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Copyright copy 2010 American Scientific PublishersAll rights reservedPrinted in the United States of America

Science ofAdvanced Materials

Vol 2 184ndash189 2010

Effect of Mn Substitution for Fe in MultiferroicBiFeO3 A First-Principles Study

Hai Wang1 Haitao Huang1lowast and Biao Wang21Department of Applied Physics and Materials Research Center The Hong Kong Polytechnic University Hong Kong China

2School of Physics and Engineering Sun Yat-sen University Guangzhou 510275 China

The effect of B-site Mn doping on the structural electronic and magnetic properties of multiferroicBiFe1minusxMnxO3 (0lex le 05) systems has been investigated based on the first-principles calculationswithin the density functional theory using virtual crystal approximation (VCA) Our structural param-eters of pure BiFeO3 agree well with experimental values and previous theoretical results B-site Mndoping has significant effect on the electronic and magnetic properties of BiFeO3 which are deter-mined by Fe 3dminusO 2p and Fe 3dminusFe 3d interactions The induced magnetism may beascribedto the superexchange interaction of Fe3+ndashO2+ndashMn3+ The total magnetization depends on the Mncontent rather than the volume effect of unit cell The results may shed some light on the controllingand tuning of the multiferroic properties of BiFeO3

Keywords First Principles Multiferroic BFO

1 INTRODUCTION

Recently magnetoelectric or multiferroic materials haveattracted increasing attention12 owing to the rich physicalphenomena resulting from multi-order parameter interac-tions and promising potential applications on the magneticcontrol of ferroelectric polarization and vice versa3 Indeedthere are few magnetic ferroelectrics in nature becauseferroelectricity seems to suppress magnetism4 Althoughsome multiferroic composite materials show large mag-netoelectric effect5 single phase multiferroic materialswith strong coupling of ferroelectric and magnetic order-ings are still attractive6 Among them BiFeO3 (BFO) isan interesting multiferroic oxide at room temperature Itexhibits both ferroelectricity with high Curie tempera-ture (TC asymp 830 C) and G-type antiferromagnetic proper-ties below TN (asymp370 C)7 The antiferromagnetic natureof BFO results in weak magnetism and weak magneto-electric coupling of BFO8 Therefore in order to inducemagnetism the spiral magnetic structure of BFO shouldbe destroyed For example it can be done by doping ofother ions or by making low-dimensional structures9 in theform of thin films10 or nanoparticles11 First principles cal-culation has predicted that the spontaneous polarization ofBFO single crystal is as high as 100 Ccm212 HoweverBFO films often show a polarization one order of magni-tude lower than the theoretical value due to sizable leakage

lowastAuthor to whom correspondence should be addressed

current There have been extensive efforts to reduce theleakage current through doping a small amount of otherelements at A- (such as Ca Sr Ba Pb13 and La14) orB-site (such as Cr15 Sc16 and Ti17)Here we focus on Mn-doped BFO which exhibits a

magnetocapacitance effect18 at room temperature betterproperties in terms of leakage current19 and better mul-tiferroic properties20 In fact BiFeO3 and BiMnO3 werefound to form a solid solution in the entire composi-tion range when prepared at a high pressure of severalGPa BiFe1minusxMnxO3 (BFM) system has an orthorhom-bic structure in the composition range of 02 le x le 06while BiMnO3-type monoclinic structure appears whenx ge 0621 In the BFM system only when x le 02 was itfound to possess a polar BiFeO3-type structure and weakferromagnetic moment at room temperature By contrastit was reported that the BFO-type rhombohedral structurecan be preserved up to 30 of Mn in the BFM system byusing different preparation methods1822 Further increasein the Mn content up to 50 while maintaining the rhom-bohedral structure in BFM can be achieved by co-dopingof La at the A-site23 As Mn content is increased the lat-tice constants (a and c and unit cell volume decreasewhile ca ratio is basically unchanged suggesting that thecrystal shape remains unchanged It is well-known that Mndoped BFO results in a magnetic ordering transition egfrom the long-range spiral spin antiferromagnetic orderingto a collinear antiferromagnetic ordering with spins alongc axis Both the structures before and after the transition

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Wang et al Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study

are of G-type antiferromagnetic one2425 The experimen-tal data on the effect of Mn-doping however seem tobe quite contradictory On one hand magnetization reduc-tion was reported in 5 Mn-doped BFO system26 On theother hand Mn doped BFO system gave rise to a spon-taneous magnetization that increased with increasing Mncontent20ndash22 The enhanced magnetization was attributed toeither the canting of antiferromagnetically ordered spinsby structural distortions27 or the breakdown of the balancebetween antiparallel sublattice magnetization of Fe3+ dueto the substitution of metal ions with a different valence28

Up to now the optimum composition in the BFM sys-tem is still unclear Also unclear are the factors (eg vol-ume effect or local structural distortion) that control themultiferroic properties of BFM A comprehensive under-standing on the effect of Mn doping on structural elec-tronic and magnetic properties of BFO is still lackingalthough a dozen of theoretical papers on BFO has beenpublished8122930

2 METHOD

In this work a series of B-site Mn-doped hypotheti-cal crystals BiFe1minusxMnxO3 (x = 0010203 and 05)were selected for first principles study The calculationswere performed using highly accurate full-potential lin-earized augmented plane-wave method (FP-LAPW) asimplemented in WIEN2k code31 Exchange and correlationeffects are treated within the generalized gradient approxi-mation (GGA)32 The muffin-tin radii are 25 20 20 and16 au for Bi Fe Mn and O respectively To control thesize of basis set for the wave functions RmtKmax was set to80 The well-converged basis sets consist of about 1023LAPW functions and 86 local orbitals chosen for O 2s Fe3p Fe 3d and Bi 6p states Integrations in the recipro-cal space were performed by using improved tetrahedronmethod33 and a 12times 12times 12 mesh was used to represent292 k-points in the irreducible Brillouin zone (BZ)To examine the effect of Mn substitution on the

multiferroic properties of BFO we have calculated the

Table I Experimental and calculated lattice constant a (Aring) rhombohedral angel (deg) unit cell volume V (Aring3 and atomic fractional coordinateswhere a rhombohedral symmetry was assumed Here PAW represents projector augmented wave method NCPP and USPP stand for norm-conservingand ultrasoft pseudopotential respectively

a V V Vexp Fe (x x x O (x y z

Expa 56343 59348 12460 02208 05279 03948 09333Expb 56301 59343 12430 02207 0523 0422 0939Expc 56370 59344 12477 02208 05244 03972 09344Expd 56345 59348 12461 02199 05267 09367 03961Cale 54590 60360 11598 minus69 02308 05423 09428 03980Calf 55000 60180 11500 minus69 02310 0399 0541 0946Calg 56970 59235 12848 31 02232 05342 09357 03865Calh 56600 57320 12043 minus33 02210 0530 0936 0389Cali 56720 59240 12772 25 02240 05353 09367 03882

aReference [11] bReference [47] cReference [31] dReference [48] eReferences [12 18] VASP-PAW-LDA fReferences [42 43] ABINIT-NCPP-LDA gReference [41]VASP-PAW-GGA hReference [49] PWSCF-USPP-LDA iPresent work WIEN2k-FP-LAPW-GGA

structural electronic and magnetic properties of BFMwith different Mn contents using the virtual crystalapproximation (VCA) method Our calculations presentedhere employed the experimental lattice parameters724

where inner atomic coordinates were optimized The opti-mizations were performed using the MINI package ofWIEN2k The rhombohedral structure with space groupR3 (No 146) was used for VCA calculations In the rhom-bohedral structure set Bi and Fe ions occupy the wyckoffposition 1a (x x x with O ions at 3b (x y z Forthe composition of BiFe05Mn05O3 apart from the VCAmethod we have also conducted the calculation based ona supercell structure consisting of two BFO formula unitswith one of the two Fe sites replaced by Mn

3 RESULTS AND DISCUSSION

31 Structure

Pure BiFeO3 has a rhombohedral structure with spacegroup R3c where Bi atom sits at the origin7 First ofall we performed full structural optimization of the lat-tice parameters and the atomic positions for pure BiFeO3The structural parameters obtained are listed in Table IIn our calculations the homogeneous and collinear G-typeantiferromagnetic structure rather than the real spiral spinstructure were used Similar approximation was also usedin pure BFO12 Our results are in better agreement withexperimental values than othersrsquo work because of the useof FP-LAPW method It is clear that GGA is necessary forthe correct prediction of the equilibrium volume and innerstructural distortions This is consistent with a conclusiondrawn from the first-principles calculations on BFO29 Inaddition VASP-PAW-GGA method29 is found to give thesame accurate resultsTable II shows calculated structural parameters of pure

BFO and doped BFM systems with different Mn con-tents The results reveal that the addition of Mn ionsinduces larger off-center displacements than those in pureBFO system suggesting observable structural distortion

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Table II Calculated structure parameters of BFM with differentMn contents (0 10 20 30 and 50) using VCA method and theexperimental structure parameters of pure BFO11 BFM50 stands forBiFe05Mn05O3 supercell with one of the Fe sites substituted by Mn Therhombohedral structure with space group R3 (No 146) and the exper-imental structural parameters of BFO were adopted in the calculationBi and FeMn ions locate at 1a (x x x while O ions at 3b (x y z

