Fabrication of half metallicity in a ferromagnetic metal
Fabrication of half metallicity in a ferromagnetic metal
Kalobaran Maiti∗
Department of Condensed Matter Physics and Materials’ Science,
Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai - 400 005, INDIA
(Dated: August 15, 2021)
We investigate the growth of half metallic phase in a ferromagnetic material using state-of-the-art
full potential linearized augmented plane wave method. To address the issue, we have substituted Ti
at the Ru-sites in SrRuO3, where SrRuO3 is a ferromagnetic material. Calculated results establish
Ti4+ valence states (similar to SrTiO3), which was predicted experimentally. Thus, Ti substitution
dilutes the Ru-O-Ru connectivity, which is manifested in the calculated results in the form of
significant band narrowing leading to finite gap between t2g and eg bands. At 75% substitution, a
large gap (> 2eV) appears at the Fermi level, ǫF in the up spin density of states, while the down spin
states contributes at ǫF characterizing the system a half-metallic ferromagnet. The t2g − eg gap can
be tailored judiciously by tuning Ti concentrations to minimize thermal effects, which is often the
major bottleneck to achieve high spin polarization at elevated temperatures in other materials. This
study, thus, provides a novel but simple way to fabricate half-metallicity in ferromagnetic materials,
which are potential candidates for spin-based technology.
PACS numbers: 85.70.Ay, 75.30.-m, 71.70.Ch, 71.15.Ap
The search of half metallic ferromagnetic materials has
seen an explosive growth in the recent times due to its
potential technological applications. In these materials,
the electronic density of states (DOS) at the Fermi level,
ǫF corresponds to only one kind of spin, while the other
spin density of states exhibit an energy gap at ǫF . Thus,
in the polarized condition, electronic conduction strongly
depends on the spin of the charge carriers; the material
is insulating for one kind of spin and metallic for the
other. This unique property makes them ideal candidates
for the development of spin-based electronics. Various
theoretical studies predicted half metallicity in Heusler
alloys [1], double perovskites [2], manganates [3], CrO2
[4], graphene nanoribbons [5] etc. However, experimen-
tal studies on very few materials such as manganates [3]
and CrO2 [4], etc. exhibit half metallicity at low temper-
atures. Thermal fluctuations often lead to a reduction in
spin polarization at elevated temperatures [6] making it
difficult for technological applications.
In this study, we investigate the evolution of the elec-
tronic density of states in SrRu1−xTixO3 as a function
of x. SrRuO3 is a ferromagnetic metal with Curie tem-
perature of 165 K. Spin polarization at ǫF is found to be
negative in the ferromagnetic ground state [7, 8]. SrTiO3,
on the other hand, is a band insulator. Various experi-
mental studies [9, 10] suggest (4+) valence state of Ti in
the intermediate compositions (similar to SrTiO3), which
corresponds to 3d0 electronic configuration. Thus, in ad-
dition to disorder effect, Ti substitution leads to a dilu-
tion of Ru-O-Ru connectivity. Transport measurements
in SrRu1−xTixO3 exhibit a range of novel phase tran-
sitions involving disorder induced correlated metal, An-
derson insulator, correlated insulator and band insulators
[11] for different values of x.
Using ab initio calculations, we find that Ti substitu-
tion at Ru-sites in ferromagnetic SrRuO3 leads to half
FIG. 1: (color online) Crystal structure of SrRu0.25Ti0.75O3.
In order to obtain the structure of SrRuTiO3, we replaced Ti2
by Ru, and all the Ti and Ru sites are made equivalent.
metallicity. Here, reduced Ru-O-Ru connectivity due to
Ti-substitution leads to significant narrowing of Ru 4d
band and thus, the up spin band moves below ǫF . In-
terestingly, the energy gap between t2g and eg bands can
be tuned by Ti-concentration. 75% substituted sample
exhibits gap as high as 2 eV. Experimental realization of
such method on different systems would provide a new
direction in the search of HMFs for spin-based technol-
The electronic density of states of SrRu1−xTixO3 for
x = 0.0, 0.5, 0.75 and 1.0 were calculated using state-
of-the-art full potential linearized augmented plane wave
method (FLAPW) within the local spin density approxi-
mations (LSDA) using WIEN2K software [12]. The crystal
structure of SrTiO3 is cubic with the lattice constant, a =
3.905 Å. SrRuO3 possesses close to cubic structure with
small orthorhombic distortion. This is manifested clearly
by the similar density of states (DOS) of SrRuO3 in real
structure vis-a-vis in the equivalent cubic structure [7].
