PHYSICAL REVIEW B 78, 115101 共2008兲

Structural and electronic properties of SrFeO2 from first principles
J. M. Pruneda,1 Jorge Íñiguez,1 Enric Canadell,1 Hiroshi Kageyama,2 and Mikio Takano3
1Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), Campus UAB, 08193 Bellaterra, Spain
2Department of Chemistry, Graduate School of Science, Kyoto University, Sakyo, Kyoto 606-8502, Japan
3Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan

共Received 3 April 2008; revised manuscript received 15 July 2008; published 2 September 2008兲
We report on a first-principles study of SrFeO2, an infinite-layer oxide with Fe atoms in a perfect squareplanar coordination down to essentially 0 K. Our results reveal that this striking behavior relies on the double
occupation of the 3dz2 orbitals of high-spin Fe2+. Such an electronic state results from electrostatic andhybridization effects, the latter enabling a large reduction in the intra-atomic exchange splitting of the z2
electrons.
DOI: 10.1103/PhysRevB.78.115101

PACS number共s兲: 71.20.⫺b, 71.15.Mb, 71.70.Ch

I. INTRODUCTION

Tsujimoto et al.1 recently reported on SrFeO2, an unusual
infinite-layer oxide with iron in square-planar coordination.
This compound exhibits a number of puzzling structural andphysical properties that remain unexplained and are, in fact,
apparently incompatible with each other. An illustrative example of the open questions pertaining to SrFeO2 is the absence of any structural instability in the material down to thelowest temperatures 共⬃4.2 K兲. This behavior is most unexpected since the physical measurements reported by
Tsujimoto et al. 共i.e., their Mössbauer data兲 suggest that Fe2+
is in a high-spin state of the type 共xz , yz兲3共xy兲1共z2兲1共x2− y 2兲1, which should lead to a Jahn-Teller structural distortion
to remove the 共xz , yz兲 degeneracy. Another striking observation pertains to the Néel temperature for the antiferromagnetic phase transition of SrFeO2, which is remarkably high
共473 K兲 for what seems to be a magnetically twodimensional 共2D兲 crystal. Taking into account the fundamental interest and the variety of possible applications of SrFeO2
and related materials displaying similar features,2 there isclearly a pressing need for an independent confirmation andphysical explanation of all such intriguing properties.
Recently, a first-principles study of SrFeO2 by Xiang
et al.3 confirmed the peculiar magnetic properties of thecompound and suggested that its surprising behavior may berelated to an unusual electronic structure with doubly occupied 3dz2 orbitals. In this paper, we go beyond the work ofRef. 3 and fully exploit the first-principles approach topresent a comprehensive study of SrFeO2. Here, in addition
to the magnetic properties, we confirm the structural stabilityof the observed infinite-layer phase of SrFeO2 down to essentially 0 K. We also resolve the apparent incompatibility
between the measured Mössbauer spectrum and the structural and 共computed兲 electronic properties of the compound.
Finally, we also report on a systematic study that allows us to
identify the physical origin of the peculiar electronic structure of the compound, with doubly occupied 3dz2 orbitals ofhigh-spin Fe2+, and highlights the importance of intra-atomic
exchange effects.
II. METHODOLOGY

We used a spin-polarized generalized gradientapproximation4 共GGA兲 to density functional theory 共DFT兲
1098-0121/2008/78共11兲/115101共5兲

as implemented in the code VASP 共Ref. 5兲 and employed
the “LDA+ U” correction of Dudarev et al.7 for the
Fe-3d electrons 共we used U = 4 eV and checked that ourqualitative results are already obtained at the GGA level兲.
We employed the projector augmented wave 共PAW兲 method6
to represent the ionic cores, solving explicitly for thefollowing electrons: 4s, 4p, and 5s of Sr; 3p, 3d, and 4sof Fe; and 2s and 2p of O. The electronic wave functions were described with a plane-wave basis truncated at
400 eV. Typically, we worked with the 16-atom cell depicted in Fig. 1, which is highly symmetric and compatible
with the magnetic ground state of the system, and used a4 ⫻ 4 ⫻ 4 grid for Brillouin-zone integrations. These calculation conditions were checked to render accurate results.
We also used PWSCF 共Ref. 8兲 and ABINIT,9 two different
DFT codes, for some of the electronic structure analysis
and the electric-field-gradient calculations, respectively.
The LDA+ U schemes implemented in PWSCF 共Ref. 10兲
and ABINIT 共Ref. 11兲 differ in some details from that of
Dudarev et al.; we have checked that our results do notdepend significantly on the specific LDA+ U used. Wavefunction figures were prepared using the visualization software XCRYSDEN.12

Sr
O
z
y

J1

x

Fe

J3
c

J2
2a

FIG. 1. 共Color online兲 16-atom SrFeO2 cell considered in mostof our calculations. The ground-state magnetic structure is sketched;
the lattice and exchange constants are defined.