0 10 20 30 50 BFM50

Bi1x 00000 00000 00000 00000 00000 00000Bi2x 05000 04996 04996 04992 04990 04959Fe1x 02254 02259 02247 02226 02216 02235Fe2x 07254 07261 07256 07247 07263 07127O1x 05405 05412 05391 05355 05324 05315O1y 09399 09415 09412 09431 09472 09257O1z 03888 03882 03882 03878 03891 03825O2x 00406 00441 00432 00439 00474 00441O2y 08888 08896 08903 08925 08973 08808O2z 04399 04385 04382 04365 04338 04387

within rhombohedral symmetry This is consistent withthe experimental observations24 atomic thermal displace-ments increase with increasing Mn content As Mn contentincreases the structural distortions decrease only slightlywithout substantial variation We have recalculated thestructure parameters by using the experimental values24 ofMn-doped BFO and have found that the same conclusioncan be obtained The total energy ofBiFe05Mn05O3 calculated by VCA method is lower than

that of BFM50 supercell with one of the two Fe ionsreplaced by Mn This indicates that random arrangementof Fe and Mn ions is more energetically favorable In addi-tion the doping of Mn ions into BFO sharply increases itstotal energy indicating that introduction of Mn into BFO

Fig 1 Majority spin band structure of pure antiferromagnetic BFO (left panel) and BFM50 (right panel) along high-symmetry directions in BZ

is difficult as suggested by Bi et al34 We have also per-formed the volume optimization on BFM with different Mncontents and the results (not shown here) obtained con-firm what is experimentally observed23 that is as the Mnconcentration increases both the lattice constants a and cdecrease as well as unit cell volume while ca ratio isbasically unchanged

32 Electronic Properties

For pure BFO the major spin band structure equals tothe minor spin band structure due to its antiferromagneticnature The introduction of Mn into BFO has a significanteffect on the majority spin band structure which bringsabout a larger band-gap while its effect on the minor-ity spin band structure is negligible Shown in Figure 1are the calculated band structures of pure BFO and 50Mn BFM systems along the high-symmetry directions inthe BZ (only majority spin states are shown) Here theFermi level is located at the top of valence band and isset to 0 eV For pure BFO in the valence band (VB) theenergy band located at the lowest region of [minus19minus17] eVis mainly occupied by O 2s states The bands at aboutminus10 eV are Bi 6s states The upper part of VB around[minus7 0] eV is dominated by Fe 3d states mixed with someO 2p and lesser Bi 6p states The conduction band (CB)region at about 1 to 3 eV is dominated by Fe 3d states Bi6p states occupy the region of36 eV Above 8 eV strongmixing occurs among Bi 6p Fe 3d and O 2p states Thetop of VB is located between ndashZ (only 0015 eV higherthan the energy at Z) very close to Z while the bottomof the conduction band sits at Z point Hence an indirect

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Wang et al Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study

(very close to direct) band gap of 106 eV is formedbetween the top of the O 2p valence band and the bottomof the Fe 3d conduction band The calculated band gapis very close to the experimental value of 13 eV 35 andprevious theoretical results1236 The electrical propertiesof BFO is determined by charge transfers from the occu-pied O 2p to unoccupied Fe 3d states and dndashd transitionbetween Fe 3d valence and conduction bands35 Our calcu-lated band structures agree quite well the results obtainedby VASP-PAW method12 indicating the latter is as preciseas the FP-LAPW method used in this study The electronicband structures of Mn-doped BFO are found to be quitesimilar to those of pure BFOFigure 2 shows the total density of states of pure and

Mn-doped BiFeO3 Because Mn doping is hole dopingthe Fermi level of BFM systems should be shifted down-ward as compared to pure BFO and electrons will fillholes in the Mn 3d band For 50 Mn-doped BFM sys-tem its spin-up band gap is about 10 eV greater thanthat in pure BFO while the spin-down band gap remainsessentially unchanged As found by Neaton et al12 theFe partial density of states in BFO is quite different forthe two spin states (spin up and spin down Fe1 and Fe2respectively) From the partial density of states of Fe (notshown here) one can draw the conclusion that Fe existsin +3 oxidation state in pure BFO compound indicating ad5 high-spin electronic configuration (detailed explanationcan be found in Ref [37]) Likewise Mn also exists inthe +3 oxidation state Based on the ionic radii of FeMnin six-coordinate octahedral environment the combinationof Fe2+Mn4+ ions has an average ionic radius of 079 Aringwhich is slightly larger than that of Fe3+38 Therefore theunit cell volume of BFM system with Fe2+Mn4+ oxida-tion state should be higher than that of pure BFO This is

Fig 2 Total density of states in pure 10 and 50 Mn-doped BFOsystems (only the majority spin states are shown while the minority spinstates of doped BFO are similar to the majority spin states of pure BFO)The top of the valence band is set at 0 eV

contradictory to the experimental results23 where no bigdifference in unit cell volume was found Since the aver-age ionic radius of the Fe3+Mn3+ couple is closer to thatof Fe3+ ions in pure BFO both Fe and Mn in BFM systemare likely to be in the +3 oxidation state Moumlssbauer andXPS measurements on La01Bi09Fe1minusxMnxO3 revealed thatall Fe ions exist in the +3 oxidation states and hence Mnsubstitution does not introduce any mixed valence into thesystem25 Recently X-ray absorption spectroscopy39 showsthat mixed valence states of Fe2+ and Fe3+ exist in pureBFO and Mn-doped BFO However since the content ofFe2+ does not change with the introduction of Mn dopantthe existence of Fe2+ can be ascribed to oxygen vacanciesrather than Mn doping39

33 Magnetic Properties

Because Fe and Mn are magnetic ions we first examinedthe stability of magnetic ordering of B-site Fe and Mnatoms It is found that the antiferromagnetic ordering isstable for BFO and it gives a ferrimagnetic structure forthe ground-state of BFM The calculated total and localmagnetic moment (MM) of BFM with different Mn con-tents are given in Table III It is shown that pure BFOhas an antiferromagnetic nature and the total MM is zeroalthough local MMs are not exactly equal Local MM ofBi is very small since Bi is strongly diamagnetic Fe ionhas the largest local MM (369 B) which is very closeto the experimental value7 (375 B) and previous theoret-ical one30 (365 B) It is greatly reduced from the formalvalue of 5 B for high-spin Fe3+ ions Similarly the cal-culated local MM value of Mn (about 3 B) is also muchsmaller than the formal value of 4 B for high spin Mn3+

ions The reduction of local MM is caused by the strongFeMn 3dndashO 2p hybridization In addition O ions alsohave a slight MM of 007 B which is the result of thehybridization between Fe 3d and O 2p states The oxygenMM values are about two orders of magnitude smaller thanthose of FeMn (see Table II) and hence FeMn ions arethe main source of magnetism in BFM Previous theoret-ical calculations have shown that the canting of magneticmoments was not significantly affected by the presence of

Table III Calculated total and local magnetic moment (Bfu) ofBFM with different Mn contents (0 10 20 30 and 50) using VCAmethod BFM50 stands for the calculated results based on BiFe05Mn05O3

supercell with one of the Fe sites substituted by Mn The experimentalstructural parameters of BFO11 were used for all the calculations

0 10 20 30 50 BFM50

Bi1 minus0003 +0001 +0003 +0005 +0006 minus0004Bi2 +0003 +0003 +0006 +0008 +0010 minus0006Fe1 +3689 +3598 +3514 +3382 +3175 minus3673Fe2 minus3690 minus3748 minus3812 minus3861 minus3907 +3142O1 +0069 +0044 +0035 +0021 +0012 +0112O2 minus0068 minus0058 minus0062 minus0054 minus0053 +0033Total 0 minus0200 minus0400 minus0600 minus1000 minus1000

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Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study Wang et al

oxygen vacancies and no increase in macroscopic magne-tization due to oxygen vacancies could be found37 Henceoxygen vacancies cannot be considered as the main reasonfor the suppression of spin modulation40

Experimentally there are contradictory reports on theMn-doping effect on magnetic properties of BFM It isreported that the average MM and the ordering tempera-ture decrease with increasing Mn concentration in BFMsystem1824 Naganuma et al26 reported that 5 Mn-doping has negligible effect on the magnetization behaviorA general trend of increased magnetization with increasingMn content in BFM has also obtained a lot of experimentalsupports2122 The calculated spontaneous magnetization(eg total MM) of BFM which increases linearly withincreasing Mn content is consistent with this trend2022

We believe that the total magnetization in BFM comesfrom the FendashOndashMn antiferromagnetic superexchange inter-actions rather than the antiferromagnetic superexchangeinteractions of FendashOndashFe and MnndashOndashMn which basicallycancel the magnetization of BFM system Similar phe-nomenon has been found in LaFeO3ndashLaCrO3 systems41

Recent study on Bi2FeMnO6 epitaxial thin films also sup-ported this mechanism36 When Mn content is 50 theinduced magnetic moment is about 10 B per FendashMncouple which is expected for the antiferromagnetic order-ing between Fe3+ and Mn3+ ionsPure BFO shows a pressure-induced magnetic transi-

tion from high-spin state to low-spin one42 Here we havestudied the pressure effect by examining the volume depen-dence of the total and local MMs in BFM systems with 10and 50 Mn and the results are given in Tables IV and Vrespectively It is found that the total MM in BFM is inde-pendent of the unit cell volume while the local MM isclosely related to the volume effect The local MMs onFe and O sites increase with increasing unit cell volumewhile those on Bi sites show the opposite trend In addi-tion the contribution from A-site Bi ions to the total mag-netization of BFM systems is very small since its localMM is one and three orders of magnitude smaller thanthat on O and Fe sites respectively With increasing Mncontent a small but linear enhancement in magnetizationcan be observed23 This may be due to the fact that therandom positioning of Fe and Mn ions has frustrated the(anti)ferromagnetic properties41

Table IV Calculated local magnetic moment (Bfu) of BFM with10 Mn under different unit cell volumes V0 stands for the theoreticalequilibrium volume The total MM equals to minus0200 Bfu which isindependent of the unit cell volume

