atoms (M TM , M Re and M S ), respectively, and the characteristics of TM doped ReS2 . The doped systems will become magnetic semiconductors (MS) or nonmagnetic semiconductors (NS).

2. Computational model and methods

Dopant atom

E b (eV)

M tot (μB )

M TM (μB )

M Re (μB )

The calculations adopted the Vienna ab initio simulation package and implemented within spin-polarized density functional theory [29]. The generalized gradient approximation of the Perdew– Burke–Ernzerhof (PBE) functional was used to describe the exchange–correlation interactions. The plane wave basis cutoff energy was 500 eV. The structures were relaxed until the Hellman– Feynman forces were satisfied and the changes in energy were <0.01 eV Å−1 and 1.0 × 10−5 eV. Monkhorst–Pack k-point meshes of 16 × 16 × 1 and 36 × 36 × 1 were used for the optimization of geometry and electronic structure calculations, respectively. Because the electronic structure remained almost unchanged from the monolayer structure to a thickness of a few layers, a 2 × 2 supercell containing 48 atoms was used to model the monolayer ReS2 structure [Fig. 1(a)], which was formed by cleavage from the (0001) surface of the bulk ReS2 with a vacuum layer of at least 15 Å to avoid interactions between adjacent layers. TM atoms (Cr, Mn, Fe or Co) were substituted for an Re atom to give a doped concentration of 6.25%. Cr induced p-type doping and Mn doping was isovalent, whereas Fe and Co induced n-type doping.

Cr Mn Fe Co

8.44 8.07 8.24 8.93

0.98 0 0.99 1.83

1.04 0 0.63 1.18

0.03 0 0.42 0.43

M S (μB )

State

−0.08

MS NS MS MS

0

−0.07 0.22

3. Results and discussion The calculated lattice constants of bulk ReS2 are a = 6.41 Å, b = 6.51 Å and c = 6.53 Å, agreeing fairly well with the experimental results (a = 6.41 Å, b = 6.51 Å and c = 6.46 Å) [26]. The electronic structure in Fig. 1(b) shows that pure monolayer ReS2 is a direct band gap (E g = 1.43 eV) semiconductor, which is an excellent match to the experimental result (E g = 1.55 eV) [16]. Additionally, though PBE method generally underestimate the band gap of the semiconductor, but they can give a reasonable description of the magnetism [30]. These can indicate the feasibility of our PBE method. The valence band maximum (VBM) and conduction band minimum (CBM) in pure ReS2 are mainly composed of the Re 5d and S 3p states. ReS2 is a nonmagnetic semiconductor because the band structure in spin-up and spin-down channels displays symmetrical. However, when the host Re atom is substituted by a 3d TM (Cr, Mn, Fe or Co) atom, there is a change in the band structure and the systems display remarkable properties. We first investigated the stability of TM doped ReS2 . The binding energy can be calculated as E b = E v + E TM − E, where E v

Fig. 2. Formation energies of Cr, Mn, Fe, Co doped ReS2 under Re-rich and S-rich conditions.

represents the host with an Re vacancy, E TM is the energy of the doped TM atom in the bulk phase and E refers to the doped system [31]. The calculated binding energies for Cr, Mn, Fe and Co doping are 8.44, 8.07, 8.24 and 8.93 eV, respectively (Table 1). The positive values indicate that TM doped ReS2 systems have good stability. Additionally, we calculated the formation energies of these TM doped ReS2 under S-rich and Re-rich conditions, the calculated details can be found in Ref. [32,33]. As shown in Fig. 2, TM doping is much easier to be achieved under S-rich condition and the doped systems are energetically favorable because their formation energies are negative. An isolated Cr atom has a 3d5 4s1 configuration, whereas an Re atom has a 5d5 4s2 configuration. Doping with Cr can therefore provide a hole to form p-type doping. The unpaired valence electron is split under the tetrahedral field of the ReS2 crystal and induces magnetism in the ReS2 . Fig. 3(a) shows that ReS2 doped

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Fig. 3. Band structure and atom partial density of states of ReS2 doped with (a) Cr, (b) Mn, (c) Fe and (d) Co.

