Strain induced Jahn-Teller distortions in BaFeO3: A first-principles study

Imene Cherair,1, ∗ Eric Bousquet,2 Michael Marcus Schmitt,2 Nadia Iles,3 and Abdelhafid Kellou1

1Theoretical Physics Laboratory, Faculty of Physics,USTHB,BP 32 El Alia, Bab Ezzouar, Algiers, Algeria.

2Theoretical Materials Physics, University of Liege(B5), B 4000 Liege, Belgium.3Laboratory of Thin Films Physics and Materials for Electronics, Oran 1 University, Oran, Algeria

(Dated: October 31, 2017)

The effect of epitaxial strain on structural, magnetic and electronic properties of BaFeO3 per-ovskite oxide are investigated from first principles calculations, using the Density Functional The-ory (DFT) plus the Hubbard approach (DFT+U) within the Generalized Gradient Approximation(GGA). Hybrid functional calculations, based on mixed exact Hartree-Fock (HF) and DFT exchangeenergy functionals, are also performed. For the ground state calculations,the DFT+U is found moresuitable to describe the half metallic and ferromagnetic state of cubic BaFeO3. The possible oc-curence of oxygen octahedra rotations, Jahn-Teller distortions and charge orderings through biaxialstrain are explored. The obtained results reveal that the Jahn-teller distortion is induced undertensile biaxial strain while the oxygen octahedra rotations and breathing are unusualy not observed.Then, the strained BaFeO3 is considered as a particular Jahn-Teller distorted perovskite with excep-tional properties when compared to CaFeO3 and SrFeO3. These findings lead to a strain engineeringof the JT distortions in BaFeO3, and thus for high fundamental and technological interests.

PACS numbers:Keywords: BaFeO3 perovskite, DFT+U, epitaxial strain, Jahn Teller distortions, oxygen octahedra rotations,breathing distortions.

I. INTRODUCTION

Iron perovskite oxides have raised a large interest inthe last decades because of their particular electronic andmagnetic properties. A very appealing property of thesecompounds is to have a multiferroism behavior as oftenobserved in BiFeO3 and GaFeO3

1. Unusual Fe4+ (in highvalence state) perovskites, such as cubic SrFeO3

2,3, ironstabilize in the t2g

3eg1 electronic configuration. However,

in CaFeO3, a charge disproportionation is observed. Thisis provided by the 2Fe4+ splitting into Fe5+ and Fe3+

oxidization states4,5.

BaFeO3 belongs to these few Fe4+ oxides where thetetravalent state of iron was confirmed very earlier6.The physical properties of BaFeO3 depend on oxy-gen content7–10. Mori11 demonstrated that BaFeO3−y

forms in several phases: hexagonal 6H, triclinic, rhom-bohedral and tetragonal, depending on the oxygen off-stoichiometry. The 6H-hexagonal phase has attractedmore attention because of interesting electronic and mag-netic properties such as the charge disproportionation ofFe+412,13.

Stoichiometric BaFeO3 was synthetized only recentlyby Hayashi et al.14 in 2011 where the cubic perovskitestructure was found to be stable with a lattice constanta =3.971A. The authors reported that a magnetic phasetransition takes place at 111K from paramagnetic to A-type spin spiral order with a propagation vector along the[100] direction, the crystal remains metallic at all temper-atures. By applying a small magnetic field of 0.3T, thespin sipral order is destroyed and a ferromagnetic (FM)phase is stabilized with a magnetic moment of 3.5 µB perFe ion. These features were examined theoretically by Li

et al.15. They found that the A- and G-type helical ordersin BaFeO3 are almost degenerated to the ferromagneticspin state with a small energy difference. A transitionfrom helical order to ferromagnetic order is also foundwhen the lattice constant is reduced16. Very recently,Rahman et al.17 demonstrated that the ground state ofcubic BaFeO3 is ferromagnetic. The transition from fer-romagnetic to anti-ferromagnetic state is yielded only ifdisplacements of Fe and O ions are considered. It wasalso shown from HAXPES and XAS measurements andfrom first-principle studies18 that the strong hybridiza-tion between Fe 3d and O 2p orbitals are responsible forthe negative charge transfer and metallicity.

