First-Principles Study of the Effect of Native Defects on Spin Polarization and Exchange Coupling Interaction in Semimetal V3O4.

We use first-principles calculations to investigate the mechanism of the effect of native defects on the spin polarization and exchange coupling interaction in the V3O4 semimetal material. Our results reveal that, in contrast to other neutral defects, V vacancy defects in V3O4 at A/B sites are in favor of higher spin polarization degrees and lower defect formation energies. Compared to ideal V3O4, the V vacancy defects at A/B sites cause slightly lower spin polarization degrees but much higher exchange coupling interactions. Our results suggest an effective route to mediate the spin polarization and exchange coupling by defect engineering, which promotes the applications of the V3O4 semimetal material in spintronics.

Introduction

Because of the large spontaneous spin splitting of bands around Fermi energy, spintronics devices exhibit a variety of unique spin-dependent optical and transport properties.[1−3] Among these materials, half-metallic ferromagnets with an ultra-high spin polarization degree (∼100% theoretically) stemming from the existence of only one-spin direction at the Fermi level have excellent prospects for spintronic devices.[4−7]

Vanadium oxides have attracted extensive attention for their unique electrical properties because of the prolific valence state of vanadium ions.[8,9] It is interesting that almost all of the binary vanadium oxides can be expressed using a simple formula: VO2 (n is an integer ≥1) or VO2 (n is an integer ≥2), while V3O4 is an exception, because of the lack of an identified integer to confirm the above simple formula.[8,10] There are few reports on the magnetic property of V3O4 in contrast to other vanadium oxides with VO2 and VO2 formulae, such as VO, V2O3, and V2O5. As displayed in Figure a, cubic V3O4 is an isomorphism of Fe3O4, which has an inverse spinel structure of AB2O4. As shown in Figure b, the octahedral six-coordinated B sites in the V3O4 structure, twice as abundant as A sites, are equally occupied by V3+ (3d2 state) and V2+ (3d3 state), thereby in favor of high spin configuration via t2g2↑–t2g3↑, respectively; whereas the tetrahedral four-coordinated A sites are occupied by the remaining V3+ with the 3d2 state in favor of smaller spin configuration via t2g2↓. Therefore, the different spin configurations of vanadium ions at different sites would result in a half-metallic state in the cubic V3O4 structure. As reported by Xiao et al., the first-principles density functional theory (DFT) calculation results indicated that V3O4 was half-metallic and the ultrasmall V3O4 quantum dots with an average size of 4.8 nm obtained via a facile solvothermal method displayed ferromagnetism in the temperature range from 16 to 32 K and exhibited superparamagnetic behavior above 32 K with negligible remnant magnetization and coercivity in hysteresis loops.[8] However, the Curie temperature should be improved in view of the practical applications in spintronic devices and the impact of native defects on magnetic property of the V3O4 semimetal material is unclear.

Figure 1

Schematic representation of the crystal and electronic structure for cubic V3O4. (a) Unit cell of cubic V3O4; (b) schematic spin structure of V3+ and V2+ in octahedral and tetrahedron sites, respectively; (c) the calculated DOSs of the ideal cubic V3O4. The Fermi level (EF = 0 eV) is indicated by the black-dotted vertical line.

Macroscopic ferromagnetism is determined by spin polarization, which further depends on the difference between the spin-up and spin-down DOS at the Fermi level.[11,12] Curie temperature is determined by spin exchange coupling, which further depends on the difference in the total energies (ΔE) between antiferromagnetic (AFM) and ferromagnetic (FM) states.[13−18] In addition, the native defects could mediate carriers and introduce defect energy levels near the Fermi level, which provides an effective method to alter the spin polarization and spin exchange coupling interaction.[19−21] Furthermore, it has been a long-standing goal to mediate intrinsic ferromagnetism without clustering of the magnetic elements and magnetic second phases introduced by a magnetic transition-metal dopant, which has led to the idea of d0 ferromagnetism.[22,23] Therefore, a complete understanding of the physics of the role of native defects in spin polarization and exchange coupling interaction of the V3O4 semimetal material provides an essential and effective method to mediate this d0 ferromagnetism and Curie temperature, which is a key element in the application of the V3O4 semimetal material in spintronics.

