Lin JuYing DiTong-shui XuYong-ji ZhngLi Sun

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

I.INTRODUCTION

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.Na0.5Bi0.5TiO3(NBT)was found to be ferroelectric(rhombohedral symmetry)at room temperature with its Curie temperature near 320°C[2–9].NBT has been considered to be an excellent candidate for lead-free piezoelectric ceramics due to its large remnant polarization(38μC/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 ABO3structure,with mixed site occupancy of Na+and Bi3+ions at A-site,and Ti4+at the octahedrally coordinated B-site.

Recently,Liet al.found the electrical behavior of NBT is highly sensitive to low levels of A-site nonstoichiometry. For the series of Na nonstoichiometric compositions,Na0.50+yBi0.50TiO3+0.50y(y=0.01 and?0.01),the Na-de ficient 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].Zhanget 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 O2on the FM should be considered.Furthermore,O2molecule is one of the most important gases taking up more than 20%in air.Sequential steps of physisorption,chemisorption and dissociation of O2on 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 O2molecules electronically depleten-type materials such as MoS2and MoSe2,which weakens electrostatic screening,leading to the drastic enhancement in photoluminescence[40].Moreover,unlike the case for other basic adsorbates,O2is particularly interesting because it carries electron spin derived from unpaired electrons.Thus,O2molecules 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 O2adsorption 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 O2adsorption should be considered.Motivated by the question above,in the present work we have carried out a systematicab initioinvestigation of the combination effect of cation vacancies and O2adsorption on ferromagnetism of NBT(100)surface.

II.THEORETICAL METHODS AND MODELS

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 con figurations are named V1,V2 and V3,respectively.

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 Viennaab initiosimulation package(VASP)code[44,45].The plane-wave cutoffenergy was 400 eV.The total energy was converged to be 1.0×10?4eV/atom,while the Hellman-Feynman force was smaller than 0.02 eV/?A.Before starting the surface calculations,we optimized the bulk structure firstly.The 1×1×2 periodic supercell for NBT with a rhombohedral perovskite structure(R3c group)containing 60 atoms was chosen.A G-centered mesh of 3×3×1k-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 effectiveUparameter(Ueff=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+Umay not accurately describe the experimental value of band gap,LDA+Uapproach 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(Ueff=5.8 eV),the calculated lattice constantsa,b,cthe NBT bulk are 5.50,5.50,13.51 ?A,and anglesα,β,γof the NBT bulk are 90°,90°,and 120°,respectively,which match(within 1%)well with the experimental data[50].The lattice parametersa,b,c,and angleα,β,γfor rhombohedral phase are reported as 5.4887 ?A,5.4887 ?A,13.5048 ?A,90°,90°,120°by Jones and Thomas[50].After optimization,the(100)surface was cleaved from the bulk,followed by the construction of a 15?A vacuum layer added to the supercell of the layers.For the surface,specialkpoints were generated with the 4×1×1 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.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.

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 energiesEf(j)are de fined below[53]:

whereEtot(NBT)andEtot(NBT,[j])are the total energies of the perfect surface and the surface with a speciesjvacancy,respectively.Etot(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.

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 totalDOS 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 0.68μB.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 2.00μB,respectively.

TABLE I Calculated values of the vacancy formation energies Ef,and the total net magnetic moments Mtot(v),calculated for the NBT(100)surface with a Na/Ti/Bi vacancy.

B.Geometric and electronic structures of O2adsorption 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 O2adsorption 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 O2adsorption on the NBT(100)surface with a Na vacancy.After geometry optimization,we found that O2desorbs or deviates from the surface for all the geometries we tried,indicating that O2cannot chemisorb on the surface.Examining the various possible physical adsorption sites X for O2on the NBT(100)surface, five adsorption sites(X=O1,O2,Na,Ti,Bi)are considered,labeled R1?R5 in FIG.4.The initial angle(β)of O?O?X is 180°.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 con firmed 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(Eads)of the oxygen molecule on the NBT surface with a Na vacancy is calculated from:

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 O2physisorption 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.

FIG.4 Top(left)and side(right)views of the optimized geometry of NBT(100)surface with a Na vacancy.The con figuration of the surface with O2absorbed 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 O2absorption 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 O2physisorption site R1?R5,respectively.Density plots show equal density surfaces of 0.00 e/?A3.The blue region corresponds to a density loss and the yellow region to a density gain.

whereEtotis the total energy of the whole adsorbed system in the equilibrium state,Esurfcorresponds to the energy of the relaxed NBT surface with a Na vacancy calculated in the same conditions(k-points,cutoffand unit cell)andE(O2)is the energy of the relaxed O2molecule.According to this de finition,a negative value ofEadsindicates that the adsorption is exothermic(stable)with respect to a free O2molecule and a positive value indicates endothermic(unstable)reaction.

