The magnetic and optical properties of 3d transition metal doped SnO₂ nanosheets

Abstract

Based on first-principles calculations, we study the electronic structure, magnetic properties and optical properties of transition metal (TM) doped SnO₂NSs. Computational results indicate that pristine SnO₂NSs is a direct gap semiconductor with nonmagnetic states. Cr, Mn, Fe atom doping can induce 2μ_B, −3μ_B and 2μ_B magnetic moment, respectively, while Ni atom doped SnO₂NSs keeps the nonmagnetic states. More interestingly, Fe doped SnO₂NSs becomes an indirect gap semiconductor, and the Cr, Mn and Ni atom doping maintain the character of direct gap semiconductor. For optical properties, the optical absorption edge shows red shift phenomenon for a TM atom (Cr, Mn, Fe or Ni) doped SnO₂NSs. In addition, the tensity of absorption, reflection and refraction coefficient are enhanced significantly in the visible light region, which may be very useful for the design of solar cells, photoelectronic devices and photocatalysts.

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1. Introduction

Dilute magnetic semiconductors (DMSs) have attracted extensive attention in experimental and theoretical studies because of their potential application in spintronic devices.^1–5 For practical applications, it is required that DMSs are half-metallic (HM) or ferromagnetic (FM) around room temperature. However, DMSs usually have a rather low Curie temperature (T_C), so it is desirable find a new method to improve the T_C of DMSs. Recently, the reported DMSs can obtain high T_C by doping with transition metal (TM) elements, such as ZnO,^6–8 In₂O₃,⁹ TiO₂,¹⁰ CeO₂ (ref. 11) and so on.

As a typical wide-gap semiconductor with band gap E_g = 3.6 eV, SnO₂ has received considerable interest for its wide variety of practical applications, such as photovoltaic devices, transparent conducting electrodes, gas sensors, solar cells, panel displays and ferroelectric transparent thin-film transistors.^12–17 More recently, TM-doped SnO₂ has become one of the hottest research topics in spintronics. Room temperature (RT) ferromagnetism has been observed in V,¹⁸ Cr,^19,20 Mn,²¹ Fe,^22,23 Co²⁴ and Ni²⁵ doped SnO₂. Research in this field now mainly concentrates on SnO₂ bulk while seldom reports on SnO₂ nanosheets theoretical calculations. The nanosheets structure may have many excellent properties because of its larger specific surface area. SnO₂ nanosheets have higher lithium storage properties with high reversible capacities and good cycling performance due to a large specific surface area.²⁶ Compared to SnO₂ bulk, SnO₂NSs with larger band gap are more suitable for tuning band gap to obtain better optical properties. And high optical transmittance,²⁷ good gas-sensing optical properties are found in transition metal doped SnO₂ film. More interestingly, SnO₂ nanosheets (NSs) were by fabricated Wang et al.²⁸ in experiments, and the T_C was estimated to be about 300 °C, indicated its potential value in spintronic devices. The results provide an opportunity to study two-dimensional (2D) SnO₂NSs. Gul Rahman et al.²⁹ reported intrinsic magnetism in nanosheets of SnO₂ and found that it is easier to create vacancies, which are magnetic, at the surface of the sheets for SnO₂NSs different thicknesses. Research by Luan et al.³⁰ found a strong localized magnetic moment in Co-doped SnO₂NSs. For optical properties, Huang³¹ reported that the capacity to absorb becomes stronger in the visible region for SnO₂NSs doped with increasing Ag concentrations.

In the present work, we perform first principles calculations to study the electronic, magnetic and optical properties of TM element doped SnO₂NSs, where the TM atom substitutes Sn atom for Cr, Mn, Fe or Ni in 2D SnO₂NSs. Our results show that the doped TM atom could induce magnetic moment, except Ni, and the magnetic moment mainly comes from the 3d orbital of the TM atom. The optical properties can get significantly improved in the visible region.

