Lin Ju，Tong-shui Xu，Yong-ji Zhng，Li Sun?.School of Physics nd Electric Engineering，Anyng Norml University，Anyng 455000，Chin.Deprtment of Physics，Tiyun University of Technology，Tiyun 030024，Chin

(Dated:Received on February 2，2016；Accepted on May 4，2016)

The origins of magnetism in transition-metal doped Na0.5Bi0.5TiO3system are investigated by ab initio calculations.The calculated results indicate that a transition-metal atom substitution for a Ti atom produces magnetic moments，which are due to the spin-polarization of transition-metal 3d electrons.The characteristics of exchange coupling are also calculated，which shows that in Cr-/Mn-/Fe-/Co-doped Na0.5Bi0.5TiO3system，the antiferromagnetic coupling is favorable.The results can successfully explain the experimental phenomenon that，in Mn-/Fe-doped Na0.5Bi0.5TiO3system，the ferromagnetism disappears at low temperature and the paramagnetic component becomes stronger with the increase of doping concentration of Mn/Fe/Co ions.Unexpectedly，we find the Na0.5Bi0.5Ti0.67V0.33iO3system with ferromagnetic coupling is favorable and produces a magnetic moment of 2.00μB，which indicates that low temperature ferromagnetism materials could be made by introducing V atoms in Na0.5Bi0.5TiO3.This may be a new way to produce low temperature multiferroic materials.

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First-Principles Study of Magnetism in Transition Metal Doped Na0.5Bi0.5TiO3System

Lin Jua，Tong-shuai Xua，Yong-jia Zhangb，Li Sunb?
a.School of Physics and Electric Engineering，Anyang Normal University，Anyang 455000，China
b.Department of Physics，Taiyuan University of Technology，Taiyuan 030024，China

(Dated:Received on February 2，2016；Accepted on May 4，2016)

The origins of magnetism in transition-metal doped Na0.5Bi0.5TiO3system are investigated by ab initio calculations.The calculated results indicate that a transition-metal atom substitution for a Ti atom produces magnetic moments，which are due to the spin-polarization of transition-metal 3d electrons.The characteristics of exchange coupling are also calculated，which shows that in Cr-/Mn-/Fe-/Co-doped Na0.5Bi0.5TiO3system，the antiferromagnetic coupling is favorable.The results can successfully explain the experimental phenomenon that，in Mn-/Fe-doped Na0.5Bi0.5TiO3system，the ferromagnetism disappears at low temperature and the paramagnetic component becomes stronger with the increase of doping concentration of Mn/Fe/Co ions.Unexpectedly，we find the Na0.5Bi0.5Ti0.67V0.33iO3system with ferromagnetic coupling is favorable and produces a magnetic moment of 2.00μB，which indicates that low temperature ferromagnetism materials could be made by introducing V atoms in Na0.5Bi0.5TiO3.This may be a new way to produce low temperature multiferroic materials.

Transition-metal atom，Substitution，Magnetic moment，F(xiàn)irst-principles calculation.

I.INTRODUCTION

Ⅰn recent years，multiferroic materials have drawn increasing interest due to their attractive physical properties and potential applications in spintronics，information storage and sensors[1-4].The coupling between the magnetic and electric properties could lead to magnetoelectric effect[1]in which the magnetization can be controlled by application of electric fields，and vice versa.Multiferroic properties have been found in some oxides with perovskite structure[5-7].The observed single-phase multiferrioc materials are few[8]，due to the contradiction between the conventional mechanism for cation off-centering in ferroelectrics(which generally requires d0orbitals)，and the formation of magnetic moments(which usually results from partially filled d or f orbitals).Related studies on magnetic ferroelectrics have signalled a revival of interest in this phenomenon [2].Several reports show that doping of transition metal ions in a ferroelectric oxide could induce ferromagnetism，a similar case to that of diluted magnetic semiconductors[9，10].

Na0.5Bi0.5TiO3attracts much attention as a promising environmental friendly lead-free ferroelectric material due to its possible applicability to electromechanical actuators，sensor，and transducers[11].Ⅰt is one among the non-lead free relaxor ferroelectrics having very high remanent polarization Pr=36μC/cm2with a coercive field of about 70 kV/cm[12].At temperatures below 255?C Na0.5Bi0.5TiO3has a rhombohedral structure with R3c space group which has anti-phase (ˉaˉaˉa)octahedral tilting and ion displacements along the[111]direction of the pseudo-cubic cell，making Na0.5Bi0.5TiO3exhibit unique ferroelectric and piezoelectric properties[13].Ⅰn such systems inducing a multifunctional behavior by site specific substitution will be inevitable.Ⅰn Na0.5Bi0.5TiO3，diluted magnetic behavior has been observed by transition-metal substitution at B-site，such as Fe-/Mn-/Co-doped Na0.5Bi0.5TiO3[14-16].All the results above indicate that the substitutional doping with transition metals play a very important role in tuning the electronic and magnetic properties of Na0.5Bi0.5TiO3and related systems.However，the mechanisms of electronic and magnetic of TM-doped Na0.5Bi0.5TiO3remain unclear.

