Mechanistic Analysis of Oxygen Vacancy Formation and Ionic

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Article

Mechanistic Analysis of Oxygen Vacancy Formation and Ionic Transport in SrFeO 3

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Tadashi Ota, Hidetoshi Kizaki, and Yoshitada Morikawa J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11904 • Publication Date (Web): 30 Jan 2018 Downloaded from http://pubs.acs.org on February 4, 2018

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The Journal of Physical Chemistry

Mechanistic Analysis of Oxygen Vacancy Formation and Ionic Transport in Sr3Fe2O7−δ Tadashi Ota,∗,† Hidetoshi Kizaki,†,‡,¶ and Yoshitada Morikawa∗,†,‡,¶ †Department of Precision Science and Technology, Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan ‡Elements Strategy Initiative for Catalysis and Batteries, Kyoto University, Katsura, Kyoto 615-8520, Japan ¶Research Center for Ultra-Precision Science and Technology, Graduate School of Engineering, Osaka University E-mail: [email protected]; [email protected]

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Abstract The elucidation of the oxygen ionic transport mechanism in atomic scale is important for finding the essential element of the higher efficiency and the wider oxygen content range in the application such as three-way catalysis or SOFC. In this study, the oxygen ionic transport properties of Sr3 Fe2 O7−δ are investigated as a function of its oxygen content by using density functional theory within the GGA+U methods. The calculated activation energy in Sr3 Fe2 O6.0 exhibits a higher migration barrier of 1.35 eV, while those in Sr3 Fe2 O6.25−6.75 are below 1.09 eV. To elucidate the difference of activation energy in Sr3 Fe2 O7−δ , we calculated the electronic and magnetic properties, which vary depending on the oxygen content and should affect the oxygen ionic transport. In our calculation, the energy band gap of 2.2 eV and the G-type antiferromagnetic ordering in Sr3 Fe2 O6.0 are well reproduced. The insulating phase in Sr3 Fe2 O6.25−6.5 is reproduced and the magnetic phase transition from antiferromagnetic to incommensurate antiferromagnetic ordering within the planar FeO2 is also reasonably reproduced within our collinear calculation. In terms of the oxygen diffusion, we found that the vacancy at the O3 site between the bilayers of FeO6 is energetically the most stable and the vacancy at the apical O3 site moves more easily to an adjacent equatorial O1 site of FeO6 than in other directions for vacancy redistribution. The obtained activation energy of the O1 → O3 pathway is 1.09 eV, which agrees with the experimental value. The added O3 atom induces Jahn-Teller distortion, which is related not only with the insulating phase in Sr3 Fe2 O6.25−6.5 but also with the lower activation energy in Sr3 Fe2 O6.25−6.75 , compared with Sr3 Fe2 O6.0 .

Introduction The mechanistic analysis of ion transport and the design of new materials for fast oxideion conductors are very important for developing catalysts for oxygen reduction reaction (ORR) and electrolytes in solid-oxide fuel cells (SOFCs), oxygen-storage materials, oxygenseparation membranes, and methane-conversion reactors. 1–7 For these applications, materials 2


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must be mechanically robust and exhibit excellent ion-transport properties. To satisfy such strict requirements, reasonably good structural stability and proper ionic conductivity must be balanced because a higher structural stability could reduce the mobility of oxygen ions and vice versa. Many perovskite-related materials have been explored in previous research. 8–10 Among them, the family of Ruddlesden-Popper An+1 Bn C3n+1 oxides has been studied for use in ionic-conducting applications, such as SOFCs and oxygen-storage materials, operating at intermediate or high temperatures (300-900◦ C). 11–15 In particular, Sr3 Fe2 O7−δ , which contains no rare-earth elements, has recently been found to exhibit high structural stability and high oxygen-ion conductivity. 14,15 Beppu et al. revealed that Sr3 Fe2 O7−δ shows higher performance in the oxygen storage capacity and the rate of oxygen release and storage, compared with the conventional Pt/Ce2 Zr2 O8 used in three way catalysts. 14 It is also experimentally shown that Sr3 Fe2 O7−δ is more sustainable under H2 reductive conditions than perovskite SrFeO3−δ . SrFeO3−δ decomposes to Fe metal or Sr3 Fe2 O6 at above 850 K, while Sr3 Fe2 O7−δ can tolerate large oxygen deficiencies without decomposing at high temperatures. Even under a severe reductive condition, the space group I4/mmm seems to be preserved. 14 It is experimentally shown that Sr3 Fe2 O7−δ has a water-containing derivative phase holding water in SrO rock-salt layers under an ambient atmosphere. 16–18 The water containing derivative in Sr3 Fe2 O7−δ is still kept in symmetry group I4/mmm, although the derivative phases decompose to SrCO3 after a long exposure to ambient atmosphere. 17,18 While the previous research showed that Sr3 FeMO7−δ (M=Ni,Mn,Ti) are more difficult to have the derivative phase with water and have the longer stability compared with the Sr3 Fe2 O7−δ , to elucidate the primitive mechanism of the oxygen ionic transport, Sr3 Fe2 O7−δ without substitution of another transition metal is investigated in the present study. 18 Sr3 Fe2 O7−δ crystallizes in the Ruddlesden-Popper strontium ferrite structure, which comprises bilayers of SrFeO3−δ perovskite separated by SrO rock-salt layers, as shown in Figure 1. O1 is the equatorial oxygen site within the planar layer of FeO6 , O2 is the apical oxygen site in the SrO layers, and O3 is the apical oxygen site between the bilayers of FeO6 . Oxygen vacancies were experimentally