Ti-substitution in SrRuO3 leads the system towards cu-
http://arxiv.org/abs/0704.0321v1
�� �� �� � � � �  !"
/0 12 34 5 6 7 8 9 :;
?@A BCDE
^_` ab cd efg
lmn op qr stu
z{| } ~� ���
��� �� ��
¡¢£¤¥¦ §¨©ª
FIG. 2: (color online) (a) TDOS, (b) Ti 3d PDOS, (c) Ru 4d
PDOS, (d) O 2p PDOS and (e) Sr 4d PDOS of SrRu1−xTixO3.
Thin and thick solid lines represent DOS corresponding to x
= 0.5 and 0.75, respectively.
bic structure. Thus, we have considered cubic structure
for all the calculations in this study. A typical unit cell
for SrRu0.25Ti0.75O3 is shown in Fig. 1. There are 8 for-
mula units in the unit cell constructed by doubling the
lattice constant of SrTiO3. In order to preserve cubic
symmetry, three types of Ti are considered occupying
corners (Ti1), edge centers (Ti2) and face centered posi-
tions (Ti3). The body centered position is occupied by
Ru. There are three non-equivalent oxygens; O1 forms
the octahedra around Ti1-sites, O2 forms the octahedra
around Ru-sites and the rest of the oxygen positions are
occupied by O3. Thus, the connectivity between Ru-sites
occurs via Ru-O2 bondings. The muffin-tin radii (RMT )
for Sr, Ru, Ti and O were set to 1.16 Å 0.95 Å 0.95 Å and
0.74 Å respectively. The convergence for different calcu-
lations were achieved considering 512 k points within the
first Brillouin zone. The error bar for the energy conver-
gence was set to < 0.25 meV per formula unit. In every
case, the charge convergence was achieved to be less than
10−3 electronic charge.
In Fig. 2, We show the total DOS calculated for
SrRu1−xTixO3 (x = 0.5 and 0.75) and the partial DOS
obtained by projecting the eigenstates onto the Ti 3d,
Ru 4d, O 2p and Sr 4d states. The figure exhibits 5
distinctly separable features. The energy region -1.5 eV
to -5 eV is primarily contributed by O 2p partial DOS
with negligible contributions from other electronic states.
Thus, these contributions are characterized due to the
non-bonding O 2p states. Sr 4d partial DOS shown in
Fig. 2(e) appear above 5 eV. The peak appears to shift
towards higher energy with increasing x. This can be
·¸ ¹º »¼ ½¾ ¿ À Á Â Ã ÄÅ
ÑÒÓÔÕ
×ØÙÚÛ
ÝÞ ßà
áâãäå
íîïðñ
óô õö
÷øùúûü ýþÿ�
�	���

�� ��
�����
89:;<
FIG. 3: (color online) (a) TDOS, (b) Ti 3d and Ru 4d PDOS,
(c) O 2p PDOS and (d) Sr 4d PDOS of SrTiO3 and SrRuO3.
Dashed line represent Sr 4d PDOS rescaled by 20 times.
understood by comparing the same in the end members,
SrTiO3 and SrRuO3 as demonstrated in Fig. 3. Sr 4d
states appear at much higher energies in SrTiO3 com-
pared to that in SrRuO3. One reason for such a large
shift may be related to the shift of the Fermi level to
the top of the O 2p band in SrTiO3. However, the shift
of Sr 4d band in the intermediate compositions, where
the Fermi level is pinned by the occupancy of the Ru 4d
band, indicates that the Madelung potential at Sr-sites
increases with the increase in Ti concentrations.
