Transition Metal Doped Tin Monoxide Monolayer: A First-Principles

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Transition Metal Doped Tin Monoxide Monolayer: A First-Principles Study Yiren Wang, Sean Li, and Jia Bao Yi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12282 • Publication Date (Web): 01 Feb 2018 Downloaded from http://pubs.acs.org on February 5, 2018

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The Journal of Physical Chemistry

Transition Metal Doped Tin Monoxide Monolayer: A First-Principles Study Y.R. Wang, S. Li, J.B.Yi* School of Materials Science and Engineering, UNSW, Sydney, NSW, 2052 Email: [email protected]; Tel: 61-293854837. Abstract

Using first principles calculations, the structural and electronic properties of monolayer SnO doped with 3d transition metals from V to Ni were investigated. The results indicate that the substitutional doping is preferred under oxygen rich conditions for all transition metals. In addition, all dopants induce magnetism by forming TMsub except for Ni. Such magnetic behaviour is due to the interaction between the dopants and the surrounding Sn/O atoms. The stability and origin of magnetism are investigated by considering different defect complexes. The results show that defect complex composed of substitutional dopant and oxygen vacancy has the same magnetic moment as that of substitutional dopant of TMsub alone while the magnetic moments of defect complex composed of ubsubstitutional, TMsub and tin vacancy, VSn vary significantly. The moments of defect complex, such as (Cosub +VSn) and (Nisub +VSn), are enhanced compared to that of the substitutional alone. On the other hand, the magnetic moments of (Fesub +VSn) and (Mnsub +VSn) maintain the same as that of substitutional dopants alone. Whereas, (Crsub +VSn) and (Vsub +VSn) have lower magnetic moments than that of single TMsub.

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Introduction Graphene, a typical two-dimensional (2D) material, is one of the most interesting research topics over the past decade 1. Graphene can be exfoliated from graphite, which has a layered honeycomb structure. The carbon atoms in graphite within the plane are bonded covalently and the layers are coupled via the weak van der Waals force. The weak coupling between the interlayers enables the layers of graphite to be separated easily to obtain the graphene. The exfoliation of single-layer graphene from graphite has paved ways for the cleavage of the layered materials into single atomic layered 2D materials. 2D structures were thought to be unstable until the discovery of graphene which presents stable and unique mechanical, thermal, electronic and magnetic properties

2-3

. It is promising for the applications in various fields, such as

sensors, electronic devices and spintronics devices. The exotic properties of graphene have inspired many researchers to explore other 2D materials derived from group IV elements like silicene, group II-V and group III-V compounds including BN and GaN, as well as transition-metal dichalcogenides such as MoS2, WS2 and NbSe2, etc.

Recently, studies have gained insights into a new member of 2D materials family: metal oxide. The exfoliation of layered oxides has been achieved successfully in layered manganese oxide, titanium oxide, niobium oxide and cobalt oxide

4-7

. 2D

metal oxide materials have shown various electronic properties: for instance, 2D transition metal oxide like TiO2 is usually semiconducting while MnO2 nanosheets are found to be redoxable or semimetallic 8, rendering wide applications in electronic devices with their unique electronic properties. High performance supercapacitors have been fabricated using RuO2 nanosheets 9; field-effect transistors (FET) can be obtained with Ti0.87O2 and Ti0.91O2 nanosheets via layer-by-layer assembly 6; room


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temperature ferromagnetism was observed in magnetic oxide nanosheets like Ti1xCoxO2(x≤0.2) xCoxO2

10

, Ti1-xFexO2(x≤0.4)

11

, and Ti1-xMnxO2(x≤0.4)

12

. Moreover, 2D Ti1-

was calculated to be ferromagnetic with spin-orbit coupling anisotropy

13-14

.

Two-dimensional metal oxides are therefore believed to have great potential in the applications of various electronic and spin-electronic devices.

Recently, 2D tin monoxide monolayer has been successfully fabricated experimentally and it possesses promising properties for the application of field effect transistors (FET), making it one of the most interesting candidates for the family of metal oxide 2D materials

15

. Tin monoxide (SnO) has a unique layered tetragonal structure with

both Sn and O atoms in four coordinate pyramids. The bottom of the square pyramid is formed by the four oxygen atoms arranged in regular tetrahedral geometry while tin atoms sit alternatively on the top of pyramids. Electron densities are observed to be asymmetric along the vertical axis due to the long pairs of the 5s electrons of Sn. These electrons do not contribute to the bonding but dipole-dipole interaction between SnO layers.