This paper reports on the underlying mechanism of the effect of intrinsic defects on the spin polarization and exchange coupling interaction in the V3O4 semimetal material using first-principles calculations. The spin-polarized density of states (DOS) of ideal cubic V3O4 and V3O4 with different intrinsic neutral defects are extensively studied to clarify the impact of neutral defects on the spin polarization in cubic V3O4. In addition, the formation energies of different neutral defects in O-rich and V-rich cubic V3O4 are calculated to investigate the most energetically favorable defects. To reveal the role of defects in mediating the exchange coupling interaction of the V3O4 semimetal material, we compare ΔE values between the AFM and FM states of defective V3O4 to those of the ideal V3O4. The crucial mechanism of the role of native defects in mediating the spin polarization and exchange coupling interaction of the V3O4 semimetal material would provide an effective route to mediate this d0 ferromagnetism and Curie temperature, promoting the applications of semimetal V3O4 in spintronics.

Computational Details

The first-principles calculations were performed by using DFT in the Vienna Ab initio Simulation Package (VASP) to study the native defects in cubic V3O4. The electron–electron interactions were computed by the projector-augmented-wave method, and the correlation and exchange part of the density functional was treated within the generalized gradient approximation functional of the Perdew–Burke–Ernzerhof functional. Considering the strong association of V 3d electrons, the on-site Coulomb interaction U scheme was adopted to correct the electron–electron correlation. For the V 3d electrons, the Hubbard parameter U was chosen as 4.5 eV to improve the prediction of the computation, which is also supported by the previous study of V3O4.[8] In order to investigate the defect effect on spin polarization of cubic V3O4, a model configuration of the cubic V3O4 2 × 2 × 1 supercell of the primitive cell with different native defects was constructed. The cutoff energy was set to be 570 eV, and the convergence thresholds were set at values of 0.001 eV for energy and 0.05 eV/Å for force, respectively. A 3 × 3 × 5 k-point mesh was used with a γ-centered grid. For the ideal V3O4 systems, the ionic positions, cell volumes, and cell shapes were allowed to be relaxed. In the case of the intrinsic defects in V3O4 systems, the ionic positions were allowed to be relaxed, while the cell dimensions were kept fixed.

Results and Discussion

The calculated DOS curves (Figure c) of the ideal cubic V3O4 demonstrate that the spin-down states display a broad band gap being insulating. Whereas the spin-up states being metallic exhibit no gap, and are fully polarized at the Fermi energy mainly originating from the 3d states of V atoms. The calculation results indicate that V3O4 exhibits a typical half-metallic character resulting from the difference between the spin-up and spin-down DOS at the Fermi level, resulting in a total magnetic moment of 7.00 μB per formula unit. Based on Bader charge analysis, the less electronegative V atoms lose 1.82/1.67 electrons per atom at A/B sites and the more electronegative O atoms obtain 1.29 electrons per atom. Thus, ideal V3O4 can be written as V(A)V(B)2O4 in view of the V atoms at B sites twice as abundant as A sites, and further can be written as V(A)+1.82(V(B)+1.67)2(O–1.29)4.[24] Moreover, the larger average valence state of the V atom at the A site than that of the V atom at the B site illustrates that more electrons are transferred from the V atoms at A sites to the nearest neighbor O atoms than from the V atoms at B sites, which mainly results from the smaller V(A)–O bond length of 1.85 Å than the V(B)–O bond length of 2.05 Å to form a stronger chemical bond.