096 V0 098 V0 100 V0 102 V0 104 V0

Bi1 0002 0001 0001 0001 minus0001Bi2 0001 0002 0002 0003 minus0003Fe1 3492 +3519 3539 3560 3576Fe2 minus3646 minus3669 minus3689 minus3705 minus3719O1 0041 +0043 0045 0047 0049O2 minus0054 minus0057 minus0059 minus0062 0065

Table V Calculated local magnetic moment (Bfu) of BFM with50 Mn under different unit cell volume V0 stands for the theoreticalequilibrium volume The total MM equal to +100 Bfu which isindependent of the unit cell volume

096 V0 098 V0 10 V0 102 V0 104 V0

Bi1 minus0009 minus0010 minus0010 minus0011 minus0012Bi2 minus0009 minus0008 minus0007 minus0006 minus0005Fe1 3535 3558 3577 3589 3600Fe2 minus2827 minus2875 minus2914 minus2946 minus2977O1 0091 0097 0101 0106 0111O2 0024 0026 0028 0029 0031

4 CONCLUSIONS

In summary we have examined the effect of Mn doping onthe structural electronic and magnetic properties of BFOsystem based on first-principles calculations Our resultsconfirm the multiferroic properties of Mn-doped BFO sys-tem DOS and local MM suggest that both Fe and Mn ionsare in +3 oxidation state The spontaneous magnetizationof the system is dependent on Mn content while indepen-dent of the unit cell volume and local structural distortionssuggesting the highly stable magnetism Our results maybe effective for other B-site doped BFO systems

Acknowledgments This work was supported by grantsfrom the Research Grants Council of the Hong Kong Spe-cial Administrative Region (Project PolyU 517107E) andfrom the Hong Kong Polytechnic University (Projects NoG-YF71 and G-YH07)

References and Notes

1 M Fiebig J Phys D Appl Phys 38 R123 (2005)2 W Eerenstein N D Mathur and J F Scott Nature 442 759 (2006)3 T Lottermoser T Lonkai U Amann D Hohlwein J Ihringer and

M Fiebig Nature 430 541 (2004)4 N A Hill J Phys Chem B 104 6694 (2000)5 H Huang and L M Zhou J Phys D Appl Phys 37 3361 (2004)6 T Zhao A Scholl F Zavaliche K Lee M Barry A Doran M P

Cruz Y H Chu C Ederer N A Spaldin R R Das D M KimS H Baek C B Eom and R Ramesh Nature Mater 5 823 (2006)

7 F Kubel and H Schmid Acta Crystallogr B 46 698 (1990)8 C Ederer and N A Spaldin Phys Rev B 71 060401 (2005)9 J Chen X R Xing A Watson W Wang R B Yu J X Deng

L Yan C Sun and X B Chen Chem Mater 19 3598 (2007)10 R Ramesh and N A Spaldin Nature Mater 6 21 (2007)11 T J Park G C Papaefthymiou A J Viescas A R Moodenbaugh

and S S Wong Nano Lett 7 766 (2007)12 J B Neaton C Ederer U V Waghmare N A Spaldin and K M

Rabe Phys Rev B 71 014113 (2005)13 V A Khomchenko D A Kiselev J M Vieira A L Kholkin

M A Sa and Y G Pogorelov Appl Phys Lett 90 242901 (2007)14 Y H Lee J M Wu and C H Lai Appl Phys Lett 88 042903

(2006)15 P Baettig C Ederer and N A Spaldin Phys Rev B 72 214105

(2005)16 S R Shannigrahi A Huang N Chandrasekhar D Tripathy and

A O Adeyeye Appl Phys Lett 90 022901 (2007)17 X D Qi J Dho R Tomov M G Blamire and J L MacManus-

Driscoll Appl Phys Lett 86 062903 (2005)

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Wang et al Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study

are of G-type antiferromagnetic one2425 The experimen-tal data on the effect of Mn-doping however seem tobe quite contradictory On one hand magnetization reduc-tion was reported in 5 Mn-doped BFO system26 On theother hand Mn doped BFO system gave rise to a spon-taneous magnetization that increased with increasing Mncontent20ndash22 The enhanced magnetization was attributed toeither the canting of antiferromagnetically ordered spinsby structural distortions27 or the breakdown of the balancebetween antiparallel sublattice magnetization of Fe3+ dueto the substitution of metal ions with a different valence28

Up to now the optimum composition in the BFM sys-tem is still unclear Also unclear are the factors (eg vol-ume effect or local structural distortion) that control themultiferroic properties of BFM A comprehensive under-standing on the effect of Mn doping on structural elec-tronic and magnetic properties of BFO is still lackingalthough a dozen of theoretical papers on BFO has beenpublished8122930

2 METHOD

In this work a series of B-site Mn-doped hypotheti-cal crystals BiFe1minusxMnxO3 (x = 0010203 and 05)were selected for first principles study The calculationswere performed using highly accurate full-potential lin-earized augmented plane-wave method (FP-LAPW) asimplemented in WIEN2k code31 Exchange and correlationeffects are treated within the generalized gradient approxi-mation (GGA)32 The muffin-tin radii are 25 20 20 and16 au for Bi Fe Mn and O respectively To control thesize of basis set for the wave functions RmtKmax was set to80 The well-converged basis sets consist of about 1023LAPW functions and 86 local orbitals chosen for O 2s Fe3p Fe 3d and Bi 6p states Integrations in the recipro-cal space were performed by using improved tetrahedronmethod33 and a 12times 12times 12 mesh was used to represent292 k-points in the irreducible Brillouin zone (BZ)To examine the effect of Mn substitution on the

multiferroic properties of BFO we have calculated the

Table I Experimental and calculated lattice constant a (Aring) rhombohedral angel (deg) unit cell volume V (Aring3 and atomic fractional coordinateswhere a rhombohedral symmetry was assumed Here PAW represents projector augmented wave method NCPP and USPP stand for norm-conservingand ultrasoft pseudopotential respectively

a V V Vexp Fe (x x x O (x y z

Expa 56343 59348 12460 02208 05279 03948 09333Expb 56301 59343 12430 02207 0523 0422 0939Expc 56370 59344 12477 02208 05244 03972 09344Expd 56345 59348 12461 02199 05267 09367 03961Cale 54590 60360 11598 minus69 02308 05423 09428 03980Calf 55000 60180 11500 minus69 02310 0399 0541 0946Calg 56970 59235 12848 31 02232 05342 09357 03865Calh 56600 57320 12043 minus33 02210 0530 0936 0389Cali 56720 59240 12772 25 02240 05353 09367 03882

aReference [11] bReference [47] cReference [31] dReference [48] eReferences [12 18] VASP-PAW-LDA fReferences [42 43] ABINIT-NCPP-LDA gReference [41]VASP-PAW-GGA hReference [49] PWSCF-USPP-LDA iPresent work WIEN2k-FP-LAPW-GGA

structural electronic and magnetic properties of BFMwith different Mn contents using the virtual crystalapproximation (VCA) method Our calculations presentedhere employed the experimental lattice parameters724

where inner atomic coordinates were optimized The opti-mizations were performed using the MINI package ofWIEN2k The rhombohedral structure with space groupR3 (No 146) was used for VCA calculations In the rhom-bohedral structure set Bi and Fe ions occupy the wyckoffposition 1a (x x x with O ions at 3b (x y z Forthe composition of BiFe05Mn05O3 apart from the VCAmethod we have also conducted the calculation based ona supercell structure consisting of two BFO formula unitswith one of the two Fe sites replaced by Mn

3 RESULTS AND DISCUSSION

31 Structure

Pure BiFeO3 has a rhombohedral structure with spacegroup R3c where Bi atom sits at the origin7 First ofall we performed full structural optimization of the lat-tice parameters and the atomic positions for pure BiFeO3The structural parameters obtained are listed in Table IIn our calculations the homogeneous and collinear G-typeantiferromagnetic structure rather than the real spiral spinstructure were used Similar approximation was also usedin pure BFO12 Our results are in better agreement withexperimental values than othersrsquo work because of the useof FP-LAPW method It is clear that GGA is necessary forthe correct prediction of the equilibrium volume and innerstructural distortions This is consistent with a conclusiondrawn from the first-principles calculations on BFO29 Inaddition VASP-PAW-GGA method29 is found to give thesame accurate resultsTable II shows calculated structural parameters of pure

BFO and doped BFM systems with different Mn con-tents The results reveal that the addition of Mn ionsinduces larger off-center displacements than those in pureBFO system suggesting observable structural distortion

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Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study Wang et al

Table II Calculated structure parameters of BFM with differentMn contents (0 10 20 30 and 50) using VCA method and theexperimental structure parameters of pure BFO11 BFM50 stands forBiFe05Mn05O3 supercell with one of the Fe sites substituted by Mn Therhombohedral structure with space group R3 (No 146) and the exper-imental structural parameters of BFO were adopted in the calculationBi and FeMn ions locate at 1a (x x x while O ions at 3b (x y z