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demonstrated to exist at the O3 site at low temperatures for the entire range from Sr3 Fe2 O7 to Sr3 Fe2 O6 . 19 In terms of the oxygen ionic transport, it is experimentally reported that the activation energy is 0.6−1.3 eV at low temperature below 850◦ C, while 2.0−2.3 eV at higher temperature over 850◦ C. 11,12,20–23 In these researches, the filled O1 oxygen atom is suggested to migrate toward the vacant O3 site during the migration at low temperature. The activation energy of O1→O3 pathway is estimated as 0.9−1.4 eV at the lower temperature, while that of O1→O1 pathway is 1.5−2.2 eV at the higher temperature using classical force field calculations. 24 On the other hand, another research using density functional theory for (Sr,La)3 Fe2 O7−δ showed that the O1→O1 pathway, whose migration barrier is 0.7−0.9 eV, is the most plausible at the lower temperature, while the O1→O3 and O1→O2 pathway occur at higher temperature in addition to O1→O1 pathway. 25 The clarification of the oxygen ionic transport mechanism in atomic scale enables us to understand the essential element both for the higher efficiency and for the wider oxygen content range, which are very important for the application of the ORR such as three-way catalysis or SOFC. The influence of the oxygen stoichiometry and the magnetic ordering on the oxygen ionic transport in atomic scale, however, has not been studied. The oxygen stoichiometry in the Ruddlesden-Popper series, containing Fe 3d and O 2p orbitals, is found to give rise to a severe change in the electronic and magnetic behaviors. The Sr3 Fe2 O6.0 exhibits G-type antiferromagnetic ordering, with antiferromagnetic Fe spins along both the intra- and inter-layers. When the oxygen content increases from 6.0 to 6.75, the ferromagnetic ordering appears in the planar direction. The fully oxygenated Sr3 Fe2 O7 exhibits incommensurate antiferromagnetic ordering. 26–28 Therefore, to evaluate the activation barrier energy accurately, we must consider the influence of the oxygen stoichiometry and the magnetic configuration on the ionic transport. In this paper, we discuss the atomic structures including Jahn-Teller distortion, electronic and magnetic structures for oxygen content from Sr3 Fe2 O6.0 to Sr3 Fe2 O7.0 using first-principles electronic structure calculations. Then, we investigate the ionic transport processes across O1, O2 and O3 sites and the effect of the oxygen content on the

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activation energies in Sr3 Fe2 O6.0−6.75 .

Methods All of our calculations were performed by using the STATE (Simulation Tool for Atom Technology) program package, which has been successfully used for both semiconductors and metal structures. 29,30 The electronic structures were calculated by using density functional theory (DFT) within the generalized gradient approximation (GGA) method with the Perdew-Burke-Ernzerhof (PBE) exchange correlation energy and GGA+U functionals. 31–37 The Coulomb U and exchange J interaction parameters for the localized Fe 3d electrons were set to U = 5 eV and J = 1 eV. The energy cutoffs for the wave functions and the augmentation charge were 25 Ry and 225 Ry, respectively. The atomic configurations were relaxed by using the generalized direct inversion in the iterative subspace (GDIIS) scheme. The Brillouin zone was sampled with a 12 × 12 × 4 Monkhorst-Pack k-point mesh. 38 While Sr3 Fe2 O6 has a layered square pyramidal configuration, Sr3 Fe2 O7 is the n = 2 member of the Ruddlesden-Popper An+1 Bn C3n+1 family of structures. This family of structures consists of two-dimensional BO6 octahedra in the ab plane and a thickness of n octahedra parallel to the c direction. It has a tetragonal structure with a = 3.89 (Å) and c= 20.04 (Å) for Sr3 Fe2 O6.0−6.75 and a = 3.85 (Å) and c= 20.15 (Å) for Sr3 Fe2 O7.0 and a symmetry group of I4/mmm. The atomic configurations of Sr3 Fe2 O7 and Sr3 Fe2 O6 are given in Figure 1. The O3 site connects the octahedra of Sr3 Fe2 O7 in the c axis, but this site is not occupied for Sr3 Fe2 O6 . The O2 and O1 sites are located at the apical and equatorial sites of the octahedra, respectively. In the calculated unit cell, there are four O3 sites in the crystalline structure. We calculated Sr3 Fe2 O6.25 by adding one O atom into the O3 site of Sr3 Fe2 O6 . Similarly, Sr3 Fe2 O6.5 and Sr3 Fe2 O6.75 are calculated by adding two and three more O atoms into the O3 sites, respectively. The behavior of the magnetic phase in the ferrites was investigated experimentally and found to exhibit antiferromagnetic ordering for the fully deoxygenated

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Sr3 Fe2 O6 and incommensurate antiferromagnetic ordering for the oxygenated Sr3 Fe2 O7 . In our study, structures with G-type, C-type, and A-type antiferromagnetic ordering and ferromagnetic ordering were calculated within collinear magnetic configurations. The G-type has a configuration of antiferromagnetic Fe spins along both the intra- and inter-layers. The C-type has antiferromagnetic ordering within the layers but ferromagnetic ordering between the layers. The A-type consists of antiferromagnetic ordering between the layers and ferromagnetic ordering within the layers. Ferromagnetic ordering contains all ferromagnetic Fe spins. In this paper, the oxidation reaction energy ∆ H is calculated (on a per O2 molecule basis) as follows. 39,40 ∆H =

E(M Ox+0.25 ) − E(M Ox ) −

0.25 E(O2 ) 2

0.25 2

(1)