Fig. 4. Spin density of ReS2 doped with (a) Cr, (b) Mn, (c) Fe and (d) Co. Isovalue is 0.02 eV Å−3 .

with Cr has the properties of a magnetic semiconductor because spin-splitting occurs between the spin-up and spin-down channels. The dopant bands resulting from hybridization among the Cr-3d, Re-5d and S-3p states appear in the band gap of ReS2 , which is close to the valance bands, further indicates p-type doping. The magnetism mainly origins from the dopant Cr atom, with only a small amount from the neighboring Re and S atoms [Fig. 4(a)]. The

magnetic moment of the Cr atom is 1.04 μB and, although the spin of the Cr atom is anti-parallel to the neighboring Re atoms, the up-spins are much larger than the down-spins, the positive total magnetic moment with 0.98 μB can be achieved in Cr doped ReS2 (Table 1). For doping with Mn, the number of valence electrons of Mn (3d5 4s2 ) is equal to that of Re (5d5 5s2 ) and therefore the dop-

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Fig. 5. Orbital decomposed partial density of states (PDOS) and schematic diagram of the d orbital splitting of ReS2 doped with (a) Cr, (b) Mn, (c) Fe and (d) Co. c f means crystal field splitting and ex means intra-atomic Hund’s exchange splitting.

ing is isovalent. The dopant bands contribute from Mn-3d, Re-5d and S-3p states and appear near the valence band maximum, thus, the band gap reduces to 1.16 eV. The electronic structure is symmetrical in both the spin-up and spin-down channels, the system remains a nonmagnetic semiconductor [Fig. 3(b)]. Doping with Fe and Co results in n-type doping because the Fe and Co atoms have 3d6 4s2 and 3d7 4s2 configurations and have one and two valence electrons more than the Re atom, respectively. Their electronic structures [Fig. 3(c) and 3(d)] show significant spin-splitting between the spin-up and spin-down channels, demonstrating their magnetic character. The dopant bands in the band gaps are close to the conduction bands, confirming the ntype semiconductor properties. The local dopant bands near the Fermi level (E F ) mainly come from Fe 3d (Co 3d), Re 5d states, indicating the contribution to the magnetism from the dopant TM and neighboring Re atoms, which can be verified by the spin density shown in Fig. 4(c) and 4(d). The total magnetic moments are 0.99 and 1.83 μB , the magnetic moments of Fe and Co are 0.63 and 1.18 μB , respectively, and the magnetic moments of the neighboring Re atoms are 0.42 and 0.43 μB for ReS2 doped with Fe and Co, respectively. This clearly shows that tunable magnetism can be achieved in ReS2 by doping with TM atoms. To investigate the origin of magnetism in TM-doped ReS2 , we explored the orbital decomposed partial density of states of 3d TM atoms (Fig. 5). According to ligand field theory, the 3d states of TM atoms can be split into a single a1 (dz2 ) state and two twofold degenerate e 1 (dxy ,x2 − y 2 ) and e 2 (dxz, yz ) states. Intra-atomic (Hund’s) exchange splitting (ex ) determines the energy difference of the e 1 orbital between the up-spin and down-spin states, whereas crystal field splitting (c f ) determines the energy difference between the e 1 and e 2 orbitals [10,34,35]. For TM doped ReS2 , the spin-splitting near the Fermi level mainly results from the exchange splitting and crystal field splitting of the 3d states of the TM. For Mn doped ReS2 [Fig. 5(b)], ex is zero and therefore the systems are non-