0 10 20 30 50 BFM50

Bi1x 00000 00000 00000 00000 00000 00000Bi2x 05000 04996 04996 04992 04990 04959Fe1x 02254 02259 02247 02226 02216 02235Fe2x 07254 07261 07256 07247 07263 07127O1x 05405 05412 05391 05355 05324 05315O1y 09399 09415 09412 09431 09472 09257O1z 03888 03882 03882 03878 03891 03825O2x 00406 00441 00432 00439 00474 00441O2y 08888 08896 08903 08925 08973 08808O2z 04399 04385 04382 04365 04338 04387

within rhombohedral symmetry This is consistent withthe experimental observations24 atomic thermal displace-ments increase with increasing Mn content As Mn contentincreases the structural distortions decrease only slightlywithout substantial variation We have recalculated thestructure parameters by using the experimental values24 ofMn-doped BFO and have found that the same conclusioncan be obtained The total energy ofBiFe05Mn05O3 calculated by VCA method is lower than

that of BFM50 supercell with one of the two Fe ionsreplaced by Mn This indicates that random arrangementof Fe and Mn ions is more energetically favorable In addi-tion the doping of Mn ions into BFO sharply increases itstotal energy indicating that introduction of Mn into BFO

Fig 1 Majority spin band structure of pure antiferromagnetic BFO (left panel) and BFM50 (right panel) along high-symmetry directions in BZ

is difficult as suggested by Bi et al34 We have also per-formed the volume optimization on BFM with different Mncontents and the results (not shown here) obtained con-firm what is experimentally observed23 that is as the Mnconcentration increases both the lattice constants a and cdecrease as well as unit cell volume while ca ratio isbasically unchanged

32 Electronic Properties

For pure BFO the major spin band structure equals tothe minor spin band structure due to its antiferromagneticnature The introduction of Mn into BFO has a significanteffect on the majority spin band structure which bringsabout a larger band-gap while its effect on the minor-ity spin band structure is negligible Shown in Figure 1are the calculated band structures of pure BFO and 50Mn BFM systems along the high-symmetry directions inthe BZ (only majority spin states are shown) Here theFermi level is located at the top of valence band and isset to 0 eV For pure BFO in the valence band (VB) theenergy band located at the lowest region of [minus19minus17] eVis mainly occupied by O 2s states The bands at aboutminus10 eV are Bi 6s states The upper part of VB around[minus7 0] eV is dominated by Fe 3d states mixed with someO 2p and lesser Bi 6p states The conduction band (CB)region at about 1 to 3 eV is dominated by Fe 3d states Bi6p states occupy the region of36 eV Above 8 eV strongmixing occurs among Bi 6p Fe 3d and O 2p states Thetop of VB is located between ndashZ (only 0015 eV higherthan the energy at Z) very close to Z while the bottomof the conduction band sits at Z point Hence an indirect

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Wang et al Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study

(very close to direct) band gap of 106 eV is formedbetween the top of the O 2p valence band and the bottomof the Fe 3d conduction band The calculated band gapis very close to the experimental value of 13 eV 35 andprevious theoretical results1236 The electrical propertiesof BFO is determined by charge transfers from the occu-pied O 2p to unoccupied Fe 3d states and dndashd transitionbetween Fe 3d valence and conduction bands35 Our calcu-lated band structures agree quite well the results obtainedby VASP-PAW method12 indicating the latter is as preciseas the FP-LAPW method used in this study The electronicband structures of Mn-doped BFO are found to be quitesimilar to those of pure BFOFigure 2 shows the total density of states of pure and

Mn-doped BiFeO3 Because Mn doping is hole dopingthe Fermi level of BFM systems should be shifted down-ward as compared to pure BFO and electrons will fillholes in the Mn 3d band For 50 Mn-doped BFM sys-tem its spin-up band gap is about 10 eV greater thanthat in pure BFO while the spin-down band gap remainsessentially unchanged As found by Neaton et al12 theFe partial density of states in BFO is quite different forthe two spin states (spin up and spin down Fe1 and Fe2respectively) From the partial density of states of Fe (notshown here) one can draw the conclusion that Fe existsin +3 oxidation state in pure BFO compound indicating ad5 high-spin electronic configuration (detailed explanationcan be found in Ref [37]) Likewise Mn also exists inthe +3 oxidation state Based on the ionic radii of FeMnin six-coordinate octahedral environment the combinationof Fe2+Mn4+ ions has an average ionic radius of 079 Aringwhich is slightly larger than that of Fe3+38 Therefore theunit cell volume of BFM system with Fe2+Mn4+ oxida-tion state should be higher than that of pure BFO This is

Fig 2 Total density of states in pure 10 and 50 Mn-doped BFOsystems (only the majority spin states are shown while the minority spinstates of doped BFO are similar to the majority spin states of pure BFO)The top of the valence band is set at 0 eV

contradictory to the experimental results23 where no bigdifference in unit cell volume was found Since the aver-age ionic radius of the Fe3+Mn3+ couple is closer to thatof Fe3+ ions in pure BFO both Fe and Mn in BFM systemare likely to be in the +3 oxidation state Moumlssbauer andXPS measurements on La01Bi09Fe1minusxMnxO3 revealed thatall Fe ions exist in the +3 oxidation states and hence Mnsubstitution does not introduce any mixed valence into thesystem25 Recently X-ray absorption spectroscopy39 showsthat mixed valence states of Fe2+ and Fe3+ exist in pureBFO and Mn-doped BFO However since the content ofFe2+ does not change with the introduction of Mn dopantthe existence of Fe2+ can be ascribed to oxygen vacanciesrather than Mn doping39

33 Magnetic Properties

Because Fe and Mn are magnetic ions we first examinedthe stability of magnetic ordering of B-site Fe and Mnatoms It is found that the antiferromagnetic ordering isstable for BFO and it gives a ferrimagnetic structure forthe ground-state of BFM The calculated total and localmagnetic moment (MM) of BFM with different Mn con-tents are given in Table III It is shown that pure BFOhas an antiferromagnetic nature and the total MM is zeroalthough local MMs are not exactly equal Local MM ofBi is very small since Bi is strongly diamagnetic Fe ionhas the largest local MM (369 B) which is very closeto the experimental value7 (375 B) and previous theoret-ical one30 (365 B) It is greatly reduced from the formalvalue of 5 B for high-spin Fe3+ ions Similarly the cal-culated local MM value of Mn (about 3 B) is also muchsmaller than the formal value of 4 B for high spin Mn3+

ions The reduction of local MM is caused by the strongFeMn 3dndashO 2p hybridization In addition O ions alsohave a slight MM of 007 B which is the result of thehybridization between Fe 3d and O 2p states The oxygenMM values are about two orders of magnitude smaller thanthose of FeMn (see Table II) and hence FeMn ions arethe main source of magnetism in BFM Previous theoret-ical calculations have shown that the canting of magneticmoments was not significantly affected by the presence of

Table III Calculated total and local magnetic moment (Bfu) ofBFM with different Mn contents (0 10 20 30 and 50) using VCAmethod BFM50 stands for the calculated results based on BiFe05Mn05O3

supercell with one of the Fe sites substituted by Mn The experimentalstructural parameters of BFO11 were used for all the calculations

0 10 20 30 50 BFM50

Bi1 minus0003 +0001 +0003 +0005 +0006 minus0004Bi2 +0003 +0003 +0006 +0008 +0010 minus0006Fe1 +3689 +3598 +3514 +3382 +3175 minus3673Fe2 minus3690 minus3748 minus3812 minus3861 minus3907 +3142O1 +0069 +0044 +0035 +0021 +0012 +0112O2 minus0068 minus0058 minus0062 minus0054 minus0053 +0033Total 0 minus0200 minus0400 minus0600 minus1000 minus1000

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Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study Wang et al

oxygen vacancies and no increase in macroscopic magne-tization due to oxygen vacancies could be found37 Henceoxygen vacancies cannot be considered as the main reasonfor the suppression of spin modulation40

Experimentally there are contradictory reports on theMn-doping effect on magnetic properties of BFM It isreported that the average MM and the ordering tempera-ture decrease with increasing Mn concentration in BFMsystem1824 Naganuma et al26 reported that 5 Mn-doping has negligible effect on the magnetization behaviorA general trend of increased magnetization with increasingMn content in BFM has also obtained a lot of experimentalsupports2122 The calculated spontaneous magnetization(eg total MM) of BFM which increases linearly withincreasing Mn content is consistent with this trend2022

We believe that the total magnetization in BFM comesfrom the FendashOndashMn antiferromagnetic superexchange inter-actions rather than the antiferromagnetic superexchangeinteractions of FendashOndashFe and MnndashOndashMn which basicallycancel the magnetization of BFM system Similar phe-nomenon has been found in LaFeO3ndashLaCrO3 systems41

Recent study on Bi2FeMnO6 epitaxial thin films also sup-ported this mechanism36 When Mn content is 50 theinduced magnetic moment is about 10 B per FendashMncouple which is expected for the antiferromagnetic order-ing between Fe3+ and Mn3+ ionsPure BFO shows a pressure-induced magnetic transi-

tion from high-spin state to low-spin one42 Here we havestudied the pressure effect by examining the volume depen-dence of the total and local MMs in BFM systems with 10and 50 Mn and the results are given in Tables IV and Vrespectively It is found that the total MM in BFM is inde-pendent of the unit cell volume while the local MM isclosely related to the volume effect The local MMs onFe and O sites increase with increasing unit cell volumewhile those on Bi sites show the opposite trend In addi-tion the contribution from A-site Bi ions to the total mag-netization of BFM systems is very small since its localMM is one and three orders of magnitude smaller thanthat on O and Fe sites respectively With increasing Mncontent a small but linear enhancement in magnetizationcan be observed23 This may be due to the fact that therandom positioning of Fe and Mn ions has frustrated the(anti)ferromagnetic properties41

Table IV Calculated local magnetic moment (Bfu) of BFM with10 Mn under different unit cell volumes V0 stands for the theoreticalequilibrium volume The total MM equals to minus0200 Bfu which isindependent of the unit cell volume