Eight V3O4 systems with native neutral defects under O-rich (Figure a–d) and V-rich (Figure e, f) conditions provide a further insight into the mechanism of the impact of native neutral defects on spin polarization in half-metallic V3O4: (a) a V(A) vacancy created by removing one V atom at the A site, denoted as the V(A) vacancy; (b) a V(B) vacancy created by removing one V atom at the B site, denoted as the V(B) vacancy; (c) one V atom at the A site replaced by an O atom denoted as the OV(A) antisite; (d) one V atom at the B site replaced by an O atom denoted as the OV(B) antisite; (e) an O vacancy created by removing one O atom, denoted as the O vacancy; and (f) one O atom replaced by a V atom denoted as the VO antisite.

Figure 2

Model configuration of the cubic V3O4 2 × 2 × 1 supercell of the primitive cell with neutral defects. (a) V(A) vacancy; (b) V(B) vacancy; (c) OV(A) antisite; (d) OV(B) antisite; (e) O vacancy; and (f) VO antisite.

For an in-depth understanding of the role of native neutral defects under O-rich conditions in modulating the spin polarization of half-metal V3O4, we calculate and compare the spin-polarized DOS of the four V3O4 systems with one native neutral V vacancy and Ov antisite defect at different V(A) and V(B) sites, as shown in Figure a–d. Theoretical calculations in Figure a demonstrate that one neutral V vacancy at the V(A) site introduces the half-occupied defect states in the spin-down channel in the original forbidden band gap close to the bottom of the conduction band mainly composed of V 3d orbitals, which decreases the difference in spin DOS between spin-up and spin-down near the Fermi level compared to the perfect V3O4 system. Therefore, the overall V3O4 system with one neutral V vacancy at the V(A) site has a smaller spin polarization degree with a smaller magnetic moment of 6.12 μB per formula unit. In the case of one neutral V vacancy at the V(B) site (Figure b), compared to the perfect V3O4 system, two impurity states appear in the original wide band gap below and above the Fermi energy in the spin-down channel, respectively, which results in the lower spin polarization degree near Fermi energy. The calculated magnetic moment of 6.11 μB per formula unit is slightly less than that of the neutral V vacancy at the V(A) site because of the more impurity states induced by the neutral V vacancy at the V(B) site in the original wide band gap near Fermi energy in the spin-down DOS. As shown in Figure c, one neutral Ov antisite at the A site introduces six impurity states below Fermi energy in the spin-down channel, and three of the six impurity levels in lower energy mainly stem from the O 2p orbitals, the other three impurity levels in higher energy mainly come from the V 3d orbitals. The calculated magnetic moment for one neutral Ov antisite at the A site is 3.78 μB per formula unit much smaller than that of the perfect V3O4 system, because of the six impurity states in the spin-down channel greatly reducing the spin polarization degree. For one neutral Ov antisite at the B site (Figure d), the four impurity acceptor levels are introduced in the spin-down channel below the Fermi energy, and three of the four impurity acceptor levels in lower energy mainly stem from the O 2p orbitals, another one impurity level in higher energy mainly originates from the V 3d orbitals. The calculated magnetic moment of the V3O4 system with one neutral Ov antisite at the B site is 5.60 μB per formula unit lower than that of the perfect V3O4 system because of the four impurity levels introduced by the neutral Ov antisite at the B site in the spin-down DOS decreasing the total spin polarization degree, but is higher than that of the neutral Ov antisite at the A site.

Figure 3

Spin-polarized total and partial DOS of four native neutral defective V3O4 cases under O-rich conditions: a neutral V vacancy (a) at the V(A) site, (b) at the V(B) site, and a neutral Ov antisite defect (c) at the V(A) site, (d) at the V(B) site, respectively. The black-dotted vertical line indicates the position of the Fermi level (EF = 0 eV).