The investigations of SnO mainly focused on thin films structures, which exhibit native p-type conductivity and are ideal for fabricating high-mobility p-channel thin film electronic devices, such as gas sensors and thin film transistors

16-22

. Several

computational studies have been carried out to explore the structural, electronic, optical and magnetic properties of SnO to elucidate the defect chemistry of SnO

23-29

.

Briefly, tin vacancy is the major native defect under oxygen-rich atmosphere and responsible for the observed p-type conductivity

23

. However, the existence of oxygen

vacancy and tin interstitials can enhance the electron mobility under Sn-rich



environment. It is important to clarify the defects chemistry since defects have shown strong influence on the properties of oxide based semiconductors 30-38. Good examples are the effects of defects or defect complexes on the magnetic properties in the research of oxide based magnetic semiconductors

35-38

. Cation vacancies or oxygen

vacancies have been found to be the origin of the ferromagnetism in pure oxide semiconductors, such as ZnO and TiO2

33-34, 39-40

. In addition, these defects play

important role in the ferromagnetism of transition metal doped oxide based diluted magnetic semiconductors and the ferromagnetism can be tuned by defect engineering 41-44

.

In the research of diluted magnetic semiconductors, transitional metals have been widely used as dopants to realize ferromagnetism. Similarly, theoretical study on SnO bulk systems doped with a series of transition metals including Sc, V, Cr, Mn, Fe, Co, Ni, and Cu doped was also conducted

45

. Formation energies have been extensively

calculated to predict the preferable doping sites and the calculation results indicate that the doping sites can strongly influence the magnetic properties. For example, the spin polarization induced by transition metal doping can be neutralized if two TM dopants are located closely.

However, it is exceptional for V doping, which has strong

ferromagnetic behaviour if the dopants are clustering and therefore promising for the fabrication of magnetic semiconductors 45.

Although intensive research efforts have been devoted to bulk SnO, the report related to 2D SnO is very limited. The research interest was triggered by the stability of 2D SnO as a semiconductor with a bandgap energy of ~3.95 eV predicated with HSE06 functionals.46 Subsequently multiferroic was found from the monolayer SnO using


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HSE06 and PBE-vdW functionals, respectively

47

. It was believed that the

ferromagnetism can be achieved in monolayer SnO with a hole density of 2-3×10

14

cm-2. Such a phenomenon may originate from Mexican-hat band dispersion. Ferroelasticity and multiferroicity can be stabilized using a generalized Landau model, suggesting great potential of 2D SnO in achieving multi-functional electronic devices47. Theoretical study carried out by Ma et al. confirmed the stability of monolayer SnO and the semiconducting nature of monolayer SnO with an indirect bandgap of 2.62 and 3.33 eV using PBE and HSE06 functionals 48. More recently, few layers of SnO films were successfully fabricated on sapphire substrates using pulsed laser deposition

15

. The structural, optical and transport properties were measured,

which showed that 2D SnO could be a potential candidate in fabricating room temperature 2D FET.

Until now, there is no experimental or theoretical works on the monolayer SnO doped with transition metals as well as considering the defect or defect complex effects on the structural, electronic and magnetic properties. In this work, we have used first principles calculations to study the electronic and magnetic properties of 2D SnO by considering both defects and transition metal doping. Detail calculations have shown that all the doping is preferable at rich oxygen environment. Transition metal doping alone can induce magnetism except for Ni. However, the defect complex formed by substitutional Ni and tin vacancy, (Nisub +VSn) shows a spin polarized state. Our calculations indicate that defects or defect complexes have strong influences on the electronic and magnetic properties of 2D SnO.