magnetic. For ReS2 doped with Cr [Fig. 5(a)], c f is 1.34 eV and ex is 1.19 eV. The crystal field splitting induced by the structural asymmetry is larger than the exchange splitting induced by doping with Cr. This indicates that there is competition between exchange splitting and crystal field splitting in TM doped ReS2 . By contrast, c f becomes 0.99 eV, less than the ex of 1.84 eV for ReS2 doped with Fe, and c f is 0.77 eV, less than the ex of 1.77 eV for ReS2 doped with Co. Similarly, the magnetism of the systems mainly origin from the competition between crystal field splitting and exchange splitting. Exchange splitting is dominant in n-type doping with Fe and Co [Fig. 5(c) and 5(d)] and the magnetic moment is larger when there is a greater difference between c f and ex . To further investigate the magnetic coupling of the TM dopants, the supercells are enlarged to four unit cells. There are 96 atoms in the system, the two doped TM atoms are separated by 3.40, 3.66 and 3.49 Å for ReS2 doped with Cr, Fe, and Co, respectively, in the near-neighbor coupling interaction, whereas the distances in the long-range coupling interaction are 12.82 Å (Fig. 6). As far as coupling between the TM dopants, we consider not only ferromagnetic coupling but also antiferromagnetic coupling [33]. The total magnetic moments are 1.97, 1.98 and 3.66 μB for Cr-, Fe- and Co-doped ReS2 , respectively, they are twofold of one TM atom doping and independent of the distance between the two TM dopants. For Crdoping with near-neighboring coupling interaction, the energy of the ferromagnetic state is 1.52 meV lower than the antiferromagnetic state, displaying a weak ferromagnetic character. By contrast, the stable state in the long-range coupling interaction is the antiferromagnetic state because the energy of this state is 113.65 meV lower the ferromagnetic state. This means ReS2 doped with Cr can be easily tuned from weak ferromagnetic coupling to strong antiferromagnetic coupling by varying the distance between the TM atoms. ReS2 doped with Fe shows strong antiferromagnetic coupling in the near-neighboring coupling interaction, with  E M = −91.59 meV, but weak ferromagnetic coupling in the long-range

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Fig. 6. Top views of ReS2 doped with pairs of (a) Cr, (b) Fe and (c) Co in (upper panel) near-neighbor and (lower panel) long-range coupling interactions between the TM dopants. Table 2 Distance between two TM dopant atoms (d), total magnetic moments of the pair of ReS2 dopes with a TM (M tot ), the energy difference between the antiferromagnetic (AFM) and ferromagnetic (FM) state ( E M = E AFM − E FM ) and the Curie temperature (T c ). System

d (Å)

M tot (μB )

 E M (meV)

T C (K)

Cr

3.40 12.82

1.97 1.97

1.52 −113.65

11.76 –

Fe

3.66 12.82

1.98 1.98

−91.59 1.00

– 7.74

3.49 12.82

3.66 3.66

72.89 0.82

563.86 6.35

Co

coupling interaction, with  E M = 1.0 meV. For ReS2 doped with Co, the energies of the ferromagnetic states are lower than the antiferromagnetic states both in near-neighboring and the long-range coupling, with  E M = 72.89 meV and  E M = 0.82 meV, respectively, indicating that Co dopants favor ferromagnetic coupling and Co-doped ReS2 is a ferromagnet. See Table 2. The Curie temperature (T C ) is an important parameter of DMSs, it can be estimated as k B T C = (2/3) E M using the Heisenberg model with mean field approximation [33,35]. For ReS2 doped with Co, T C is 563.86 and 6.35 K for near-neighboring coupling and long-range coupling interactions, respectively, indicating that ReS2

doped with Co may be an ideal low-dimensional DMS as a result of its good stability, long-range ferromagnetic interaction and high Curie temperature. 4. Conclusions Based on density functional theory electronic structure calculations and magnetic analysis, we show that it is possible to tune 1T -ReS2 from a nonmagnetic semiconductor to a DMS by doping with TMs. The magnetism comes from the dopant TM atom and the neighboring Re and S atoms and results from competition between exchange splitting and crystal field splitting. ReS2 doped with Co is considered to be an ideal DMS as a result of its strong ferromagnetism with long-range ferromagnetic ordering, high T C (above room temperature) and good stability. These findings provide a feasible strategy by which to engineer the band structure of a new member of the TMDC family at the atomic level and pave the path for future applications of ReS2 in nanoelectronic and spintronic devices. Acknowledgement This work is supported by the National Natural Science Foundation of China (11774302, 11574263 and 11674276), the Qinglan

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