Matsui et al.19,20 reported that BaFeO3 films werefound to be highly insulator with a weak ferromagnetismat T > 300K. However, Callender et al.21 observed metal-licity and strong ferromagnetism at TC=235K that wereattributed to the anionic deficiency. Both studies showeda pseudo cubic structures. In contrast, Taketani et al.22

found the BaFeOy−3 films have a tetragonal structurewith an antiferromagnetic order. In addition, the de-crease of oxygen vacancies increases the ferromagnetismin these films. Chakraverty et al.23, synthesized fullyoxidized BaFeO3 films by pulsed-laser deposition.Theyfound that the films are ferromagnetic insulators with anoptical gap of 1,8 eV. This result was also confirmed bya X-ray study24 which showed that the films have Fe4+

valence state.Epitaxial strain in thin films technology is a well es-

tablished technique to tune the perovskite propertiesand to induce new phases not observed in the uncon-strained bulk crystals.25–28 Strain and interface effectscan also be used together to observe new properties asin SrFeO3/SrTiO3 films29, in which oxygen octahedra

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rotations are induced in SrFeO3 by SrTiO3. Motivatedby these observations and the suggestion of Matsui etal.19,20 that BaFeO3 may become a new magnetoelec-tric material, we propose in this work to study the effectof epitaxial strain on the properties of BaFeO3. Usingfirst principles calculations, we investigate through bi-axial strain the possible induced-occurence of a metal-insulator transition, magnetic phase transitions, oxygenoctahedra rotations (OOR), Jahn-Teller (JT) distortionsand charge orderings .

II. COMPUTATIONAL DETAILS

Our calculations have been performed using theDensity Functional Theory, within the projected aug-mented wave (PAW) method30, as implemented in Abinitpackage31–34. The electronic exchange-correlation en-ergy is described with the Generalized Gradient Approx-imation (GGA-PBE)35. To improve the treatement ofthe localized Fe-3d electrons, the GGA plus Hubbard U(GGA+U) method has been employed36, with the on-site coulomb effective U (U =4eV). The U values weretested from 0 to 8 eV. A good agreement of the bulkBaFeO3 properties with the experimental data is foundfor U=4eV. This value was also used in previous theo-retical works16,37. PAW atomic data files have been usedfrom the JTH table (v0.1)38 with the following valencestates configurations: (5s25p66s2) for Ba, (3s23p63d74s1)for Fe and (2s22p6) for O. The convergence on total en-ergy of 10−4Ha is reached for a plane wave energy cut-off of 20 Ha and PAW energy cutoff of 40 Ha. TheMonkhorst-Pack scheme grid of 8× 8× 8, 6× 6× 4 and4×4×4 for the 5 atoms unit cells, 20 atoms supercell and40 atoms supercell, respectively were sufficient to reachthe above energy criterion. Structural relaxations werecarried out until the Helmann-Feynman forces becomeless than 10−6Ha/Bohr. The effect of epitaxial stain wasinvestigated through strained bulk calculations39 with a

misfit strain defined as(

a−a0

a0

), where a0 is the calculated

equilibrium lattice parameter of the five atoms unit cell,and a is the in-plane imposed cell parameter taken equalto√

2a0. The space-group is determined with FINDSYMsymmetry analysis software40. The Glazer notations41 isused to describe the octahedral distortions.

In order to check the accuracy of the pseudopoten-tials (PAW) calculations, additional calculations basedon the Full Potential Linearized Augmented Plane Wave(FP-LAPW) method were performed, as implemented inWien2k code42. The wave functions, electron charge den-sities, and potentials, inside the muffin-tin spheres are ex-panded in terms of the spherical harmonics up to angularmomentum lmax = 10, while the plane-waves are used inthe interstitial region. The muffin-tin spheres radii RMT

of 2.0, 1.9 and 1.2 a.u are used for Ba, Fe and O respec-tively. Convergence is reached for 60 special k-pointsin the irreducible Brillouin zone and RMT ∗ Kmax = 8,

where Kmax is the plane wave cut-off.To explore the effect of the Exchange and Correlation