The previous study has revealed that calculating the oxygen molecule include the overbinding error in DFT with GGA. 39,40 In this study, the calculated oxidation reaction energy is downshifted by the correction ∆h0O2 = 1.36 eV/O2 for the fitting to the experimental chemical potential. 39 To compare the calculated oxidation reaction energy with the experiment, the chemical potential of oxygen molecule, which is fixed by the condition of thermodynamic stability in the surrounding gas phase, is estimated. The temperature and pressure dependence is defined as

µO2 (T, pO2 ) = µ Õ2 (T, p0 ) + kB T ln(

pO2 ). p0

(2)

µ Õ2 (T, p0 ) is based on the experimental values from thermodynamic table at p0 =1 atm. 41,42 Jahn-Teller distortion, which is the local distortion around the iron atom, does not occur for Sr3 Fe2 O6.0 , while it occurs in Sr3 Fe2 O7.0 because of the existence of Fe4+ . Two Jahn-Teller √ distortion modes, Q2 and Q3 , are represented by Q2 = (1/ 2)(X1 − X4 − Y2 + Y5 ) and Q3 √ = (1/ 6)(2Z3 − 2Z6 − X1 + X4 − Y2 + Y5 ), respectively, as shown in Figure 2 35,36,43,44 In the result and discussion, only Q3 mode is discussed because Q2 mode is always zero in this system.

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Sr3Fe2O6

Sr3Fe2O7 perovskite layer 2

Fe O2

O2

O1 Sr

O1 O3

perovskite layer 1

perovskite layer 2 Figure 1: Crystal structures of elementary units of Ruddlesden-Popper ferrites Sr3 Fe2 O6 and Sr3 Fe2 O7 . Strontium and iron cations are represented by green and yellow spheres, respectively. Oxygen atoms are represented by red circles in octahedra around iron cations.

(b)

(a)

z

z

3

3 4

5

4 2

5

y

1 x

2

y

1 x

6

6

Figure 2: (a) The normal mode Q2 and (b) The normal mode Q3 (Q2 , Q3 > 0). Iron and oxygen atoms are represented by yellow and red spheres, respectively.

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ΔH oxidation reaction energy/eV μO2 chemical potential / eV -1.00

105

1

105

-1.50

ΔH, μO2

10-5 -2.00

1

pO2 (atm) 1

10

-2.50 6.00

-10

6.25 6.50 6.75 7.00 600K 900K 1000K Oxygen content 7-δ

Figure 3: Oxidation reaction energy of Sr3 Fe2 O6.0−7.0 . Oxidation reaction energy ∆H is calculated on basis of Eq. 1. Dependence on µO2 (T, pO2 ) has been cast into pressure scale at T=600 K, 900K and 1000 K.

Results and discussion Magnetic and electronic structures of Sr3 Fe2 O6.0−7.0 The electronic structures, magnetic properties and oxygen reaction energy with the oxygen content from Sr3 Fe2 O6.0 to Sr3 Fe2 O7.0 are investigated within the GGA+U . The calculated oxidation reaction energy and chemical potential of Sr3 Fe2 O6.0−7.0 is shown in Figure 3. A higher value of ∆H indicates less likely oxidized. The oxidation reaction energy of Sr3 Fe2 O6.75−7.0 exhibits higher oxidation reaction energy than that of Sr3 Fe2 O6.0−6.75 . The higher oxidation reaction energy in Sr3 Fe2 O6.75−7.0 corresponds to the experimental result that reversible redox cycle occurs between Sr3 Fe2 O6.0 and Sr3 Fe2 O6.75 and Sr3 Fe2 O6.75−7.0 is relatively difficult to oxidize. 14 Based on the calculated results, at the oxygen partial pressure, pO2 = 1 atm and T = 900 K, Sr3 Fe2 O7.0−δ is oxidized up to Sr3 Fe2 O6.75 , while Sr3 Fe2 O6.75−7.0 is difficult to intake the oxygen atom at 900 K. This result is reasonably consistent with the experimental observation that it is oxidized up to Sr3 Fe2 O6.75 at 773 K, although the temperature range is slightly different between theory and experiment by 127 K. 14 Regarding the electronic structures, the total and local densities of states in Sr3 Fe2 O6.0 , Sr3 Fe2 O6.25 and Sr3 Fe2 O6.5 within the GGA+U approximation are shown in Figure 4. The

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20 10 Total 0 10 20

Fe1

0.5 0 0.5

O1

0.5 0 0.5

-8

Sr3Fe2O6.5

Sr3Fe2O6.25

Sr3Fe2O6

20 10 Total 0 10 20

20 10 Total 0 10 20

d 3z2-r2

0.5 0 0.5

Fe1

d x2-y2

0.5

Fe2

0.5 0 0.5

Fe1

0.5

Fe2

0

0 0.5

0.5

-6

-4

2

0

-2

4

O1 Fe1

O1

O3

px

0.5 0 0.5

Energy/eV

Fe2

O3

O3’

pz

0.5 0

0.5 0 0.5

O1

O3

0.5 0 0.5

0.5 z

-8

-4

-6

y x atomic configuration

-2

2

0

4

-8

-4

-6

Energy/eV

-2

0

2

4

Energy/eV

Figure 4: Total and local densities of states in Sr3 Fe2 O6.0 , Sr3 Fe2 O6.25 and Sr3 Fe2 O6.5 within GGA+U approximation. Fermi level is at 0 eV. Black and red lines represent eg and t2g states, respectively. Arrows in lower left figure depict change in atomic configuration when O3 oxygen atom is inserted. Sr3Fe2O7

