Nitrogen-induced ferromagnetism in BaO

Abstract

Density functional theory with local spin density approximation has been used to propose possible room temperature ferromagnetism in N-doped NaCl-type BaO. Pristine BaO is a wide bandgap semiconductor, however, N induces a large density of states at the Fermi level in the non-magnetic state, which suggests magnetic instability within the Stoner mean field model. Spin-polarized calculations show that N-doped BaO is a true half-metal, where N has a large magnetic moment, which is mainly localized around the N atoms, and a small polarization at the O sites is also observed. The origin of magnetism is linked to the electronic structure. The ferromagnetic (FM) and antiferromagnetic (AFM) coupling between the N atoms in BaO reveal that doping N atoms have a FM ground state, and the calculated transition temperature (T_C), within the Heisenberg mean field theory, theorizes possible room temperature FM in N-doped BaO. Nitrogen also induces ferromagnetism when doping occurs at the surface O sites and it has a smaller defect formation energy than bulk N-doped BaO. The magnetism of N-doped BaO has also been compared to that of Co-doped BaO, and we believe that N has a greater potential for tuning the magnetism in BaO than Co.

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I. Introduction

Inducing magnetism in non-magnetic oxides is one of the main areas of interest in the research community. Generally, many oxides are insulators and, without magnetic impurity atoms, non-magnetic. However, recent theoretical and experimental research of oxides has shown ferromagnetism with defects or light elements, e.g., C, N, Li.^1–9 In the past decade, density functional theory (DFT) has played a vital role in either proposing new magnetic materials or elucidating the origins of defect-driven magnetism in oxides.^{3–5,10–16} To date, there are a few oxides that show room temperature (RT) ferromagnetism, e.g., ZnO, SnO₂, In₂O₃, CeO₂.^13,17–19 Light elements can not only be used to develop magnetism in oxides, but also to stabilize intrinsic defects in the host materials.^20,21 Through the combined efforts of theoreticians and experimentalists, we are now certain that magnetism in oxides can be induced by non-magnetic impurities.^6,7,22,23 Now, it is known that magnetism develops in non-magnetic oxides where the impurity atoms have a finite local magnetic moment and these local magnetic moments interact to form a net magnetic moment in the host material. Those materials in which magnetism is induced by doping non-magnetic impurities, for which the substitutional atom can have a finite magnetic moment and the 2p-electrons of the doped atom play an essential role in governing the magnetism in the host material, are generally considered as d⁰ magnetic materials. These non-magnetic impurity atoms can also form impurity bands in the bandgap of the host material, and ferromagnetic behavior can be expected if the Fermi energy lies within these impurity bands.

BaO is an oxide with interesting structural and electronic properties. It can be used as a NO₃ storage device for catalysis.²⁴ BaO is also considered as a precursor to the well known ferroelectric perovskite oxide BaTiO₃, which can have an either TiO₂ or BaO terminated surface when BaTiO₃ is grown on a suitable substrate as a thin film. Possible magnetism in TiO₂ has been extensively studied,⁷ however, less attention has been given to impurities in BaO and there are no detailed theoretical and experimental studies on induced magnetism in it. It has been experimentally observed that bulk BaO naturally occurs in a B1 (NaCl) structure.²⁵ Recently, experimental reports have claimed the growth of ultrathin BaO films on a SrTiO₃ (001) substrate and the formation of BaO nanoparticles on reconstructed SrTiO₃ (001), while a locally ordered c(4 × 4) BaO structure has been observed on the disordered sample surface.²⁶ Tan et al.²⁷ have also observed RT ferromagnetism in N-doped BaTiO₃ and the origin of the magnetism was correlated with the presence of N. Therefore, studying the electronic properties of BaO is of great importance for the development of new applications, specially in the area of magnetism. Hence, we propose to add a new functionality to BaO, i.e. magnetism. We show that N in BaO has a ferromagnetic (FM) ground state and the transition temperature T_C, which is the temperature at which a material goes from a paramagnetic (disorder phase) state to a magnetic phase (order phase) state, is above room temperature.