2. Computational details

The electronic properties and band structures were performed employing the vienna ab initio simulation package (VASP),³² and the optical properties were carried out by using the WIEN2k simulation package which implements a full potential linearized augmented plane wave (FLAPW) method.³³ The exchange–correlation (XC) functional was approximated with a generalized gradient approximation (GGA)³⁴ and GGA + U³⁵ as proposed by the Perdew–Bueke–Emzerhof (PBE). And a 400 eV cutoff energy for the plane-wave basis set was used. Two-dimensional periodic boundary conditions were applied to the TM-doped SnO₂NSs while a vacuum region of 12 Å is set along the direction perpendicular to the SnO₂NSs surface to avoid mirror interaction. The k-point meshes for Brillouin zone were generated using a 9 × 9 × 1 Monkhorst–Pack grid.³⁶ All atomic positions in all structures were fully relaxed until all atomic forces converged to be less than 0.02 eV Å⁻¹.

3. Results and discussion

3.1 Formation energy

Firstly, we used pristine SnO₂NSs, which is modeled with a 4 × 4 × 1 supercell containing sixteen SnO₂ units, as shown in Fig. 1. We found that it forms a sandwiched structure as seen from the side view of SnO₂NSs Fig. 1(b). These structures are similar to MoS₂NSs³⁷ and TiO₂NSs³⁸ in previous reports. In the top view of SnO₂NSs Fig. 1(a), the tin atom is substituted by TM atom at the site of X. The optimized lattice parameters are 3.2 Å and the length of Sn–O bond is 2.11 Å, which is consistent with Luan’s³⁰ research. In Fig. 1(c), we show the total density of states (TDOSs) for pristine SnO₂NSs. It presents nonmagnetic behavior due to the electron wave function dose not exhibiting spin polarization in spin-up and spin-down channels. The band structure of pristine SnO₂NSs is as shown in Fig. 1(d). The band gap is about 2.75 eV, which is close to the experimental value in Huang’s³¹ report. Thus, pristine SnO₂NSs is also a direct gap semiconductor, which is in agreement with the bulk SnO₂ calculated results.^39,40

Fig. 1 (a) Top view of pure SnO₂NSs (the position of Sn is denoted by X) (b) side view of pure SnO₂NSs (c) TDOS of pure SnO₂NSs (d) the band structure of pure SnO₂NSs.

Next, we investigated the effect of TM atom (Cr, Mn, Fe or Ni) substitution for Sn atom in SnO₂NS. The doping atom is located at X shown in Fig. 1(a). In order to evaluate the stability of TM-doped SnO₂NSs, we calculated the defect formation energy (E_f) defined as E_f = E_X:SnO2 − E_SnO2 + u_Sn − u_X,⁴¹ where E_X:SnO2 and E_SnO2 are the total energies of the TM-doped SnO₂NSs and SnO₂NSs supercell, and u_Sn, u_X are the chemical potentials of Sn and TM atom (Cr, Fe, Mn or Ni), respectively. The values of E_f are shown in Table 1. Compared with pristine SnO₂NSs, the Cr, Mn doped SnO₂NSs release 0.56 eV, 0.37 eV in energy and Fe, Ni doped SnO₂NSs absorb 0.35 eV, 1.75 eV in energy, respectively. This indicates that Cr, Mn as a dopant can obtain a more stable structure than pristine SnO₂NSs. After structural optimization, we found that all the bond lengths of TM–O bond (d_X–O) were shorter than the Sn–O bond (2.11 Å), see Table 1, because of the smaller ionic radius of the TM atom (Cr, Fe, Mn or Ni) which substitutes the Sn atom. And the bond length of TM–O atom gets shorter with an increase of atomic number.