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Computational methods Ab-initio density functional theory (DFT) calculations were performed to investigate the electronic and magnetic properties of two-dimensional tin monoxide. All the calculations were carried out in the Vienna ab initio simulation package (VASP)49 with generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof (PBE)

50

combined with projector augmented wave (PAW)

51

. GGA+U

methods were applied as well to describe the d states of the TM dopants. U=3.3, 3.7, 3.9, 5.4 6.2 and 3.25 eV are adopted for Co, Cr, Mn, Fe, Ni and V doped SnO monolayers respectively. The values of U are chosen based on our calculations and references

52-55

. Grimme DFT-D2 approach

56

was adopted to describe the van der

Waals interactions between the interlayers in SnO bulk for lattice optimization. A 4×4 monolayer tin monoxide with 32 Sn atoms and 32 O atoms, as shown in Fig. 1(a), was employed with a cut-off energy set to 500 eV and a Monk-horst pack k-point mesh of 3×3×1 for structural optimizations while in self-consistent calculations, a 5×5×3 kpoint mesh was adopted. A vacuum distance of 15 Å along the z direction was added to avoid the interactions between adjacent layers. The total energy convergence was set to less than 10-5 eV and the force on each atom was less than 0.02 eV/Å in both structural optimizations and the self-consistent calculations.

Results and discussion As shown in Fig. 1 (a), monolayer SnO consists of three atomic layers with an alternating tetragonal structure. The two layers of tin atoms and one layer of oxygen atoms are arranged in alternating pyramid structures. The optimized unit-cell monolayer SnO has lattice constants of a=b=3.805 Å, which is in good agreement with other calculation results (3.803 Å

47

) and the experimental value of bulk SnO (3.7986


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Å

57

). The average length of the Sn-O bond is 2.251 Å. The calculated total and

projected density of states (TDOS and PDOS) of the 4×4 supercell are demonstrated in Fig. 1(b). It shows that pristine monolayer SnO is a wide band gap semiconductor with a calculated bandgap of about 2.95 eV, agreeing well with other calculations, such as 3.00 eV 47 and 2.62 eV 48.

FIG. 1. (a) The atomic structure of 4×4 monolayer tin monoxide from top view and side view. The rectangle in top view denotes the primitive cell of SnO. (b) The calculated total DOS and partial DOS of pristine 4×4 monolayer tin monoxide. The Fermi level indicated by the grey line has been set to zero.

It is known that defects can be easily formed in monolayer 2D materials during the exfoliation and there are a large amount of native defects in 2D materials 58. Therefore, before investigating the substitutional system, we first examined the SnO monolayer with a single vacancy defect. In this case, an oxygen vacancy (VO) is created by removing an oxygen atom from the supercell and no obvious lattice displacement can be observed after the structural relaxation as denoted in dashed sphere in Fig. 2 (a). VO prefers nonmagnetic ground state and does not produce any magnetism, which can be



confirmed by the symmetry of spin-up and spin-down bands near the Fermi level in total density of states.

FIG. 2. The atomic structures, spin densities and total density of states of 4×4 monolayer SnO with VO (a) and spin densities and total density of states of 4×4 monolayer SnO VSn (b) after structural relaxation. The dashed spheres indicate the vacancy sites and the Fermi levels indicated by the grey lines have been set to zero. The numbers in the top view of the structures suggest the different positions of the TM elements when forming defects (a) (VO+TMsub) and (b) (VSn+TMsub).

However, atomic displacements are observed in Fig. 2 (b) when Sn vacancy (VSn) exists. The O atoms around the vacancy shift away against the vacancy position for 0.278 Å. The bond lengths between these O atoms and two adjacent Sn atoms at lower layer are 2.136 Å while the bonds with the Sn atoms at upper layer are slightly stretched to be 2.140 Å. VSn is spin-polarized and has a total magnetic moment of 2.00


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µB as shown in Fig. 2 (b). The spin densities are mainly located on the four first nearest-neighbouring (1NN) and the four second nearest-neighbouring (2NN) Sn atoms as well as the 16 O atoms surrounded. These neighbouring can be classified as 1NN, 2NN, and 3NN by the different distances to the vacancy site. The partial density of states (PDOS) of these atoms are shown in Fig. 3, and it is a ferromagnetic halfmetal. We can see that the magnetism originates from p orbitals of the surrounding Sn and O atoms around the vacancy site. The spin-down state of 2p orbitals of 1NN and 2NN O atoms and 5p orbitals of 1NN Sn atoms is partially occupied which contributes to the magnetic moment of VSn, while the 5s orbitals of Sn atoms have no contribution to the magnetic moment. The magnetism is mainly attributed to the mediation between unpaired electrons via p-p interaction. The local magnetic moments of these atoms are listed in Table 1. The local magnetic moments of the other Sn and O atoms are close to zero which can be neglected.

TABLE 1. The calculated average local magnetic moments of the Sn and O atoms around the VSn.