(XC) interaction on the electronic structure, several XCfunctionals are tested and compared to the GGA+U one.For this purpose, CRYSTAL1443 code based on the lin-ear combination of atomic orbitals method (LCAO) andatom centered Gaussian basis sets is also used. Hybridfunctionals require exact Hartree-Fock (HF) exchangecalculations mixed with the exchange energy of someusual DFT exchange functional. In this work, three addi-tionnal functionals are tested : the hybrid Becke-1 Wu-Cohen (B1WC)44, Heyd-Scuseria-Ernzerhof HSE0645,46

and HSEsol47. We tested the exact exchange mixing pa-rameter of B1WC (16%) for values going from 10% to25%. The lattice parameters and atomic positions arefully optimized and relaxed taking into account carefullyconvergence tests. The atomic distortions are consistentwith the space group Pm3m (5 atoms) and tetragonalP4/mbm (10 atoms). To find the stable magnetic config-urations, the 5 atoms unit cell of the cubic structure wasextended to 20-atom supercell. We used a Monkhorst-Pack scheme with 8× 8× 8, 6× 6× 8 and 6× 6× 4 forthe k-point sampling of the 5, 10 and 20 atoms unit cellsrespectively. The basis sets for Barium, Iron and Oxygenwere taken from references 48, 49 and 50 respectively.

III. RESULTS AND DISCUSSIONS

A. Bulk properties

The ferromagnetic (FM) state of the cubic BaFeO3

(space group Pm3m) is reviewed. The obtained latticeparameter, magnetic moment, bulk modulus and its pres-sure derivative are reported in the Table I. Our resultsfor full potential (Wien2k) and PAW (Abinit) methodsare very close to each other as well as to the availableexperimental and theoretical ones. The best agreementwith the experimental lattice parameter a is obtained forU = 4 eV. Our calculations show a magnetic moment ofv 4 µB (U = 4 eV). This result is consistent with thet2g3 ↑ eg1 ↑ electronic configuration of Fe4+ and withrecent works on BaFeO318,51.

The LCAO calculations using CRYSTAL14 and hy-brid functional HSE06 functional give the lattice con-stant of 3.95 A as DFT+U (U = 0 eV) calculations. TheB1WC and HSEsol underestimate the lattice parametera of about 0.04 A. The mixing of the HF exchange withinthe B1WC functional has not affected the lattice parame-ter. However, increasing this mixing parameter increasesthe magnetic moment of Fe from ∼ 3.6µB (10 % mixing)to ∼ 3.9µB (25 % mixing). This means that the mixingparameter tends to localize the charge on Fe-d orbitals.

The total density of state (DOS) obtained from thetested XC functionals are reported in the Fig 1. TheFig 1 (a) - (c) show the obtained DFT+U DOS usingWien2k and Abinit codes. BaFeO3 is metallic for bothup and down spin channels without the Hubbard U cor-

3

TABLE I: The optimized lattice parameter a0, magnetic mo-ment µ ,bulk modulus B0 and its pressure derivative Bp ofcubic BaFeO3.

a0(A) B0(GPa) Bp µ(µB)Present U=0eV 3.950 132.6 4.77 3.60work U=4eV 3.990 124.7 4.59 4.01Abinit U=8eV 4.046 117.1 4.13 4.33Present U=0eV 3.955 136.1 4.92 3.66work U=4eV 3.995 132.3 4.50 4.02Wien2k U=8eV 4.044 131.6 2.29 4.16

10% B1WC 3.915 - - 3.62Present 16% B1WC 3.913 - - 3.76work 25% B1WC 3.912 - - 3.93Crystal14 HSE06 3.955 - - 3.97

HSEsol 3.916 - - 3.91

Other Th.GGA 3.956 a 139.0 a 4.30 a 3.65 b

works Th.GGA+U 4.026 a 116.0 a 4.50 a 4.03 b

Exp. 3.971 c 167.6 d - 3.50 c

a Ref. [52]b Ref. [18]c Ref. [14]d Semiempirical value in Ref. [53]