Ⅰn order to address exactly these above questions，we explore the electronic and magnetic properties of bulk of Na0.5Bi0.5TiO3with transition metals doping via the first-principles density functional theory(DFT). Results demonstrate that，for Na0.5Bi0.5TiO3system，magnetic moments can be induced when one Ti atom is substituted by a TM(TM=V，Cr，Mn，F(xiàn)e，and Co) atom.We also compared the energies of ferromagnetic and antiferromagnetic couplings between two TM atoms substitutions in Na0.5Bi0.5TiO3super-cell.The type of preferential magnetic coupling of system depends upon both the doped transition-metal atoms and the distributions of the Ti atoms substituted.The TM doping concentration was defined as the molar ratio of TM/(TM+Ti).

II.COMPUTATIONAL DETAILS

DFT calculations were performed using the planewave pseudopotential method in the Vienna ab initio simulation package(VASP)[17，18].The projector augmented wave(PAW)[19，20]potentials were employed. Considering the fact that LDA may underestimate the Coulomb repulsion and tend to localize the charge density，strong correlation effects were introduced by means of the LDA+U scheme[19].Ⅰn our LDA+U calculation，the on-site effective U parameter(Ueff=U-J=5.8 eV) was proposed by Dudarev et al.[21].The calculated lattice constants of(a=b=5.49?A，c=13.51?A，and α=β=90?，γ=120?)are in good agreement with reported results by Jones and Thomas[13].Special k points were generated with a 3×3×3 grid based on Monkhorst-Pack scheme.We constructed a rhombohedral Na0.5Bi0.5TiO3periodic supercell containing 30 atoms，where a Ti atom is substituted by a TM atom (TM=V，Cr，Mn，F(xiàn)e，and Co).Such substitution corresponds to Na0.5Bi0.5Ti0.84V0.16O3and the doping level is 16%.An energy cutoff of 400 eV was used for the plane wave expansion of the electronic wave function.The cases of pure Na0.5Bi0.5TiO3and TM atoms (TM=V，Cr，Mn，F(xiàn)e，and Co)doped Na0.5Bi0.5TiO3are considered.The total energy is converged to be 1.0×10-4eV/atom，while the Hellman-Feynman force is smaller than 0.01 eV/?A in the optimized structure.

III.RESULTS AND DISCUSSION

TherhombohedralNa0.5Bi0.5TiO3，acomplex perovskite-structure compound with Na and Bi ions at the A site of ABO3with a Na:Bi ratio of 1:1 are shown in Fig.1.The density of state(DOS)for the pure system Na0.5Bi0.5TiO3is given in Fig.2(a).Ⅰn addition，the total DOS for pure Na0.5Bi0.5TiO3system also shows that no spin-polarization emerges around the Femi energy level，indicating that the pure Na0.5Bi0.5TiO3is nonmagnetic，as there are no unpaired electrons，the results are in good agreement with Zhang’s report[22].

Experimentalevidencehasshownthatthe transition-metalatomsreplacetheTiatomsat B-site[14，15].Calculations have been performed on Na0.5Bi0.5Ti0.84V0.16O3(TM=V，Cr，Mn，F(xiàn)e and Co).

FⅠG.1 The schematic crystal structure of rhombohedral Na0.5Bi0.5TiO3.

The total DOSs of Na0.5Bi0.5Ti0.84V0.16O3(TM=V，Cr，Mn，F(xiàn)e，and Co)are shown in Fig.2(b)-(f).An obvious spin-split in the spin-up and spin-down total DOS at/near the Fermi level can be found.Clearly，V-，Cr-，F(xiàn)e-，and Co-doped Na0.5Bi0.5TiO3are all half-metals and magnetic with 100%spin polarization. The Mn-doped Na0.5Bi0.5TiO3is magnetic semiconductors，because both the majority and minority spin DOSs are zero at the Fermi level and there is a clear spin polarization between the DOSs of the two spin channels around the Fermi level.According to our calculations，the values of magnetic moments are 1.00，2.00，3.00，2.00，and 1.01μBfor 16%V-，Cr-，Mn-，F(xiàn)e-，and Co-doped Na0.5Bi0.5TiO3，respectively.The total energies of the supercell with Na0.5Bi0.5Ti0.84TM0.16O3(TM=V，Cr，Mn，F(xiàn)e and Co)for spin-polarized and nonspin-polarized modes are also calculated.The correspondingenergydifference?EN-M=EN-EM between the total energies of nonmagnetic state ENand the magnetic state EMare 0.12，0.64，1.32，0.47 and 0.07 eV for 16%V-，Cr-，Mn-，F(xiàn)e-，and Codoped Na0.5Bi0.5TiO3，respectively.All the results show that the magnetic state is more stable than the nonmagnetic one.Figure 3(a)-(e)show the spin-density distribution(spin-up minus spin-down) for Na0.5Bi0.5Ti0.84TM0.16O3(TM=V，Cr，Mn，F(xiàn)e，and Co).The spin density is mainly distributed on the TM atoms.