096 V0 098 V0 100 V0 102 V0 104 V0

Bi1 0002 0001 0001 0001 minus0001Bi2 0001 0002 0002 0003 minus0003Fe1 3492 +3519 3539 3560 3576Fe2 minus3646 minus3669 minus3689 minus3705 minus3719O1 0041 +0043 0045 0047 0049O2 minus0054 minus0057 minus0059 minus0062 0065

Table V Calculated local magnetic moment (Bfu) of BFM with50 Mn under different unit cell volume V0 stands for the theoreticalequilibrium volume The total MM equal to +100 Bfu which isindependent of the unit cell volume

096 V0 098 V0 10 V0 102 V0 104 V0

Bi1 minus0009 minus0010 minus0010 minus0011 minus0012Bi2 minus0009 minus0008 minus0007 minus0006 minus0005Fe1 3535 3558 3577 3589 3600Fe2 minus2827 minus2875 minus2914 minus2946 minus2977O1 0091 0097 0101 0106 0111O2 0024 0026 0028 0029 0031

4 CONCLUSIONS

In summary we have examined the effect of Mn doping onthe structural electronic and magnetic properties of BFOsystem based on first-principles calculations Our resultsconfirm the multiferroic properties of Mn-doped BFO sys-tem DOS and local MM suggest that both Fe and Mn ionsare in +3 oxidation state The spontaneous magnetizationof the system is dependent on Mn content while indepen-dent of the unit cell volume and local structural distortionssuggesting the highly stable magnetism Our results maybe effective for other B-site doped BFO systems

Acknowledgments This work was supported by grantsfrom the Research Grants Council of the Hong Kong Spe-cial Administrative Region (Project PolyU 517107E) andfrom the Hong Kong Polytechnic University (Projects NoG-YF71 and G-YH07)

References and Notes

1 M Fiebig J Phys D Appl Phys 38 R123 (2005)2 W Eerenstein N D Mathur and J F Scott Nature 442 759 (2006)3 T Lottermoser T Lonkai U Amann D Hohlwein J Ihringer and

M Fiebig Nature 430 541 (2004)4 N A Hill J Phys Chem B 104 6694 (2000)5 H Huang and L M Zhou J Phys D Appl Phys 37 3361 (2004)6 T Zhao A Scholl F Zavaliche K Lee M Barry A Doran M P

Cruz Y H Chu C Ederer N A Spaldin R R Das D M KimS H Baek C B Eom and R Ramesh Nature Mater 5 823 (2006)

7 F Kubel and H Schmid Acta Crystallogr B 46 698 (1990)8 C Ederer and N A Spaldin Phys Rev B 71 060401 (2005)9 J Chen X R Xing A Watson W Wang R B Yu J X Deng

L Yan C Sun and X B Chen Chem Mater 19 3598 (2007)10 R Ramesh and N A Spaldin Nature Mater 6 21 (2007)11 T J Park G C Papaefthymiou A J Viescas A R Moodenbaugh

and S S Wong Nano Lett 7 766 (2007)12 J B Neaton C Ederer U V Waghmare N A Spaldin and K M

Rabe Phys Rev B 71 014113 (2005)13 V A Khomchenko D A Kiselev J M Vieira A L Kholkin

M A Sa and Y G Pogorelov Appl Phys Lett 90 242901 (2007)14 Y H Lee J M Wu and C H Lai Appl Phys Lett 88 042903

(2006)15 P Baettig C Ederer and N A Spaldin Phys Rev B 72 214105

(2005)16 S R Shannigrahi A Huang N Chandrasekhar D Tripathy and

A O Adeyeye Appl Phys Lett 90 022901 (2007)17 X D Qi J Dho R Tomov M G Blamire and J L MacManus-

Driscoll Appl Phys Lett 86 062903 (2005)

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Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study Wang et al

Table II Calculated structure parameters of BFM with differentMn contents (0 10 20 30 and 50) using VCA method and theexperimental structure parameters of pure BFO11 BFM50 stands forBiFe05Mn05O3 supercell with one of the Fe sites substituted by Mn Therhombohedral structure with space group R3 (No 146) and the exper-imental structural parameters of BFO were adopted in the calculationBi and FeMn ions locate at 1a (x x x while O ions at 3b (x y z

0 10 20 30 50 BFM50

Bi1x 00000 00000 00000 00000 00000 00000Bi2x 05000 04996 04996 04992 04990 04959Fe1x 02254 02259 02247 02226 02216 02235Fe2x 07254 07261 07256 07247 07263 07127O1x 05405 05412 05391 05355 05324 05315O1y 09399 09415 09412 09431 09472 09257O1z 03888 03882 03882 03878 03891 03825O2x 00406 00441 00432 00439 00474 00441O2y 08888 08896 08903 08925 08973 08808O2z 04399 04385 04382 04365 04338 04387

within rhombohedral symmetry This is consistent withthe experimental observations24 atomic thermal displace-ments increase with increasing Mn content As Mn contentincreases the structural distortions decrease only slightlywithout substantial variation We have recalculated thestructure parameters by using the experimental values24 ofMn-doped BFO and have found that the same conclusioncan be obtained The total energy ofBiFe05Mn05O3 calculated by VCA method is lower than

that of BFM50 supercell with one of the two Fe ionsreplaced by Mn This indicates that random arrangementof Fe and Mn ions is more energetically favorable In addi-tion the doping of Mn ions into BFO sharply increases itstotal energy indicating that introduction of Mn into BFO

Fig 1 Majority spin band structure of pure antiferromagnetic BFO (left panel) and BFM50 (right panel) along high-symmetry directions in BZ

is difficult as suggested by Bi et al34 We have also per-formed the volume optimization on BFM with different Mncontents and the results (not shown here) obtained con-firm what is experimentally observed23 that is as the Mnconcentration increases both the lattice constants a and cdecrease as well as unit cell volume while ca ratio isbasically unchanged

32 Electronic Properties

For pure BFO the major spin band structure equals tothe minor spin band structure due to its antiferromagneticnature The introduction of Mn into BFO has a significanteffect on the majority spin band structure which bringsabout a larger band-gap while its effect on the minor-ity spin band structure is negligible Shown in Figure 1are the calculated band structures of pure BFO and 50Mn BFM systems along the high-symmetry directions inthe BZ (only majority spin states are shown) Here theFermi level is located at the top of valence band and isset to 0 eV For pure BFO in the valence band (VB) theenergy band located at the lowest region of [minus19minus17] eVis mainly occupied by O 2s states The bands at aboutminus10 eV are Bi 6s states The upper part of VB around[minus7 0] eV is dominated by Fe 3d states mixed with someO 2p and lesser Bi 6p states The conduction band (CB)region at about 1 to 3 eV is dominated by Fe 3d states Bi6p states occupy the region of36 eV Above 8 eV strongmixing occurs among Bi 6p Fe 3d and O 2p states Thetop of VB is located between ndashZ (only 0015 eV higherthan the energy at Z) very close to Z while the bottomof the conduction band sits at Z point Hence an indirect

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Wang et al Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study

(very close to direct) band gap of 106 eV is formedbetween the top of the O 2p valence band and the bottomof the Fe 3d conduction band The calculated band gapis very close to the experimental value of 13 eV 35 andprevious theoretical results1236 The electrical propertiesof BFO is determined by charge transfers from the occu-pied O 2p to unoccupied Fe 3d states and dndashd transitionbetween Fe 3d valence and conduction bands35 Our calcu-lated band structures agree quite well the results obtainedby VASP-PAW method12 indicating the latter is as preciseas the FP-LAPW method used in this study The electronicband structures of Mn-doped BFO are found to be quitesimilar to those of pure BFOFigure 2 shows the total density of states of pure and

Mn-doped BiFeO3 Because Mn doping is hole dopingthe Fermi level of BFM systems should be shifted down-ward as compared to pure BFO and electrons will fillholes in the Mn 3d band For 50 Mn-doped BFM sys-tem its spin-up band gap is about 10 eV greater thanthat in pure BFO while the spin-down band gap remainsessentially unchanged As found by Neaton et al12 theFe partial density of states in BFO is quite different forthe two spin states (spin up and spin down Fe1 and Fe2respectively) From the partial density of states of Fe (notshown here) one can draw the conclusion that Fe existsin +3 oxidation state in pure BFO compound indicating ad5 high-spin electronic configuration (detailed explanationcan be found in Ref [37]) Likewise Mn also exists inthe +3 oxidation state Based on the ionic radii of FeMnin six-coordinate octahedral environment the combinationof Fe2+Mn4+ ions has an average ionic radius of 079 Aringwhich is slightly larger than that of Fe3+38 Therefore theunit cell volume of BFM system with Fe2+Mn4+ oxida-tion state should be higher than that of pure BFO This is

Fig 2 Total density of states in pure 10 and 50 Mn-doped BFOsystems (only the majority spin states are shown while the minority spinstates of doped BFO are similar to the majority spin states of pure BFO)The top of the valence band is set at 0 eV

contradictory to the experimental results23 where no bigdifference in unit cell volume was found Since the aver-age ionic radius of the Fe3+Mn3+ couple is closer to thatof Fe3+ ions in pure BFO both Fe and Mn in BFM systemare likely to be in the +3 oxidation state Moumlssbauer andXPS measurements on La01Bi09Fe1minusxMnxO3 revealed thatall Fe ions exist in the +3 oxidation states and hence Mnsubstitution does not introduce any mixed valence into thesystem25 Recently X-ray absorption spectroscopy39 showsthat mixed valence states of Fe2+ and Fe3+ exist in pureBFO and Mn-doped BFO However since the content ofFe2+ does not change with the introduction of Mn dopantthe existence of Fe2+ can be ascribed to oxygen vacanciesrather than Mn doping39