115101-1©2008 The American Physical Society

PHYSICAL REVIEW B 78, 115101 共2008兲

PRUNEDA et al.

(a)

TABLE I. Computed properties of the P4/mmm phase of
SrFeO2 共measured lattice parameters in parentheses兲.

DOS
4

Structure: a = b = 4.01 Å共3.99 Å兲 ; c = 3.42 Å共3.47 Å兲Elastic constants 共GPa兲:
B = 125, C11 = C22 = 317, C33 = 164, C12 = 78,
C13 = C23 = 51, C44 = C55 = 95, C66 = 125
Infrared active modes 共cm−1兲:
159 and 276 共A2u兲; 183, 301, and 531 共Eu兲
Magnetic couplings 共meV兲: J1 = 1.75, J2 = 6.58, J3 = −0.26

up

4

down

E(eV)

2

2

0

0
z

2

(c)

-2

-2
4s

-4

(b)

-4

xz,yz

III. BASIC RESULTS

-6

-6
xy

A. Structural stability and magnetic interactions

2

x -y

2

Γ X R

We begin by showing that our DFT methods reproduce
the main results reported in Ref. 1. To investigate the stability of the highly symmetric phase of SrFeO2, we first determined the structural parameters that minimize the energy of
the crystal under the constraints that the P4/mmm spacegroup is preserved, and the magnetic order is the antiferromagnetic 共AFM兲 one found experimentally. Our results,
shown in Table I, are in good agreement with the measurements. We then computed the elastic constants and thephonons that are compatible with the cell of Fig. 1. The
results, summarized in Table I, indicate that the P4/mmm
phase of SrFeO2 is stable upon symmetry-lowering structural
distortions, thus confirming it as the ground state of the material at 0 K. It is worth noting that, while obviously anisotropic, the computed elastic constants and phonon frequencies present values that are acceptable for a threedimensional 共3D兲 crystal 共for SrFeO3 we obtained C11= 300 GPa and C12 = 140 GPa兲, which suggests this infinitelayer phase is robustly 共meta-兲stable.
We then studied the magnetic interactions in SrFeO2. We
considered all the spin arrangements compatible with the cellin Fig. 1 and confirmed that the experimentally observed
AFM pattern 共sketched in the figure兲 is the magnetic groundstate. Further, the Fe2+ ions are in a high-spin configuration
with a magnetic moment of about 3.6␮B, in agreement withexperiment. We also computed the exchange parameters of amodel Hamiltonian H = 1 / 2兺ijJijSiS j, with 兩S兩 = 2; the results
are given in Table I, following the notation defined in Fig. 1.
We found that the in-plane interactions are considerablystronger than those along the c direction; yet, the material isfar from being two-dimensional from the magnetic point ofview. Indeed, a simple 共admittedly rough兲 mean-field estimate based on our computed J’s renders a Néel temperature
above 1000 K, and the energy scale for the magnetic couplings between FeO2 planes, which we can estimate as
S2共2J1 − 8J3兲, is found to be around 260 K. Thus, our results
confirm the three-dimensional character of magnetism in
SrFeO2 and are compatible with the relatively high TN observed. We checked that values of the U parameter within the
3–6 eV range, which is typical for Fe compounds, do notaffect this conclusion.