rection (Fig 1 a). For U = 4 eV (Fig 1 b), a gap is openedin the minority spin channel resulting in an half metalliccharacter. A similar result is obtained for U = 8 eV (Fig1 c) but with an increased gap in the minority spin chan-nel and a down shift in energy of the DOS around theFermi level for the majority spin channel. These resultsare in agreement with the recent works of Mizumaki etal.18 and Rahman et al.17. All the hybrid functional cal-culations (Fig 1 d and e) give a half metallic behaviorfor the cubic structure of BaFeO3. At a qualitative level,the calculated total DOSs with the hybrid functionalsB1WC (16%), HSE06 and HSEsol show the same trendsas GGA+U for U = 4 eV. Similarly, the Hubbard U valueand the exact exchange mixing parameter of B1WC alterthe band gap width in the minority spin channel (Fig 1c). While the HSE06 and HSEsol functionals give signifi-cantly different structural parameters, there is no sizabledifference between them in the DOS (Fig 1 d). In order tofind the most stable magnetic state of cubic BaFeO3, sev-eral magnetic configurations were considered. The totalenergies of four magnetic orders (FM, A-AFM, C-AFMand G-AFM) were calculated. The FM state energy istaken as a reference. The corresponding differences intotal energies are sum up in Table II. For all the usedapproaches (DFT+U and hybrid functionals), the FMorder is always the lowest energy state (all the energiesrelative to the FM one are positive in Table II) and thenext lowest energy phase is the A-AFM. Our findings arein agreement with the previous theoretical works of Liet al.54, Ribeiro et al.37 and Cherair et al.51. It can benoticed that the energy differences between the magneticorders obtained with DFT+U are more pronounced thatthose obtained with hybrid functionals.

As it can be shown from the obtained bulk proper-ties, the DFT+U calculations with the PAW method

-5

0

5

U=0eV

AbinitWien2k

-5

0

5

(a)

(b)

U=4eV

-5

0

5

Dos

(S

tate

s/eV

/Uni

t cel

l)

(c)

U=8eV

-5

0

5 (d)

Crystal14

10% B1WC16% B1WC25% B1WC

-10 -5 0 5 10E-E

F(eV)

-5

0

5 (e)

Crystal14

HSE06HSEsol

FIG. 1: Total densities of states of the ferromagnetic cubicBaFeO3 obtained by GGA and GGA+U using Abinit andWien2k with (a) U=0eV, (b) U=4eV and (c) U=8eV, andCrystal14 (d), (e) with various Hybrid functionals .The Fermilevel energy EF is located at 0 eV.

TABLE II: Total energies (meV) of different AFM orders rel-ative to the FM phase taken as the zero energy reference.

A-AFM C-AFM G-AFMU=0 eV 375 831 1491U=4 eV 72 574 1416U=8 eV 568 895 120616 % B1WC 107 220 427HSE06 125 236 461HSEsol 126 245 474

4

TABLE III: Hybrid Functional lattice and magnetic resultsfor tetragonal ferromagnetic BaFeO3 (P4mbm) and energydifference ∆E in meV to the cubic relaxed phase calculatedwith the same hybrid exchange correlation functional.

Functional a (A) c (A) a0 (A) QJT (A) µ(µB) ∆E(meV)10 % B1WC 5.581 3.887 3.92 0.178 3.53 -21.8316 % B1WC 5.591 3.873 3.91 0.205 3.62 -35.5825 % B1WC 5.605 3.873 3.85 0.233 3.73 -59.36

HSE06 5.629 3.931 3.96 0.121 3.90 -9.31HSEsol 5.563 3.896 3.91 0.135 3.86 -4.80

(Abinit code) provide the best agreement with previ-ous experimental and theoretical ones. Accordingly, thePAW method is used in the next section to investigatethe effect of structural distortions on the energy loweringof the cubic phase.

B. Lattice distortion

1. Jahn Teller distortions

In the following, the stability of the JT distortion withrespect to the U parameter within DFT+U method isinvestigated. In a cubic octahedral environment and ahigh spin state, the degeneracy of the eg orbitals of Fe4+

is lifted by the occupancy of the fourth electron. Thisis accompanied by a change of symmetry from the cubicto the tetragonal one where the crystal distortion allowsthe energy lowering of the occupied eg orbital pointingtoward the ligands. This fact induce an elongation or acontraction of one of the Fe-O bonds and the change ofthe two others through elasticity. This is the so-calledJahn Teller (JT) effect in crystals. However, BaFeO3

does not show any JT distortions while it has a highspin Fe4+ configuration. Two different JT distortions aredefined: M-JT distortion from the M point (1/2,1/2,0.0)of the Brillouin zone, where each elongation/contractionof the Fe-O bonds are in phase along the z direction (seeFig2-b) and a R-JT distortion from the R point (1/2,1/2, 1/2) of the Brillouin zone where each contractionand elongation of the Fe-O bonds are out-of-phase alongthe z direction (see Fig 2-c). When the M-JT distortionocccurs, it lowers the symmetry from cubic to tetragonalwith the P4/mbm space group (No127) and the R-JT tothe I4/mcm space group (No140).