33 Magnetic Properties

Because Fe and Mn are magnetic ions we first examinedthe stability of magnetic ordering of B-site Fe and Mnatoms It is found that the antiferromagnetic ordering isstable for BFO and it gives a ferrimagnetic structure forthe ground-state of BFM The calculated total and localmagnetic moment (MM) of BFM with different Mn con-tents are given in Table III It is shown that pure BFOhas an antiferromagnetic nature and the total MM is zeroalthough local MMs are not exactly equal Local MM ofBi is very small since Bi is strongly diamagnetic Fe ionhas the largest local MM (369 B) which is very closeto the experimental value7 (375 B) and previous theoret-ical one30 (365 B) It is greatly reduced from the formalvalue of 5 B for high-spin Fe3+ ions Similarly the cal-culated local MM value of Mn (about 3 B) is also muchsmaller than the formal value of 4 B for high spin Mn3+

ions The reduction of local MM is caused by the strongFeMn 3dndashO 2p hybridization In addition O ions alsohave a slight MM of 007 B which is the result of thehybridization between Fe 3d and O 2p states The oxygenMM values are about two orders of magnitude smaller thanthose of FeMn (see Table II) and hence FeMn ions arethe main source of magnetism in BFM Previous theoret-ical calculations have shown that the canting of magneticmoments was not significantly affected by the presence of

Table III Calculated total and local magnetic moment (Bfu) ofBFM with different Mn contents (0 10 20 30 and 50) using VCAmethod BFM50 stands for the calculated results based on BiFe05Mn05O3

supercell with one of the Fe sites substituted by Mn The experimentalstructural parameters of BFO11 were used for all the calculations

0 10 20 30 50 BFM50

Bi1 minus0003 +0001 +0003 +0005 +0006 minus0004Bi2 +0003 +0003 +0006 +0008 +0010 minus0006Fe1 +3689 +3598 +3514 +3382 +3175 minus3673Fe2 minus3690 minus3748 minus3812 minus3861 minus3907 +3142O1 +0069 +0044 +0035 +0021 +0012 +0112O2 minus0068 minus0058 minus0062 minus0054 minus0053 +0033Total 0 minus0200 minus0400 minus0600 minus1000 minus1000

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Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study Wang et al

oxygen vacancies and no increase in macroscopic magne-tization due to oxygen vacancies could be found37 Henceoxygen vacancies cannot be considered as the main reasonfor the suppression of spin modulation40

Experimentally there are contradictory reports on theMn-doping effect on magnetic properties of BFM It isreported that the average MM and the ordering tempera-ture decrease with increasing Mn concentration in BFMsystem1824 Naganuma et al26 reported that 5 Mn-doping has negligible effect on the magnetization behaviorA general trend of increased magnetization with increasingMn content in BFM has also obtained a lot of experimentalsupports2122 The calculated spontaneous magnetization(eg total MM) of BFM which increases linearly withincreasing Mn content is consistent with this trend2022

We believe that the total magnetization in BFM comesfrom the FendashOndashMn antiferromagnetic superexchange inter-actions rather than the antiferromagnetic superexchangeinteractions of FendashOndashFe and MnndashOndashMn which basicallycancel the magnetization of BFM system Similar phe-nomenon has been found in LaFeO3ndashLaCrO3 systems41

Recent study on Bi2FeMnO6 epitaxial thin films also sup-ported this mechanism36 When Mn content is 50 theinduced magnetic moment is about 10 B per FendashMncouple which is expected for the antiferromagnetic order-ing between Fe3+ and Mn3+ ionsPure BFO shows a pressure-induced magnetic transi-

tion from high-spin state to low-spin one42 Here we havestudied the pressure effect by examining the volume depen-dence of the total and local MMs in BFM systems with 10and 50 Mn and the results are given in Tables IV and Vrespectively It is found that the total MM in BFM is inde-pendent of the unit cell volume while the local MM isclosely related to the volume effect The local MMs onFe and O sites increase with increasing unit cell volumewhile those on Bi sites show the opposite trend In addi-tion the contribution from A-site Bi ions to the total mag-netization of BFM systems is very small since its localMM is one and three orders of magnitude smaller thanthat on O and Fe sites respectively With increasing Mncontent a small but linear enhancement in magnetizationcan be observed23 This may be due to the fact that therandom positioning of Fe and Mn ions has frustrated the(anti)ferromagnetic properties41

Table IV Calculated local magnetic moment (Bfu) of BFM with10 Mn under different unit cell volumes V0 stands for the theoreticalequilibrium volume The total MM equals to minus0200 Bfu which isindependent of the unit cell volume

096 V0 098 V0 100 V0 102 V0 104 V0

Bi1 0002 0001 0001 0001 minus0001Bi2 0001 0002 0002 0003 minus0003Fe1 3492 +3519 3539 3560 3576Fe2 minus3646 minus3669 minus3689 minus3705 minus3719O1 0041 +0043 0045 0047 0049O2 minus0054 minus0057 minus0059 minus0062 0065

Table V Calculated local magnetic moment (Bfu) of BFM with50 Mn under different unit cell volume V0 stands for the theoreticalequilibrium volume The total MM equal to +100 Bfu which isindependent of the unit cell volume

096 V0 098 V0 10 V0 102 V0 104 V0

Bi1 minus0009 minus0010 minus0010 minus0011 minus0012Bi2 minus0009 minus0008 minus0007 minus0006 minus0005Fe1 3535 3558 3577 3589 3600Fe2 minus2827 minus2875 minus2914 minus2946 minus2977O1 0091 0097 0101 0106 0111O2 0024 0026 0028 0029 0031

4 CONCLUSIONS

In summary we have examined the effect of Mn doping onthe structural electronic and magnetic properties of BFOsystem based on first-principles calculations Our resultsconfirm the multiferroic properties of Mn-doped BFO sys-tem DOS and local MM suggest that both Fe and Mn ionsare in +3 oxidation state The spontaneous magnetizationof the system is dependent on Mn content while indepen-dent of the unit cell volume and local structural distortionssuggesting the highly stable magnetism Our results maybe effective for other B-site doped BFO systems

Acknowledgments This work was supported by grantsfrom the Research Grants Council of the Hong Kong Spe-cial Administrative Region (Project PolyU 517107E) andfrom the Hong Kong Polytechnic University (Projects NoG-YF71 and G-YH07)

References and Notes

1 M Fiebig J Phys D Appl Phys 38 R123 (2005)2 W Eerenstein N D Mathur and J F Scott Nature 442 759 (2006)3 T Lottermoser T Lonkai U Amann D Hohlwein J Ihringer and

M Fiebig Nature 430 541 (2004)4 N A Hill J Phys Chem B 104 6694 (2000)5 H Huang and L M Zhou J Phys D Appl Phys 37 3361 (2004)6 T Zhao A Scholl F Zavaliche K Lee M Barry A Doran M P

Cruz Y H Chu C Ederer N A Spaldin R R Das D M KimS H Baek C B Eom and R Ramesh Nature Mater 5 823 (2006)

7 F Kubel and H Schmid Acta Crystallogr B 46 698 (1990)8 C Ederer and N A Spaldin Phys Rev B 71 060401 (2005)9 J Chen X R Xing A Watson W Wang R B Yu J X Deng

L Yan C Sun and X B Chen Chem Mater 19 3598 (2007)10 R Ramesh and N A Spaldin Nature Mater 6 21 (2007)11 T J Park G C Papaefthymiou A J Viescas A R Moodenbaugh

and S S Wong Nano Lett 7 766 (2007)12 J B Neaton C Ederer U V Waghmare N A Spaldin and K M

Rabe Phys Rev B 71 014113 (2005)13 V A Khomchenko D A Kiselev J M Vieira A L Kholkin

M A Sa and Y G Pogorelov Appl Phys Lett 90 242901 (2007)14 Y H Lee J M Wu and C H Lai Appl Phys Lett 88 042903

(2006)15 P Baettig C Ederer and N A Spaldin Phys Rev B 72 214105

(2005)16 S R Shannigrahi A Huang N Chandrasekhar D Tripathy and

A O Adeyeye Appl Phys Lett 90 022901 (2007)17 X D Qi J Dho R Tomov M G Blamire and J L MacManus-

Driscoll Appl Phys Lett 86 062903 (2005)

188 Sci Adv Mater 2 184ndash189 2010

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IP 193496250Tue 22 Feb 2011 080011

RESEARCH

ARTIC

LE

Wang et al Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study

(very close to direct) band gap of 106 eV is formedbetween the top of the O 2p valence band and the bottomof the Fe 3d conduction band The calculated band gapis very close to the experimental value of 13 eV 35 andprevious theoretical results1236 The electrical propertiesof BFO is determined by charge transfers from the occu-pied O 2p to unoccupied Fe 3d states and dndashd transitionbetween Fe 3d valence and conduction bands35 Our calcu-lated band structures agree quite well the results obtainedby VASP-PAW method12 indicating the latter is as preciseas the FP-LAPW method used in this study The electronicband structures of Mn-doped BFO are found to be quitesimilar to those of pure BFOFigure 2 shows the total density of states of pure and

Mn-doped BiFeO3 Because Mn doping is hole dopingthe Fermi level of BFM systems should be shifted down-ward as compared to pure BFO and electrons will fillholes in the Mn 3d band For 50 Mn-doped BFM sys-tem its spin-up band gap is about 10 eV greater thanthat in pure BFO while the spin-down band gap remainsessentially unchanged As found by Neaton et al12 theFe partial density of states in BFO is quite different forthe two spin states (spin up and spin down Fe1 and Fe2respectively) From the partial density of states of Fe (notshown here) one can draw the conclusion that Fe existsin +3 oxidation state in pure BFO compound indicating ad5 high-spin electronic configuration (detailed explanationcan be found in Ref [37]) Likewise Mn also exists inthe +3 oxidation state Based on the ionic radii of FeMnin six-coordinate octahedral environment the combinationof Fe2+Mn4+ ions has an average ionic radius of 079 Aringwhich is slightly larger than that of Fe3+38 Therefore theunit cell volume of BFM system with Fe2+Mn4+ oxida-tion state should be higher than that of pure BFO This is