µ/ µB

1NN- Sn

2NN- Sn

1NN- O

2NN- O

3NN -O

0.070

0.059

0.099

0.045

0.033



FIG. 3. PDOS of monolayer SnO with a VSn. The Fermi level has been set to zero. The inset is an enlarge image of the PDOS near the Fermi level.

For further studying the magnetic properties of 2D SnO, we conducted the studies of substitutional effect of transition metals in monolayer SnO systems. Six elements, including V, Cr, Mn Fe, Co, and Ni, have been employed for the investigation. Those elements are common 3d elements for doping to induce ferromagnetism in 2D materials and diluted magnetic semiconductors

59-63

. The blue ball in Fig. 4(a) stands

for the substituted transition metal element.

The formation energy of the supercell with a single defect is defined as: ∑ μ , where Edefect and Esupercell are the total energies of monolayer SnO with and without defects; n stands for the number of atom i that has been removed or added and µi is the relevant chemical potential of atom i in bulk


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phase. Here, we choose Co in hcp phase, Cr and Ni in fcc structure, Fe, Mn and V in bcc structure for the calculations of formation energies. For O-rich (Sn-poor) limit, the chemical potential of O is given by the equilibrium condition between SnO and SnO2; For Sn-rich (O-poor) limit, the chemical potential of Sn is the taken from the bulk αSn.

Our calculations in both GGA and GGA+U methods suggest that most of transitionmetals doping in SnO can induce magnetism by simple substitutions except for Ni. The spin density distributions of SnO with different doping elements are shown in Fig. 4 (b). Ni substitutional in monolayer SnO still remains non spin-polarized state as that in bulk SnO 45. Ni is a TM element that exhibits strong ferromagnetic properties and is expected to be a potential magnetic dopant. However, Ni doping is not always magnetic, especially for the doping in 2D materials, such as Ni doping in MoS264. The nonmagnetic doping in 2D materials has not been explained. According to Ref.65. The nonmagnetic nature of Ni doping may be due to the charge transfer between Sn and Ni, making 3d orbitals fully filled. The calculated magnetic moments of Co, Cr, Fe, Mn, and V substitutional are 1.00, 4.00, 4.00, 3.00 and 3.00 µB separately. The magnetism mainly originates from the active d orbitals of the TM elements as seen from the spin density distributions.



FIG. 4. (a) The initial atomic structures of 4×4 monolayer SnO with a TMSn and the atomic structures and spin densities of (b) Cosub, (c) Crsub, (d) Fesub, (e) Mnsub, (f) Nisub and (g) Vsub after structural relaxations from both top and side views using GGA method. The blue ball in (a) stands for the substituted transition element. Yellow and blue iso-surfaces in (b)-(g) represent positive and negative spin densities, respectively. The iso-surface value is taken to be 0.001 bohr-3.

The calculated formation energies of monolayer SnO with single defects (i.e. VSn, VO and TMsub) are shown in Fig. 5 and listed in Table 2. VSn can form spontaneously in the system under oxygen rich condition. However, VO has lower formation energy indicating that VO will generate primarily. The formation energy of VSn will increase greatly with the existence of VO which means it is unlikely to form under this circumstance. The calculation results suggest that substitutional TM defects, TMSn, can be easily formed under the oxygen rich condition, and CrSn has the lowest formation energy among all the TM elements while CoSn has the highest one.


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Subsequently the structures with two Sn vacancies are considered, including eight possible configurations of (VSn +VSn) as numbered in Fig. 2(b). According to the total energy calculations of all the possible configurations, the most possible structure of the concerned defect complex is two VSn defects with the second nearest-neighbouring (NN) separation as shown in Fig. 6 (the second VSn in position 2 in Fig. 2 (b)). Large lattice distortion can be observed in (VSn +VSn): The system becomes symmetric along the axis of the oxygen atom between two vacancies as indicated with the dashed lines in Fig. 6. The oxygen atom moves upwards for about 2.81 Å and two tin atoms beside this oxygen atom shift towards the vacancies for 0.75 Å. This complex is calculated to show a very weak moment of merely 0.0014 µB which can be neglected. The absolute formation energy of (VSn+ VSn) is -1.88 eV at O-rich condition, which is -0.94 eV/VSn. The defect complex can be very easily formed under the O-rich condition.

FIG. 5. The calculated formation energies of 4×4 monolayer SnO with various single defects using GGA method. The inset is a zoom view of the area marked in rectangle.