Table 1 The bond length between the sit of X atom and its nearest O atoms (d_X–O), the defect formation energy (E_f) whose plus and minus represent the absorbing and releasing energy, the total magnetic moment (M), the total magnetic moment with GGA + U method (M_u) and the local magnetic moment for TM atom (M_X) whose plus and minus represent spin-up an spin-down, the charge transfer for TM atom (Q) whose minus represent losing electron

Configurations	dX–O	Ef	M	Mu	MX	Q
SnO2	2.11	—	0	—	—	—
Cr : SnO2	1.97	−0.56	2	2	1.97	−1.80
Mn : SnO2	1.96	−0.37	−3	−3	−2.85	−1.73
Fe : SnO2	1.95	+0.35	2	2	1.91	−1.57
Ni : SnO2	1.95	+1.75	0	0	0	−1.34

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3.2 Electronic structures and magnetic properties

The TDOSs and partial density of states (PDOSs) for the TM atom (Cr, Fe, Mn or Ni) doped SnO₂NSs are illustrated in Fig. 2(a)–(d), respectively. Taking Cr-doped SnO₂NSs as a representative example from Fig. 2(a), the electronic states of the valence band mainly arise from the strong hybridization between the O 2p and Sn 5p states, while the Sn 5s states make mainly a contribution to the electronic states of the conduction band. We also observe that the Fermi level shifts upward to the conduction band, indicating an n-type conductivity character, which may display a low resistivity character. Moreover, there are some impurity energy levels near the fermi level which are mainly caused by Cr 3d, O 2p and Sn 5p states. The Fe-, Mn-, Ni-doped SnO₂NSs can give the similar conclusion by analyzing the DOS. However, compared with three other TM atom (Cr, Fe, Mn) doped SnO₂NSs, the Ni-doped SnO₂NSs is different due to a symmetrical distribution of the wave functions of spin-up and spin-down channels on TDOSs. The result indicates that the other doped structures are magnetic except Ni-doped SnO₂NSs. DOS analysis further shows that the magnetic moment is mainly from TM atom 3d orbital.

Fig. 2 Total and partial DOS for (a) Cr, (b) Mn, (c) Fe, and (d) Ni atom and nearest O, Sn atoms. Fermi level is set to zero. DOS is broadened by Gaussian smearing with 0.2 eV.

In order to study the origin of the magnetism, we performed spin-polarized calculations and the spin density distributions are displayed in Fig. 3. We can find a strong localized magnetic moment except for Ni-doped SnO₂NSs and the magnetism mainly results from the doped atom. The Cr, Fe atom supplies the spin-up magnetic moment and Mn atom provides the spin-down magnetic moment, while a Ni atom does not provide the magnetic moment. To further verify the localization of the magnetic moment, we calculated the net magnetization defined as m(r) = ρ_↑(r) − ρ_↓(r), where ρ_↑(r)ρ_↓(r) is the charge density in spin-up and spin-down channel. The corresponding values of magnetic moment are shown in Table 1. The total magnetic moment (M) of Cr, Mn, Fe and Ni doped SnO₂NSs are found to be 2μ_B, −3μ_B, 2μ_B and 0μ_B, for which the Cr, Mn, Fe atom provides 1.97μ_B, −2.85μ_B, 1.91μ_B local magnetic moment (M_X), respectively. The results are similar to the case of TM atom doped TiO₂ carried out by Errico et al.⁴² Each doped TM atom contributes two valence electrons to the nearest O atom, and the unpaired electrons in Cr, Mn, Fe atoms induce the local magnetic moment. The mechanism can be understood as follow: a Cr atom loses two 3d-electrons and one electron of the 4s electrons transitions to the 3d orbit to form paired electrons. Two unpaired electrons provide 1.97μ_B spin-up local magnetic moment for Cr atom. However, the Mn and Fe atoms lose two 3d-electrons forming three unpaired spin-down electrons and two unpaired spin-up electrons, respectively. The magnetic moment can be widely applied to spintronic devices. The charge transfer (Q) for TM atom can be obtained from Bader analysis in Table 1. We found that the number electrons lost in Cr, Mn, Fe and Ni atoms is 1.80, 1.73 1.57 and 1.34, respectively, with the number of electron less than 2 due to the TM atom and O atom forming covalent bonds. We also found that the number of electrons lost tends to drop off with an increase of atomic number. The reason is that the electronegativity of atom is gradually strengthened.