Fig 2 Total density of states in pure 10 and 50 Mn-doped BFOsystems (only the majority spin states are shown while the minority spinstates of doped BFO are similar to the majority spin states of pure BFO)The top of the valence band is set at 0 eV

contradictory to the experimental results23 where no bigdifference in unit cell volume was found Since the aver-age ionic radius of the Fe3+Mn3+ couple is closer to thatof Fe3+ ions in pure BFO both Fe and Mn in BFM systemare likely to be in the +3 oxidation state Moumlssbauer andXPS measurements on La01Bi09Fe1minusxMnxO3 revealed thatall Fe ions exist in the +3 oxidation states and hence Mnsubstitution does not introduce any mixed valence into thesystem25 Recently X-ray absorption spectroscopy39 showsthat mixed valence states of Fe2+ and Fe3+ exist in pureBFO and Mn-doped BFO However since the content ofFe2+ does not change with the introduction of Mn dopantthe existence of Fe2+ can be ascribed to oxygen vacanciesrather than Mn doping39

33 Magnetic Properties

Because Fe and Mn are magnetic ions we first examinedthe stability of magnetic ordering of B-site Fe and Mnatoms It is found that the antiferromagnetic ordering isstable for BFO and it gives a ferrimagnetic structure forthe ground-state of BFM The calculated total and localmagnetic moment (MM) of BFM with different Mn con-tents are given in Table III It is shown that pure BFOhas an antiferromagnetic nature and the total MM is zeroalthough local MMs are not exactly equal Local MM ofBi is very small since Bi is strongly diamagnetic Fe ionhas the largest local MM (369 B) which is very closeto the experimental value7 (375 B) and previous theoret-ical one30 (365 B) It is greatly reduced from the formalvalue of 5 B for high-spin Fe3+ ions Similarly the cal-culated local MM value of Mn (about 3 B) is also muchsmaller than the formal value of 4 B for high spin Mn3+

ions The reduction of local MM is caused by the strongFeMn 3dndashO 2p hybridization In addition O ions alsohave a slight MM of 007 B which is the result of thehybridization between Fe 3d and O 2p states The oxygenMM values are about two orders of magnitude smaller thanthose of FeMn (see Table II) and hence FeMn ions arethe main source of magnetism in BFM Previous theoret-ical calculations have shown that the canting of magneticmoments was not significantly affected by the presence of

Table III Calculated total and local magnetic moment (Bfu) ofBFM with different Mn contents (0 10 20 30 and 50) using VCAmethod BFM50 stands for the calculated results based on BiFe05Mn05O3

supercell with one of the Fe sites substituted by Mn The experimentalstructural parameters of BFO11 were used for all the calculations

0 10 20 30 50 BFM50

Bi1 minus0003 +0001 +0003 +0005 +0006 minus0004Bi2 +0003 +0003 +0006 +0008 +0010 minus0006Fe1 +3689 +3598 +3514 +3382 +3175 minus3673Fe2 minus3690 minus3748 minus3812 minus3861 minus3907 +3142O1 +0069 +0044 +0035 +0021 +0012 +0112O2 minus0068 minus0058 minus0062 minus0054 minus0053 +0033Total 0 minus0200 minus0400 minus0600 minus1000 minus1000

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Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study Wang et al

oxygen vacancies and no increase in macroscopic magne-tization due to oxygen vacancies could be found37 Henceoxygen vacancies cannot be considered as the main reasonfor the suppression of spin modulation40

Experimentally there are contradictory reports on theMn-doping effect on magnetic properties of BFM It isreported that the average MM and the ordering tempera-ture decrease with increasing Mn concentration in BFMsystem1824 Naganuma et al26 reported that 5 Mn-doping has negligible effect on the magnetization behaviorA general trend of increased magnetization with increasingMn content in BFM has also obtained a lot of experimentalsupports2122 The calculated spontaneous magnetization(eg total MM) of BFM which increases linearly withincreasing Mn content is consistent with this trend2022

We believe that the total magnetization in BFM comesfrom the FendashOndashMn antiferromagnetic superexchange inter-actions rather than the antiferromagnetic superexchangeinteractions of FendashOndashFe and MnndashOndashMn which basicallycancel the magnetization of BFM system Similar phe-nomenon has been found in LaFeO3ndashLaCrO3 systems41

Recent study on Bi2FeMnO6 epitaxial thin films also sup-ported this mechanism36 When Mn content is 50 theinduced magnetic moment is about 10 B per FendashMncouple which is expected for the antiferromagnetic order-ing between Fe3+ and Mn3+ ionsPure BFO shows a pressure-induced magnetic transi-

tion from high-spin state to low-spin one42 Here we havestudied the pressure effect by examining the volume depen-dence of the total and local MMs in BFM systems with 10and 50 Mn and the results are given in Tables IV and Vrespectively It is found that the total MM in BFM is inde-pendent of the unit cell volume while the local MM isclosely related to the volume effect The local MMs onFe and O sites increase with increasing unit cell volumewhile those on Bi sites show the opposite trend In addi-tion the contribution from A-site Bi ions to the total mag-netization of BFM systems is very small since its localMM is one and three orders of magnitude smaller thanthat on O and Fe sites respectively With increasing Mncontent a small but linear enhancement in magnetizationcan be observed23 This may be due to the fact that therandom positioning of Fe and Mn ions has frustrated the(anti)ferromagnetic properties41

Table IV Calculated local magnetic moment (Bfu) of BFM with10 Mn under different unit cell volumes V0 stands for the theoreticalequilibrium volume The total MM equals to minus0200 Bfu which isindependent of the unit cell volume

096 V0 098 V0 100 V0 102 V0 104 V0

Bi1 0002 0001 0001 0001 minus0001Bi2 0001 0002 0002 0003 minus0003Fe1 3492 +3519 3539 3560 3576Fe2 minus3646 minus3669 minus3689 minus3705 minus3719O1 0041 +0043 0045 0047 0049O2 minus0054 minus0057 minus0059 minus0062 0065

Table V Calculated local magnetic moment (Bfu) of BFM with50 Mn under different unit cell volume V0 stands for the theoreticalequilibrium volume The total MM equal to +100 Bfu which isindependent of the unit cell volume

096 V0 098 V0 10 V0 102 V0 104 V0

Bi1 minus0009 minus0010 minus0010 minus0011 minus0012Bi2 minus0009 minus0008 minus0007 minus0006 minus0005Fe1 3535 3558 3577 3589 3600Fe2 minus2827 minus2875 minus2914 minus2946 minus2977O1 0091 0097 0101 0106 0111O2 0024 0026 0028 0029 0031

4 CONCLUSIONS

In summary we have examined the effect of Mn doping onthe structural electronic and magnetic properties of BFOsystem based on first-principles calculations Our resultsconfirm the multiferroic properties of Mn-doped BFO sys-tem DOS and local MM suggest that both Fe and Mn ionsare in +3 oxidation state The spontaneous magnetizationof the system is dependent on Mn content while indepen-dent of the unit cell volume and local structural distortionssuggesting the highly stable magnetism Our results maybe effective for other B-site doped BFO systems

Acknowledgments This work was supported by grantsfrom the Research Grants Council of the Hong Kong Spe-cial Administrative Region (Project PolyU 517107E) andfrom the Hong Kong Polytechnic University (Projects NoG-YF71 and G-YH07)

References and Notes

1 M Fiebig J Phys D Appl Phys 38 R123 (2005)2 W Eerenstein N D Mathur and J F Scott Nature 442 759 (2006)3 T Lottermoser T Lonkai U Amann D Hohlwein J Ihringer and

M Fiebig Nature 430 541 (2004)4 N A Hill J Phys Chem B 104 6694 (2000)5 H Huang and L M Zhou J Phys D Appl Phys 37 3361 (2004)6 T Zhao A Scholl F Zavaliche K Lee M Barry A Doran M P

Cruz Y H Chu C Ederer N A Spaldin R R Das D M KimS H Baek C B Eom and R Ramesh Nature Mater 5 823 (2006)

7 F Kubel and H Schmid Acta Crystallogr B 46 698 (1990)8 C Ederer and N A Spaldin Phys Rev B 71 060401 (2005)9 J Chen X R Xing A Watson W Wang R B Yu J X Deng

L Yan C Sun and X B Chen Chem Mater 19 3598 (2007)10 R Ramesh and N A Spaldin Nature Mater 6 21 (2007)11 T J Park G C Papaefthymiou A J Viescas A R Moodenbaugh

and S S Wong Nano Lett 7 766 (2007)12 J B Neaton C Ederer U V Waghmare N A Spaldin and K M

Rabe Phys Rev B 71 014113 (2005)13 V A Khomchenko D A Kiselev J M Vieira A L Kholkin

M A Sa and Y G Pogorelov Appl Phys Lett 90 242901 (2007)14 Y H Lee J M Wu and C H Lai Appl Phys Lett 88 042903

(2006)15 P Baettig C Ederer and N A Spaldin Phys Rev B 72 214105

(2005)16 S R Shannigrahi A Huang N Chandrasekhar D Tripathy and

A O Adeyeye Appl Phys Lett 90 022901 (2007)17 X D Qi J Dho R Tomov M G Blamire and J L MacManus-

