Design of ferromagnetism in Co-doped SnO₂ nanosheets: a first-principles study

Abstract

First-principles calculations are performed to study the structural, electronic and magnetic properties of Co-doped SnO₂ nanosheets (NSs), using the generalized gradient approximation (GGA) plus Hubbard U method. We find that two Co atoms have a clustering tendency and the magnetic interactions between them exhibit a ferromagnetic (FM) coupling, while the appearance of an oxygen vacancy (V_O) turns it into an antiferromagnetic (AFM) order. When the Li atom is codoped into Co-doped SnO₂NS, the interactions between Co atoms are rehabilitated to FM coupling with a high Curie temperature (T_C) of 850 K. The electronic structure analysis reveals that this is mainly attributed to the hole-induced double-exchange mechanism from s–d hybridizations between Li and Co, which finally activates a long-range FM coupling between two Co atoms. These findings could be very useful in nano-material design for spintronics.

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I. Introduction

Dilute magnetic semiconductors (DMSs) have attracted extensive attention in the past few years due to their potential applications in spintronic devices.^1,2 Since the observation of high temperature ferromagnetism (T_C close to 650 K) with a giant magnetic moment of 7.5 ± 0.5 μB/Co by Ogale et al.,² the transition metal (TM) doped SnO₂ DMSs have been identified as some of the most promising candidates. However, the magnetic origin of TM-doped SnO₂ is quite controversial nowadays, because the magnetic behavior of TM-doped SnO₂ is strongly dependent on the preparation methods and is poorly reproducible.^3,4 For example, ferromagnetism with high T_C was observed in Fe-,⁵ Cr-,⁶ V-,⁷ and Ni-doped⁸ SnO₂, and especially in the case of Mn-doped it shows a very large magnetic moment up to 20.0 μB at low doping concentration, which is far above the spin moment of Mn ion.⁹ To clarify the FM nature of TM-doped cases theoretically, many calculations based on density-functional theory (DFT) have been carried out, which recognized that the V_O may be responsible for the promotion of ferromagnetism. Those are partially in consistent with experimental results.^5,8 However, in comparison to a considerable amount of experimental data, the origin of FM order in TM-doped SnO₂ is still not well understood.

Recently, focus has shifted to the low-dimensional SnO₂NSs, of which the formation mechanism and relatively stability have been discussed.^10–15 The synthesis of the SnO₂NSs opens up new possibilities for fabricating SnO₂ based spintronics devices. Theoretically, Rahman et al.¹⁶ reported the spin-polarized states induced by C substitutions in SnO₂ surface, whereas no magnetism is observed if C atom is doped into inner oxygen site in SnO₂ thin film. These demonstrate that the surface quantum confinement effects play an important role for ferromagnetism in SnO₂ nanostructure. However, how to theoretically design and manipulate the room-temperature ferromagnetism in SnO₂NS has seldom been reported up to date.

Based on our theoretical results and orbital hybridization model, the origin of the long-range ferromagnetism in (Co, Li)-codoped systems has been discovered. The two Co atoms have a clustering tendency and the magnetic interactions between them exhibit a FM coupling, while the appearance of V_O turns it to be an AFM order. When the Li atom is codoped into SnO₂NS, the interactions between Co atoms are rehabilitated to FM coupling with a high Curie temperature (T_C) of 850 K. These findings and their fundamental mechanism should be important in the successful fabrication of the excellent SnO₂NS for spintronics applications.

II. Computational details

We preformed first-principles calculations using the Vienna ab initio simulation package (VASP) code¹⁷ based on density-functional theory (DFT) with the projector augmented wave (PAW) method¹⁸ in conjunction with the generalized gradient approximation (GGA) and strong correlation effects were introduced by means of GGA + U method,¹⁹ where U (U = 3.0 eV) has been applied to Co 3d orbital since further correction for the host material has little impact on the magnetic order.²⁰ The electronic wave functions were expanded by plane waves with the cutoff energy of 400 eV. Two-dimensional periodic boundary conditions were applied to the Co-doped SnO₂NS while a vacuum spacing of 20 Å is set along the direction perpendicular to the SnO₂NS surface to avoid the mirror interaction. All atomic positions in all structures were optimized until the forces had converged to be less than 0.01 eV Å⁻¹. For k-space integration, we use a grid of 5 × 5 × 1 k points in the first Brillouin zone.