The dashed grey line indicates the formation energy per VSn in defect complex (VSn+VSn).

From above analysis, the growth chemistry of monolayer SnO can be outlined briefly: oxygen vacancies are the dominant defects under O-poor environment and therefore the system remains nonmagnetic. Increasing the oxygen partial pressure, tin vacancies become more favourable and the system will show spin-polarized state since VSn is magnetic. However, VSn tends to cluster at high vacancy concentrations and the system becomes nonmagnetic again. Therefore, the undoped monolayer SnO can be magnetic only in a moderate oxygen partial pressure and tin vacancy concentration.

FIG. 6. The atomic structure of 4×4 monolayer SnO with the most possible configuration of (VSn +VSn) after structural relaxation. The dashed spheres denote the VSn.


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Defects play an important role in determining the properties of 2D materials. Besides single defects, like vacancies and substitutional defects, dopants can form certain defect complexes with vacancies as well. In this work, defect complexes (TMsub +VO) and (TMsub +VSn) are considered with 6 and 8 potential configurations, respectively. The possible positions for TM to substitute Sn sites are indicated in Fig. 2 (a) (TMsub +VO) and (b) (TMsub +VSn). From our study, the preferred substitutional site for all TMs to form (TMsub +VO) is in the position 3 except for Co substitutional site, which is in the position 1, as depicted in Fig. 7 (a). The defect complexes have the same value of magnetic moments as that of a single TMSn but with lower formation energies at O-poor condition. The spin densities of (TMsub +VO) in Fig. 7 show almost the same pattern as that in single TMsub that all the spins are located around the substitutional TM element and the surrounding O atoms, as shown in Fig. 4. Therefore, the same magnetic moments are observed in systems with both defect complex and single TM defects (see Table 2). The local magnetic moment of Co in (Cosub +VO) is increased, higher than that of a single Cosub. However, the spins around the vacancy sites are directly opposite to the spins around Co as illustrated in Fig. 7(a), which results in the observed equality of magnetic moments of (Cosub +VO) and Cosub.

For the defect complex composed of substitutional TM and tin vacancy, (TMsub +VSn) has the most stable structure when TM occupies the position 1 (denoted in Fig. 2), which is at the nearest-neighbouring site of the vacancy for all considered TMs. However, the magnetic moments vary significantly. As seen from Fig. 7 (b), for Co, Fe, Mn and Ni doping, spins are found not only localized around the TM atoms and their NN oxygen atoms but also around the Sn atoms, which are nearby the vacancy site and TM atoms. Although neither Nisub nor (Nisub +VO) is magnetic, (Nisub +VSn)



Page 16 of 43

prefers spin-polarized state with a total magnetic moment of 2 µB due to the interaction between the Ni atom and the surrounding Sn as well as O atoms. Based on our calculations of the magnetic moments, the six TM elements can be clarified as (Fe, Mn), (Co, Ni) and (Cr, V). The defect complexes associated with Fe and Mn have the same value of magnetic moments as the single substitutions while the magnetic moments of defect complexes formed by Co or Ni substitutional are enhanced and that of Cr, V decreases. Moreover, spins in (Cosub +VSn) and (Nisub +VSn) are not observed in the diagonal Sn atom but the other two Sn atoms around the vacancy site as well as their surrounding O atoms. For Cr and V substitutional, the spins are found around the TM atoms and nearby oxygen atoms with opposite spin directions. Therefore, the moment in (Crsub +VSn) or (Vsub +VSn) is weakened. However, the spin distributions of (TMsub +VSn) are all symmetric along the axis lines that diagonally cross the monolayer SnO through TMsub and VSn.

TABLE 2. The calculated total magnetic moments (µtotal/ µB) for defects TMsub, and defects complexes (TMsub +VSn) and (TMsub +VO) using both GGA and GGA+U methods, and the local magnetic moments (µlocal/ µB) for the TM in the relevant defects. Co