Ⅰn order to further understand the electronic structure，the atom-，orbital-，and spin-projected density of the TM atom(TM=V，Cr，F(xiàn)e and Co)d states，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.4 for V-，Cr-，F(xiàn)e-，and Co-doped Na0.5Bi0.5TiO3. Obviously，the TM 3d 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. As shown in Fig.3(c)-(e)，small induced magnetic moments are also observed for the O atoms.The differencebetween the spin-up and spin-down DOS of O pstates can be found，which can been in Fig.4(a)-(d). The O atoms around the 3d TM atoms are polarized while other O atoms are not.That is to say，the polarized electrons are decided by the distance between the O atom and the TM atom.The spin-projected DOS of spin-up orbitals(or spin-down orbitals)pass through the Fermi level and spin-down orbitals(or spin-up orbitals)can exhibit the characteristics of semiconductor. Therefore，V-，Cr-，F(xiàn)e-，and Co-doped Na0.5Bi0.5TiO3are the half-metal materials.

Subsequently，we perform spin polarized calculations on the Na0.5Bi0.5TiO3supercell with two TM(TM= V，Cr，Mn，F(xiàn)e and Co)atoms substituting for Ti atoms in the lattice.Such substitution corresponds to Na0.5Bi0.5Ti0.67TM0.33O3and the doping level is 33%. Ⅰn the supercell，we investigate three distributions of the two Ti atoms，which are replaced by TM atoms. The three cases are:(i)the two TM atoms are located at the sites of Ti1 and Ti2，respectively，(ii)the two TM atoms are located at the sites of Ti1 and Ti3，respectively，(iii)the two TM atoms are located at the sites of Ti1 and Ti4，respectively.The value of the distance between the two TM atoms located at the sites of Ti1 and Ti5 is too large(more than 9?A)，and the magnetic coupling effect is very weak.Therefore，the case of two TM atoms located at the sites of Ti1 and Ti5 is not meaningful to discuss here.

FⅠG.2 Total density of state of(a)pure Na0.5Bi0.5TiO3，(b)Na0.5Bi0.5Ti0.84V0.16O3，(c)Na0.5Bi0.5Ti0.84Cr0.16O3，(d) Na0.5Bi0.5Ti0.84Mn0.16O3，(e)Na0.5Bi0.5Ti0.84Fe0.16O3and(f)Na0.5Bi0.5Ti0.84Co0.16O3，respectively.The vertical dotted line indicates the Fermi level.

FⅠG.3Three-dimensionaliso-surfacesofmagnetizationdensityfor(a)Na0.5Bi0.5Ti0.84V0.16O3，(b)Na0.5Bi0.5Ti0.84Cr0.16O3，(c)Na0.5Bi0.5Ti0.84Mn0.16O3，(d)Na0.5Bi0.5Ti0.84Fe0.16O3，and(e)Na0.5Bi0.5Ti0.84Co0.16O3. The yellow iso-surfaces represent the spin density of spin up.The iso-value is 0.01 e/?A3.

TABLEⅠDistance between two Ti atoms substituted by TM(TM=V，Cr，Mn，F(xiàn)e，and Co)for the three cases of Na0.5Bi0.5Ti0.67TM0.33O3.

After absolutely optimized，as shown in TableⅠ，the distances between TM(TM=V，Cr，Mn，F(xiàn)e，and Co)atoms for the three cases are almost the same.Ⅰn order to deal with the effect of the magnetic coupling between the two isolated TM atoms，we evaluate the relative energies between ferro-and antiferromagnetically ordered states by LDA+U calculation.TableⅠⅠprovides the energy differences between ferromagnetic state(FM)and antiferromagnetic state(AFM) as well as magnetic moments of two TM atoms doping.Here，?Em=EAFM-EFMrepresents energy difference between antiferromagnetic state and ferromagnetic state after optimization，which enables us to estimate stable states of magnetism coupling.?Em＞0 indicates that the ferromagnetic state is more stable than the antiferromagnetic state，while?Em＜0 indicates that the antiferromagnetic state is more stable than the ferromagnetic state.The energy differences?E of structures with different distance between the two TM atoms substitution for Ti atoms in Na0.5Bi0.5TiO3are also listed in TableⅠⅠ.By comparing the total energies of the above three cases for Na0.5Bi0.5Ti0.67TM0.33O3(TM=V，Cr，Mn，F(xiàn)e，and Co)，we find that the type of preferential magnetic coupling of system depends upon both the doped transition-metal atoms and the distributions of the Ti atoms substituted.