III. Results and discussions

Firstly, we study the geometric structure of perfect SnO₂NS, which is modeled with a 4 × 4 SnO₂ supercell in the x-y plane containing sixteen SnO₂ units, with a vacuum region of 20 Å perpendicular to the SnO₂ surface, as shown in Fig. 1(a). Each Sn atom is in the center of a pseudo-octahedron composed of six-oxygen ring, in which four O atoms locate in the same plane with central Sn atom, while the otherwise two O atoms occupy the vertex sites. After structural optimization, both Sn and O sublattice are equilateral triangle with the lattice constant of 3.20 Å, less than the experimental lattice constant of bulk SnO₂ (4.74 Å).²¹ This can be attributed to a symmetric shrinking, being similar to TiO₂ nanosheets.²² The averaged Sn–O bond length (2.11 Å) is also known. Different from the planar structure in graphene,²³ the SnO₂NS forms a sandwiched structure, where Sn atoms are located in the middle of two-layered oxygen atoms, as shown of side view in Fig. 1(b).

Fig. 1 (a) Top view, (b) side view of pure SnO₂NS; (c) DOS of pure and V_O-doped SnO₂NS. Turquoise and pink balls represent Sn and O atoms, respectively.

In Fig. 1(c), we present the total and partial density of states (DOS) for perfect SnO₂NS. It can be seen that the valence band maximum (VBM) near the Fermi level (E_F) mainly consists of Sn 4d and O 2p states, while the conduction band minimum (CBM) comes from Sn 5s state. Thus the VBM–CBM gap is about 2.75 eV, larger than the theoretical value of bulk SnO₂ (about 1.90 eV) that we calculated by GGA. This can be attributed to nanometer size effect. In addition, the spin-polarized calculations indicate that the electron wave function in spin-up and spin-down channels is symmetric, exhibiting a nonmagnetic behavior. This is because that Bader analysis shows that the Sn atom is in a +2 state due to the donation of its two valence electrons to neighboring oxygen atoms, which are in a −1 state. As a result, no unpaired electrons exist in perfect SnO₂NS, in good agreement with previous results.²⁴

Next, we begin to study the effect of Co substitution for Sn atoms in SnO₂NS. We placed a single Co atom in SnO₂NS by removing one Sn atom, corresponding to a defect concentration of 2.08%, as shown in Fig. 2(a). After structural relaxation, the O–Co–O layered sandwich configurations are preserved, where the Co dopant is located in the middle of two-layered oxygen atoms. The Co–O bond length contracts by 0.17 Å significantly due to smaller ionic radius of Co atom, while the Sn–O bond length (2.11 Å) changes less. It is of note that the Co substitution for Sn atom results in the spin-polarized states due to the asymmetrical distribution of the wave functions of spin-up and spin-down channels on Co-3d states near the E_F [Fig. 2(c)]. To further verify the localization of the magnetic moment, we plot the net magnetization m(r) = ρ_↑(r) − ρ_↓(r), where ρ_↑(↓)(r) is the total charge density in the ↑↓polarized channel. The m(r) is plotted for a single isolated Co atom as shown in Fig. 2(b). The spin-density plots show clearly a strong localized magnetic moment at the Co site, which has a strong “up” d character. Meanwhile, in the direction of the bond with Co atom, the nearest-neighboring O atoms has slightly “up” p like character due to hybridization of Co-3d and O-2p states. The total magnetic moment is found to be 1.0 μB, in which the local magnetic moment is around 0.86 μB for Co atom. These can be understood as follows: a Co impurity has five quasi-localized electrons on Co-3d states. Under the symmetry notations of the local octahedral crystal field, the Co-3d states are split into the triply-degenerate t_2g and double-degenerate e_g state, the latter occurring at the higher energy than the former. Due to spin polarization, the occupied electronic configuration of Co⁴⁺ is d⁵[(t^↑_2g)³(t^↓_2g)²], exhibiting the half-metallic behavior with 100% spin-polarized current at the E_F [Fig. 2(c)]. Due to the poor description of strong Coulomb correlation and exchange interaction between electrons in GGA, we check these results with GGA + U (U = 3 eV).²⁵ It is of note that the partial occupied Co-t_2g spin-down states are further split into the double-degenerate e₂ and single a₁ states. So, the spin-down electrons of Co⁴⁺ ion becomes d²[(e^↓₂)²(a^↓₁)⁰], clearly opening the gap between the doubly-degenerate e₂ and singly-degenerate a₁ states in the vicinity of Fermi level. As s result, the Co-doped SnO₂NS transforms from half-metal to semiconductor when U is included on Co-3d states, as shown in Fig. 2(c).

