Oxygen-vacancy-induced ferromagnetism in CeO
2
from first principles
Xiaoping Han,
1
Jaichan Lee,
1,
* and Han-Ill Yoo
2
1
School of Advanced Materials Science and Engineering, SungKyunKwan University, Suwon 440-746, Korea
2
Department of Materials Science and Engineering, Seoul National University, Seoul 151-744, Korea
Received 14 October 2008; revised manuscript received 8 January 2009; published 10 March 2009
The electronic and magnetic properties of CeO
2
with various concentrations of oxygen vacancies have been
studied by first-principles calculations within the LSDA+ U method and were found to remarkably depend on
the oxygen vacancy concentration. With increasing oxygen deficiency, the electrons left behind by oxygen
removal not only localize on Ce 4 f orbitals but also on the vacancy sites. This leads to the magnetic mecha-
nism with both superexchange and polarization in the cases of heavy doping, effectively enhancing the stability
of ferromagnetism. The study reveals the magnetic properties and associated magnetic mechanisms of CeO
2
with the different oxygen deficiencies.
DOI: 10.1103/PhysRevB.79.100403 PACS numbers: 75.50.Pp, 61.72.Bb, 71.15.Mb
Global environment and energy issues have led to great
interest in ceria CeO
2
and related compounds, which can
be applied to environmentally friendly power generation,
such as solid oxide fuel cell and catalytic applications.
1–4
CeO
2
is known to be an oxygen vacancy reservoir with a
high capacity for storing and releasing oxygen vacancies.
Such a high oxygen vacancy storage capacity is essential in a
wide variety of applications. To this end, oxygen vacancy
often plays a vital role in changing materials properties, fur-
ther influencing oxide-based device characteristics and reli-
ability. For example, the high performance of CeO
2
as an
oxygen buffer and active support for noble metals in cataly-
sis relies on an efficient supply of lattice oxygens at reaction
sites governed by oxygen vacancy formation.
5,6
Moreover,
CeO
2
is widely used for ionic conducting oxides due to the
role of oxygen vacancy.
It is well known that the stoichiometrical CeO
2
is para-
magnetic. When an oxygen atom is released from CeO
2
, two
electrons are left behind and are believed to strongly localize
at the f -level traps on two Ce atoms, which causes the formal
valence of two neighboring Ce atoms to change from +4 to
+3. This will give rise to net spin in the Ce f states, inducing
the magnetism. However, little effort has been done to study
the magnetic properties of oxygen-deficient CeO
2
. Further-
more, most previous studies have been limited to slightly
reduced CeO
2
, while CeO
2
is known to be an effective oxy-
gen vacancy reservoir. In fact, high oxygen deficiency in
CeO
2
is a very likely situation in a wide range of applica-
tions since the oxides are often exposed to various environ-
ments, such as a highly reducing atmosphere or a high-
temperature condition. In this study, we therefore have
examined the localization behavior of CeO
2
with various de-
grees of oxygen deficiency as well as the associated mag-
netic properties and their origins. This study reveals that the
electrons are localized not only on the Ce 4 f state but also on
the oxygen vacancy site i.e., the electron localization ten-
dency on the Ce 4 f state weakens when the oxygen defi-
ciency becomes large. These electrons remaining on the oxy-
gen vacancy site are polarized by the reduced ions,
eventually leading to the evidently enhanced ferromagnetic
ordering in highly oxygen deficient CeO
2
.
First-principles methods, implemented in the Vienna ab
initio simulation package VASP,
7
were used to study the
electronic and magnetic properties of CeO
2-x
, particularly,
the effects of oxygen vacancy doping concentration
x = 3.13%, 6.25%, 12.5%, and 25% corresponding to 2 2
2, 1 2 2, 1 1 2, and 1 1 1 supercells with one
oxygen vacancy, respectively. In all calculations, the projec-
tor augmented wave method PAWRef. 8 with the frozen-
core approximation was used for the ion-electron interac-
tions. Exchange correlation interactions were described by
the PAW local spin density approximation LSDA. Due to
the strong Coulomb interaction of the localized Ce 4 f elec-
trons, the standard density-functional theory DFT calcula-
tions were inadequate for a satisfactory electronic structure
prediction. Many recent reports
9–12
have proven that DFT
calculation with the correction of Hubbard U parameter
DFT+ U is effective for CeO
2-x
and related compounds.
Dudarev’s spherical LDA+ U methods
13
were employed in
this study. The optimal combination of U =8 eV and
J =1 eV for Ce 4 f orbitals was found to improve the predic-
tion of the electronic structure. The Brillouin-zone BZ in-
tegration was performed on a well-converged Monkhorst-
Pack k-point grid. The plane-wave kinetic energy cutoff was
set to be 400 eV. Atomic positions and lattice parameters
were optimized until the atomic forces were smaller than
0.02 eV / Å.
First, a CeO
1.969
supercell was used to model a low dop-
ing concentration case x = 0.0313, where one oxygen atom
is removed from a 96-atom 2 2 2 supercell of pure CeO
2
.
Figure 1a shows the total density of states DOS of
CeO
1.969
. The peak just below the Fermi level represents the
localized f states, which are mainly on two Ce ions that are
the nearest neighbors to the O vacancy. The gap between the
O2p valence-band edge and occupied f state is 1.4 eV,
which agrees well with the experimental value of 1.2–1.5
eV.
14
Figures 1b–1d show the total DOSs of CeO
2-x
x = 0.0625, 0.125, and 0.25. The existence of the gap states
in these figures reveals the electron localization. These local-
ized states are also due to the 4 f states of the reduced Ce ion,
originating from the electrons by oxygen removal. The inte-
gration analysis using Bader analysis
15
shows that each of
the two reduced Ce ions has 0.98, 0.97, 0.93, and 0.91 elec-
trons for the cases of x = 0.0313, 0.0625, 0.125, and 0.25,
PHYSICAL REVIEW B 79, 100403R2009
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