Sr3Fe2O6.75 Total

20 10 0 10 20

Total

0.5

0.5

Fe1

Fe1

0

0.5

0.5

Fe2

0

0.5

0.5

O1

0

0.5

0.5

O3

0

0 0.5

0.5

-8

0 0.5

0.5

O3

0 0.5

0.5

O1

0 0.5

0.5

Fe2

20 10 0 10 20

-6

-4

-2

0

2

-8

4

-6

-4

Energy/eV

-2

0

2

4

Energy/eV

Figure 5: Total and local densities of states in Sr3 Fe2 O6.75 and Sr3 Fe2 O7.0 within GGA+U approximation. Fermi level is at 0 eV. 9



Sr3Fe2O6.25

Sr3Fe2O6 1.74 eV FM 1.73 eV AAFM2 1.71 eV AAFM1 FM’ 1.31 eV 0.87 eV AAFM4 0.85 eV AAFM3 0.01 eV CAFM 0.0 eV GAFM GAFM

(a)

(b)

(a)

3.0 eV AAFM1,2 2.6 eV FM’ AAFM1 1.35 eV 2.16 eVAAFM4 0.75 eV 2.11 eVAAFM3 FM 0.73 eV 1.37 eVCAFM AAFM2 GAFM 0.40 eV 1.35 eVGAFM CAFM 0.30 eV AAFM4 0.04 eV AAFM3 0.0 eV

CAFM

AAFM1

AAFM2

(b) 1.64 eV FM 1.63 eV AAFM1 1.39 eV AAFM2 1.21 eV GAFM 1.10 eV CAFM 0.96 eVAAFM3 0.90 eVAAFM4

GAFM CAFM FM AAFM2 AAFM1

AAFM3

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Sr3Fe2O6.5

Sr3Fe2O6.75 Sr3Fe2O7

(a)

(a)

(b)

1.57 eV 1.34 eV 0.91 eV 0.80 eV 0.90 eV 0.60 eV

2.30 eVGAFM

GAFM CAFM FM

(b)

GAFM

AAFM2 CAFM

1.62 eV

FM’

FM

1.08 eVAAFM1

1.14 eV 0.82 eV AAFM2 0.81 eV FM 0.42 eV

perovskite layer 2

2.56 eV

CAFM

1.75 eV

1.81 eV CAFM

0.06 eV 0.76 eV AAFM1 AAFM1 0.05 eV AAFM2 0.01 eV 0.0 eV FM 0.0 eV

AAFM4

GAFM

AAFM1 AAFM2 FM

0.43 eV 0.01 eV 0.0 eV

Vacancy position in perovskite layer 1 (a)

(b)

perovskite layer 1 UP DN

V V

Figure 6: Total energy difference between structures with vacancies at O1 and O3 sites in Sr3 Fe2 O6.0−6.75 considering G-type, C-type, and A-type antiferromagnetic and ferromagnetic spin configurations. Black and white circles indicate iron ions with up and down spin magnetic moments, respectively. Four spin configurations are considered for A-type antiferromagnetic configurations. Vacancy at O1 site was located within perovskite layer 1, as shown in figure. total and local densities of states in Sr3 Fe2 O6.75 and Sr3 Fe2 O7.0 are shown in Figure 5. Detail discussion of the electronic structure based on the oxygen content is described in the later sections. In terms of the magnetic properties, the total energies of Sr3 Fe2 O6.0−7.0 with ferromagnetic, G-type, C-type, and A-type antiferromagnetic ordering were calculated within the collinear framework, as shown in the lower left panel of Figure 6. Four types of Atype antiferromagnetic configurations are considered for Sr3 Fe2 O6.0 and Sr3 Fe2 O6.25 . The AAFM1 and AAFM2 consist of ferromagnetic ordering within the layers in the planar direction and antiferromagnetic ordering within or between the perovskite layers. The AAFM3 and AAFM4 have ferromagnetic ordering within the planar layer of the perovskite layer 1 and G-type antiferromagnetic ordering in the perovskite layer 2 in the lower left panel of Figure 6. Structures (a) and (b) are considered in the calculation, as shown in the right panel of Figure 6. Structure (a) has a vacancy at the O3 site, while structure (b) has the vacancy at the O1 site. Structure (b) is the most important atomic configuration for oxygen ion trans10


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port, as discussed later. In the calculated models of Sr3 Fe2 O6.25−6.75 (a), only one O3 atom exists within perovskite layer 1 in the lower panel of Figure 6. The structures of Sr3 Fe2 O6.5 (a) and Sr3 Fe2 O6.75 (a) have one and two O3 atoms in perovskite layer 2, respectively. Bond lengths for Sr3 Fe2 O6.0−7.0 around the iron atoms by computation and experiment are shown in Table 1. 28,45 In case of Sr3 Fe2 O6.25−6.75 , some of iron atoms have O3 atoms as a ligand because the O3 atoms are partially filled. The local bond lengths in Table 1 are those around the iron atoms with O3 atoms as a ligand, while the average bond lengths are the average of all bond lengths for Fe-O1, Fe-O2 and Fe-O3 bonds. The Jahn-Teller distortion, Q3 mode, is calculated in the Table 2. The Jahn-Teller distortion from Sr3 Fe2 O6.25−6.75 is estimated based on the local and average bond lengths around iron atoms, same as the bond lengths in Table 1. The electronic structure, magnetic properties and Jahn-Teller distortion of each oxygen content in Sr3 Fe2 O6.0−7.0 are discussed in the following subsections. Table 1: Bond lengths of Sr3 Fe2 O7.0−δ around iron atom. In the calculation, local values are bond lengths around iron atoms with O3 atoms as a ligand, while average values are average of all bond lengths for Fe-O1,Fe-O2 and Fe-O3.