共QS兲 of about 1 mm/s and in accordance with the usual picture from crystal-field theory, the authors of Ref. 1 assumed
the 共xz , yz兲3共xy兲1共z2兲1共x2 − y 2兲1 electronic configuration forthe 3d electrons of Fe2+. However, in such conditions a JahnTeller distortion is expected to lift the degeneracy associatedwith the 共xz , yz兲 orbitals, at odds with the experimental results. Our calculations readily clarify this question. As shownin Fig. 2, the DFT electronic structure of SrFeO2 does notagree with the one proposed in Ref. 1. We found that thesixth 3d electron of high-spin Fe2+ goes to the z2 minorityspin orbital. At variance with the 共xz , yz兲 3d orbitals of Fe,
the z2 state is not degenerate with any other; and, thus, its
occupancy cannot cause any symmetry-lowering distortion
that reduces the energy. Hence, this electronic configurationis compatible with the stability of the P4/mmm phase. Further, we also checked that the calculation results are compatible with the Mössbauer data. We address this point below
after having discussed the electronic structure of SrFeO2 inmore detail.

B. Electronic structure

IV. DISCUSSION

57

Based on their Fe Mössbauer spectroscopy results
showing a temperature-independent quadrupole splittingR(b)−4.1eVup2|ψ| = 0.00122|ψ| = 0.002 |ψ| = 0.01(c)
−1.6eV
down
FIG. 2. 共Color online兲 Panel 共a兲: computed electronic structureof SrFeO2 around the Fermi energy, which is set to 0 eV. The partial
density of states corresponding to the 3d and 4s orbitals of a particular Fe atom is indicated. The dashed line depicts the total DOS
divided by a factor of four. Panels 共b兲 and 共c兲: representative⌫-point eigenstates with dominating z2 character indicated by arrows in the band structure of panel 共a兲. The plotted isosurfaces
correspond to the indicated values of the squared modulus of the
wave function.

Our DFT calculations provide us with a coherent pictureof SrFeO2, accounting for the structural and magnetic prop-

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STRUCTURAL AND ELECTRONIC PROPERTIES OF SrFeO…

PHYSICAL REVIEW B 78, 115101 共2008兲

erties of the material. Yet, that picture relies on a result, thedouble occupation of the z2 orbitals of Fe2+, which may seemcounterintuitive based on the common knowledge in molecular and solid-state chemistry. We will thus focus on this key
issue: Why are the z2 orbitals of Fe2+ doubly occupied in
SrFeO2?
Let us start with a word of caution: Many apparently satisfying answers to the above question do not resist a rigorous
analysis. For example, it may be tempting to postulate thatthe double occupation of the z2 orbitals is determined by thefact that, as compared with the other 3d’s, they suffer fromnegligible Coulomb repulsion because they find no O2− ionsalong the direction perpendicular to the FeO2 plane. Thiskind of argument has been invoked in several occasions3,13
and is supported by extended Hückel calculations we have
performed. However, it is not consistent with our DFT electronic structure: It implies that the z2 orbitals should be thelowest-lying ones for both the majority- and minority-spin
electrons of high-spin Fe2+, which is in evident disagreementwith the results in Fig. 2. Ultimately, the failure of this argument suggests that independent-electron effects cannot fully
explain the electronic structure of SrFeO2.
To address the above question, we proceeded by eliminating possibilities in a systematic way. Our key observations
are the following. As already discussed, our calculations
show SrFeO2 should be regarded as a 3D crystal, and one
can thus conjecture that interactions along the c direction,
particularly between neighboring Fe atoms, might play a rolein stabilizing the doubly occupied z2 orbital. In order to investigate this possibility, we considered the limit case inwhich such interactions are totally suppressed. More precisely, we studied an idealized system composed of an isolated FeO2 layer, fixing the number of electrons in the calculation so as to keep the Fe and O atoms in the ionization
states they have in SrFeO2. We denote this virtual 2D crystal
as “Fe2+共O2−兲2 + bg”, where “bg” refers to the homogeneous
charge-compensating background introduced to stabilize thematerial. Interestingly, the partial density of states 共pDOS兲
obtained for Fe2+共O2−兲2 + bg is essentially identical to the result for SrFeO2 in Fig. 2, indicating that out-of-plane interactions play no role in determining the electronic structure of
SrFeO2. Recognizing that the significance of the results witha charge background may be questionable, we also ran calculations for SrFeO2 with a significantly increased c lattice
constant and ratified this conclusion.
Next, we turned our attention to the interactions within
the FeO2 planes. We ran calculations for a = b lattice constants increased and decreased up to ⫾10% of their equilibrium values and found that the most significant changes inthe electronic structure pertain to the x2 − y 2 electrons of iron.
This is not surprising as these are the electrons forming ␴bonds with the oxygen atoms. With regard to the z2 electrons,
we observed no effect worth noting, which clearly indicatesthat the Fe-O interactions are not the key to understand the
double occupation of the z2 orbitals. In particular, these results rule out the possibility that ␲-donor interactions withthe oxo ligands, which would destabilize the xy, xz, and yz
orbitals, are at the origin of the double occupation of z2.
These conclusions are ratified by a standard Fe-O overlap
population analysis. We also checked that the electronic