II. Computational methods

To study the magnetism of N-doped BaO, we performed calculations in the framework of density functional theory (DFT),²⁸ using a linear combination of atomic orbital basis as implemented in the SIESTA code.²⁹ A double-ζ polarized basis set for all atoms was used. The local spin density approximation³⁰ (LSDA) was adopted for describing exchange–correlation interactions. We used standard norm-conserving pseudopotentials³¹ in their fully nonlocal form.³² A cutoff energy of 400 Ry for the real-space grid was adopted. The sampling of k-space was performed with the Monkhorst and Pack (MP) scheme with a regularly spaced mesh of 18 × 18 × 18. The convergence with respect to k-point sampling and cutoff energy was carefully checked.

To investigate the magnetism and electronic structure of N-doped BaO, we considered the 2 × 2 × 1 (Ba₄O₃N₁), 2 × 2 × 2 (Ba₈O₇N₁), and 2 × 2 × 3 (Ba₁₂O₁₁N₁) supercells of the primitive unit cell of NaCl-type BaO. Calculations were also carried out using a 3 × 3 × 3 (Ba₂₇O₂₆N₁) supercell. In all these supercells, N was doped at the O sites due to the small difference in their atomic size and electronegativity. For the magnetic properties of the BaO (001) surface, we considered the conventional unit cell of BaO, and used different n × m × z symmetric slabs of thickness z, defined as a monolayer of BaO. We investigated n = 1, m = 1, z = 8 (Surf₁) and n = 2, m = 1, z = 8 (Surf₂) surfaces of BaO and doped N at the O sites on both sides of the BaO surface. We added a vacuum region of about ∼10 Å, so that the two surfaces do not interact with each other through the vacuum region. Additional simulations, using plane waves plus pseudopotentials, as implemented in the Quantum Espresso (QE) code,³³ were also carried out to further test the validity of our results. The atomic positions were relaxed, using a conjugate-gradient algorithm,³⁴ until the residual Hellmann–Feynman force on a single atom converged to less than 0.05 eV Å⁻¹. Test calculations, using LSDA + U, were also carried out by considering the on-site Coulomb correction (U = 6.0 eV, our previously optimized value²⁰) between the p-orbital electrons of O.^20,35,36

III. Results and discussion

First, we calculated the optimized lattice constant of NaCl-type BaO, which was found to be 5.40 Å, as shown in Fig. 1(a). The calculated lattice constant is comparable to the previously calculated 5.47 ų⁷ and experimental 5.52 ų⁸ values. Our DFT estimated value is smaller than the experimental value due to the underestimation problem of DFT-LDA. Using the optimized lattice constant, we calculated the band structure, which is shown in Fig. 1(b). We see that BaO is a wide bandgap semiconductor and the calculated bandgap at the X point is ∼1.62 eV. The band is degenerate at G point [2π/α (0, 0, 0)], but this degeneracy is removed at X point where the band has less curvature (large effective mass) compared to point G. The electronic density of states (DOS) shows that bands near the Fermi energy (E_F) are mainly derived from the O p-orbitals [see Fig. 2(a)]. The LSDA calculated indirect (Γ − X) bandgap is ∼2.0 eV, in agreement with previous LDA calculations.³⁹ However, the experimental and GW calculated value is 3.88 eV.^39–41 We then used LSDA + U and the LSDA + U calculated bandgap was found to be ∼3.6, which is comparable with the GW calculated and experimental values.

Fig. 1 (a) The calculated lattice constant vs. energy of pristine BaO (black line), Ba₈O₇N₁ (blue line), and Ba₁₂O₁₁N₁ (green line). (b) The band structure of pristine BaO. The horizontal line (black) shows the Fermi energy, which is set to zero.

Fig. 2 The calculated total and atom projected density of states (PDOS) of non-magnetic Ba₄O₃N₁ (a), where the green dotted lines show the PDOS (O-pris) and total DOS (pris) of pristine BaO. The spin-polarized (magnetic) total and PDOS of Ba₄O₃N₁, Ba₈O₇N₁, and Ba₁₂O₁₁N₁ are shown in (b), (d), and (e), respectively. Panel (c) shows the LSDA + U DOS of Ba₄O₃N₁. The green dotted lines in the total DOS panels show the total DOS of pristine BaO (pris) of the same supercells. The total magnetic moment per N atom and local magnetic moment of N and O are also shown. The O and N PDOS is represented by solid (red) lines. The vertical lines represent the Fermi energy, which is set to zero.