TMsub

TMsub

Cr

Fe

Mn

Ni

V

µlocal

µtotal

µlocal

µtotal

µlocal

µtotal

µlocal

µtotal

µlocal

µtotal

µlocal

µtotal

GGA

0.943

1

3.436

4

3.492

4

2.97

3

0

0

2.290

3

GGA+U

0.992

1

3.441

4

3.494

4

4.545

5

0

0

2.549

3

GGA

1.343

1

3.431

4

3.477

4

3.00

3

0

0

2.332

3


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+ VO

GGA+U

1.736

1

3.436

4

3.483

4

4.576

5

0

0

2.623

3

TMsub

GGA

1.573

3

2.133

2

3.231

4

3.471

3

0.396

2

1.017

1

+VSn

GGA+U

1.498

3

2.17

2

3.260

4

3.909

5

0.411

2

1.241

1

The electron charge densities of TMsub, (TMsub +VO) and (TMsub +VSn) are shown in Fig. 8. The overlap of the electrons of Co and 1NN-O ions in (Cosub +VSn) observed in Fig. 8 (a) indicates possible exchange coupling between Co and the surrounding atoms. The magnetic moment of (Cosub +VO) is therefore enhanced compared to Cosub . In addition, the local magnetic moment of Co atom is enhanced as well when forming the defect complex as listed in Table 3. For Cr substitution, there is almost no difference between the charge density of Crsub and (Crsub +VO), as seen from Fig. 8 (b). The local magnetic moments of both defects are very close, suggesting that a similar magnetic interaction may dominate the magnetism in both defects. The lower electron densities around the defect complex and the local magnetic moments are attributed to the lower total magnetic moments in (Crsub +VSn). No remarkable change of charge densities and local magnetic moments are observed in the three kinds of Fe-related defects, suggesting a relative stable magnetic moment in Fe doped SnO. Though the local magnetic moments of Mn ion in (Mnsub +VSn) are enhanced, the exchange interactions between the Mn ion and the surrounding O ions are greatly weakened as seen from Fig. 8 (d). Therefore, the values of the total magnetic moments of Mn-related defects remain the same. For Ni doping, magnetic moment is found in (Nisub +VSn) only and the electrons of Ni ion overlap with the nearby O ions, thus inducing the exchange interaction for the formation of magnetism.



The electron densities in Fig. 8 (f) are very different in three concerned defects, resulting in distinct magnetic behaviours in V doped SnO. Higher electron charge densities can be observed in the Sn and O ions, which is different from both (Vsub +VO) and (Vsub +VSn). However, the interactions between V and the surrounding O and Sn ions are much less active, which lead to the spins directed in different orientations as depicted in Fig. 7 (l). Therefore, the local magnetic moment of V in (Vsub +VSn) decreased significantly. Subsequently, the overall magnetic moment in (Vsub +VO) remains the same while it is decreased in (Vsub +VSn).


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FIG. 7. The calculated spin densities of 4×4 monolayer SnO with (a) (Cosub +VSn), (b) (Crsub +VSn), (c) (Fesub +VSn), (d) (Mnsub +VSn), (e) (Nisub +VSn), (f) (Vsub +VSn), (g) (Cosub + VO), (h) (Crsub + VO), (i) (Fesub + VO), (j) (Mnsub + VO), (k) (Nisub + VO), (l) (Vsub + VO) after structural relaxations from top view. Yellow and blue iso-surfaces represent positive and negative spin densities. The iso-surface value is taken to be 0.002 bohr-3. The dashed spheres indicate the vacancy sites.



FIG. 8. The calculated charge densities of 4×4 monolayer SnO with TMsub, (left) (TMsub +VO) (middle) and (TMsub +VSn) (right) subsequently, with TM= (a) Co, (b) Cr, (c) Fe, (d) Mn, (e) Ni, and (f) V. The images in each rectangle are taken from the (001) plane (upper) and (010) planes (lower) through the TM atom. The dashed spheres indicate the vacancy site. The saturation level is set from 0 to 0.7 e/bohr3 and blue to red. The core areas with the highest charge densities are removed for all ions except for the TM for better illusion.

GGA+U calculations were performed for describing the strong correlation between the d electrons in TM dopants as well. The calculated results of the GGA+U method have been summarized in the Table 2. According to our calculations, the results obtained from GGA method have shown good consistence with that from GGA+U method.


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Specifically, for Cr, Fe, Ni, and V doped SnO, the computational results are roughly the same in both GGA+U and GGA methods. Similar values of total and local magnetic moments of the doped systems are obtained. The spin and electron density distributions of Cr doped SnO monolayer calculated using GGA+U are shown in Fig.9 as an example. No obvious change of the spin and electron charge distributions can be found between GGA and GGA+U method, suggesting that GGA can describe these systems correctly.