Fig. 2 (a) Optimized structure and (b) spin density distribution of SnO₂NS containing a substitutional Co atom; (c) DOS of single Co-doped SnO₂NS with U = 0, U = 3. Turquoise, pink and blue balls represent Sn, O, Co atoms, respectively. The positions of Sn are denoted by 0–4.

To analyze its magnetic nature, we studied the coupling between two Co atoms in SnO₂NS. The Co dopants are still substituted for Sn sites, corresponding to the doping concentration of 4.17%. Since there are only four nonequivalent sites for the incorporation of Co dopants into SnO₂NS, we perform spin-polarized calculations for these configurations, such as I(0,1), II(0,2), III(0,3), and IV(0,4), as shown in Fig. 2(a). For each configuration, the magnetic energy difference, ΔE_FM = E_AFM − E_FM, and the relative energy Δε with respect to the ground state of configurations I(0,1) are also presented in Table 1. It is of note that I(0,1) is energetically the lowest among four structures, demonstrating that it is the ground state and Co dopants have a clustering tendency, whether the U is considered or not. The ΔE_FM in the ground state I(0,1) is found to be 14 meV, lower than that of AFM state. However, this difference decreases to be 2 meV when U is applied to Co-3d orbital, indicating the AFM and FM state might coexist. Especially, AFM states can be observed in the structure III(0,3) and IV(0,4) when the distance between two Co atoms is larger than 6.0 Å. The magnetic interactions could be understood as the competition between two exchange interactions: the super-exchange (SXC) interaction between the filled t^↓_2g electrons which gives a result of AFM, and the double-exchange (DXC) interaction between the partially filled t^↑_2g orbitals, leading to be FM.^26,27 The latter one depends on the electron hopping between the neighboring Co atoms, and the local atomic arrangements and local orbital ordering of the two t^↓_2g electrons of the neighboring atoms, which control the magnitude of the two competing interactions. If the orbital orientation is such that the hopping is small, the AFM-SEC dominates as in case III and IV. The reason of the formation of SXC-AFM is that the triple degenerate spin-up orbitals of two Co atoms (Co₁,Co₂) are fully occupied and the electrons of Co₂ atom have an inversion (changes from t^↑↑↑_2g to t^↓↓↓_2g), resulting in an indirect hopping between two Co atoms by the bonding O atoms. When the electron hopping is relatively large, the FM-DXC overwhelms the AFM-SXC, resulting in a net FM interaction as in case I. The plot of Fig. 3(d) illustrates this competition.