The total energy variation with the amplitude of theJT distortions is reported in Fig (3-a). For U = 0 eV, theM- and R-JT patterns drive an energy double well andthus allow the energy lowering of the crystal with re-spect to the cubic reference (gain of energy of v 50 and100 meV for the M- and R-JT, respectively). Increasingthe value of U tends to reduce this gain of energy suchas beyond U = 4 eV the double wells are suppressed andare transformed into a single well for both M- and R-JTdistortions. Consequently, it should be emphasized thatthe U parameter stabilizes the cubic symmetry against

FIG. 2: Schematic representation of Jahn-Teller and octa-hedral distortions within the perovskite ABO3 structure. a)Undistorted ideal cubic perovskite structure. b) Jahn Tellerat M point (JT-M). Octahedra in consecutive layers exhibitidentical distortion. c) Jahn-Teller at R point (JT-R). Oc-tahedra in consecutive layers exhibit opposite distortion. d)In phase rotation at M - point (a0a0c+ in Glazer Notation).Consecutive Octahedra rotate about the same angle and di-rection. e) Out-of Phase rotation R point (a0a0c− in Glazernotation). Consecutive octahedra rotate about the same an-gle in opposite directions.

the JT distortions. To reproduce the cubic phase ob-served experimentally a U parameter larger than 4 eVshould be used for BaFeO3. This result goes well withBoukhvalov et al. findings55, who found that the JTdistortion of BiMnO3 is strongly dependent on the U pa-rameter; larger U reduces the JT distortions. They at-tributed this effect to the increase of the Mn-O distancesdue to the MnO6 octahedra expansion.

On Table III are reported our results of the structuraloptimizations using CRYSTAL14 code with various hy-brid exchange correlation functionals. We have used a su-percell of 10 atoms restricted to the P4mbm space group.According to our findings, for all hybrid functionals, theJT distortion lowers the energy with respect to the cu-bic reference phase. Hence, the hybrid functionals fail topredict the correct cubic ground-state of BaFeO3. The

5

B1WC functional gives the strongest energy gain (tenmeV depending on the HF/DFT exchange mixing). Theamplitude of the JT distortion, the tetragonality andthe magnetic moment on the Fe site are increased byincreasing the HF exchange percentage. However, theHSE functionals gives smaller energy gain and the cor-responding JT effect is energetically closer to the cubicphase (∆E < 10 meV). Nonetheless, all the functionalsfail to predict the undistorted cubic ground state eventhough HSE06 has been developed specifically for metal-lic systems46. Our findings are in agreement with thefirst-principles study using the HSE06 functional for theLaMO3 3 d0 → d8 (M = Sc - Cu) compounds. In thisstudy, HSE06 delivered accurate results except for themetallic paramagnets LaNiO3 and LaCuO3

56. The use ofDFT+U and a large enough U is thus better adapted tothe study of BaFeO3 than the hybrid functionals. We willthus focus our study with the DFT+U approach in therest of the paper. It is intersting to note that in KCuF3

36

the U parameter is necessary to observe the JT distortionand in LaMnO3

57;58 the U parameter has the tendencyto enlarge the amplitude of the JT distortions. This is inopposition to what we observe in BaFeO3. In the case ofBaFeO3, the negative charge transfert is such that the in-crease of the U parameter tends to increase the energeticinterval between the Fe-d and O 2p orbitals. In otherwords, larger is the U parameter less hybridized are Fe-dand O-2p orbitals and then less favorable is the JT insta-bility which requires Fe-d and O-2p hybridization. Thiscan suggest that the covalency of the bonds in BaFeO3

is low which is required to observe an undistorted cubicground state.

2. Oxygen octahedra rotations

Oxygen octahedra rotations (OOR) are the most com-mon distortions observed in perovskite crystals.41;59;60

We thus checked whether such octahedra rotations canbe present in BaFeO3. However, from the Goldshmidtfactor61 and from the experiment, it is unlikely that oxy-gen rotations appear. Accordingly, to confirm this fact,we studied the two most common OOR present in per-ovskites: The in-phase rotations of successive octahedra(a0a0c+ in the Galzer notation, see Fig 2-d for its rep-resentation), which appears at the M point of the Bril-louin zone and the out-of-phase rotations (a0a0c−), whichcomes from the R point (see Fig 2-e for its representa-tion). If present independently in one direction, theseOOR lower the cubic symmetry to tetragonal one, withspace groups P4/mbm (127) and I4/mcm (140) for thea0a0c+ and a0a0c− cases, respectively.