Next, the impact of the native neutral defects under V-rich conditions on the spin polarization of half-metal V3O4 are investigated. The computed spin-polarized DOS of two V3O4 systems with a neutral O vacancy and VO antisite defects are shown in Figure a,b. As observed in Figure a, a neutral O vacancy introduces impurity acceptor levels above the valence bands in both the spin-up and spin-down channels, which are mainly contributed by the coupling between V 3d and O 2p orbitals. The impurity acceptor levels in the spin-up channel crossing the Fermi level are found to be partially filled, whereas in the spin-down channel appearing below the Fermi energy are completely filled, resulting in an asymmetric spin-up and spin-down DOS near Fermi energy and inducing a total magnetic moment of 4.19 μB per formula unit. The smaller spin polarization degree and magnetic moment compared with those of the pure V3O4 system are probably because of the fully occupied impurity levels in the spin-down channel introduced by the neutral O vacancy decreasing the splitting degree between the spin-up and spin-down states near the Fermi level. In the neutral VO antisite defect case (Figure b), one neutral VO antisite defect only introduces some acceptor levels, which mainly comes from coupling between the V 3d and O 2p orbitals in the spin-down channel leading to a smaller band gap in the vicinity of the Fermi level. The majority spin state maintains the metallic nature because of the top of the valence band cutting the Fermi level. Therefore, compared with ideal V3O4, the V3O4 system with one neutral VO antisite defect maintains semimetallic nature with a smaller magnetic moment of 4.35 μB per formula unit. Therefore, all the above neutral defects under O rich and V rich conditions are in favor of lower magnetic moments and spin polarization degrees compared to those of the ideal V3O4, which mainly results from the introduction of impurity energy levels in spin-down decreasing the difference between the spin-up and spin-down DOS near the Fermi level. Among these neutral defects, the V vacancy defects at both A and B sites contribute the highest magnetic moment and spin polarization degree.

Figure 4

Spin-polarized total and partial DOS for two native neutral defective V3O4 cases under V-rich conditions (a) with one neutral O vacancy and (b) with one neutral VO antisite defect. The black vertical-dotted line indicates the Fermi level (EF = 0 eV).

To evaluate the thermodynamic stability of these native neutral defects, we calculate their formation energies under V-rich and O-rich conditions, respectively. For ideal V3O4, the chemical potentials μV and μO must satisfy the following growth conditions[25]where μV is the chemical potential of the ideal V3O4. Under O rich conditions, considering thermodynamic corrections, we use the experimental value of 5.23 eV for the binding energy of the O2 molecule.[26] The atomic energy of oxygen is −1.90 eV calculated from a spin-polarized calculation. Then, by subtracting the above binding energy from 2× atomic energy of oxygen, we get −9.03 eV for the chemical potential μO. Therefore, the chemical potential μO is −4.52 eV defined as the oxygen-rich limit, and the chemical potential μV is obtained according to eq . In the V rich case, the chemical potential μV is −8.95 eV calculated from the metal vanadium, and the chemical potential μO is obtained according to eq . The neutral defect formation energies are defined as eq (27,28)where Edefecttot is the total energy of the supercell containing the neutral defect, E0tot is the total energy of the host supercell, n– and n+ are the number of atoms being removed and added, respectively, and μ– and μ+ are the corresponding chemical potentials.

Under O rich conditions, one V vacancy defect energy at the A/B site in the V23O32 system in comparison to the ideal V24O32 system is obtained according to eqs and 2

Under O rich conditions, one OV antisite defect energy at the A/B site in the V23O33 system in comparison to the ideal V24O32 system is obtained according to eqs and 2

Under V rich conditions, one O vacancy defect energy in the V24O31 system in comparison to the ideal V24O32 system is obtained according to eqs and 2

Under V rich conditions, one VO antisite defect energy in the V25O31 system in comparison to the ideal V24O32 system is obtained according to eqs and 2

