Vacancy-enhanced ferromagnetism in Fe-doped rutile TiO
2
Jun Chen,
1,2
Paul Rulis,
1
Lizhi Ouyang,
3
S. Satpathy,
4
and W. Y. Ching
1,
*
1
Department of Physics, University of Missouri-Kansas City, Kansas City, Missouri 64110, USA
2
Institute of Applied Physics and Computational Mathematics, Beijing, China, 100088
3
Department of Physics and Mathematics, Tennessee State University, Nashville, Tennessee 37221, USA
4
Department of Physics, University of Missouri, Columbia, Missouri 65211, USA
Received 30 September 2006; published 8 December 2006
Based on a series of supercell density functional calculations of Fe-doped TiO
2
both with and without O
vacancy V
O
, we show that V
O
plays an important role in determining the magnetic properties of the dilute
magnetic semiconductors DMS. Without V
O
, two Fe atoms in rutile lattice are ferromagnetically coupled
except at a separation distance of 3.57 Å, where they are antiferromagnetically coupled. The V
O
introduces two
electrons into the conduction bands of rutile, which are either captured by the Fe dopants or form a shallow
impurity state. The ferromagnetic FM coupling J between two Fe atoms is enhanced, through the enhance-
ment of the FM double exchange if V
O
is sufficiently close.
DOI: 10.1103/PhysRevB.74.235207 PACS numbers: 75.50.Pp, 61.72.Ji, 75.10.Lp, 75.30.Hx
I. INTRODUCTION
Recent studies on dilute magnetic semiconductors DMS
for room temperature spintronics applications concentrate
mostly on Mn-doped GaAs Refs. 1–3 and GaN
compounds.
4,5
Co doped TiO
2
was also reported to be a
promising magnetic oxide semiconductor MOS with n type
of carriers.
6,7
However, the reported Curie temperature T
c
is
quite low which limits its practical applications. Further-
more, controversies regarding the nature of the samples arise
and much of the claim cannot be validated.
8–11
More re-
cently, it was reported that doping Fe in reduced rutile has
p-type carriers and a higher T
c
Ref. 12. The reported mag-
netic moment per Fe M
s
is as high as 2.4
B
. The possibil-
ity of room temperature ferromagnetic semiconductors with
a high T
c
is very exciting. There have been several reports on
Fe doping in TiO
2
with conflicting results and
interpretations
13–19
which could be the source of much of the
discrepancy. These different observations arise from different
samples prepared in different laboratories. The atomic-scale
structure of Fe-doped TiO
2
has not been precisely character-
ized and there are lingering doubts as to the validity of the
data and the origin of the observed ferromagnetism FM.
Most likely, the presence of O vacancies V
O
in these ma-
terials play an important role but this has not been thor-
oughly investigated.
To understand the role of the vacancies in determining the
magnetic properties of the oxide-based DMS, we study the
Fe-doped rutile TiO
2
with and without V
O
using density
functional theory DFT. We find that vacancies enhance the
FM in two distinctly different ways, either through the for-
mation of a shallow impurity state of a nearest-neighbor Fe
-V
O
complex or through the capture of the vacancy electrons
by the Fe atoms and the subsequent enhancement of the FM
double exchange. In the next section, we briefly outline our
method of calculation. The results of the supercell calcula-
tions on Fe-doped TiO
2
without and with V
O
are presented
and discussed in Sec. 3. The last section is for conclusions,
emphasizing the importance of O vacancy in dilute magnetic
oxide semiconductors.
II. METHOD OF CALCULATION
The rutile TiO
2
crystallizes in a tetragonal cell a
=4.594 Å, c = 2.959 Å, space group P4
2
/ mnm. In this study,
we used a 2 2 4 supercell 32 Ti and 64 O atoms and
replace Ti atoms by one, two or three Fe atoms correspond-
ing to concentration ratios of x =1/32, 1/16, and 3/32 in
Fe
x
Ti
1-x
O
2
which are close to the experimentally reported
values
12
of x =0.02, 0.06, and 0.08. We then considered the
cases of single V
O
, 1 Fe and 1 V
O
, 2Fe and 1 V
O
, and 1 Fe
and 2 V
O
. For a 96-atom supercell, the maximum interatomic
separations for Ti-Ti, Ti-O, and O-O are restricted to 7.49 Å,
6.88 Å, and 7.48 Å, respectively because of the periodic
boundary condition. In each case, a large number of defect
configurations were identified for ab initio study. For each
model, the structure was fully relaxed using DFT as imple-
mented in the Vienna ab initio Simulation Package VASP in
the spin-polarized mode.
20,21
We used the PWA-GGA poten-
tial for the exchange and correlation and a high energy cutoff
of 600 eV. Eight k points were used in the irreducible Bril-
louin zone of the supercell. The total energy TE attained an
accuracy of at least 0.001 eV and the residual force con-
verged to about 0.01 eV/Å. For perfect TiO
2
, VASP results
show a slight expansion of the lattice 1% for a, 0.7% for c.
The calculated vacancy formation energy for V
O
is 2.71 eV.
This accuracy is fairly typical of calculations based on DFT.
Substitution of a Ti by an Fe reduces the supercell size
slightly and the Fe-O bonds 1.904 Å, 1.908 Å are shorter
than the original rutile Ti-O bonds 1.949 Å and 1.980 Å.
They are comparable to the Fe-O bonds in Fe
3
O
4
1.862 Å
and 1.936 Å. The energy of substitution for a single Fe is
4.18 eV. The calculated Fe moment M
S
and that of the
whole cell are 1.67
B
and 1.72
B
, respectively since the
neighboring O ions are found to be slightly polarized in the
same direction.
III. RESULTS AND DISCUSSION
Figures 1a and 1b shows the density of states DOS of
TiO
2
with 1 V
O
and 1 Fe, respectively. The one electron DOS
PHYSICAL REVIEW B 74, 235207 2006
1098-0121/2006/7423/2352075 ©2006 The American Physical Society 235207-1