Ti 3d partial DOS appears 2 eV above the Fermi level.
This clearly demonstrates that the occupancy of Ti 3d
states is essentially zero and hence correspond to Ti4+
valency. Such valence states was predicted in the x-ray
photoemission spectra [9]. This study provides evidence
of such effect theoretically within the effective single par-
ticle approach itself. The width of the Ti 3d t2g band is
significantly small in x = 0.5 sample (∼ 0.65 eV), which
increases to 1.5 eV in x = 0.75 sample and 2.5 eV at x
= 1.0 (see Fig. 3).
Ru 4d partial DOS exhibit three regions. The narrow
and intense feature between the energy range -1.6 to 0.5
eV correspond to the electronic states having t2g sym-
metry. The electronic states above 1.8 eV appears due
to Ru 4d states having eg symmetry. Notably, the O
2p states also contribute in all the three energy regions.
Thus, DOS appearing below -5 eV can be attributed to
the Ru 4d - O 2p bonding states having a large O 2p
character, and the energy region above -1.5 eV are the
anti-bonding states having primarily Ru 4d character.
Most interestingly, both the compounds exhibit metallic
ground state. However, the t2g bandwidth, W reduces
significantly with the increase in x. While W is close to
2.6 eV in SrRuO3, it is about 1.7 eV for x = 0.5 and 0.54
eV for x = 0.75. Such reduction in W is understand-
able as Ti-substitution leads to a significant reduction
in the hopping interaction strength due to the reduced
degree of Ru-O-Ru connectivity. This is clearly evident
in Fig. 1; if we assume homogeneous distribution of Ru
and Ti atoms in the solid, all the RuO6 octahedra are
separated by TiO6 octahedra at x = 0.5. At x = 0.75,
the number of Ru-[O-Ti-O]-Ru connectivity reduces to
half of that at x = 0.5. Subsequently, U/W (U = local
Coulomb interactions strength) will increase significantly
and presumably play a role in the transport properties
in these compositions [11].
In order to understand the bonding of Ru 4d electronic
states with various O 2p states, we compare the Ru 4d t2g
and eg bands with the 2p bands corresponding to O1, O2
and O3 for x = 0.75 and 0.5 sample in Fig. 4(a) and 4(b),
respectively. All the oxygens are equivalent in the x = 0.5
sample. The energy distribution of O2 2p partial DOS is
almost identical in Fig. 4(a) to that observed in Ru 4d
partial DOS. This is expected as the RuO6 octahedra is
formed by O2 atoms only. The width of the O2 2p band
is significantly larger than that of O1 and O3. The most
interesting observation is that the t2g and eg bands are
separated by a distinct energy gap. This gap is already
visible in Ru 4d partial DOS of x = 0.5 sample in Fig.
4(b) and is absent in SrRuO3 as shown in Fig. 3 and in
the literature as well [7, 13].
We calculate the crystal field splitting of the Ru 4d
band by measuring the separation of the center of gravity
of the Ru 4d t2g and eg bands as shown in Fig. 4 by closed
circles in both the compositions. It is evident that crystal
field splitting, ∆ remains almost the same (∼ 2.1 eV) in
both the compositions and is very close to 2 eV found
in SrRuO3. Thus, the large energy gap between the t2g
and eg bands appears purely due to the band narrowing.
Such effect has strong implication in the magnetic phase
as described below.
It is already well established that the magnetic ground
state can be exactly described by these band structure
calculations [7, 14, 15, 16]. Thus, we have calculated the
ground state energies for ferromagnetic arrangement of
moments of the constituents using local spin-density ap-
proximations. Interestingly, the eigen energy for the fer-
romagnetic ground state in x = 0.5 sample is 5.67 meV/fu
lower than the lowest eigen energy for the non-magnetic
solution. This is higher than 1.2 meV/fu observed in
SrRuO3 in real structure and significantly smaller than
30.4 meV/fu observed in the equivalent cubic struc-
ture of SrRuO3. This energy difference between the
non-magnetic and magnetic solutions increases to 33.95
meV/fu in x = 0.75. All these results suggest that the
stability of the ferromagnetic ground state increases with
the decrease in the degree of charge delocalization of the
CD EF GH I J K L M
TU VW XY Z [ \ ] ^
bcd ef gh
ij kl
mn op
qrs tu vwxyz{|}
²³´ µ¶
·¸¹º»¼ ½¾¿À
FIG. 4: (color online) Ru 4d partial DOS with t2g and eg
symmetry are compared with the O 2p partial DOS in (a)
SrRu0.25Ti0.75O3 and (b) SrRu0.5Ti0.5O3.