Table 1 The Co–Co distance (Å), d_Co–Co, the relative energies Δε (meV) with respect to that of the (0,1) structure, the energy difference ΔE (meV) between FM and AFM states, (ΔE = E_AFM − E_FM), coupling, and the total magnetic moment M_T (μB) for all configurations in Co-doped SnO₂NS with GGA(+U), respectively. PM stands for paramagnetic

Configurations	dCo–Co (Å)	Δε (meV)	ΔE (meV)	Coupling	MT (μB)	MCo (μB)
U = 0
(0,1)	3.10	0	14	FM	2	0.88
(0,2)	5.50	87	208	FM	2	0.88
(0,3)	6.35	185	0	PM	0	—
(0,4)	8.45	140	0	PM	0	—
U = 3
(0,1)	3.11	0	2	PM	2	1.2
(0,2)	5.51	61	0	PM	0	—
(0,3)	6.35	146	−401	AFM	0	−1.2/1.2
(0,4)	8.45	103	−406	AFM	0	−1.2/1.2

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Fig. 3 Spin density distribution of double Co-doped SnO₂NS: (a) FM state and (b) AFM state with U = 0, (c) FM state with U = 3; (d) schematic diagram of this competition between AFM state and FM state.

In Fig. 3(a)–(c), we also present the spin-density distributions of SnO₂NS in the ground state I(0,1) with U = 0 and U = 3 eV, respectively. It can be seen that the net spin magnetic moment (0.88 μB) introduced by Co atom are localized in Co-3d orbitals [Fig. 3(a)], while the small contributions from the neighboring oxygen atoms (0.14 μB) are also obtained. When U = 3 eV is included, the strong coulomb interaction U increases clearly the localization of Co-3d electrons due to the further split of t_2g states in spin-down channel [Fig. 3(c)], resulting in a net magnetic moment 0.95 μB. Fig. 4 presents the corresponding total and partial DOS with U = 0 and U = 3 eV, respectively. It is of note that, similar to the isolated substituted case, the transitions from half-metal to semiconductor properties are still observed.

Fig. 4 DOS of double Co-doped SnO₂NS with U = 0, U = 3.

It is reported that V_O is more likely to appear in the SnO₂NS. In order to analyze the effect of V_O on the magnetic coupling, we consider three types of V_O sites on SnO₂NS, termed as bridging-V_O, neighboring-V_O, and further-V_O, and distinguish specific V_O occupation sites by marking V_B, V_N, and V_F, as shown in Fig. 5(a). In Table 2, we list the calculated total energies with respect to the V_B occupation sites. The formation energy of this system could be defined as

E_f = E(V_O–Co–SnO₂) + E(O) − E(Co–SnO₂),

where E(V_O–Co–SnO₂) and E(Co–SnO₂) are the total energy of the Co–SnO₂ with and without O vacancy respectively, while E(O) is the total energies of 1/2O₂. According to the definition, the formation energy of V_B is −2.53 eV, smaller than that of perfect Co-doped SnO₂NS (0.98 eV), indicating that V_O is easily formed. Especially, the induced V_B defect, i.e., Co–V_B–Co complex [Fig. 5(b)], is energetically more stable by 745 meV and 1242 meV than the other two, respectively. Unfortunately, the magnetic coupling between two Co atoms is AFM (−109 meV), instead of being FM order [Fig. 6]. In this case, the geometric analysis shows that the optimized distance between two Co atoms in Co–V_B–Co complexes is found to be 3.12 Å, larger than that (2.93 Å) without oxygen vacancy, resulting in a bond angles (124.2°) of Co–V_B–Co complex larger than that (105.5°) in Co–O–Co cases. According to the SEC Heisenberg model, the intensity of the magnetic interaction between TM ions is determined by the exchange integral J_ij, which is proportional to the energy difference for a kind of anion-mediated structure.²⁸ So the change in the orbital nature of the Co states near the Fermi level in the proximity of V_B now favors AFM-SEC over FM-DEC, leading to a net AFM coupling.