structure of SrFeO2 is essentially independent of the spinarrangement, and we can thus neglect interatomic exchange
effects in this discussion.
We are thus led to conclude that the double occupation of
the z2 orbitals must involve some sort of intra-atomic mechanism associated with the iron atoms. Indeed, this is the correct perspective to understand the electronic structure of
SrFeO2. Let us note a well-known effect that appears to be
critically important in this compound: As a result of the tetragonal point symmetry at the Fe site, the z2 orbital is fully
symmetric and can hybridize with the formally empty Fe-4s
state. In fact, the pDOS of Fig. 2 clearly shows such a hybridization occurs, being particularly important for the majority spin. As illustrated in panels 共b兲 and 共c兲 of Fig. 2, themajority-spin-wave functions with a significant 4s − 3dz2
mixing are characterized by 共i兲 a shrinking of the z2-likecentral ring, and 共ii兲 a deformation, as well as greater relative
weight, of the lobes extending out of plane. In contrast, theminority-spin electrons display a nearly pure z2 character.
Note also that the very different structure of the z2 pDOS forthe majority 共roughly triple-peaked兲 and minority 共singlepeaked兲 spins is consistent with this different mixing. Of
course, this peculiar behavior reflects a mechanism by which
the crystal minimizes its energy: Having different spin-up
and spin-down z2-like electrons results in a reduction in their
Coulomb repulsion and, accordingly, in the corresponding
intra-atomic exchange splitting ⌬. Indeed, the relatively
small ⌬ associated with the z2 electrons is obvious from Fig.
2. For a given orbital type, ⌬ can be estimated as the difference between the centers of mass of the spin-up and spindown bands; our calculations indicate that ⌬ is about 2.9 eV
for the z2 orbitals, while the other 3d’s present ⌬’s of morethan 6 eV.
We have thus identified a mechanism that allows SrFeO2
to reduce its energy by adopting an electronic configuration
with doubly occupied z2 orbitals. Now we ask ourselves
whether this mechanism, which only relies on having theappropriate local symmetry at the Fe site, is sufficient to
explain the computed electronic structure. To check this, we
performed the following computational experiment: We considered the 3D crystal “Fe2+共O2−兲3 + bg” sketched in Fig. 3,
fixing the number of electrons in order to retain the Fe-3d6
configuration. For simplicity, we assumed a ferromagnetic
order, which we checked has no effect on the electronic configuration of Fe. We fixed the in-plane lattice constant in the
SrFeO2 value and monitored the evolution of different electronic solutions14 as the cubic crystal 共dFeO⬘ = 2 Å兲 undergoes a tetragonal distortion. As shown in Fig. 3, only one
electronic solution is found in the cubic case: The minorityspin 3d electron occupies a combination of t2g orbitals 共from
which the xy orbital is selected as soon as the tetragonal
distortion occurs兲, closing the gap of the crystal. In contrast,
for the largest values of dFeO⬘ considered, several solutions
occur, the ground state corresponding to doubly occupied z2
orbitals. Interestingly, the solution with doubly occupied z2
already exists at dFeO⬘ = 2.14 Å; yet, the “xy-to-z2” crossover
only occurs at dFeO⬘ = 2.50 Å. These results show a mere
symmetry breaking, and the possibility of having 4s-3dz2
mixing will not cause the double occupation of the z2 orbitals. Rather, a relatively large tetragonal distortion, which re-115101-3

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PRUNEDA et al.