As for the JT distortion, we report in Fig (3-b) theenergy versus the a0a0c+ and a0a0c− distortions for U =0 and U = 4 eV. Contrary to the JT distortions, theOOR are always stable whatever the value of U withsteep single energy well. As expected from the Goldshmittolerance factor, we thus confirm that the OOR are not

favorable in BaFeO3.

3. Breathing-type distortion

The third type of perovskite distortions that we cananalyze is the so called breathing of the oxygen octahe-dra. This type of distortion is associated with a chargeordering of the transition metal cation where the differ-ences of charge from site to site change the bond lengthwith the surounding oxygens. This ends up with an alter-nating dilatation and contraction of the octahedra fromsite to site (See Fig 4 for a visualization of the breathingdistortion). The iron usually prefers to have an oxida-tion state of 2+ or 3+. In BaFeO3 the Fe4+ could havea tendency to split into the two oxidation states 3+ and5+ (d5 and d3 orbital filling respectively) to lower theenergy of the system and thus exhibiting a breathing dis-tortion of the oxygen octahedra. Such a distortion wouldlower the symmetry to the Fm3m space group (number225).62 This is not observed in experiments. To confirmthis fact, we investigate the effect of the breathing dis-tortion in BaFeO3. We report the variation of the totalenergy versus several breathing distortions in Fig (3-c)for U =0 and 4 eV. We find that whatever the value of Uthe breathing distortion forms a steep single well. Thus,we confirm that the breathing distortion is unlikely to bepresent in BaFeO3. Our finding agrees with the recentwork of Maznichenko et al.63, who used DFT and XAS,XMCD experiments and they concluded that the oxida-tion of Fe in BaFeO3 is +4 and it can change from +4 to+3 only if oxygen vacancies are present.

4. Polar distortions

BaFeO3 is a metallic compound. Accordingly, we donot expect any polarization that can be present in thecrystal. This is due to the full screening of the charges.Distortions that break the inversion center can be ob-served in metallic perovskite but it is related to stericor geometric effect,64;65. However, these distortions areabsent in BaFeO3. As for the OOR and the breathing dis-tortions, we do not find that polar-like distorions lowerthe energy of the cubic phase of BaFeO3. The absenceof all these distortions is consistent with the absence ofphonon instabilities, already reported in the cubic phaseof BaFeO3.51

C. Epitaxial strain effect

Epitaxial strain is nowadays a well known techniqueto tune the properties of perovskites. In some cases, thistechnique can also induce new phases absent in the un-constrained bulk crystal. We propose in the following tocheck whether epitaxial strain can induce the aforemen-tioned structural instabilities discussed in the previous

6

- 0 . 0 2 - 0 . 0 1 0 . 0 0 0 . 0 1 0 . 0 2

0

5 0 0

1 0 0 0

1 5 0 0

- 0 . 0 2 - 0 . 0 1 0 . 0 0 0 . 0 1 0 . 0 2

0

2 5 0

5 0 0

- 0 . 0 2 - 0 . 0 1 0 . 0 0 0 . 0 1 0 . 0 2

0

1 0 0 0

2 0 0 0

3 0 0 0

Energ

y (me

V/ Su

percel

l)

J T a m p l i t u d e ( F r a c t i o n a l u n i t s )

M - J T ( U = 0 e V ) R - J T ( U = 0 e V ) R - J T ( U = 4 e V ) R - J T ( U = 6 e V ) R - J T ( U = 8 e V )

( a )

O O R a m p l i t u d e ( F r a c t i o n a l u n i t s )

a 0 a 0 c + ( U = 0 e V ) a 0 a 0 c - ( U = 0 e V ) a 0 a 0 c + ( U = 4 e V ) a 0 a 0 c - ( U = 4 e V )

( b )

B r e a t h i n g a m p l i t u d e ( f r a c t i o n a l u n i t s )

F e 4 + ( U = 0 e V ) F e 4 + ( U = 4 e V ) F e 3 + , 5 + ( U = 0 e V ) F e 3 + , 5 + ( U = 4 e V )

( c )

FIG. 3: Energy wells with respect to the amplitude of (a) Jahn-Teller (JT)distortion (b) Oxygen octahedra rotations (OOR)and (c) Breathing-type distortion.The cubic energy is taken as zero