Fig. 5 (a) Structure employed to define various configurations of Co-doped SnO₂NS with oxygen vacancy (V_O). The positions of V_O are denoted by V_B, V_N, V_F. (b) The optimized structure and spin density distribution of Co-doped SnO₂NS with V_O. (c) Schematic plot of the coupling mechanism for Co-doped SnO₂NS with V_O.

Table 2 The relative energies Δε (meV) with respect to that of the V_B structure, the energy difference ΔE (meV) between FM and AFM states(ΔE = E_AFM − E_FM), coupling, and the total magnetic moment M_T (μB) for different V_O locations in V_O–Co-doped SnO₂NS by GGA method. PM stands for paramagnetic

Locations (VO)	Δε (meV)	ΔE (meV)	Coupling	MT (μB)	MCo (μB)
VB	0	−109	AFM	0	−1.6/1.6
VN	745	0	PM	0	—
VF	1242	0	PM	0	—

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Fig. 6 DOS of double Co-doped SnO₂NS with V_O.

On the other hand, another possible explanation of the AFM mechanism on Co–V_B–Co complex is that the coupling between Co atoms depends on the electron distributions in Co orbitals. The systematic plot of d level occupation is shown in Fig. 5(c). The presence of V_O makes the point group lower from O_h to C_4v. The t_2g states are no longer degenerate, further splitting into one doubly degenerate e state (d_xz, d_yz) and one singly degenerate a state (d_xy), while the e_g state is splitting into two single degenerate a₁(d_z2) and a₂(d_x²−y²) states. We don't concern a₁ and a₂ states due to their high energy. The bonding levels of e and a states and the anti-bonding level of e state are fully filled by Co-3d electrons in spin-up and spin-down channels. When the SnO₂NS is in an XY plane, due to the crystal-field splitting, O-2p levels are also split into one doubly degenerate state (p_x, p_y) and one singly degenerate state (p_z), in which the latter occurs with the higher energy. When one O atom is removed, O-p_z orbital will preferentially lose its two electrons, resulting in the anti-bonding level of singly degenerate a state fully occupied. Hence, the oxygen-deficient Co-doped SnO₂NS is an AFM order. Thus, we conclude that the strength of AFM interactions between the Co atoms is determined by not only the AFM-SEC mechanism but also the crystal-field induced orbital energy splitting in Co-doped SnO₂NS.

Recent experiments reported that Li can be easily incorporated into SnO₂ lattice.²⁹ Hence, it is expected that Li co-doping should introduce redundant positive charges into the lattice and neutralize the additional charges introduced by Co dopants, and thus can confine the formation of AFM order between Co atoms, thus promotes ferromagnetism in Co-doped SnO₂NS. To check this scenario, we consider four configurations, i.e., (i) two Co atoms with an intermediate Li substituting for O atom (Co–Li_O–Co complex) [1.08 eV], (ii) two Co atoms with a neighboring Li substituting for O atom [−2.00 eV], (iii) two Co atoms with a distant Li substituting for O atom [−0.82 eV], and (iv) two Co atoms with Li substitution for Sn sites (Co–Li_Sn–Co complex) [−2.40 eV]. We also define the formation energy as