It is important to consider atomic relaxation in N-doped BaO. Usually, the doping impurity at the host site can either compress or elongate the bond lengths depending on the atomic size of the impurity atom. In some cases, the impurity atom can also be located at an interstitial site and form a defect complex.²⁰ We therefore relaxed all the atomic coordinates of BaO : N and no significant changes in the atomic position of N at the O sites were found. To further confirm this, both Ba₈O₇N₁ and Ba₁₂O₁₁N₁ were considered and their optimized lattice constant calculated, which is 5.40 Å for both systems [see Fig. 1(a)]. This lattice constant is approximately equal to our optimized lattice constant of pristine BaO, which shows that N can easily dope the O sites without any structural distortion.

Fig. 2(a) shows the calculated total and atom projected (P) DOS of N-doped BaO in the non-magnetic state. For comparison purposes, the total PDOS of pristine BaO is also shown. It can be clearly seen that the DOS of doped and pristine BaO are the same in the conduction and valence bands. However, near the Fermi energy (E_F), the DOS of the doped system is drastically changed and the material shows metallic behavior, in contrast to pristine BaO, which is an insulator. The PDOS demonstrates that the main peak at the Fermi energy arises mainly from contributions from the p-orbitals of N. The N atoms in BaO form an impurity band in the bandgap of BaO. A small impurity-derived peak can also be seen at 2.0 eV just below the E_F, and this peak is hybridized with the p-orbitals of the O atoms. Therefore, the O and N atoms are only hybridized near the Fermi energy. No significant changes in the PDOS of O can be seen when the O sites are doped with N, except a small shoulder derived by the N p-orbitals near the Fermi energy. The calculated results show that the top of the valence band consists of N 2p electrons, which are higher than O 2p electrons. The large DOS at the Fermi energy D(E_F) in N-doped BaO shows that there is an instability towards magnetism within the Stoner mean field theory of magnetism.⁴² Within the Stoner model, which was mainly proposed for itinerant electron systems, the large D(E_F) can lead to a large Pauli susceptibility which is large enough for the band to split spontaneously, and therefore magnetism in N-doped BaO can be expected.