ÇÈ É Ê Ë Ì
ÍÎ Ï Ð Ñ Ò
Ö× ØÙ ÚÛ Ü Ý Þ ß
àá âã äå æ ç è é
î ï ð ñ
ò ó ô õ
ùú ûü ýþ ÿ
�� �� �� �
��
� �� ���� �� ��
'()* +,-.
23 4567
[\]^_ `abc
ghij kl mnop
qr st
���� ����
�� ���� ����
 Energy (eV)
ª«¬­ ®¯°±
FIG. 5: (color online) Up and down spin density of stated
corresponding to (a) Ru 4d in SrRu0.5Ti0.5O3, (b) O 2p in
SrRu0.5Ti0.5O3, (c) Ru 4d in SrRu0.25Ti0.75O3, and (d) O
2p in SrRu0.25Ti0.75O3. This figure demonstrates that band
narrowing in Ru 4d band leads to a gap in the up spin channel
leading to half metallicity.
valence electrons.
The spin magnetic moment centered at Ru-sites is
found to be about 0.6 µB in x = 0.5 sample. Inter-
estingly, magnetic moment at the interstitial electronic
states is significantly large (∼ 0.36 µB). The moment
at the O sites is about 0.05 µB. The Ti sites also ex-
hibit very small moment (∼ -0.03 µB). Thus the total
magnetic moment of the solid becomes 1.24 µB per Ru-
atom. This is very similar to that observed (1.2 µB) in
SrRuO3. The magnetic moments increase significantly
with the increase in x. The moments at Ru site becomes
0.88 µB in x = 0.75 sample. The moments of the intersti-
tial states and 2p states at O2 sites also enhance to 0.66
µB and 0.066 µB, respectively. Thus, the total moment
turns out to be 1.99 µB, which is very close to the spin
only value of 2 µB corresponding to Ru 4t
2g electronic
configuration. It is to note here that although the local
moment of the highly extended 4d states is significantly
smaller than the spin only value as opposed to the case
in 3d transition metal oxides [15], Ru 4d moment induces
a large degree of polarization in the interstitial and O 2p
electrons. These results evidently suggest applicability
of Stoner description to capture magnetic properties of
these systems.
In order to investigate the exchange splitting and the
character of density of states in the vicinity of ǫF , we plot
the spin-resolved DOS corresponding to Ru 4d and O 2p
partial DOS in Fig. 5. In the x = 0.5 sample, both the up
and down spin states contribute at ǫF and the exchange
splitting is found to be about 0.47 eV. This is again very
similar to the case in SrRuO3 [7]. The exchange splitting
increases to 0.65 eV in x = 0.75 sample as shown in the
figure. Interestingly, the up spin band moves significantly
below ǫF and the contributions at ǫF appears only due
to the down spin states indicating a half-metallic behav-
ior. No contribution of the up spin states observed in
the total density of states (not shown here). Considering
the paucity of half-metallic materials for various tech-
nological applications, achieving half metallicity in the
ferromagnetic SrRuO3 by Ti-substitution is remarkable.
It is believed that the half metallicity can be achieved
via strong d − d hybridization in Heusler alloys involv-
ing two transition metal elements in the compound [17].
