Chinese Journal of Polar Since  2018, Vol. 31 Issue (2): 177-183

The article information

Lin Ju, Ying Dai, Tong-shuai Xu, Yong-jia Zhang, Li Sun
鞠林, 戴瑛, 徐同帅, 张雍家, 孙礼
Combination Effect of Cation Vacancies and O2 Adsorption on Ferromagnetism of Na0.5Bi0.5TiO3(100) Surface: ab initio Study
Chinese Journal of Polar Since, 2018, 31(2): 177-183
化学物理学报, 2018, 31(2): 177-183

Article history

Received on: August 26, 2017
Accepted on: November 30, 2017
Combination Effect of Cation Vacancies and O2 Adsorption on Ferromagnetism of Na0.5Bi0.5TiO3(100) Surface: ab initio Study
Lin Jua,b, Ying Daib, Tong-shuai Xua, Yong-jia Zhangc, Li Sunc     
Dated: Received on August 26, 2017; Accepted on November 30, 2017
a. School of Physics and Electric Engineering, Anyang Normal University, Anyang 455000, China;
b. School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China;
c. Key Lab of Advanced Transducers and Intelligent Control System, Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China
*Author to whom correspondence should be addressed. Li Sun,
Abstract: The combination effect of cation vacancies and O2 adsorption on ferromagnetism of Na0.5Bi0.5TiO3(100) surface is studied by using density functional theory.An ideal Na0.5Bi0.5TiO3(100) surface is non-magnetic and the cation vacancy could induce the magnetism.By comparing the formation energies for Na, Bi and Ti vacancy, the Na vacancy is more stable than the others.Therefore, we focus on the configuration and electric structure for the system of O2 molecule adsorption on the Na0.5Bi0.5TiO3(100) surface with a Na vacancy.Among the five physisorption configurations we considered, the most likely adsorption position is Na vacancy.The O2 adsorption enhances the magnetism of the system.The contribution of spin polarization is mainly from the O 2p orbitals.The characteristics of exchange coupling are also calculated, which show that the ferromagnetic coupling is favorable.Compared with the previous calculation results, our calculations could explain the room-temperature ferromagnetism of Na0.5Bi0.5TiO3 nanocrytalline powders more reasonably, because of taking into account adsorbed oxygen and cation vacancies.Moreover, our results also show that adsorption of O2 molecule as well as introduction of cation vacancies may be a promising approach to improve multiferroic materials.
Key words: O2 adsorption     Cation vacancies     Ferromagnetism     First-principles calculation    

Lead-based ceramics, such as PZT, PMN-PT and PZN-PT, with their high piezoelectric coefficients, are widely used as the materials for actuator, sensors and transducers in the electronic industry [1]. However, the toxicity of lead has raised connecting with these lead-based piezoelectric materials. Therefore, lead-free functional materials are highly desirable for environment-friendly applications. Na$_{0.5}$Bi$_{0.5}$TiO$_3$ (NBT) was found to be ferroelectric (rhombohedral symmetry) at room temperature with its Curie temperature near 320 ℃ [2-9]. NBT has been considered to be an excellent candidate for lead-free piezoelectric ceramics due to its large remnant polarization (38 μC/cm2) and coercive field (73 kV/cm) at room temperature. It is also the base material for newly discovered family of oxide ion conductors with promising application in solid oxide based fuel cell [10]. NBT has a distorted perovskite ABO$_3$ structure, with mixed site occupancy of Na$^+$ and Bi$^{3+}$ ions at A-site, and Ti$^{4+}$ at the octahedrally coordinated B-site.

Recently, Li et al. found the electrical behavior of NBT is highly sensitive to low levels of A-site nonstoichiometry. For the series of Na nonstoichiometric compositions, Na$_{0.50+y}$Bi$_{0.50}$TiO$_{3+0.50y}$ ($y$=0.01 and -0.01), the Na-deficient composition, which is close to stoichiometric NBT, exhibits near-intrinsic electronic conduction, and is an excellent dielectric. Starting compositions with Bi/Na>1 will lead to such insulating composition(s) which can be used to suppress leakage conductivity for piezoelectric and high temperature capacitor applications [11].