To confirm that N-doped BaO can present magnetism within the Stoner mean field theory, we further carried out spin-polarized calculations. The spin-polarized electronic density of states of Ba₄O₃N₁ is shown in Fig. 2(b). The total DOS clearly shows that N induces magnetism in BaO when doped at the O sites. The spin-polarized structure shows that the non-magnetic impurity band in the bandgap [see Fig. 2(a)] is mainly due to the contribution from minority spins. Large exchange splitting at N sites can also be seen, as expected in the Stoner mean field theory. For comparison, we also show the total DOS of pristine BaO and one can easily judge that the conduction band of Ba₄O₃N₁ in the spin-up state is identical to that of BaO. The 2p states of nitrogen are located at the top of the valence band, which are mainly derived from the anion p-states, resulting in the hybridization of the electron wave functions of the 2p orbitals. The majority spin-states of nitrogen also hybridize with oxygen 2p states, promoting the impurity band which connects to the top of the valence band. Such chemical process gives rise to a bandgap in the majority spin states. The minority spins, on the other hand, create an impurity band in the bandgap which includes the E_F. As a result, this impurity band is broadened, having about 0.38 eV half-width, and the approximated exchange splitting is 0.80 eV. The majority spins are completely occupied and behave just like an insulator, whereas the minority spins are partially occupied and have a metallic nature. Such electronic structure is the fingerprint of half-metal ferromagnets,^43,44 which have applications in the area of spin electronics. The total and local magnetic moments of Ba₄O₃N₁ were also calculated, and the calculated total magnetic moment is 1.0 μ_B per unit cell. The PDOS clearly shows that the magnetic moment arises mainly from contributions from the N p-orbitals and the local magnetic moment at the N site is ∼0.74 μ_B. A small induced magnetic moment (∼0.20 μ_B) at the nearby O sites is also observed. The PDOS of O shows some unoccupied minority spin states, which were occupied in the pristine BaO, suggesting that the holes induced by N are also localized at the O p-orbitals. We repeated the same calculations by doping N at the O sites in 2 × 2 × 2 and 2 × 2 × 3 supercells, and interestingly, we found half-metallic behavior in all these doped systems [see Fig. 2(d and e)] and the magnetic moments were mainly localized at the N sites. It is also noticeable that N does not polarize the whole valence band, it polarizes only the valence electronic states near the Fermi energy. Such behavior of N in BaO is different from that of transition metals in oxides/semiconductors, which usually polarize the whole valence band.⁴⁵ The band-width of N decreases and the band is narrowed as the concentration of N in BaO is reduced [see Fig. 2(e)], which further increases the localization of the 2p states of N. This localization of the N 2p states may further increase the observation/suppression of ferromagnetism/antiferromagnetism in BaO, which is discussed in the following paragraph. The total magnetic moment per N atom is 1.0 μ_B, which indicates that the total magnetic moment is independent of the N concentration. In all these N-doped BaO systems, the calculated magnetic moment is consistent with Hund’s rules indicating that the N dopant exists as a N²⁻ (s²p⁵) anion, illustrating that each N impurity introduces one 2p hole, the strong Hund-type exchange makes the nitrogen 2p spin-up orbitals completely occupied, and the spin-down states are partially filled [Fig. 2(b–e)]. As a result, one can expect the (ferro)magnetism in N-doped BaO to be stabilized mainly by a predominant double-exchange mechanism.⁴² Before we address the question of FM or AFM coupling between the N atoms, the above calculations were also performed for Ba₂₇O₂₆N₁ and Ba₃₂O₃₁N₁, and we confirmed that N in BaO has a spin-polarized band structure. We also confirmed the above conclusions using the QE code. It is also important to comment on the magnetism of N-doped BaO using LSDA + U. The LSDA + U calculated total and PDOS of Ba₄O₃N₁ are shown in Fig. 2(c). As expected, the N forms an impurity band in the bandgap of BaO and N-driven oxygen p states can also be seen in the gap region of BaO. Similar observations have also been observed in the self-interaction correction (SIC) for C-doped BaO.⁴⁶ The local magnetic moment of N (O) is increased (decreased), but the total magnetic moment of the unit cell remains unchanged, i.e., 1.0 μ_B. Similar conclusions were also drawn when LSDA + U calculations were performed for Ba₈O₇N₁and Ba₁₂O₁₁N₁, consistent with our previous work.²⁰

As predicted, N can induce half-metallic magnetism in insulator BaO. However, there remains a question on whether N-doped BaO can have a FM order above room temperature, and whether the exchange coupling is sufficiently large to give rise to possible RT ferromagnetism. Magnetism is a cooperative phenomenon and a single N in BaO can not determine the true magnetic ground state. Therefore, we considered 2 × 2 × 3 and 3 × 3 × 3 supercells of BaO and doped two N atoms at different O sites. The distance between the two N atoms d was varied, as it was the FM and AFM coupling between them. For comparison purposes, we kept the same N–N separation in both supercells, and the results are summarized in Table 1. It is interesting to see that both BaO : N systems have a FM ground state, and the total magnetic moment of the unit cell is 2.0 μ_B (i.e., 1.0 μ_B per N). All the systems remained half-metallic as well. The strength of the exchange interactions, J, can be judged from ΔE = E_AFM − E_FM, where E_AFM(E_FM) is the total energy of the supercell in the AFM (FM) state. This exchange energy can be further used to estimate T_C. Using the Heisenberg mean field model (k_BT_C = 2ΔE/3),^47,48 the estimated T_C was found to be close to room temperature, indicating the possibility of room temperature ferromagnetism in BaO : N systems. One can also see that both systems have different transition temperatures due to different N concentrations in BaO. Note that, usually, mean field theory overestimates T_C but it can give an indication of possible RT FM. Therefore, RT ferromagnetism in N-doped BaO is expected, if properly prepared. It is encouraging to mention that our estimated T_C matches that of N-doped BaTiO₃²⁷ and other magnetic oxides,^9,21 indicating that the magnetism is mainly attributed to N impurities.