The parameters of the system,including the optimized distance(d)between O2molecule and NBT(100)surface with a Na vacancy,the optimized O?O bond length of O2molecule,the optimized angle(β)of O?O?X molecule,and the adsorption energy(Eads)are listed in Table II.From Table II,We can clearly see that the values ofEadsfor con figuration 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 de finition ofEads,these negative values ofEadsindicate that all these physisorptions are stable with respect to a free O2molecule.Since having the lowest adsorption energy,the con figuration R3 is found to be the most stable and the O2molecule most likely adsorbs on the site of Na vacancy on NBT(100)surface,which is different from the case of O2molecule absorbed on the ideal Na0.5Bi0.5TiO3(100)surface.It is reported that the O2molecule prefers to adsorb on the Bi site of stoichiometric Na0.5Bi0.5TiO3(100)surface[41].The difference may be due to the distortion caused by the Na vacancy.As displayed in Table II,the distances between O2and NBT surface are different,when the O2molecule adsorbs at the different sites of the NBT(100)surface.The values ofdfor con figuration of R1,R2,R3,R4 and R5 are 2.892,2.824,2.187,3.074,and 3.312 ?A,respectively.The values ofβfor con figuration of R1,R2,R4 and R5 are 112.19°,151.15°,117.73°,and 147.85°,respectively. For the case of stoichiometric Na0.5Bi0.5TiO3(100)surface,at the corresponding physisorption position,the distances between O2molecule and the surface are 2.892,2.824,2.531,3.074,and 3.359?A,and the optimized angles are 104.40°,133.64°,179.11°,112.72°,and 134.99°,respectively[41].However,the Na vacancy does not affect the O?O bond lengths of the O2molecule very much.The O?O bond lengths for the con figuration of R1(1.231?A),R2(1.229?A),R3(1.226?A),R4(1.232?A)and R5(1.230?A)are nearly the same as that of a free O2molecule(1.234?A),which is similar to the case of stoichiometric Na0.5Bi0.5TiO3(100)surface[41].

TABLE II The calculated results of the NBT(100)surface containing a Na vacancy with one O2molecule adsorption(Eadsin eV/atom).

C.The magnetic properties of O2adsorption on NBT(100)surface with a Na vacancy

Next,the magnetic properties of the O2adsorption 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 2.62μB,respectively.As is mentioned above,the total magnetic moment of NBT surface with a Na vacancy is 0.68μB,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 O2free value of 2.0 μB,suggesting the adsorption process almost unaffects the O2molecular magnetic moments in these physisorbed structures.

FIG.7 The partial DOSs(a)?(d)of NBT(100)surface with a Na vacancy and O2physisorption 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.

TABLE III The relative energies of nonmagnetic state EN and the magnetic state EM(ΔEN?M=EN?EM),the total net magnetic moments(Mtotal)when O2adsorption 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 differencebetween the total energies of nonmagnetic stateENand the magnetic stateEMare 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 con figuration R1?R5 mainly concentrates in the O2molecule which is almost the same as the spin density of isolated O2molecule 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 con figuration R1?R5,which is made up of O 2p orbitals.

For purpose of dealing with the effect of the magnetic coupling between the two adsorbed O2molecules,subsequently,we also compared the energies of ferromagnetic and antiferromagnetic couplings by LDA+Ucalculation.Here,represents energy difference between antiferromagnetic state and ferromagnetic state after optimization,which enables us to estimate stable states of magnetism coupling.The ΔEmis 24.765 meV for the physisorbed structure,so the ferromagnetic coupling is more stable and the value of magnetic moment is 4.88μB.

Since the ferromagnetic moment of ideal NBT(100)surface with a O2molecule adsorption is reported to be about 2.0μB[41],the results above also suggest that the Na vacancy could strengthen the ferromagnetic property induced by O2molecule adsorption.Hence,the combined action of introducing Na vacancy and O2molecule adsorption could more efficiently regulate the ferromagnetic moment of the NBT nanocrystalline materials than the single action.

IV.CONCLUSION

We have presented detailed DFT studies of the combine effect of cation vacancies and O2adsorption 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 O2is unfavorable at all adsorption sites,we find the configuration R3 is the most stable and the O2molecule adsorption enhances the magnetism of these systems.The corresponding energy difference ΔEN?Mfor physisorption sites R1?R5 shows that the magnetic state is more stable than the nonmagnetic one.The con figuration R3 induces spin polarization with hybridized O 2p orbitals at Fermi level.In addition,the ferromag-netic coupling state of con figuration 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.

V.ACKNOWLEDGEMENTS

This work was supported by the National NaturalScience Foundation ofChina (No.11547176,No.11704006)and Henan College Key Research Project(No.15A140017).

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