3
The atomic structures and relative stability of LaO- and FeO
2
-terminated
LaFeO
3
(001) surfaces
Since LaFeO
3
(001) has alternating LaO +1 and FeO
2
-1 layers, the surface presents either a LaO- or an FeO
2
-termination, and finite slabs should have nonzero dipole moments. Stabilization of the polar surfaces requires geometric and/or electronic reconstruction of the atomic layers, even including the formation of vacancies and adsorption of other species on the surface.
1
Indeed, upon full optimization of LaO- and FeO
2
-terminated surfaces, it was found that the geometric and electronic structures of the two surfaces undergo some modification, as shown in Table S1.
There,
 d =d relaxed
-d ideal ij ij ij
is the change in the relaxed interlayer spacing between layer i and j from the ideal surface structure, where the positions of layers are determined by the average vertical coordinates of the cations in each layer. Overall, the distortion of oxygen octahedra and the atomic-layer rumpling in the top two layers are pronounced, however, it does not penetrate further than 3-4 layers. The distance between the outermost and second layers of the LaO- and FeO
2
-terminated surfaces is compressed by 0.15 and 0.16 Å, while that between the second and the third layers is expanded by 0.07 and 0.13 Å, respectively, finally converging to values close to zero for both surfaces. Therefore, it is reasonable to use the 7-layer thick slabs for our studies of the properties of bare surfaces and the interactions between Pd metal and
LaFeO
3
(001).
To stabilize the polar surfaces, the electronic structures usually undergo self-consistent charge redistribution, which is more complex than that of the classic model based on the formal ionic charges. Thorough insight can be obtained by Bader charge analysis.
2 The atomic and layer charges for both terminations of LaFeO
3
(001), as well as the bulk values, are presented in Table S1. Because of the strong hybridization of La and Fe with O, the charges deviate from the perfect ionic limit.

For LaFeO
3
bulk, the charges were calculated to be +2.07, +1.92 and -1.33, instead of the formal +3, +3 and -2 for La, Fe and O, respectively. Similarly, the charges of electron-rich LaO and electron-poor FeO
2
terminations are changed from ± 1 to
+0.65 and -0.5, respectively. The additional electrons and holes are also roughly delocalized over three and four layers of LaO- and FeO
2
-terminated surfaces, respectively, with the result that the layer charges are strongly modified. Finally, the differences between these layer charges and the LaFeO
3
bulk values achieve convergence by the third and fourth layers of the LaO- and FeO
2
-terminated surfaces, as presented in Table S1. Correspondingly, the magnitude of the Fe atom magnetic moments were calculated to be 3.62 and 4.14 μ
B
in the second and fourth layers of
LaO-terminated surface and 4.0 and 4.12
μ
B
in the first and third layers of
FeO
2
-terminated surface, respectively, while the magnetic moments of O and La atoms are negligible.
The thermodynamic stability of a surface in contact with an oxygen atmosphere is closely related to temperature T and oxygen pressure p . If the surface is in equilibrium with atomic reservoirs, the stability is characterized by the surface Gibbs free energy, which is defined as:
 
1
2A

E slab

N

La La

N

Fe Fe

N

O O

PV

TS

(1)
At 0 K and typical pressures, the PV and TS terms can be neglected with respect to other contributions. For the LaFeO
3
bulk system, the chemical potential of the compounds can be written as a sum of the chemical potential of each component within this crystal:

LaFeO
3
 
La
 
Fe

3

O
(2)
Combining (2) with (1) and eliminating the
 term, we can obtain:
Fe
 
1
2A


E slab
 
N
La

N
Fe
 
La

N
Fe

LaFeO
3
 
N
O

3N
Fe
 
O


(3)
Introducing the variation of the chemical potentials (

O

1
2

O gas
2
  
O
and

La
  bulk
La
  
La
) in Eq.(3) , we can obtain:

 
1
2A

1
2A
E slab
 
N
La

N
Fe
  bulk
La

N
Fe

LaFeO
3

N
La

N
Fe
  
La
 
N
O

3N
Fe
  
O

1
2

N
O

3N
Fe
 
O gas
2 (4)
Since the system is in thermodynamical equilibrium, the surrounding O
2
atmosphere acts as an ideal reservoir for the surfaces. As suggested in Refs. 3-5, the ab initio total energy of an isolated O
2
was chosen as a reference to calculate the oxygen chemical potential as functions of temperature T and oxygen partial pressure p . It is well known that traditional DFT methods would overestimate the binding energy of O
2
.
4, 6, 7
However, this intrinsic weakness doesn’t affect the calculations significantly, because the oxygen chemical potential variation rather than the chemical potential itself is used
as the variable.
4, 8
Under the ideal gas approximation, the oxygen chemical potential
variation Δμ
O
(T, p ) can be expressed as:
 
O
 
O
T p 0 )

1
2 k T
B ln


 p
 p
0 
 , (5)
The μ
O
(T, p
0
) term determined by the contribution from molecular vibration and rotation, is given by 3 :

O
T p 0 )

1
2
( , 0 )- (0 , 0 )

1
2
 ( , 0 )

S (0 , 0 ) (6)
At the standard pressure p
0
= 1 atm, by using the experimental enthalpy and entropy of
O
2
from thermodynamical tables, 9 μ
O
(T, p 0 ) can be derived, as listed in Table S2.
Employing Eq. (5), we can obtain the dependence of Δμ
O
(T, p ) as a function of the given temperature T and oxygen pressure p . Since the surfaces were oxidized in air, the specific oxygen partial pressure p is approximately 0.2 atm.
Furthermore, Δμ
O
(T, p ) can be varied experimentally within certain boundaries under the thermodynamic equilibrium conditions. The chemical potential of the compound can be rewritten as:

LaFeO
3
  bulk
La
  bulk
Fe

3
2
 gas
O
2
 
H 0 f
(7)
 bulk
La
,
 bulk
Fe
,
 gas
O
2 are the energies of the La atom in the hcp bulk metal, the Fe atom in the bcc bulk structure and the O atom in the gas phase O
2
molecule, respectively.
So, we can get the Gibbs free energy of formation

H
0 f by


H f
0 


La
  bulk
La

Fe
  bulk
Fe



3

O

3
2
 gas
O
2

(8)
The chemical potential in compounds for each species must be less than the chemical potential in its bulk phase, otherwise the compound would be unstable and decompose into elemental phases. So,

La
  bulk
La
,

Fe
  bulk
Fe
and

O

1
2
 gas
O
2
(9)
Thus, 1
3

H f
0   
O

0 ,

H
0 f
  
La

0 . Here,

H f
0
is the 0 K formation heat of
LaFeO
3
bulk, which is calculated to be -10.34 eV. The stability of LaO- and
FeO
2
-terminated LaFeO
3
(001) surfaces as a function of temperatures T (at p = 0.2 atm) and oxygen partial pressure (at T = 1000 K) is shown in Figure S1. Note that the formation of a surface will be exothermic and spontaneous if Ω becomes negative, leading the crystal to decompose. Therefore, the surface slab can be stable on the condition that Ω is positive. As illustrated in Figure S1, only the FeO
2
-terminated surface is available under conditions where the temperature is higher than 1700 K
(with p
O2
= 0.2 atm), which is comparable to the transition temperature of 1500 K obtained by Lee et. al.
,
4
or the oxygen partial pressure is lower than 10
-10
atm (at T =
1000 K), assuming that the phase transition from orthorhombic to tetragonal or cubic doesn’t happen. The LaO-terminated surface is thermodynamically more stable under the oxygen chemical potential μ
O
(T, p ) in the range of -2.20~-1.00 eV, i.e., at temperatures between 800 and 1700 K ( p
O2
= 0.2 atm) or the oxygen partial pressure between 10 0 to 10 -10 atm (T = 1000 K). The FeO
2
-terminated surface turns out to be more stable under the oxygen chemical potential higher than -1.0 eV, corresponding to a temperature lower than 800 K ( p
O2
= 0.2 atm) or the oxygen partial pressure higher than 10
0
atm (T = 1000 K). The results are slightly in disagreement with the conclusion from Ref. 10 in which the authors claimed that the LaO-terminated surface is not stable over a wide range of oxygen chemical potential, the extent of which was not explicitly provided.

1
2
3
4
5
6
7
8
9
10
A. Asthagiri and D. Sholl, Phys. Rev. B 73 (2006).
R. F. W. Bader, Atoms in Molecules: A Quantum Theory (Oxford University Press, New York,
1990).
K. Reuter and M. Scheffler, Phys. Rev. B 65 (2001).
C.-W. Lee, R. Behera, E. Wachsman, S. Phillpot, and S. Sinnott, Phys. Rev. B 83 (2011).
E. Heifets, S. Piskunov, E. Kotomin, Y. Zhukovskii, and D. Ellis, Phys. Rev. B 75 (2007).
Y.-L. Lee, J. Kleis, J. Rossmeisl, and D. Morgan, Phys. Rev. B 80 (2009).
L. Wang, T. Maxisch, and G. Ceder, Phys. Rev. B 73 (2006).
E. Heifets, J. Ho, and B. Merinov, Phys. Rev. B 75 (2007).
D. R. Stull and H. Prophet, JANAF Thermochemical Tables, 2nd ed. (U.S. National Bureau of
Standards, Washington, DC, 1971).
I. Hamada, A. Uozumi, Y. Morikawa, A. Yanase, and H. Katayama-Yoshida, J. Amer. Chem.
Soc. 133 , 18506 (2011).
Table S1 Geometric relaxation (
 d =d relaxed
-d ideal ij ij ij
in Å) and the atomic Bader charges (AC in e) and total charge associated with each layer (LC in e) in the LaO- and FeO
2
-terminated
LaFeO
3
(001) surfaces.
LaO-terminated FeO
2
-terminated
Layer Δd ij
LaO
FeO
2
-0.15
AC LC Layer Δd ij q
La
=1.99
q
O
=-1.34
0.65 FeO
2 q
Fe
=1.87 q
O
=-1.34 -0.81 LaO
-0.16 q q
Fe
La
=1.88
AC q
=2.08 q
O
O
=-1.19
=-1.29
LC
-0.5
0.79
LaO
FeO
2
Bulk
0.07
0.03 q
La
=2.07 q
O
=-1.33 0.74 FeO
2
0.13 q
Fe
=1.93 q
O
=-1.31
0.02 q
Fe
=1.92 q
O
=-1.34 -0.76 LaO q
La
=2.07 q
Fe
=1.92 q
O
=-1.33 q
LaO
=0.74 q
FeO2
=-0.74
-0.69 q
La
=2.08 q
O
=-1.32 0.76
Table S2 Temperature dependence of oxygen chemical potential μ
O
(T, p 0 ) at the standard pressure of p 0 =1 atm.
T μ
O
(T, p 0 ) T μ
O
(T, p 0 )
100
300
500
1000
-0.08 eV
-0.27 eV
-0.50 eV
-1.10 eV
1500
2000
2500
3000
-1.75 eV
-2.43 eV
-3.14 eV
-3.87 eV

Figure S1.
Surface free energy of LaO- and FeO
2
-terminated LaFeO
3
(001) as functions of temperature at given oxygen partial pressure p =0.2 atm (left panel) and of oxygen partial pressure at give temperature of 1000 K (right panel), respectively.