O’

Energy (eV)-22d FeO’

-24

-26

xy
2

z
xz,yz

-28
2

2.5

3

3.5

dFeO’ (Å)
FIG. 3. 共Color online兲 Computed energy of various electronicsolutions of the Fe2+共O2−兲3 + bg virtual system 共see text兲 as a function of the distance dFeO⬘ between the central Fe atom and theapical oxygens O⬘.

sults in both a more anisotropic environment for the Fe atom
and a reduction in the Coulomb repulsion for the z2 orbitals,
is required. Finally, we also checked that changes in the inplane lattice constant have a minor effect on the xy-to-z2
crossover.
It is not easy to estimate the universality of these effects.
It may seem surprising, for example, that such an electronicsolution is not found in molecules with Fe2+ centers. However, after reviewing the literature for some well-known
cases,15 we have the impression that the electronic structureof iron is often conditioned by the nature of the ligands or bya reduced atomic symmetry that precedes any electronic effect associated with the metal atom itself. This suggests thatsuch systems may not be appropriate to look for effects suchas the one discussed here. As for crystalline materials, weonly know of one candidate to present this kind of effect: themineral gillespite 共BaFeSi4O10兲, which contains Fe2+ ions ina square-planar coordination and displaying a high-spin configuration with doubly occupied z2 orbitals.13 An appealing
possibility, though, would be to synthesize other compoundsof the SrFeO2 family. Indeed, we found that crystals such as
RbCoO2 and YFeO2 present a similar pattern of electroniclevels with doubly occupied z2 orbitals. More precisely, ourcalculations predict that RbCoO2 displays a Co-3d6 highspin configuration with a doubly occupied z2; thus, this material might remain in the high-symmetry P4/mmm phasedown to 0 K, exactly as SrFeO2. On the other hand, YFeO2
exhibits a Fe-3d7 high-spin configuration where, in addition
to having a doubly occupied z2, the last 3d electron goes to a
共xz , yz兲 state that closes the band gap; hence, this crystal
should undergo a Jahn-Teller distortion.
Finally, let us discuss the compatibility between the valueof the QS obtained from 57Fe Mössbauer spectroscopy,

which is about 1 mm/s, and the double occupation of the z2
orbitals, which is expected to result in QS values of 2–3
mm/s. We should begin by noting that SrFeO2 is not the only
compound exhibiting this seemingly contradictory behavior.
Indeed, the Fe2+ atoms in the above-mentioned gillespite
have been reported to display QS values below 0.6 mm/s inthe 80–650 K temperature range.16 As for SrFeO2, we computed the electric-field gradient at the Fe site and the corresponding QS, obtaining a value of about 0.8 mm/s. We also
checked that varying U between 0 and 6 eV renders QS
results in the 0.6–0.9 mm/s range, with the greater values
corresponding to the smaller U’s. This clearly shows thathaving an electronic structure with doubly occupied z2 orbitals is not incompatible with the relatively small QS values
measured. As to the mechanism that causes such a reductionin the observed QS with respect to its expected value, twopossibilities can be mentioned: 共i兲 that the lattice contribution to the QS is comparable to the one coming from the 3delectrons of iron,16 which would lead to a cancellation as
their signs are known to be opposite or 共ii兲 that the splittings
associated with iron’s 3d electrons are unusual in SrFeO2.
Interestingly, our results seem to support the latter possibility: The spread in energy of the majority-spin z2 and x2 − y 2electrons 关see Fig. 2共a兲兴 will imply a relatively large spatial
spread of the corresponding Wannier functions,17 whichmight result in unusually small quadrupole splittings. However, a detailed analysis of this issue is not trivial and goesbeyond the scope of this paper.
V. SUMMARY

We have used first-principles methods to show that
SrFeO2, an unusual high-spin Fe2+ layered phase recently
reported, is free from structural instabilities and exhibits
strong magnetic interactions. Our results reveal that thisstriking behavior relies on the double occupation of the 3dz2
orbitals of high-spin Fe2+. Such an electronic state resultsfrom electrostatic and hybridization effects, the latter enabling a large reduction in the intra-atomic exchange splitting of the z2 electrons. Our simulation results also accountfor a concomitant decrease in the quadrupole splitting that isobserved in the Mössbauer spectrum, solving apparent contradictions in the experimental results.
ACKNOWLEDGMENTS

We acknowledge discussions with E. Molins. Our work
was funded by the Catalan 共Grant No. SGR2005-683兲 andSpanish 共Grants No. FIS2006-12117-C04-01 and No.
CSD2007-00041兲 governments, CSIC 共Grant No. PIE200760I015兲, and the Marie Curie program.

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