calculation (Å) local Fe − O1 Fe − O2 Fe − O3 average Fe − O1 Fe − O2 Fe − O3 experiment (Å) Fe − O1 Fe − O2 Fe − O3

Sr3 Fe2 O6.0

Sr3 Fe2 O6.25

Sr3 Fe2 O6.5

Sr3 Fe2 O6.75

Sr3 Fe2 O7.0

1.98 1.91 -

2.03 1.96 1.91

2.03 1.96 1.91

1.97 1.95 1.94

1.93 1.96 1.97

1.98 1.91 -

1.97 1.92 1.91

1.96 1.94 1.91

1.95 1.94 1.94

-

1.98 1.89 -

1.98 1.93 2.07

1.94 1.93 2.00

1.94 1.93 1.98

1.92 1.94 1.95

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Table 2: Jahn-Teller distortion of Sr3 Fe2 O6.25−7.0 . Q3 mode are estimated based on calculation and experiment in Angstrom units. Local values in calculation are estimated by bond lengths only around iron atoms with O3 atoms as a ligand, while average values are calculated by all bond lengths in unit cell.

calculation local average experiment

Sr3 Fe2 O6.25

Sr3 Fe2 O6.5

Sr3 Fe2 O6.75

Sr3 Fe2 O7.0

-0.15 (-0.09)

-0.15 (-0.06)

-0.04 (-0.02)

0.06 -

(0.03)

(0.04)

(0.04)

(0.04)

Sr3 Fe2 O6.0 The calculated insulating phase with the electronic gap of 2.2 eV agrees very well with the experimental value (2.3 eV), as shown in Figure 4. 22 In the total and local density of states for Sr3 Fe2 O6 , the strong hybridization of the Fe 3d and O 2p states generates bonding and anti-bonding states near the Fermi level, where the top of the valence band is an anti-bonding eg state. As for the magnetic structure, the most stable spin configuration is found to be the G-type antiferromagnetic configuration, which is also consistent with the experimental result, as shown in Figure 6. 26 Here, the GGA+U method is applied, because the calculated results within the GGA underestimated the energy gap(1.0 eV, not shown here), although the GGA still correctly predicts that the G-type antiferromagnetic spin configuration is the most stable spin configuration. In the case of Sr3 Fe2 O6.0 (b), we performed SCF calculation starting from the totally ferromagnetic (FM) ordering. However, the FeO2 plane just above the O3 atom, which moved from the neighboring O1 site, became antiferromagnetically ordered, while other spin configurations kept ferromagnetic ordering. Therefore, totally FM ordering could not be obtained for this structure. We denote this magnetic ordering as FM’, as shown in Figure 6. Regarding the atomic structure, the calculated bond lengths of FeO1 and Fe-O2 in Sr3 Fe2 O6.0 become 1.98 Å and 1.91Å, respectively. The calculated bond lengths agree very well with the experimental results. Jahn-Teller distortion does not occur for Sr3 Fe2 O6.0 , because Fe4+ does not exist in Sr3 Fe2 O6.0 .

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Sr3 Fe2 O6.25 As for the electronic structure, the total and local densities of states for Sr3 Fe2 O6.0 and Sr3 Fe2 O6.25 are shown in the Figure 4. The main structural difference between Sr3 Fe2 O6.0 and Sr3 Fe2 O6.25 is the existence of an O3 atom close to the O1 in Sr3 Fe2 O6.25 , as shown in the lower-left panel of Figure 4. By adding the O3 atom, the d3z2 −r2 state at the Fe1 site hybridizes strongly with the pz orbital of the added O3 atom and is partially shifted above the Fermi level because of the anti-bonding character of the d3z2 −r2 orbital, leading to the strengthening of the Fe1-O3 bond. Furthermore, the anti-bonding electron of the dx2 −y2 state at the Fe2 site is also extracted and accommodated into the minority spin states of the Fe2 site, leading to the strengthening of the Fe2-O1 bond. Because of the re-distribution of the electrons induced by adding the O3 atom, the Fe1 atoms move towards the O3 atom, and the O1 atom relaxes towards the Fe2 atom, as shown in the lower left panel of Figure 4. Here, the iron atom at Fe1 site near the O3 atom becomes Fe4+ due to the extraction of the anti-bonding eg state electron, while the iron atom at Fe2 site keeps Fe3+ , where the extracted electron at Fe2 site moves from majority spin towards the minority spin of the same Fe2 site. The electronic structure of Sr3 Fe2 O6.25 exhibits the insulating phase. This insulating property is related with the distortion in Sr3 Fe2 O6.25 . The addition of the O3 atom changes the atomic configuration and gives rise to the Q3 mode of Jahn-Teller distortion, as shown in Table 2. The Jahn-Teller distortion removes the degeneracy and the electronic structure of Sr3 Fe2 O6.25 becomes the insulating phase. This result also corresponds with the small polaron mechanism discussed in the previous experimental research. 20 Regarding the magnetic properties, the stable magnetic ordering is found to be AAFM3 for Sr3 Fe2 O6.25 , as shown in Figure 6. This AAFM3 configuration has parallel spins within the planes parallel to the a and b axis in perovskite layer 1 with O3 atom, while G-type antiferromagnetic ordering is maintained in perovskite layer 2 without O3 atom. The experimental research also shows that the magnetic configuration of Sr3 Fe2 O6.25 exhibits the antiferromagnetic ordering, which agrees well with the calculated result. 26 13



Sr3 Fe2 O6.5 The electronic structure of Sr3 Fe2 O6.5 becomes a small gap insulator which agrees with the experimental result. 46 The atomic structure of Sr3 Fe2 O6.5 has O3 atoms in both perovskite layer 1 and layer 2 in the lower left panel of Figure 6. On the other hand, the stable spin configuration is found to be AAFM1, which has parallel spins in the planar direction for both perovskite layers. The experimental result also shows ferromagnetic ordering in the planar direction for Sr3 Fe2 O6.5 . 26 Based on the stable magnetic ordering in Sr3 Fe2 O6.25−6.5 , one can see that the parallel spin configuration in the planar direction is stabilized by the addition of O3 atom in the perovskite layers in the lower left panel of Figure 6.