Some theoretical works have so far attempted to develop basic understanding of this lead-free ferroelectric material and its structural, electronic, ferroelectric, dielectric properties of pristine NBT [12-14], and effects of A-site nonstoichiometry, O-vacancy, and doping on its properties [15-19]. Zhang et al. found the Na vacancies could introduce the ferromagnetism in the bulk NBT, indicating the NBT nanocrystalline is a potential multiferroic material [20]. The multiferroic materials have drawn increasing interest due to their attractive physical properties and potential applications in spintronics, information storage and sensors [21-24]. Multiferroic properties have been found in some oxides with perovskite structure [25-31]. The coupling between the magnetic and electric properties could lead to magnetoelectric (ME) effect in which the magnetization can be controlled by application of electric fields, and vice versa [21, 32-36].

In our previous studies, we reported that nanocrystalline NBT powders were prepared by sol-gel method present ferromagnetism (FM) at room temperature, which is induced by Na vacancies. The vacuum annealing weakens the FM, while the annealing in oxygen atmosphere greatly enhances the FM [15], indicating that the effect of O$_2$ on the FM should be considered. Furthermore, O$_2$ molecule is one of the most important gases taking up more than 20% in air. Sequential steps of physisorption, chemisorption and dissociation of O$_2$ on semiconductor surfaces have attracted much attention because of their close relation with catalytic processes, corrosion and oxide formation [37-39]. Previous experiment has shown that physisorbed O$_2$ molecules electronically deplete $n$-type materials such as MoS$_2$ and MoSe$_2$, which weakens electrostatic screening, leading to the drastic enhancement in photoluminescence [40]. Moreover, unlike the case for other basic adsorbates, O$_2$ is particularly interesting because it carries electron spin derived from unpaired electrons. Thus, O$_2$ molecules can change the electronic and magnetic properties of the NBT surface containing cation vacancies. However, the earlier calculations focused on the affects of cation vacancies alone on the magnetism of NBT [15, 20]. Though, we reported the O$_2$ adsorption affects on the magnetism of ideal NBT(100) surface lately [41], as is well-known, it is difficult to synthesize the ideal NBT(100) surface, due to the volatilization of bismuth and sodium in the preparation process. Therefore, in order to explain the room-temperature FM on NBT samples, both the factors of cation vacancies and O$_2$ adsorption should be considered. Motivated by the question above, in the present work we have carried out a systematic ab initio investigation of the combination effect of cation vacancies and O$_2$ adsorption on ferromagnetism of NBT(100) surface.


Spin-polarized density functional theory (DFT) calculations were performed using the projector augmented wave (PAW) [42, 43] method with a plane-wave basis set as implemented in the Vienna ab initio simulation package (VASP) code [44, 45]. The plane-wave cutoff energy was 400 eV. The total energy was converged to be 1.0$\times$10$^{-4}$ eV/atom, while the Hellman-Feynman force was smaller than 0.02 eV/Å. Before starting the surface calculations, we optimized the bulk structure firstly. The 1$\times$1$\times$2 periodic supercell for NBT with a rhombohedral perovskite structure (R3c group) containing 60 atoms was chosen. A G-centered mesh of 3$\times$3$\times$1 $k$-points is used to sample the Brillouin zone. As is known to all, both local density and generalized gradient approximations within DFT have the band gap underestimation problem due to the self-interaction error [46]. Here, the band gap obtained from local density approximation (LDA) for NBT bulk is 1.32 eV, which is much smaller than the experimental value (3.26 eV) [47]. To cover the shortage, the value of 5.8 eV was chosen for the on-site effective $U$ parameter ($U_{\rm{eff}}$=$U-J$) for Ti 3d orbitals [15, 20, 41, 48, 49]. The band gap of NBT bulk is improved with the value of 2.12 eV. Even though LDA+$U$ may not accurately describe the experimental value of band gap, LDA+$U$ approach indeed has some redeeming features for revealing parameters characterizing the structural stability and the existence of magnetic moment [15, 48, 49]. With in LDA+$U$ ($U_{\rm{eff}}$=5.8 eV), the calculated lattice constants $a$, $b$, $c$ the NBT bulk are 5.50, 5.50, 13.51 Å, and angles $\alpha$, $\beta$, $\gamma$ of the NBT bulk are 90$^{\circ}$, 90$^{\circ}$, and 120$^{\circ}$, respectively, which match (within 1%) well with the experimental data [50]. The lattice parameters $a$, $b$, $c$, and angle $\alpha$, $\beta$, $\gamma$ for rhombohedral phase are reported as 5.4887 Å, 5.4887 Å, 13.5048 Å, 90$^{\circ}$, 90$^{\circ}$, 120$^{\circ}$ by Jones and Thomas [50]. After optimization, the (100) surface was cleaved from the bulk, followed by the construction of a 15 Å vacuum layer added to the supercell of the layers. For the surface, special $k$ points were generated with the 4$\times$1$\times$1 grid based on Monkhorst-Pack scheme [51]. The (100) surface has received much attention for NBT perovskite oxide [15, 48, 49]. As shown in FIG. 1, the NBT(100) surface is modeled by a 6-layer. The atoms in the bottom layer of NBT(100) are held in their bulk positions, and the coordinates of all others are varied to minimize the energy. The first layer means the surface layer, containing a Na atom, a Bi atom, two Ti atoms, and six O atoms. For adsorption system, the PBE+D2 (D stands for dispersion) method with the Grimme vdW correction is adopted to describe long-range vdW interactions [52].