As listed in Table , under V-rich conditions, both formation energies of the O vacancy and VO antisite defects are ultra high, suggesting that defects are less energetically favorable under V rich conditions. The oxygen atom bridges the V–O–V bond, and based on Bader charge analysis the strong bonds exist between the V and O atoms, which makes the strong exchange coupling between the V–O atoms observed in the spin polarized DOS (Figures –4) leading to the half-metallic ferromagnetism in V3O4. Therefore, the medium oxygen is hard to be removed to form the O vacancy and replaced by V atoms to form the VO antisite defects, which probably results in the high formation energies of the O vacancy and VO antisite defects. In addition, this similar case of the high formation energy of the O vacancy has been reported by the previous studies.[29,30] Moreover, under O rich conditions, the defect formation energies of the neutral V vacancy and OV antisite defects at B sites are both much lower than those at the A site because of the larger V(B)–O bond length (2.05 Å) than the V(A)–O bond length (1.85 Å) to form a weaker chemical bond, manifesting that the neutral V vacancy and the OV antisite defects are more likely to occur at B sites. In addition, the neutral V vacancy defect should be the main defect form because of the lowest defect formation energies among the various types of defects being studied.

Table 1

Calculated Neutral Defect Formation Energies (Ef) of Intrinsic Defects of V3O4

	O rich
	V vacancy		OV antisite		V rich
defect type	A site	B site	A site	B site	O vacancy	VO antisite
Ef (eV)	2.22	–0.04	15.21	3.98	18.54	22.43

Of particular importance is an understanding of the impact of native neutral defects on magnetic exchange coupling, which provides an effective route for mediating the curie temperature of semimetal V3O4. Owing to the lowest defect formation energies, the highest magnetic moments and spin polarization degrees of neutral V vacancy defects at A and B sites in contrast to other defects, we mainly study the role of the neutral V vacancy defect at different sites in influencing the magnetic coupling exchange of the V3O4 material. Curie temperature is determined by exchange coupling strength, which further depends on the difference in the total energies (ΔE) between the AFM and FM states.[31−33] As illustrated in Figure , the FM state is obtained from the collinear spin-polarized optimization of identical spin directions of the V atoms, and the AFM state is just reversing the inter-plane V spin directions in the lattice. The calculated positive and negative ΔE values correspond to FM and AFM ground states, separately. The room-temperature ferromagnetism should be achieved for ΔE values larger than thermal energy at room temperature (30 meV).[34] As listed in Table , the ΔE values of the ideal V3O4 system and defective V3O4 system with two neutral V vacancies at two A/B sites are all much larger than 30 meV, suggesting the existence of FM exchange couplings at room temperature and the much higher Curie temperatures than room temperature. Moreover, the comparative analysis of the above V3O4 systems indicates that the V3O4 systems with two neutral V vacancy defects at two A/B sites both favor higher FM transition temperatures in comparison to the ideal V3O4 system. Hence, the neutral V vacancy defects at A and B sites in the V3O4 system, as compared with the ideal V3O4, cause slightly lower spin polarization degrees, but much higher magnetic exchange coupling interactions.

Figure 5

(a,b),(c,d), and (e,f) Are the FM and AFM magnetic configurations of the ideal cubic V3O4 unit cell, V3O4 unit cell with two neutral V vacancies at A sits, and V3O4 unit cell with two V vacancies at B sits, respectively. Yellow up and green down arrows indicate the spin up and spin down states at V atoms, separately.

Table 2

Calculated Total Energies of FM and AFM States for the Ideal V3O4 System and the Defective V3O4 System with Two Neutral V Vacancies at Two A/B Sites

		V3O4 with two neutral V vacancies
energy	ideal V3O4	A site	B site
FM (eV)	–420.24990	–390.24036	–393.22177
AFM (eV)	–420.01781	–388.46047	–392.05486
ΔE (meV)	232.09	1779.89	1166.91

Conclusions

In summary, the crucial mechanism of spin polarization and exchange coupling interaction mediated by native defects is investigated in semimetal V3O4 using first-principles calculations. As revealed using the theoretical calculation results, in contrast to other neutral defects, the V vacancy defects at A and B sites are both in favor of higher spin polarization degrees and lower defect formation energies. In comparison to the ideal V3O4, the V vacancy defects in V3O4 at A and B sites both cause slightly lower spin polarization degrees, but much higher exchange coupling interactions. Our results suggest an effective route to mediate the spin polarization and exchange coupling interaction by defect engineering, promoting the applications of semimetal V3O4 in spintronics.