Sr3 Fe2 O6.75−7.0 The calculated electronic structure shows half-metallic, which cannot reproduce the experimental result with insulating phase, as shown in Figure 5. As for the magnetic properties, in case of Sr3 Fe2 O6.75 , the stable magnetic ordering is ferromagnetic in the computation, where the parallel spins within the a and b axes in the experiment are well reproduced. 26 In case of Sr3 Fe2 O7.0 , the stable spin configuration becomes the ferromagnetic ordering within the collinear calculation. The calculated result of the ferromagnetic structure is not consistent with the incommensurate helical antiferromagnetic structure with the spin canting of 51 degrees in the planar direction observed in the experiment. 26 The experimentally observed spin canting of Sr3 Fe2 O7.0 is more similar with ferromagnetic ordering than antiferromagnetic ordering in the planar direction. The calculated result in Figure 6 shows that the magnetic structure with ferromagnetic ordering in the planar direction such as AAFM1, AAFM2 and FM ordering are more stable than those with antiferromagnetic ordering of CAFM and GAFM. The stable magnetic structures obtained by the calculation agree with the experimental result within the collinear approximation. We have investigated the different calculation models of Sr3 Fe2 O7.0 with the lower symmetry to reproduce experimentally observed insulating phase presumably arising from charge disproportion. However, we can14


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not reproduce charge disproportion and insulating phase of Sr3 Fe2 O7.0 . This discrepancy could be due to the collinear treatment of the magnetic ordering in our calculations. The distortion mode Q3 in Sr3 Fe2 O7 is 0.06 Å and 0.04 Å (∆ 0.02 Å) in the computation and experiment, respectively. The calculated distortion Q3 is slightly overestimated compared with the experimental one, and the difference between the experiment and computation is small enough to estimate the Jahn-Teller distortion in Sr3 Fe2 O7 . Although the previous study showed that the magnitude of Jahn-Teller distortion calculated by using the GGA+U method is underestimated for LaMnO3 compared with the experimental value, another piece of research recently revealed that the GGA+U method reasonably well reproduces JahnTeller distortion for LaMnO3 . 35,36 Trend in the magnetic structure The magnetic order for Sr3 Fe2 O6.0 is understood by the strong antiferromagnetic superexchange interaction, which can be weakened as the oxygen content increases in Sr3 Fe2 O7.0−δ . To demonstrate the detail of the exchange interactions, the exchange parameters J∥ and J⊥ are estimated as the total energy differences between the antiferromagnetic and ferromagnetic configurations for Sr3 Fe2 O6.0−7.0 , as shown in Figure 7. J∥ is defined as the exchange interaction between the nearest neighboring iron ions in the parallel direction within the perovskite layers, while J⊥ is defined as that in the perpendicular direction, as shown in Figure 7. J∥ and J⊥ are considered as follows. J∥ = Hex(↑↓) − Hex(↑↑) (in plane)

J⊥ = Hex(↑↓) − Hex(↑↑) (out of plane)

(3) (4)

The sign of exchange parameter J∥ changes as δ in Sr3 Fe2 O7.0−δ increases. J∥ in Sr3 Fe2 O6.0 without an O3 oxygen atom occupancy is strongly negative, indicating a strong antiferromagnetic interaction parallel to the perovskite layers for both structures (a) and (b) due

15



to the strong superexchange interaction within the parallel iron layers. For Sr3 Fe2 O6.25−7.0 , J∥ is positive and increases as the occupancy of the O3 site increases, implying that the occupancy of O3 atoms strengthens the ferromagnetic interaction in the parallel direction of the iron layer. In contrast, J⊥ is weakly negative for Sr3 Fe2 O6.0 due to the lack of O atoms at the O3 sites, but it increases to be nearly equivalent in value to J∥ for Sr3 Fe2 O6.75−7.0 with more O3 atoms. The exchange interaction of J⊥ through the SrO rock-salt layers is less than 5 meV and relatively smaller than that through perovskite layers. Detailed analysis of the origin for the exchange interaction should be investigated in the future work.

(2) J// > 0, J < 0

(1) J// < 0, J < 0 (a) Vacancy at O3 site (b) Vacancy at O1 site

Perpendicular exchange Parallel exchange interaction J// /eV interaction J /eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 28

0.1 0.05

Sr3Fe2O6.25(a),(b) perovskite layer 1 Sr3Fe2O6.5(a),(b) perovskite layer 1,2 Sr3Fe2O6.75(a),(b) perovskite layer 1

Sr3Fe2O6(a) perovskite layer 1,2 Sr3Fe2O6(b) perovskite layer 2 Sr3Fe2O6.25(a),(b) perovskite layer 2 Sr3Fe2O6(b) perovskite layer 1

Sr O

0 -0.05 -0.1

J

0.1 0.05

J//

J// J//

J

Fe

or

(3) J// > 0, J > 0

0

Sr3Fe2O6.75(a),(b) perovskite layer 2 Sr3Fe2O7.0 perovskite layer 1,2

-0.05 -0.1

6.00 6.25 6.50 6.75 7.00

J//

J

Oxygen content 7-δ Figure 7: Parallel and perpendicular exchange interactions for each perovskite layer of Sr3 Fe2 O6.0−7.0 . Perovskite layer definition is same as in Figure 6.