Table 1 Calculated total magnetic moment M (in μ_B), ΔE = E_AFM − E_FM per cell (in eV), transition temperature T_C (in K), and defect formation energy E_f per N (in eV) of N-doped BaO (3 × 3 × 3). Ba_rich and O_rich shows E_f under Ba-rich and O-rich conditions, respectively. The first column shows N–N separation d (in Å). Values in brackets correspond to the 2 × 2 × 3 supercell

d	M	ΔE	TC	Ef
				Barich	Orich
3.82	2.0 (2.0)	0.064 (0.077)	495 (597)	−1.05 (−1.07)	5.42 (5.40)
6.61	2.0 (2.0)	0.035 (0.089)	271 (689)	−1.02 (−1.08)	5.45 (5.40)

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The formation enthalpy H_f of BaO was calculated using where E (BaO), E (Ba), and E (O₂) are the total energies of NaCl-type BaO, BCC Ba and molecular oxygen, respectively. The calculated H_f was found to be −6.49 eV, which is comparable to the previously calculated (−5.64,³⁷ −5.19 ⁴⁹) and experimental (−5.74 ⁵⁰) values. We followed our previous approach²⁰ and calculated the defect formation energy E_f of N in BaO under Ba-rich and O-rich conditions because the defect formation energy strongly depends on growth conditions and chemical potential.²⁰ The calculated E_f values of Ba₄O₃N₁, Ba₈O₇N₁, and Ba₁₂O₁₁N₁ in Ba-rich (O-rich) conditions are −1.15 (5.33), −1.14 (5.34), and −1.15 (5.45) eV, respectively. It is clear to see that N in BaO has a negative defect formation energy under Ba-rich conditions, which further increases the possibility of introducing N in BaO. Note that the LSDA + U calculated E_f of Ba₄O₃N₁ is about 6.6 eV in O-rich conditions, which is increased by including the U parameter – similar behavior has also been observed in other oxides.²⁰ We then varied the distance d between the two N atoms, using 2 × 2 × 3 and 3 × 3 × 3 supercells, and calculated E_f under different growth conditions. The calculated E_f per N atom of both systems in the FM states is shown in Table 1. The calculated E_f values are in the range of single N-doped BaO, and therefore we can not expect the clustering of N in BaO when doping the O sites. The formation energy depends on the N concentration in BaO. We may conclude that all the studied systems have negative formation energies under Ba-rich environments. Such calculated results can help experimentalists to dope N in BaO. The role of intrinsic defects (vacancies) can not be ignored when a sample is synthesised, these intrinsic defects may interact with the impurity atom, and such interactions may further decrease the E_f of the impurity atom.²⁰ There is also an experimental report on N-induced ferromagnetism in BaTiO₃,²⁷ which suggests the possibility of N-doping at the O sites in BaO. Experimental work will be very helpful to further analyse the possibilities of N-doped BaO.