FIG. 9 The calculated (GGA+U) spin(up) and charge (bottom) densities of 4×4 monolayer SnO with (a) Crsub, (b) (Crsub +VO) and (c) (Crsub +VSn) subsequently. The images in each rectangle are taken from the (001) plane through the Cr atom. The dashed spheres indicate the vacancy site. The saturation level is set from 0 to 0.7 e/bohr3 and blue to red. The core areas with the highest charge densities are removed for all ions except for the Cr for better illusion.



In Co doped SnO, the preferred configurations of the defects and defect complexes are the same in both calculations. The results from GGA+U method suggest that Cosub is magnetic as well as (Cosub+VO) and (Cosub +VSn). The values of the magnetic moments calculated from GGA+U method are the same as those from GGA method, showing good consistence. Moreover, the local magnetic moment of Co is slightly enhanced to 0.992 µB in Cosub, 1.736 µB in (Cosub+ VO) and 1.498 µB in (Cosub+VSn).

For Mn doped system, according to our calculations, Mnsub, (Mnsub +VO) and (Mnsub +VSn) have the same value of magnetic moments of 5.0 µB. However, the calculated magnetic moments are 3.0 µB using GGA method. Nevertheless, the local magnetic moments of Mn atoms show the same variation trend when forming defect complexes using both methods. It should also be noted that the preferred configuration of (Mnsub +VO) would change to position 4 instead of position 3 and (Mnsub +VSn) from position 1 to position 3 using GGA+U method. And the energy difference between the two configurations is about 346 meV. All the other dopants occupy the same doping sites using two different methods. The calculated results of the spin and electron density distributions of Mn doped SnO monolayer are shown in Fig.10. The spins distributions obtained from GGA+U method show the same pattern as that from GGA method. For Mnsub and (Mnsub +VO), spins are mainly located on the Mn and the surrounding O atoms as well as the diagonal Sn and O atoms around the vacancy site in SnO with the defect (Mnsub +VSn). Migration of the local electron density from Mn ion to oxygen ions can be observed from Mnsub to (Mnsub +VO), while no obvious difference can be found when (Mnsub +VSn) is formed. Obvious exchange interaction between the substitutional Mn and surrounding O atoms can be observed in Fig. 10 (a) and (b).


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Hybridization between the Mn d and O p orbitals yields a strong ferromagnetic nearest-neighbouring exchange in Mnsub and (Mnsub +VO). For (Mnsub +VSn), a similar p-p exchange as discussed in VSn is observed around the vacancy site besides the p-d hybridization. The complex therefore presents same value of magnetic moments with combined effect of both interactions. Though the calculated values of total and local magnetic moments of Co and Mn doped SnO systems are different in GGA+U and GGA methods, similar trends can be obtained in both calculations. Therefore, our GGA calculations is reliable for discussing the possible doping effect.

FIG. 10 The calculated spin(up) and charge (bottom) densities of 4×4 monolayer SnO with (a) Mnsub, (b) (Mnsub +VO) and (c) (Mnsub +VSn) subsequently. The images in each rectangle are taken from the (001) plane through the TM atom. The dashed spheres indicate the vacancy site. The saturation level is set from 0 to 0.7 e/bohr3 and



Page 24 of 43

blue to red. The core areas with the highest charge densities are removed for all ions except for the TM for better illusion.

Due to the thermo-equilibrium, the formation energies of defect complexes can be defined similarly to that of a single defect as

( ∑ ∙ ) . 2

Here EDC and Esupercell are the total energies of monolayer SnO with and without defect complexes separately; Ni stands for the numbers of atoms of type i that have been added to (negative) or removed from (positive) the supercell when defect complex is created, and Mi represents the relevant chemical potentials of these atoms, which are afore mentioned.

Based on the equation, the results for the formation energies of the concerned defects and defect complexes are summarized in Table 3. It should be noticed that the formation energies of (TMsub +VO) can be negative values related to the chemical potentials of TM from the definition. The complex (TMsub +VO) should be very likely to form. However, VO is known to be very unstable under O-rich environment, which suggests the complex may form only under O-poor conditions.

TABLE 3. Calculated formation energies (Ef/eV) for defects TMsub, and defect complexes (TMsub +VSn) and (TMsub +VO) in the most possible configurations at Opoor and O-rich extreme conditions.