FIG. 4: structural representation of breathing distortion.

section. We thus analyze the stability of the JT, OORand breathing distortions against the application of a bi-axial strain. The biaxial strain can be simulated by fix-ing the two in-plane lattice parameters to simulate theepitaxial growth on a square lattice substrate where theout-of-plane lattice parameter is allowed to relax.26 Wethus define the epitaxial strain as η = a−a0

a0where a0 is

the fully relaxed unconstrained cubic lattice parameterand a is the imposed cell parameter (a = b). We per-formed all of our calculation with strains ranging from−4% to +4 % and with GGA+U = 4eV.

In Fig ( 5-a), we report the total energy of both M-JT

and R-JT phases versus epitaxial strain for the FM, G-, C-, and A-type magnetic orders (the undistorted FMphase. The atomic positions are considered in their highsymmetry positions, but with the optimized c cell pa-rameter corresponding to a fixed a = b in-plane cell pa-rameters. We can see from Fig ( 5-a) that the FM undis-torted high symmetry reference is stable for compressiveepitaxial strain going from −4% to 0%. This fact is alsoobserved up to a tensile strain of +1%. However, beyond+1% of tensile strain, both FM R-JT and M-JT phasesbecome lower in energy than the high symmetry refer-ence structure. Thus, we can conclude that the tensileepitaxial strain stabilizes the JT distortions. When com-paring the energy of the R-JT and M-JT phases undertensile strain larger than +1%, we find that the M-JThas the lowest energy (the energy difference is 3, 8 ,12and 9 meV/supercell at 1, 2, 3 and 4% of tensile strain,respectively). Our present calculations show that beyonda critical tensile epitaxial strain BaFeO3 exhibits a phasetransition from the aristotype phase to an orbital order-ing associated to the M-JT distortion. The critical valueof +1% (represented by a dashed vertical line in Fig (5) isstrongly dependent on the Hubbard value U . In Fig (6),we plot the variation of the critical strain (ηc), necessaryto observe the JT ordering, with the value of U . We canobserve that ηc increases with the value of U . We canalso see that with U = 2 eV, the critical strain is −2%,

7

which means that the JT appears even at 0% strain andthus compressive epitaxial strain destroy the JT. Then,a value of U & 4 eV is needed to describe the BaFeO3

groundstate. In any case, qualitatively, we find that itexists a critical tensile epitaxial strain beyond which aJT phase transition is stabilized in BaFeO3.For all the epitaxial strain values explored in our studywe find that the FM phase is always the stable magneticphase (in Fig (5-a). The energies of the A-, C- and G-type phases are always higher in energy than the FMphase). We also notice that for compressive epitaxialstrain, the energies of the A-type and the FM orderingare close. More interesting, we found that for strongerstrain between -7% and -8%, the A-AFM state becomeslower in energy. In Fig (5-b), we report the amplitudeof the JT-distortions for both R-JT and M-JT for thefour magnetic orderings. Consistent with the Fig (5-a),we find that the JT distortions become non zero at anepitaxial strain larger than +1% for the FM phase. Wealso observe the same apparition of the JT distortions forA-,C- and G- type magnetic ordering at similar criticalstrain as for the FM phase. We also checked the pos-sibility to induce OOR and breathing distortions at allvalues of strain but they never appear. This confirmsthat these distortions are not favorable under epitaxialstrain in BaFeO3.

In Fig (7), we report the total and partial densitiesof states for the undistorted FM high-symmetry refer-ence structure (column a in Figure 7) and the FM (M-JT) phase of BaFeO3 under tensile strain of +4% value(column b in Figure 7) and thus within the GGA+U(U =4eV) calculations. We observe half metallicity inthe case of the undistorted high symmetry structure (seeFigure 7-a) with a gap opened in the minority spin chan-nel, similarly to the unstrained bulk. In the presence ofM-JT distortions (see Figure 7-b), the the split of the Fe3d states is broadened with respect to the undistortedcase (Figure 7-a) but no gap is opened. The JT distor-tions narrow the t2g and eg bandwidth and shift the O2p states above the Fermi level, resulting in a metallicbehavior even for the minority spin. The same observa-tion in orthorhombic BaFeO3 were reported by Rahmanet al.66. We note that the Fe 3d states are lower in en-ergy than the O 2p states, which confirms a negativecharge transfer in BaFeO3 and might explain that thegap is not opened (the 2p orbitals are less localized thanthe 3d orbitals). Recently, an metal-insulator transitionin BaFeO3 thin films is demonstrated experimentally byTsuyama et al.67. According to our calculations, sucha transition is not present in strained bulk crystal. Theexperimentally observed metal-insulator transition couldoriginate from surface effects of the film or from oxygenvacancies, the later will directly affect the O 2p statespresent at the Fermi level and responsible for metallicityin BaFeO3. The possibility to control the electronic statemodification offers a tremendous technological applica-tion, specially in the magnetic information manipulationand has been shown in strained magnetite68;69 that ex-