Fig. 3 The spin density distribution of TM-doped SnO₂NSs. (a) Cr-doped SnO₂NSs (b) Mn-doped SnO₂NSs (c) Fe-doped SnO₂NSs (d) Ni-doped SnO₂NSs, yellow and blue represent spin-up and spin-down.

Further, the band structures of TM atom (Cr, Mn, Fe or Ni) doped SnO₂NSs are illustrated in Fig. 4. In Fig. 4, the arrows ↑ and ↓ represent spin-up and spin-down, respectively. Around the Fermi level, some rather localized energy bands emerged, which mainly originate from 3d states of TM atom. The emergence of impurity energy levels may make electronic transition more active from the occupied bands to the unoccupied. This may be helpful to improve the optical properties. For the case of Cr, Mn, and Ni doping, the band structure still remains the character of direct gap semiconductor, while Fe doped SnO₂NSs become an indirect gap semiconductor. We can obtain the same conclusion with DOS from band structures: the Cr, Mn, and Fe doped SnO₂NSs can introduce magnetic moment while the Ni atom can not.

Fig. 4 Electronic band structures for (a) Cr, (b) Mn, (c) Fe and (d) Ni adsorbed stanene. Fermi level is set to zero. The arrows ↑ and ↓ represent spin-up and spin-down, respectively.

Unfortunately, the GGA method usually underestimates the binding energy of d states and yields incorrect behavior for strongly correlated magnetic systems. In order to check our results, we include an on-site Coulomb correlation interaction as given by the GGA + U method, where U (U = 3.0 eV) are used to calculate the TM atom 3d orbit. This is essential for obtaining accurate values for band structures and band gaps.⁴³ The Sn atom 4d orbit is far from the Fermi level and has little impact on the magnetic properties. In Fig. 5, we show the total DOS and partial DOS with GGA + U method. Compared with the GGA results, the Fermi energy level shifts down to the valence band, and the amount of impurity energy level is declined around the Fermi energy level. More interestingly, the band gap using the GGA + U method is larger than when using the GGA method, and shows that the GGA underestimates that the TM atom 3d orbitals hybridize quite strongly with oxygen 2p orbitals. The magnetic moments of GGA + U are listed in Table 1. We found that the GGA + U method obtains the same results for magnetism, which indicates that the results of the GGA method can qualitatively reflect the properties of TM atom doped SnO₂NS. The band gap slightly increased and the magnetic moments remained unchanged, which demonstrates that the results of GGA method are reliable.

Fig. 5 Total and TM atom 3d partial DOS with U = 3 (a) Cr, (b) Mn, (c) Fe, and (d) Ni. Fermi level is set to zero. DOS is broadened by Gaussian smearing with 0.2 eV.

3.3 Optical properties

The optical properties of TM atom doped SnO₂NSs have also been calculated in our work. The optical properties of the medium can be derived from the complex dielectric function ε(ω) = ε₁(ω) + iε₂(ω).⁴⁴ The real part of the dielectric function ε₁(ω) can be evaluated from the imaginary part via the Kramers–Kronig transform, and the imaginary part of the dielectric function ε₂(ω) momentum matrix elements between the occupied and unoccupied electronic states. The imaginary part of the dielectric function formulas is calculated as follows,⁴⁵
where subscripts C and V represent conduction band and valence band, respectively, BZ is the first Brillouin zone, k is reciprocal lattice vector, ω is angular frequency, E_V(k) and E_C(k) are intrinsic energy level of valence band and conduction band, respectively, |M_CV(K)|² is momentum matrix element.