TMsub

Co

Cr

Fe

Mn

Ni

V

Ef

Ef

Ef

Ef

Ef

Ef

O-

O-

O-

O-

O-

O-

O-

O-

O-

O-

O-

O-

rich

poor

rich

poor

rich

poor

rich

poor

rich

poor

rich

poor

-2.16

2.02

-3.74

0.45

-3.16

1.02

-3.57

0.61

-2.60

1.59

-3.64

0.55


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VSn+TMsub VO+TMsub

-1.83

2.36

-1.88

-2.77

1.41

-2.71

-2.43

1.76

-2.42

-2.76

1.42

-2.34

-1.65

2.53

-2.16

-3.16

1.02

-2.64

Formation energies of (TMsub +VSn) as functions of oxygen chemical potentials are shown in Fig. 11 and they decrease significantly compared to that of a single VSn. Moreover, (TMsub +VSn) can be easily formed under high oxygen chemical potentials. It should also be noted that (Vsub +VSn) becomes the most stable defect complex among all concerned TM and (Nisub +VSn) has the highest formation energy, which is different from the situation in a single TMsub.

FIG. 11. The calculated formation energies of 4×4 monolayer SnO with (TMsub +VSn). The inset is a zoom view of the area marked in rectangle. The dashed grey line indicates the formation energy per VSn in defect complex (VSn+VSn).



Based on afore calculations, we find that magnetism in monolayer SnO can be achieved by transition-metals doping. The TM-doped monolayer becomes magnetic at low oxygen partial pressure since the favourable defect complex (TMsub +VO) is magnetic except for Ni doping. The magnetism observed at this stage is contributed by p-d interaction of Sn-O and TM-O atoms. Increasing the oxygen pressure, more VSn defects are generated, and (TMsub+VSn) becomes dominant if the TM doping concentrations are relatively low. The TM dopants tend to occupy the VSn sites and eventually VSn sites are fully filled with TM dopants if TM doping concentration is high. Hence, TMsub is the preferred defect. The monolayer SnO remains magnetic via strong p-d interaction between transition-metals and their surrounding O atoms.

Conclusions In summary, pristine monolayer SnO is nonmagnetic. The magnetism of VSn appears in a particular oxygen partial pressure and tin vacancy concentration. Doping with transition-metals including Co, Cr, Fe, Mn, Ni, and V can induce magnetism to monolayer SnO under certain circumstances. The TM dopants all show stable magnetism from the substitutional TM defects alone or the defect complex formed by the substitutional TM plus VO defect in monolayer SnO except for Ni doping. The magnetism is mainly originated from d orbitals of the TM and p orbitals of the O atoms at the nearest-neighbouring sites. Nisub and (Nisub +VO) remain nonmagnetic nature in monolayer SnO. Moreover, the magnetic moment of (TMsub +VO) is the same as that of a single TMsub, and their electron and spin densities are like each other. On the other hand, all the TM related defect complexes (TMsub +VSn) are magnetic, including (Nisub +VSn). The magnetic moment of (TMsub +VSn) is different from that of a single TMsub since p-d exchange interactions are observed in Sn and O atoms, which contribute to the overall moments. The value of the magnetic moments of (TMsub +VSn)


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for TM elements like Co, and Ni is enhanced compared to a single TMsub, and the moment of (Fesub +VSn) or (Mnsub +VSn) maintains the same. On the other hand, (Crsub +VSn) or (Vsub +VSn) shows lower magnetic moments. In addition, different charge and spin patterns are observed, indicating different magnetic interactions. Magnetism can therefore be expected in transition-metals doped monolayer SnO in future experimental researches. The TM doping attributes to the possible magnetism in two ways: first, substitutional TM defects can induce magnetism via hybridization between the d orbitals of doped elements and the p orbitals of O atoms; second, the TM can form defects complexes with VSn which is magnetic as well. The formation energy of VSn can thus be lowered and enhance the magnetization. This study has shown a possible way to achieve magnetism in monolayer SnO and the magnetism can be manipulated by the selection of appropriate TM elements and defect engineering.

Acknowledgements The computational work was completed on the National Computational Infrastructure (NCI), Canberra, Australia. J.B. Yi acknowledges the support of the Australia Research Council discovery project grants DP140103041 and future fellowship FT160100205.



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Transition Metal Doped Tin Monoxide Monolayer: A First-Principles

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