To propose BaO for practical applications, e.g., in the area of thin films, it is essential to study the electronic and magnetic properties of N-doped surface O sites in BaO, Surf₁. We found that N can also induce magnetism in the BaO (001) surface, and the magnetism is mainly localized at the N sites as shown in Fig. 3(a and b). Surface oxygen atoms have a negligible magnetic moment and N has a large magnetic moment (0.97 μ_B) when doped at the surface O sites, as expected for surface N atoms. No induced magnetic moment at the sub-surface atoms was found, which is different from other doped oxides.^1,51 The PDOS of surface O atoms is shifted towards the Fermi energy compared to clean surface O atoms, indicating that the bandgap of the BaO (001) surface is reduced due to surface states driven by N–O hybridization. The majority spins of N are occupied and the minority spins are partially occupied. The calculated surface spin densities of N, O, and Ba atoms are shown in Fig. 3(c), and it is evident no spin-polarization at the surface O and Ba atoms is observed. The spin density is mainly localized around the N atoms. We then used a n × m × z surface (Surf₂) and doped two N atoms at two different O sites and considered the FM and AFM coupling between the N atoms. Here, we have also found that the FM coupling between the surface N atoms has a lower energy than that of the AFM coupling. As the concentration of N atom increases, a small magnetic moment at the surface O atoms is also induced, but the sub-surface O atoms do not show any induced magnetic moment [Fig. 3(b)]. No surface relaxation or reconstruction was observed when all the atoms were fully relaxed. The calculated E_f of N at surface O sites in Ba-rich (O-rich) condition is −1.58 (4.90) eV for Surf₁. For Surf₂, when two N atoms are doping surface O sites, the E_f per N in Ba-rich (O-rich) conditions is −1.48 (5.00) eV when the distance between the two surface N atoms is 3.82 Å; whereas, when the separation between the two N atoms is 5.40 Å, the calculated E_f per N in Ba-rich (O-rich) condition is −1.60 (4.88) eV. Surface N-doped BaO has a smaller defect formation energy than bulk N-doped BaO, similar to other oxides.⁵¹ Note that a smaller surface E_f corresponds to a larger N–N bond distance suggesting that N prefers isolation than clustering in the BaO (001) surface.

Fig. 3 The LSDA calculated surface atomic projected DOS of Surf₁ (a) and Surf₂ (b). The top panels show the PDOS of surface O atoms (red lines) along with the PDOS of clean surface O atoms (green lines). The middle panels show the PDOS of surface N atoms (red lines). The bottom panels show the PDOS of sub-surface O atoms denoted as O_Su. The local magnetic moments of N and O atoms are also shown. The vertical lines represent the Fermi energy, which is set to zero. (c) The calculated surface spin density of Surf₁, where red, green, and yellow balls represent the Ba, O, and N atoms, respectively. The spin density of Surf₁ is calculated on a large surface to show zero polarization at the surface O atoms. The inset shows the scale of the spin density.

We have shown that N in BaO can display possible room temperature ferromagnetism either in bulk or surface doped systems, and finally, we would like to compare it to Co-doped BaO. Our preliminary results clearly indicate that a Co atom at either O or Ba sites induces magnetism with a larger (about 3 times) E_f than that in BaO : N systems. Therefore, we believe that N doping in BaO has the potential to easily tune the magnetism and be superior to Co-doped BaO. Further experimental work would be needed to demonstrate the potential of BaO : N for possible applications in the area of spin electronics. We also believe that our results can also be helpful for BaO terminated surfaces of BaTiO₃.

IV. Summary

To summarize, DFT was used to investigate potential magnetism in N-doped NaCl-type BaO. Pristine BaO is known to be a non-magnetic wide bandgap semiconductor, and N atoms at the O sites induce an impurity band in the bandgap of BaO. It has been discussed that N in BaO can also induce magnetism and the magnetism arises mainly from contributions by the N atoms. The minority impurity-driven band is narrowed with decreasing N concentrations in BaO. The origin of magnetism was elucidated from the atom projected density of states. All the considered scenarios with different N concentrations in BaO showed half-metallic behavior. The ferromagnetic and antiferromagnetic interactions between the N atoms were also considered, and they revealed that N-doped BaO is a ferromagnetic material. The transition temperature was also calculated using the Heisenberg mean field model, and it was found to be above room temperature. The magnetic interaction between the N atoms is limited to next-nearest-neighbor interactions. The surface magnetism of N-doped BaO (001) was also studied by doping surface O sites with N. N atoms at surface O sites also showed a ferromagnetic ground state, and the magnetism was mainly limited to the BaO surface. No induced magnetic moments were observed at the sub-surface O sites. The defect formation energy showed that N has a smaller formation energy than bulk N-doped BaO. The magnetism of N-doped BaO was also compared to that of Co-doped BaO, and it was concluded that magnetic N-doped BaO can easily be achieved. LSDA + U calculations also supported the ferromagnetism in N-doped BaO.

Acknowledgements

The author acknowledges insightful discussions with Víctor M. García-Suárez and the cluster facilities of NCP, Pakistan.

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