FIG. 1 Top (left) and side (right) views of the optimized structure of clean NBT(100) surfaces. The atoms in the broken line are the vacancy atoms and the configurations are named V1, V2 and V3, respectively.
Ⅲ. RESULTS AND DISCUSSION A. Geometric structure, electronic structure and magnetic properties of NBT(100) surface with a Na/Bi/Ti vacancy

We took the vacancy formation energies to testify the stability of vacancy defects, and the vacancy formation energies $E_{\rm{f}}(j)$ are defined below [53]:

$ - {E_{\rm{f}}}\left( j \right) = {E_{{\rm{tot}}}}9{\rm{NBT) }} - \left\{ {{E_{{\rm{tot}}}}\left( {{\rm{NBT}},\left[ j \right]} \right) + {E_{{\rm{tot}}}}\left( j \right)} \right\} $ (1)

where $E_{\rm{tot}}$(NBT) and $E_{\rm{tot}}$(NBT, [$j$]) are the total energies of the perfect surface and the surface with a species $j$ vacancy, respectively. $E_{\rm{tot}}(j)$ is the total energy per atom in elemental solid. Usually, the smaller vacancy formation energy means the easier appearance for the vacancy in the NBT(100) surface.

In order to calculate the vacancy formation energy of NBT(100) surface containing a cation vacancy, one metal atom (Na, Bi or Ti) is removed from the stoichiometric structure, which corresponds to 16.7%, 16.7%, and 8.3% for Na, Bi, and Ti vacancies in the system, respectively. The three kinds of surfaces are optimized and shown in FIG. 2. The calculated vacancy formation energy for NBT(100) surface is listed in Table Ⅰ. The formation energies for Na, Bi and Ti vacancy are 8.854, 12.089, and 20.024 eV, respectively. It shows that the Na vacancy is the most easily to appear among the three kinds of cation vacancy.

FIG. 2 The optimized structure of clean NBT(100) surfaces with a Na vacancy (V1) (a), a Ti vacancy (V2) (b) and a Bi vacancy (V3) (c), respectively.
Table Ⅰ Calculated values of the vacancy formation energies $E_{\rm{f}}$, and the total net magnetic moments $M_{\rm{tot}}(v)$, calculated for the NBT (100) surface with a Na/Ti/Bi vacancy.

In addition, the magnetism of stoichiometric NBT(100) surface has been calculated by LDA+$U$ [15]. It is reported that there is no spin polarization emerging around the Fermi energy level, indicating that stoichiometric NBT(100) surface is nonmagnetic, since there are no unpaired electrons. The total DOS for rhombohedral NBT(100) surface with a single Na vacancy are shown in FIG. 3(a). The spin polarization of the total DOS at the Fermi level indicates that the introduction of Na vacancy could introduce magnetic moments in rhombohedral NBT(100) surface and the obtained total magnetic moment is 0.68 μ$_\rm{B}$. Similarly, the Bi vacancy and Ti vacancy also could introduce magnetic moments in the surface and, as shown in Table Ⅰ, the total magnetic moment is 2.99 and 2.00μ$_\rm{B}$, respectively.