Oxygen ion transport of Sr3 Fe2 O6.0−7.0 Oxygen ion transport pathway Based on the discussion of each oxygen content from Sr3 Fe2 O6.0 to Sr3 Fe2 O7.0 in the previous section, the electronic structure and magnetic configuration of Sr3 Fe2 O6.0−6.75 is reasonably 16


J

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well reproduced by the calculation. In terms of the electronic structure of Sr3 Fe2 O6.75−7.0 , a small gap insulator is experimentally shown, while it is metallic in our calculated results. 26 However, in the present study, we focus on the ionic diffusion process in Sr3 Fe2 O7−δ with the oxygen content range of Sr3 Fe2 O6.0−6.75 . Therefore, it is essential that the insulating phase of Sr3 Fe2 O7−δ be reasonably reproduced for the electronic structure of the oxygen content range of Sr3 Fe2 O6.0−6.5 in the present study. For example, the insulating phase of Sr3 Fe2 O6.0−6.5 , including the electronic gap of 2.2 eV in Sr3 Fe2 O6.0 is well reproduced in our calculations. Furthermore, the magnetic properties in Sr3 Fe2 O6.0−6.75 are rather well reproduced by the present calculations. The experimental result shows that the commensurate antiferromagnetic order in Sr3 Fe2 O6.0 and ferromagnetic ordering appear as the oxygen content increases to Sr3 Fe2 O6.75 . This trend is reasonably reproduced by the present calculations, as shown in Figure 6. To investigate the mechanism of oxygen ion transport on the basis of first-principles calculations, the activation energies of the possible pathways are explored for Sr3 Fe2 O6.5 . Here, we assume that the magnetic ordering is A-type antiferromagnetic (AAFM1) ordering for all configurations. Three types of structures with one vacancy and six ionic pathways are shown in Figure 8. The vacancy exists at the O3, O1, or O2 site, and two possible pathways are considered for each model. The activation energies are calculated by using the climbing image nudged elastic band (CI-NEB) method. The obtained total and activation energies are shown in Table 3 and Figure 9. Among the three possible positions of oxygen vacancy, we found that the vacancy at the O3 site is energetically favorable, which agrees with the experimental results. 14,19 The total energies of the structure with a vacancy at O3 site are 0.76 eV and 1.74 eV, more stable than those with vacancies at the O1 and O2 sites, respectively. The activation energy of oxygen migration for the O1→O3 pathway is 1.09 eV and it is found to be the lowest among other plausible pathways across the O1, O2 and O3 sites, as shown in Figure 9. Second possible pathways other than O1→O3 are the O1→O1 and O1→O2 pathways, whose activation energies are 1.34eV(0.76 →2.10eV)

17



Page 18 of 28

and 1.26eV(0.76→2.02eV), respectively. The O3→O3 pathway exhibits a considerably high value of 3.28 eV because it is difficult for the oxygen atom to pass through due to the narrow space between the strontium atoms.

(i)

(ii)

(iii)

O2→O1

O2→O2

O2’→O2 V

O1→O3 O3→O3

V

V

O1→O1

Figure 8: Schematic picture of oxygen vacancy positions and six ion-transport pathways in Sr3 Fe2 O6.5 . Configurations in (i), (ii), and (iii) represent structures with vacancies at O3, O1, and O2 positions, respectively. Table 3: Total energies and activation energies for structures with vacancies at O3, O1, and O2 sites for Sr3 Fe2 O6.5 . Total energy of structure with vacancy at O3 site was set to zero. vacancy at O3 site vacancy at O1 site vacancy at O2 site total energy/eV 0.00 0.76 1.74 O3 → O3 O1 → O3 O1 → O1 O2 → O1 O2 → O2 O2 → O2’ activation energy/eV 3.28 1.09 2.10 2.02 3.21 3.03

Influence of stoichiometry Next, the influence of oxygen occupancy on the activation energy was examined for Sr3 Fe2 O6.0−6.75 . The migration barrier of the O1 → O3 pathway is considered because this pathway is found to be the most plausible within the oxygen ionic transport in Sr3 Fe2 O6.0−6.75 . In this calculation, the activation energy is obtained by using the CI-NEB method. As for the O1 → 18


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4

Energy/eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3.28

3.21

3 2.10

2

3.03

2.02 2.28

1.09

1.74

1.74

O2

O2

1 0.76

0.76

O1

O1

0 O3

O3

O2’