Driscoll Appl Phys Lett 86 062903 (2005)

188 Sci Adv Mater 2 184ndash189 2010

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RESEARCH

ARTIC

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Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study Wang et al

oxygen vacancies and no increase in macroscopic magne-tization due to oxygen vacancies could be found37 Henceoxygen vacancies cannot be considered as the main reasonfor the suppression of spin modulation40

Experimentally there are contradictory reports on theMn-doping effect on magnetic properties of BFM It isreported that the average MM and the ordering tempera-ture decrease with increasing Mn concentration in BFMsystem1824 Naganuma et al26 reported that 5 Mn-doping has negligible effect on the magnetization behaviorA general trend of increased magnetization with increasingMn content in BFM has also obtained a lot of experimentalsupports2122 The calculated spontaneous magnetization(eg total MM) of BFM which increases linearly withincreasing Mn content is consistent with this trend2022

We believe that the total magnetization in BFM comesfrom the FendashOndashMn antiferromagnetic superexchange inter-actions rather than the antiferromagnetic superexchangeinteractions of FendashOndashFe and MnndashOndashMn which basicallycancel the magnetization of BFM system Similar phe-nomenon has been found in LaFeO3ndashLaCrO3 systems41

Recent study on Bi2FeMnO6 epitaxial thin films also sup-ported this mechanism36 When Mn content is 50 theinduced magnetic moment is about 10 B per FendashMncouple which is expected for the antiferromagnetic order-ing between Fe3+ and Mn3+ ionsPure BFO shows a pressure-induced magnetic transi-

tion from high-spin state to low-spin one42 Here we havestudied the pressure effect by examining the volume depen-dence of the total and local MMs in BFM systems with 10and 50 Mn and the results are given in Tables IV and Vrespectively It is found that the total MM in BFM is inde-pendent of the unit cell volume while the local MM isclosely related to the volume effect The local MMs onFe and O sites increase with increasing unit cell volumewhile those on Bi sites show the opposite trend In addi-tion the contribution from A-site Bi ions to the total mag-netization of BFM systems is very small since its localMM is one and three orders of magnitude smaller thanthat on O and Fe sites respectively With increasing Mncontent a small but linear enhancement in magnetizationcan be observed23 This may be due to the fact that therandom positioning of Fe and Mn ions has frustrated the(anti)ferromagnetic properties41

Table IV Calculated local magnetic moment (Bfu) of BFM with10 Mn under different unit cell volumes V0 stands for the theoreticalequilibrium volume The total MM equals to minus0200 Bfu which isindependent of the unit cell volume

096 V0 098 V0 100 V0 102 V0 104 V0

Bi1 0002 0001 0001 0001 minus0001Bi2 0001 0002 0002 0003 minus0003Fe1 3492 +3519 3539 3560 3576Fe2 minus3646 minus3669 minus3689 minus3705 minus3719O1 0041 +0043 0045 0047 0049O2 minus0054 minus0057 minus0059 minus0062 0065

Table V Calculated local magnetic moment (Bfu) of BFM with50 Mn under different unit cell volume V0 stands for the theoreticalequilibrium volume The total MM equal to +100 Bfu which isindependent of the unit cell volume

096 V0 098 V0 10 V0 102 V0 104 V0

Bi1 minus0009 minus0010 minus0010 minus0011 minus0012Bi2 minus0009 minus0008 minus0007 minus0006 minus0005Fe1 3535 3558 3577 3589 3600Fe2 minus2827 minus2875 minus2914 minus2946 minus2977O1 0091 0097 0101 0106 0111O2 0024 0026 0028 0029 0031

4 CONCLUSIONS

In summary we have examined the effect of Mn doping onthe structural electronic and magnetic properties of BFOsystem based on first-principles calculations Our resultsconfirm the multiferroic properties of Mn-doped BFO sys-tem DOS and local MM suggest that both Fe and Mn ionsare in +3 oxidation state The spontaneous magnetizationof the system is dependent on Mn content while indepen-dent of the unit cell volume and local structural distortionssuggesting the highly stable magnetism Our results maybe effective for other B-site doped BFO systems

Acknowledgments This work was supported by grantsfrom the Research Grants Council of the Hong Kong Spe-cial Administrative Region (Project PolyU 517107E) andfrom the Hong Kong Polytechnic University (Projects NoG-YF71 and G-YH07)

References and Notes

1 M Fiebig J Phys D Appl Phys 38 R123 (2005)2 W Eerenstein N D Mathur and J F Scott Nature 442 759 (2006)3 T Lottermoser T Lonkai U Amann D Hohlwein J Ihringer and

M Fiebig Nature 430 541 (2004)4 N A Hill J Phys Chem B 104 6694 (2000)5 H Huang and L M Zhou J Phys D Appl Phys 37 3361 (2004)6 T Zhao A Scholl F Zavaliche K Lee M Barry A Doran M P

Cruz Y H Chu C Ederer N A Spaldin R R Das D M KimS H Baek C B Eom and R Ramesh Nature Mater 5 823 (2006)

7 F Kubel and H Schmid Acta Crystallogr B 46 698 (1990)8 C Ederer and N A Spaldin Phys Rev B 71 060401 (2005)9 J Chen X R Xing A Watson W Wang R B Yu J X Deng

L Yan C Sun and X B Chen Chem Mater 19 3598 (2007)10 R Ramesh and N A Spaldin Nature Mater 6 21 (2007)11 T J Park G C Papaefthymiou A J Viescas A R Moodenbaugh

and S S Wong Nano Lett 7 766 (2007)12 J B Neaton C Ederer U V Waghmare N A Spaldin and K M

Rabe Phys Rev B 71 014113 (2005)13 V A Khomchenko D A Kiselev J M Vieira A L Kholkin

M A Sa and Y G Pogorelov Appl Phys Lett 90 242901 (2007)14 Y H Lee J M Wu and C H Lai Appl Phys Lett 88 042903

(2006)15 P Baettig C Ederer and N A Spaldin Phys Rev B 72 214105

(2005)16 S R Shannigrahi A Huang N Chandrasekhar D Tripathy and

A O Adeyeye Appl Phys Lett 90 022901 (2007)17 X D Qi J Dho R Tomov M G Blamire and J L MacManus-

Driscoll Appl Phys Lett 86 062903 (2005)

188 Sci Adv Mater 2 184ndash189 2010

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ARTIC

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Wang et al Effect of Mn Substitution for Fe in Multiferroic BiFeO3 A First-Principles Study

18 C H Yang T Y Koo and Y H Jeong Solid State Commun134 299 (2005)

19 S K Singh H Ishiwara and K Maruyama Appl Phys Lett88 262908 (2006)

20 J R Sahu Solid State Sci 9 950 (2007)21 M Azuma H Kanda A A Belik Y Shimakawa and M Takano

J Magn Magn Mater 310 1177 (2007)22 M Kumar and K L Yadav Appl Phys Lett 91 242901

(2007)23 V R Palkar D C Kundaliya and S K Malik J Appl Phys

93 4337 (2003)24 I Sosnowska W Schaffer W Kockelmann K H Andersen and

I O Troyanchuk Appl Phys A 74 S1040 (2002)25 D Kothari V R Reddy A Gupta D M Phase N Lakshmi

S K Deshpande and A M Awasthi J Phys Condens Matter19 136202 (2007)

26 H Naganuma J Miura and S Okamura Appl Phys Lett93 052901 (2008)

27 W Eerenstein F D Morrison J Dho M G Blamire J F Scottand N D Mathur Science 307 1203 (2005)

28 K Ueda H Tabata and T Kawai Appl Phys Lett 75 555(1999)

29 P Ravindran R Vidya A Kjekshus H Fjellvaringg and O ErikssonPhys Rev B 74 224412 (2006)

30 P Hermet M Goffinet J Kreisel and P Ghosez Phys Rev B75 220102 (2007)

31 P Blaha K Schwarz G Madsen D Kvasicka and J LuitzWIEN2k An Augmented Plane Wave plus Local Orbitals Programfor Calculating Crystal Properties TU Wien (2001)

32 J P Perdew K Burke and M Ernzerhof Phys Rev Lett 77 3865(1996)

33 P E Blohl O Jepsen and O K Andersen Phys Rev B 49 16223(1994)

34 L Bi A R Taussig H-S Kim L Wang G F Dionne D Bono KPersson G Ceder and C A Ross Phys Rev B 78 104106 (2008)

35 T Higuchi Y-S Liu P Yao P-A Glans J Guo C Chang Z WuW Sakamoto N Itoh T Shimura T Yogo and T Hattori PhysRev B 78 085106 (2008)

36 H M Tutuncu and G P Srivastava J Appl Phys 103 083712(2008)

37 C Ederer and N A Spaldin Phys Rev B 71 224103 (2005)38 Y-H Chu M P Cruz C-H Yang L W Martin P-L Yang

J-X Zhang K Lee P Yu L-Q Chen and R Ramesh Adv Mater19 2662 (2007)

39 T Higuchi W Sakamoto N Itoh T Shimura T Hattori andT Yogo Appl Phys Express 1 011502 (2008)

40 V A Khomchenko M Kopcewicz A M L Lopes Y G PogorelovJ P Araujo J M Vieira and A L Kholkin J Phys D Appl Phys41 102003 (2008)

41 K Ueda H Tabata and T Kawai Science 280 1064 (1998)42 A G Gavriliuk V V Struzhkin I S Lyubutin S G Ovchinnikov

M Y Hu and P Chow Phys Rev B 77 155112 (2008)

Received 7 July 2009 Accepted 24 July 2009

Sci Adv Mater 2 184ndash189 2010 189