FIG. 3 The total density of states (DOSs) of (a) NBT(100) surface with a Na vacancy, (b)-(f) NBT(100) surface with a Na cacancy and five O$_2$ physisorption sites (R1-R5), respectively. The vertical dotted line indicates the Fermi energy level. The upper halves of each panel display the spin-up states and the lower halves are the spin-down states.
B. Geometric and electronic structures of O$_2$ adsorption on NBT(100) surface with a Na vacancy

Since the Na vacancy is the most possible one to appear in the NBT(100) surface, we choose the NBT(100) surface with a Na vacancy to explore the combination effect of cation vacancies and O$_2$ adsorption on ferromagnetism of NBT(100) surface. As shown in FIG. 4, the topside atom layer shows wave-shaped. There are two kinds of oxygen atom sites labeled O1 (extrude) and O2 (invaginate). We tried many different initial geometries for O$_2$ adsorption on the NBT(100) surface with a Na vacancy. After geometry optimization, we found that O$_2$ desorbs or deviates from the surface for all the geometries we tried, indicating that O$_2$ cannot chemisorb on the surface. Examining the various possible physical adsorption sites X for O$_2$ on the NBT(100) surface, five adsorption sites (X=O1, O2, Na, Ti, Bi) are considered, labeled R1-R5 in FIG. 4. The initial angle ($\beta$) of O-O-X is 180$^\circ$. Starting from the above-mentioned adsorption sites and after geometry optimization as shown in FIG. 5, five sites R1-R5 are found to be physisorption for NBT, which is confirmed by the electron density difference plots shown in FIG. 6. There is no chemical band appearing between adsorbed oxygen and the NBT(100) surface with a Na vacancy in the five cases. The adsorption energy ($E_{\rm{ads}}$) of the oxygen molecule on the NBT surface with a Na vacancy is calculated from:

$ {E_{{\rm{ads}}}} = {E_{{\rm{tot}}}} - {E_{{\rm{surf}}}} - E\left( {{{\rm{O}}_2}} \right)$ (2)
FIG. 4 Top (left) and side (right) views of the optimized geometry of NBT(100) surface with a Na vacancy. The configuration of the surface with O$_2$ absorbed at the five different sites are signed R1-R5, respectively.
FIG. 5 Top (upper row) and side (lower row) views of the optimized geometries of O$_2$ absorption sites: R1-R5 for NBT(100) surface with a Na vacancy, respectively.
FIG. 6 Electronic density changes upon (a)-(e) NBT(100) surface with a Na cacancy and O$_2$ physisorption site R1-R5, respectively. Density plots show equal density surfaces of 0.00 e/Å$^3$. The blue region corresponds to a density loss and the yellow region to a density gain.

where $E_{\rm{tot}}$ is the total energy of the whole adsorbed system in the equilibrium state, $E_{\rm{surf}}$ corresponds to the energy of the relaxed NBT surface with a Na vacancy calculated in the same conditions ($k$-points, cutoff and unit cell) and $E$(O$_2$) is the energy of the relaxed O$_2$ molecule. According to this definition, a negative value of $E_{\rm{ads}}$ indicates that the adsorption is exothermic (stable) with respect to a free O$_2$ molecule and a positive value indicates endothermic (unstable) reaction.

The parameters of the system, including the optimized distance ($d$) between O$_2$ molecule and NBT(100) surface with a Na vacancy, the optimized O-O bond length of O$_2$ molecule, the optimized angle ($\beta$) of O-O-X molecule, and the adsorption energy ($E_{\rm{ads}}$) are listed in Table Ⅱ. From Table Ⅱ, We can clearly see that the values of $E_{\rm{ads}}$ for configuration of R1, R2, R3, R4 and R5 are -0.116, -0.078, -0.204, -0.172, and -0.1485 eV/atom, respectively. According to the definition of $E_{\rm{ads}}$, these negative values of $E_{\rm{ads}}$ indicate that all these physisorptions are stable with respect to a free O$_2$ molecule. Since having the lowest adsorption energy, the configuration R3 is found to be the most stable and the O$_2$ molecule most likely adsorbs on the site of Na vacancy on NBT(100) surface, which is different from the case of O$_2$ molecule absorbed on the ideal Na$_{0.5}$Bi$_{0.5}$TiO$_3$(100) surface. It is reported that the O$_2$ molecule prefers to adsorb on the Bi site of stoichiometric Na$_{0.5}$Bi$_{0.5}$TiO$_3$(100) surface [41]. The difference may be due to the distortion caused by the Na vacancy. As displayed in Table Ⅱ, the distances between O$_2$ and NBT surface are different, when the O$_2$ molecule adsorbs at the different sites of the NBT(100) surface. The values of $d$ for configuration of R1, R2, R3, R4 and R5 are 2.892, 2.824, 2.187, 3.074, and 3.312 Å, respectively. The values of $\beta$ for configuration of R1, R2, R4 and R5 are 112.19$^\circ$, 151.15$^\circ$, 117.73$^\circ$, and 147.85$^\circ$, respectively. For the case of stoichiometric Na$_{0.5}$Bi$_{0.5}$TiO$_3$(100) surface, at the corresponding physisorption position, the distances between O$_2$ molecule and the surface are 2.892, 2.824, 2.531, 3.074, and 3.359 Å, and the optimized angles are 104.40$^\circ$, 133.64$^\circ$, 179.11$^\circ$, 112.72$^\circ$, and 134.99$^\circ$, respectively [41]. However, the Na vacancy does not affect the O-O bond lengths of the O$_2$ molecule very much. The O-O bond lengths for the configuration of R1 (1.231 Å), R2 (1.229 Å), R3 (1.226 Å), R4 (1.232 Å) and R5 (1.230 Å) are nearly the same as that of a free O$_2$ molecule (1.234 Å), which is similar to the case of stoichiometric Na$_{0.5}$Bi$_{0.5}$TiO$_3$(100) surface [41].