Vacancy position Figure 9: Calculated oxygen migration energy as function of vacancy position. Red line represents lowest activation energy of O1 → O3 pathway in Table 3. O3 oxygen migration, the calculated activation energy for Sr3 Fe2 O6.0 is 1.35 eV, while those for Sr3 Fe2 O6.25−6.75 are below 1.09 eV, indicating a large dependence on the oxygen content, as shown in Table 4. As discussed in the previous section of Sr3 Fe2 O6.25 , because of the re-distribution of the electrons induced by adding the O3 atom, the Fe1 atoms move towards the O3 atom, and the O1 atom relaxes towards the Fe2 atom, as shown in the lower left panel of Figure 4. This structural relaxation makes it easier for the Fe1-O1 bond to break and O1 atom to migrate towards the O3 ’ site. The added O3 atom makes the bonding between the Fe1 and O1 atoms easier to break and tightens the bonding between the Fe2 and O1 atoms. Here, the relaxed O1 atom is predicted to move more easily to the neighboring O3 ’site due to the addition of the O3 atom. This effect of the added O3 atom is applicable to Sr3 Fe2 O6.25−6.75 , where the atomic and electronic structure of the SrFeO3.0−δ layer is the same in the calculation. Therefore, the activation energy of Sr3 Fe2 O6.25−6.75 is lower than that of Sr3 Fe2 O6.0 in Tabel 4 because the O3 atom reduces the activation energy of the O1 → O3’ pathway. Here, Jahn-Teller distortion in Sr3 Fe2 O6.25−6.5 induced by the addition of O3 atoms is related not only with the insulating phase of the electronic structure but also with the relatively lower activation energy compared with Sr3 Fe2 O6.0 . In terms of the influence of the magnetic configuration on the activation energy, the activation energy of the oxygen ionic transport in Sr3 Fe2 O6.0−6.75 is highly related to the 19



Page 20 of 28

Table 4: Activation energies of Sr3 Fe2 O6.0−6.75 . Total energy differences between vacancies at O1 and O3 sites are calculated. Sr3 Fe2 O6.0 activation energy/eV 1.35

Sr3 Fe2 O6.25 1.03

Sr3 Fe2 O6.5 1.09

Sr3 Fe2 O6.75 1.09

total energy difference between structures (a) and (b) in Figure 6. Here, the total energies in Sr3 Fe2 O6.0−6.75 change more than 0.7 eV by the conversion of the magnetic configuration. This total energy difference is large enough to bring about the possibility of a smaller activation energy depending on the magnetic configuration. However, if we assume that magnetic ordering is the same before and after oxygen migration, the total energy difference between structures (a) and (b) would be almost the same as that for the most stable magnetic ordering. For example, in the case of Sr3 Fe2 O6.0 , the total energy difference for G-type antiferromagnetic (GAFM) ordering between structures (a) and (b) is 1.35 eV, while that for FM’ ordering is 1.29 eV(1.31→2.6 eV). In the case of Sr3 Fe2 O6.25 , the total energy difference for AAFM3 ordering was 0.96 eV, while that for FM ordering was 0.89 eV(0.75→1.64 eV), as shown in Figure 6. Therefore, the effect of the magnetic configurations on the activation energy is expected to be small in this system. Although the electronic and magnetic properties in the range of Sr3 Fe2 O6.75−7.0 are partly inconsistent with the experimental result, those of Sr3 Fe2 O6.0−6.75 are reasonably well reproduced by the present GGA+U calculations. Therefore, the transport properties of Sr3 Fe2 O6.0−6.75 discussed in the present study should be reliable. Furthermore, concerning the GGA+U approach, the calculated results have the possibility of being affected depending on the choice of parameter U . However, the difference in the activation energies between GGA and GGA+U is confirmed to be no more than 10 percent for this system. Therefore, the calculated results for the ionic transport properties in Sr3 Fe2 O7.0−δ are not affected depending on the choice of parameter U .

20


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Summary The oxygen ionic transport properties of Sr3 Fe2 O7−δ are investigated as a function of its oxygen content by using density functional theory within the GGA+U methods. The elucidation of the oxygen ionic transport in the atomic scale helps to understand the essential factors both for the higher efficiency and for the wider oxygen content range which are very important for the applications. The calculated electronic structure in Sr3 Fe2 O6.0 shows the energy band gap of 2.2 eV and the G-type antiferromagnetic ordering, which agrees very well with the experiment. The insulating phase in Sr3 Fe2 O6.25−6.5 is reproduced and the magnetic phase transition from antiferromagnetic to incommensurate antiferromagnetic ordering within the planar FeO2 is also reasonably reproduced within our collinear calculation. Regarding the oxygen ionic transport, we found that the vacancy at the O3 site between the bilayers of FeO6 is energetically the most stable and the vacancy at the apical O3 site moves more easily to an adjacent equatorial O1 site of FeO6 than in other directions for vacancy redistribution. The obtained activation energy in Sr3 Fe2 O6.0 exhibits a higher migration barrier of 1.35 eV, while those in Sr3 Fe2 O6.25−6.75 are below 1.09 eV. We found that the addition of O3 atom induces the Jahn-Teller distortion, which is related not only with the insulating phase of the electronic structure but also with the lower activation energy in Sr3 Fe2 O6.25−6.75 , compared with Sr3 Fe2 O6.0 .

Acknowledgement We thank Kosuke Beppu, Saburo Hosokawa, Tsunehiro Tanaka, Kunihiko Yamauchi and Tamio Oguchi for the valuable discussions. This work was supported by the MEXT “Elements Strategy Initiative to Form Core Research Center” program and Grants-in-Aid for Scientific Research on Innovative Areas “3D Active-Site Science (No. 26105010)” and Scientific Research (C) (No. 26410014) from the Japan Society for the Promotion of Science (JSPS). The figures in this paper were produced by the VESTA program. 47 21



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27



Graphical TOC Entry Activation energy/eV 4

03

03 01

02

01

03

03 01

02’

Energy/eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.28

3.21

3 2.10

2

3.03

2.02 2.28

1.09

1.74

1.74

O2

O2

1 0.76

0.76

O1

O1

0 O3

O3

O2’

Vacancy position

Sr3Fe2O7-δ

28


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Mechanistic Analysis of Oxygen Vacancy Formation and Ionic

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