E_f = E(Li–Co–SnO₂) + E(Sn,O) − E(Co–SnO₂) − E(Li),

where E(Li–Co–SnO₂), E(Co–SnO₂) is the total energy of the Co–SnO₂ with Li dopant and Co–SnO₂, while the E(Li), E(Sn,O) are the total energies of single Li, Sn and 1/2O₂. By calculating their formation energies as shown above, we find that Li atom is more easily to substitute for Sn atom, and the Co–Li_Sn–Co complex (−2.40 eV) is energetically more stable than other four configurations in O-rich condition [Fig. 7(a)]. Bader analysis indicates that the atomic valance states on Co, Li and nearby O atoms in Li–Co-doped SnO₂NS are +1.5, +0.9, −0.7, respectively, while the valance states on Co, O atoms in Co-doped SnO₂NS are +1.3, −1, respectively. We find that Li co-doping make the valance states of Co atoms change from +1.3 to +1.5, indicating the decrease of electronic charges on Co dopants, in consistent with the above expectation. Due to this charge-passivated effect, the FM–DEC interaction between Co ions through hole hoping induced by Li atom is preserved, and thus stabilizes the ferromagnetism in Co–Li_Sn–Co complex. We also estimates the T_C with the classical Heisenberg model in mean-field approximation, k_BT_C = 2ΔE/3x,³⁰ where x is the concentration of defects, ΔE is the energy difference (ΔE = E_AFM − E_FM = 110 meV) and k_B is Boltzmann constant and the calculated T_C is about 850 K, which is considerably higher than the room temperature (300 K). So it is high enough for the purpose of device applications above room temperature.

Fig. 7 (a) The most stable structure, (b) spin density distribution and (c) DOS of (Co–Li)-codoped SnO₂NS.

To further clarify the nature of the effort of Li-codoping on the electronic and magnetic properties, we presented the DOS for the (Co, Li)-codoped SnO₂NS, as shown in Fig. 7(c). As for Co mono-doped SnO₂NS, the Co ion introduces a donor state within the band gap, as labeled as a₁. In contrast, Li has one less valance electron than Sn, the substitution of Li on Sn site creates a impurity state near E_F labeled as a₂ in the gap. When Co and Li are co-doped into SnO₂NS, we find that a charge transfer from a₁ to a₂ as illustrated by the arrows in Fig. 7(c). As a result, the a₁ state of Co is partially filled, while the a₂ state of Li is filled and finally pushed down E_F. The results of charge transfer lead to not only the charges induced by Co and Li are mutually counteracted so that the formation of surface V_O is effectively suppressed, but also the magnetization of Co ion is notably enhanced: the moment of Co is increased from 0.88 μB/Co for Co-doped SnO₂ to 1.19 μB/Co for (Co, Li)-codoped SnO₂NS.

On the other hand, the E_F is significantly lower and the orbitals near E_F also have a change due to the surface effect, making Co-3d states mix substantially with VBM of the host. Thus, the orbital change near E_F favors a DEC interaction on the surface. In addition, the increase in the VB hybridization enhances the exchange coupling between Co atoms, and finally makes the FM interaction preferred over AFM one. When Li is codoped into this system, the VBs of this system are further shifted toward the lower energy, therefore the s bands of Li are favored to hybridize entirely with the Co 3d bands, as shown by the spin-density distributions in Fig. 7(b). This hybridization leads the holes on the acceptor levels passivated partially by donor levels, making E_F shift towards impurity band, thus exhibiting half-metallic properties. These favor the carriers hopping between Co and the host atoms, and thus can help overcoming the difficulty in the enhancement of the low mobility of carriers in wide-band-gap DMSs. As a result, this magnetic exchange creates a significant enhancement on FM–DXC, and finally activates a long-range FM coupling between the Co atoms.

IV. Conclusions

In summary, by means of DFT calculations, we established a charge-passivated codoping approach to stabilize and enhance its ferromagnetism in Co-doped SnO₂NS system as a prototype material for the DMS oxides. It is found the Co atoms have a clustering tendency and the magnetic interactions between them exhibit a FM state, while the appearance of V_O turns it to an AFM coupling. When the Li atom is codoped into SnO₂NS to substitute for Sn atom, the interactions between Co atoms are rehabilitated to FM coupling. The electronic structure analysis reveals that this is principally attributed to the hole-induced double-exchange interactions due to s-d hybridizations between Li and Co, which finally activates a long-range FM coupling between Co atoms. Our proposed model about the long-range ferromagnetism may be very useful to design the new spintronic materials.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant nos 61172028, 11274143 and 11304121), the Natural Science Foundation of Shandong Province (Grant no. ZR2010EL017), and Technological Development Program in Shandong Education Department (Grant no. J10LA16).

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