Table Ⅱ The calculated results of the NBT(100) surface containing a Na vacancy with one O$_2$ molecule adsorption ($E_{\rm{ads}}$ in eV/atom).
C. The magnetic properties of O$_2$ adsorption on NBT(100) surface with a Na vacancy

Next, the magnetic properties of the O$_2$ adsorption on NBT(100) surface containing a Na vacancy are studied. The total DOSs for physisorption sites R1-R5 are shown in FIG. 3 (b)-(f). An obvious spin-split in the spin-up and spin-down total DOS near the Fermi level can be found. As shown in the Table Ⅲ, the magnetic moments of physisorption sites R1-R5 are 2.48, 2.45, 2.43, 2.57, and 2.62 μ$_\rm{B}$, respectively. As is mentioned above, the total magnetic moment of NBT surface with a Na vacancy is 0.68μ$_\rm{B}$, so the adsorption process raise the magnetic moment of non-stoichiometric NBT surface. This may be the real reason for the increase of magnetic moments of NBT nanocrytalline powders after being annealed in oxygen atmosphere. The previous explanation for the phenomena may be less reasonable, due to the neglect of cation vacancies [41]. In addition, the augment of magnetic moments of physisorption sites R1-R5 is almost the same as O$_2$ free value of 2.0 μ$_\rm{B}$, suggesting the adsorption process almost unaffects the O$_2$ molecular magnetic moments in these physisorbed structures.

Table Ⅲ The relative energies of nonmagnetic state $E_{\rm{N}}$ and the magnetic state $E_{\rm{M}}$ ($\Delta E_{\rm{N-M}}$=$E_{\rm{N}}-E_{\rm{M}}$), the total net magnetic moments ($M_{\rm{total}}$) when O$_2$ adsorption on the NBT(100) surface with a Na vacancy.

The total energies of the physisorption sites R1-R5 for spin-polarized and nonspin-polarized modes are also calculated and shown in Table Ⅲ. The corresponding energy difference $\Delta E_{\rm{N-M}}$ ($\Delta E_{\rm{N-M}}$=$E_{\rm{N}}-E_{\rm{M}}$) between the total energies of nonmagnetic state $E_{\rm{N}}$ and the magnetic state $E_{\rm{M}}$ are 0.988, 0.941, 0.993, 1.066, and 1.083 eV for physisorption sites R1-R5, respectively. All the results show that the magnetic state is more stable than the nonmagnetic one.

In order to further understand the electronic structure, the atom-, orbital-, and spin-projected density of Na atoms s, p states, Bi atoms s, p, d states, Ti s, p, d states, and O p states are calculated and presented in FIG. 7 for physisorption sites R3. Obviously, the O 2p DOS shows an exchange splitting between the spin-up and spin-down DOS peaks at/near the Fermi level, which results in a magnetic moment. The spin density of configuration R1-R5 mainly concentrates in the O$_2$ molecule which is almost the same as the spin density of isolated O$_2$ molecule and the O 2p orbital appear in the gap of NBT. The peaks near the Fermi level for spin-down electrons appear at different positions for configuration R1-R5, which is made up of O 2p orbitals.