The imaginary part spectrum of the dielectric function for pristine and TM atom doped SnO₂NSs are shown in Fig. 6(a). The intensity of ε₂(ω) for TM atom doping is stronger than for pure SnO₂ nanosheets especially in the low energy region. The reason is that some impurity energy levels emerge around the Fermi level and the probability of electron transition becomes more common when the Sn atom is replaced by a TM atom. For Fe doped SnO₂NSs, there are two obvious peaks located at 0.2 eV and 0.6 eV. These peaks are mainly ascribed to the transition between Fe 3d states and Sn 5s, 5p states. There is one obvious peak at 0.5 eV for Cr doped SnO₂NSs. The reason is thought to be the band transition from Cr 4s orbital to Cr 3d orbital. There are some other peaks, and the tensity of dielectric function is larger in the visible light region for all TM doping models than for pure SnO₂NSs, which indicates that the TM doped SnO₂NSs are more suitable for visible photoelectric devices compared with pure SnO₂NSs. In the ultraviolet region, the trend and peaks of TM atom doping are similar to pure SnO₂NSs. As we all know, the absorption property of a semiconductor is related to its electronic band structure. The absorption coefficient can be defined as follow: In Fig. 6(b), we can see that the capacity of absorption is improved in the low energy region, which demonstrates that the TM atom doped SnO₂NSs is more suitable making a photodetector than pure SnO₂NSs. And some peaks emerge in the visible light region which are in agreement with the imaginary part spectrum of dielectric function. These peaks are ascribed to the interband transition between the TM 3d states and O 2p states. Interestingly, the absorption edges of TM doped SnO₂NSs all show red shift phenomenon, which are caused by the impurity energy levels near the Fermi level. The absorption edges of Cr, Fe or Ni doped SnO₂NSs are below 1.50 eV, which is lower than Mn doped SnO₂NSs whose absorption edge is located at around 2.20 eV. These results indicate that Cr, Fe or Ni doped SnO₂NSs have better optical properties compared with Mn doped SnO₂NSs in the visible region. But the all doped models have a wider absorption region than pure SnO₂NSs. These results show that the TM doped SnO₂NSs can be widely used in infrared and visible photodetectors.

Fig. 6 (a) The dielectric functions of pure SnO₂NSs and TM atom doped SnO₂NSs (b) optical absorption coefficient of pure SnO₂NSs and TM atom doped SnO₂NSs.

The reflectivity and refractivity of pure SnO₂NSs and TM atom doped SnO₂NSs are calculated and shown in Fig. 7. The reflectivity and refractivity enhance much in the low energy region, which also mainly originates from the impurity energy levels near the Fermi level. At the Fermi energy level, the values of refraction of pristine and Cr, Mn, Fe, Ni doped SnO₂NSs are 1.181, 1.232, 1.192, 1.247, 1.203, respectively. The Fe doped SnO₂NSs obtains the best effect while there is a minimum influence for Mn doped SnO₂NSs. The same effect of TM doping is suitable for reflectivity. The location of reflectivity and refractivity peaks are also in agreement with the imaginary part spectrum of dielectric function. In conclusion, the optical properties of TM atom doped SnO₂NSs can get significantly improved in the low energy region, while the effect is less obvious in the ultraviolet region.

Fig. 7 (a) The reflectivity of pure SnO₂NSs and TM atom doped SnO₂NSs (b) refractivity of pure SnO₂NSs and TM atom doped SnO₂NSs.

4. Conclusion

In summary, we performed a first-principles study on the electronic structure, magnetic and optical properties of TM atom doped SnO₂NSs. Computational results indicate that the pristine SnO₂NSs is a direct gap semiconductor with nonmagnetic states. Doping with Cr, Mn, Fe can induce the magnetic moment with a value of 2μ_B, −3μ_B and 2μ_B, respectively, while the Ni atom doped SnO₂NSs remains nonmagnetic. The magnetic moment results mainly from the TM atom 3d orbital. More interestingly, Cr, Mn and Ni atom doped SnO₂NSs still maintains the character of a direct gap semiconductor except for Fe atom doping. For optical properties, the absorption edge shifts to the low energy region compared to pure SnO₂NSs. More interestingly, the tensity of absorption, reflection and refraction coefficients are enhanced significantly in the visible light region. The results indicate that TM atom doped SnO₂NSs may be very useful for the design of solar cells, photoelectronic devices and photocatalysts.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant no. 61172028, 11274143 and 11304121), the Natural Science Foundation of Shandong Province (Grant no. ZR2010EL017 and ZR2013AL004), the Research Fund for the Doctoral Program of University of Jinan (Grant no. XBS1433, XBS1402 and XBS1452).

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