For the Na0.5Bi0.5Ti0.67TM0.33O3(TM=Fe and Co) system，when the two Fe/Co atoms are located at the sites of Ti1 and Ti2，the system with antiferromagnetic coupling has the lowest energy among the three cases；For the Na0.5Bi0.5Ti0.67TM0.33O3(TM=Cr and Mn) system，when the two Cr/Mn atoms are located at the sites of Ti1 and Ti3，the system with antiferromagnetic coupling has the lowest energy among the three cases. Wang et al.reported experimentally that，as Mn ions doping concentration was increased to 20%，the Mndoped Na0.5Bi0.5TiO3sample shows a strong ferromagnetism at room temperature.However，with further increasing the doping concentration of Mn ions up to 30%，the paramagnetic component becomes stronger[15]. Duan et al.found the ferromagnetism disappeared at 10 K and indicated that inside the Na0.5Bi0.5Ti1-xMnxO3particles，the antiferromagnetic coupling between the Mn ions can be formed[23]，which conformed our calculation results.For the Na0.5Bi0.5Ti0.67V0.33O3system，when the two V atoms are located at the sites of Ti1 and Ti2，the system with ferromagnetic coupling has the lowest energy among the three cases and produces amagnetic moment of 2.00μB，indicating that low temperature ferromagnetism materials could be made by introducing V atoms in Na0.5Bi0.5TiO3.This may be a new way to produce multiferroic materials.

FⅠG.4 Partial DOS of TM d states，Na s，p states，Bi s，p，d states，Ti s，p，d states，V d states，and O p states for Na0.5Bi0.5Ti0.84TM0.16O3and TM=(a)V，(b)Cr，(c)Fe and(d)Co，respectively.The vertical dotted line indicates the Fermi level.

TABLEⅠⅠThe relative energies of the states FM and AFM(?Em=EAFM-EFM)，values of the relative stabilities?E，calculated for the Na0.5Bi0.5Ti0.67TM0.33O3(TM=V，Cr，Mn，F(xiàn)e，and Co).

IV.CONCLUSION

We explore the structural，electronic and magnetic properties of TM-doped(TM=V，Cr，Mn Fe and Co) Na0.5Bi0.5TiO3alloys via the first-principles PAW potential within DFT，employing the exchange-correlation potential provided by the LDA+U.The results demonstrate that，for Na0.5Bi0.5TiO3system，magnetic moments can be induced when one Ti atom is substituted by a TM atom.On the electronic structures，the analyses of total DOSs indicate that V-，Cr-，F(xiàn)eand Co-doped Na0.5Bi0.5TiO3alloys are all half-metals and magnetic with 100%spin polarization.Ⅰt also can be found that the magnetic phase is energetically preferred to the nonmagnetic phase for all the Na0.5Bi0.5Ti0.84TM0.16O3(TM=V，Cr，Mn，F(xiàn)e and Co) systems.For V-，Cr-，F(xiàn)e-and Co-doped Na0.5Bi0.5TiO3alloys，the results of spin-projected DOS show that the spin splitting mainly comes from TM3d states. Small magnetic moments are also observed for the O atoms，which are due to the small spin polarization of p-states of O atoms.We also compared the energies of ferromagnetic and antiferromagnetic couplings between two TM(TM=V，Cr，Mn，F(xiàn)e and Co)atoms substitutions in Na0.5Bi0.5TiO3supercell，in which we investigate three distributions.For Cr-/Mn-/Fe-/Codoped Na0.5Bi0.5TiO3system，antiferromagnetic coupling is more stable.The results can successfully explain the experimental phenomenon that，in Mn/Fe doped Na0.5Bi0.5TiO3system，the ferromagnetism disappears at low temperature and the paramagnetic component becomes stronger with the increase of doping concentration of Mn/Fe/Co ions.Furthermore，we find the Na0.5Bi0.5Ti0.67V0.33O3system with ferromagnetic coupling is favorable and produces a magnetic moment of 2.00μB，which indicating that low temperature ferromagnetism materials could be made by introducing V atoms in Na0.5Bi0.5TiO3.This may be a new way to produce low temperature multiferroic materials.

V.ACKNOWLEDGMENTS

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

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