FIG. 7 The partial DOSs (a)-(d) of NBT(100) surface with a Na vacancy and O$_2$ physisorption site R3. The vertical dotted line indicates the Fermi energy level. The upper halves of each panel display the spin-up states and the lower halves the spin-down states.

For purpose of dealing with the effect of the magnetic coupling between the two adsorbed O$_2$ molecules, subsequently, we also compared the energies of ferromagnetic and antiferromagnetic couplings by LDA+$U$ calculation. Here, $\Delta E_m$ ($\Delta E_m$=$E_{\rm{AFM}}-E_{\rm{FM}}$) represents energy difference between antiferromagnetic state and ferromagnetic state after optimization, which enables us to estimate stable states of magnetism coupling. The $\Delta E_m$ is 24.765 meV for the physisorbed structure, so the ferromagnetic coupling is more stable and the value of magnetic moment is 4.88μ$_\rm{B}$.

Since the ferromagnetic moment of ideal NBT(100) surface with a O$_2$ molecule adsorption is reported to be about 2.0μ$_\rm{B}$ [41], the results above also suggest that the Na vacancy could strengthen the ferromagnetic property induced by O$_2$ molecule adsorption. Hence, the combined action of introducing Na vacancy and O$_2$ molecule adsorption could more efficiently regulate the ferromagnetic moment of the NBT nanocrystalline materials than the single action.


We have presented detailed DFT studies of the combine effect of cation vacancies and O$_2$ adsorption on ferromagnetism of NBT(100) surface. The stoichiometric NBT(100) surface is nonmagnetic, while the cation vacancy could introduce magnetic moments in the surface. We choose the NBT(100) surface with a Na vacancy as the subject of study for its most stable state among the three cation vacancy cases. From the calculation of the adsorption of molecular oxygen on the NBT(100) surface with a Na vacancy, where the chemisorption of O$_2$ is unfavorable at all adsorption sites, we find the configuration R3 is the most stable and the O$_2$ molecule adsorption enhances the magnetism of these systems. The corresponding energy difference $\Delta E_{\rm{N-M}}$ for physisorption sites R1-R5 shows that the magnetic state is more stable than the nonmagnetic one. The configuration R3 induces spin polarization with hybridized O 2p orbitals at Fermi level. In addition, the ferromagnetic coupling state of configuration R3 is more stable than the antiferromagnetic coupling state. All the results above provide useful guidelines for regulating the magnetic property of the perovskite nanocrystalline ferroelectric materials.


This work was supported by the National Natural Science Foundation of China (No.11547176, No.11704006) and Henan College Key Research Project (No.15A140017).

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鞠林a,b, 戴瑛b, 徐同帅a, 张雍家c, 孙礼c     
a. 安阳师范学院物理与电气工程学院, 安阳 455000;
b. 山东大学物理学院, 济南 250100;
c. 太原理工大学新型传感器与智能控制教育部重点实验室, 太原 030024
摘要: 本文采用第一性原理计算系统地研究了阳离子空位和吸附氧的协同作用对Na0.5Bi0.5TiO3(100)表面磁性的影响.结果表明,完美的Na0.5Bi0.5TiO3(100)表面是无磁性的,而阳离子空位可以对其引入磁性.通过Na、Bi和Ti空位形成能的对比,发现最可能稳定存在的阳离子缺陷态为Na空位.由此,主要对氧气吸附的表层含Na空位缺陷钙钛矿Na0.5Bi0.5TiO3(100)面的几何和电子结构进行了研究.在所研究的五种吸附构型中,发现氧气更容易吸附在Na空位的上方.氧气的吸附可以增强缺陷态Na0.5Bi0.5TiO3(100)的磁性,自旋极化主要由O的2p轨道电子贡献.交换耦合作用的计算结果表明,体系中铁磁相互作用比反铁磁相互作用更加稳定.本文因为同时考虑了阳离子空位和吸附氧两种外界因素,所以与之前的计算结果相比,能够更加合理地解释Na0.5Bi0.5TiO3纳米晶颗粒的室温磁性来源.研究表明吸附氧气和引入阳离子空位都是改善多铁材料的有效途径.
关键词: 吸附氧     阳离子空位     铁磁性     第一性原理计算