In transition metal oxides, often doping of large amount
of electrons or holes leads to a shift of the Fermi level
towards the energy gap of one spin channel leading to
half metallicity [3]. The primary difficulty to use these
systems in technological applications is the loss of half
metallicity at elevated temperatures, where thermal ex-
citations leads to significant mixing of various spin chan-
nels due to small energy gap at ǫF [6]. In the present
case, mechanism to achieve half metallicity is simple and
easily achievable experimentally. The most important
aspect is that the energy gap between t2g and eg bands
can be tailored judiciously by tuning the composition to
minimize thermal effects.
In summary, we investigate the possibility of fabricat-
ing half metallicity by Ti-substitution at the Ru-sites in
a ferromagnetic material, SrRuO3. The calculated re-
sults using FLAPW method within the local spin density
approximations reveal tetravalency of Ti in all the com-
positions consistent with the experimental predictions.
The Ru 4d band exhibit significant narrowing with the
increase in Ti-substitution; the crystal field splitting re-
mains almost the same across the whole series. Thus,
an energy gap develops between the t2g and eg bands,
which gradually grows with the increase in x. Conse-
quently, the up spin density of states exhibit an energy
gap at the Fermi level, while the down spin states still
contribute leading to half metallicity. Most interestingly,
the t2g − eg gap can be engineered by tuning x and thus
spin mixing effects due to thermal excitations can be min-
imized. This study thus provide a novel but simple way
to fabricate half metallicity in ferromagnetic materials,
which are potential candidates for spin based technol-
ogy. Experimental realization of this method would help
both chemists and physicists to cultivate new materials.
In addition, this study demonstrates that effective sin-
gle particle approaches provide a remarkable description
of the electronic properties of these systems, which are
predicted experimentally.
∗ Electronic mail: kbmaiti@tifr.res.in
[1] R.A. de Groot, F.M. Mueller, P.G. van Engen, and
K.H.J. Buschow, Phys. Rev. Lett. 50, 2024-2027 (1983),
[2] K.-I. Kobayashi, T. Kimura, H. Sawada, K. Terakura,
and Y. Tokura, Nature 395, 677-680 (1998).
[3] J.H. Park et al., Nature 392, 794-796 (1998).
[4] R.S. Keizer, S.T.B. Goennenwein, T.M. Klapwijk, G.
Miao, G. Xiao, and A. Gupta, Nature 439, 825-827
(2006).
[5] Y.-W. Son, M.L. Cohen, and S.G. Louie, Nature 444,
347-349 (2006).
[6] M. Ležaić, Ph. Mavropoulos, J. Enkovaara, G.
Bihlmayer, and S. Blügel, Phys. Rev. Lett. 97, 026404
(2006).
[7] K. Maiti, Phys. Rev. B 73, 235110 (2006).
[8] D.C. Worledge and T.H. Geballe, Phys. Rev. Lett. 85,
5182 (2000).
[9] J. Kim, J.-Y. Kim, B.-G. Park, and S.-J. Oh, Phys. Rev.
B 73, 235109 (2006).
[10] S. Ray, D.D. Sarma, and R. Vijayaraghavan, Phys. Rev.
B 73, 165105 (2006).
[11] K.W. Kim, J.S. Lee, T.W. Noh, S.R. Lee, and K. Char,
Phys. Rev. B 71, 125104 (2005).
[12] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, and
J. Luitz, WIEN2k, An Augmented Plane Wave + Lo-
cal Orbitals Program for Calculating Crystal Properties
(Karlheinz Schwarz, Techn. Universität Wien, Austria),
2001. ISBN 3-9501031-1-2.
[13] D.J. Singh, J. Appl. Phys. 79, 4818-4820 (1996).
[14] N. Hamada, H. Sawada, I. Solovyev, and K. Terakura,
Physica B 237-238, 11-13 (1997).
[15] D.D. Sarma, N. Shanthi, S.R. Barman, N. Hamada, H.
Sawada, and K. Terakura, Phys. Rev. Lett. 75, 1126
(1995).
[16] K. Maiti, Phys. Rev. B 73, 115119 (2006).
[17] I. Galanakis, P.H. Dederichs, and N. Papanikolaou, Phys.
Rev. B 66, 134428 (2002); ibid, 66, 174429 (2002).