- 2 5 0

0

2 5 0

5 0 0

7 5 0

- 4 - 3 - 2 - 1 0 1 2 3 4

0 . 0 0

0 . 0 4

0 . 0 8

0 . 1 2

Total

energ

y (me

V/ Su

percel

l) ( a )

( b )

JT am

plitud

e (An

gstrom

)

S t r a i n ( % )

( R - J T ) F M ( R - J T ) A - A F M ( R - J T ) C - A F M ( R - J T ) G - A F M ( M - J T ) C - A F M ( M - J T ) G - A F M ( M - J T ) A - A F M ( M - J T ) F M

FIG. 5: (a)Total energies in meV per (20-atoms supercell)of M-JT (triangles) and R-JT (circles) phases with respectto epitaxial strain for the FM, A-,C- and G-type magneticorders. (b) The JT amplitude as function of epitaxial strain .

2 4 6 8- 2

0

2

4

6

8

Critic

al stra

in (%

)

H u b b a r d U ( e V )

FIG. 6: Variation of the critical strain to destabilise the JTdistortions in BaFeO3 as function of Hubbard U.

8

- 2 0

- 1 0

0

1 0

2 0

- 1 0 - 8 - 6 - 4 - 2 0 2 4- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

- 1 0 - 8 - 6 - 4 - 2 0 2 4

Total

DOS (

States

/eV/U

nit Ce

ll)H i g h S y m m e t r y s t r u c t u r e

( a )

( M - J T ) t e n s i l e - s t r a i n e d ( 4 % )

( b )PD

OS (S

tates/

eV/U

nit Ce

ll)

E - E F ( e V )

3 d - F e - e g 3 d - F e - t 2 g 2 p - O

3 d - F e - e g 3 d - F e - t 2 g 2 p - O

E - E F ( e V )

FIG. 7: Total (top graphs) and partial (down graphs) densi-ties of state for (a) undistorted high-symmetry structure and(b) M-JT phase under +4% of strain. The Fermi level energyEF is placed at 0 eV.

hibits a half-metal to metal transition. BaFeO3 could bea new and interesting candidate for such applications dueto its simple perovskite structure that can be combinedeasily in superlattices or grown as thin film.

IV. CONCLUSION

In this paper, we have studied from DFT+U andLCAO plus hybrid exchange correlation functional theproperties of bulk and strained bulk BaFeO3. The sta-bility of BaFeO3 against the most common structural dis-tortions present in perovskites at the bulk level and un-der epitaxial strain have been investigated. As for othermetallic oxide systems, we found that BaFeO3 is welldescribed using the DFT+U approach with U ≈ 4eVrather than hybrid functionals. In agreement with ex-periments and previous reports, we find that the oxy-gen octahedra rotations and the breathing of the octahe-dra are strongly unfavorable in BaFeO3. The high sym-metry ferromagnetic half-metallic phase is more stable.More interestingly, we found that a Jahn-Teller disor-tion can be induced in BaFeO3 under tensile epitaxialstrain. We also observed that the Jahn-Teller distortionsare strongly sensitive to the values of the U parameter ofthe DFT+U technique. This makes difficult to know thecritical strain at which the Jahn-Teller distortions willappear. However, qualitatively, we can conclude thata Jahn-Teller distortion phase transition can be inducedunder tensile epitaxial strain. Our study can motivate fu-ture experimental studies growing strained thin films ofBaFeO3 in order to induce a Jahn-Teller phase transitionin the absence of other perovskite distortions.70;71 Conse-quently, the BaFeO3 thin films can be used for magneticmanipulation67 and in superlattices as a good candidateto provide robust multiferroic compounds72.

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