Electronic structure of the zigzag spin-chain compound In$_2$VO$_5$
Electronic structure of the zigzag spin-chain compound In2VO5
U. Schwingenschlögl
Institut für Physik, Universität Augsburg, 86135 Augsburg, Germany
(Dated: November 28, 2018)
Band structure calculations within the local spin-density approximation are presented in order to
investigate the electronic and magnetic properties of the zigzag spin-chain compound In2VO5. The
essential structural feature of the system is a double chain of VO6-octahedra, which leads to compet-
ing intrachain and interchain magnetic couplings. Frustration of the spin-chains is expected for the
proposed antiferromagnetic ordering at low temperatures. However, the band calculations indicate
that the experimental room temperature crystal structure is incompatible with antiferromagnetism.
Both the intrachain and interchain coupling is found to be ferromagnetic.
PACS numbers: 71.20.-b, 71.20.Be
Keywords: density functional theory, band structure, magnetism, spin-chain
Magnetism in low-dimensional quantum spin systems
results in fascinating physical properties when the spin
ordering is frustrated due to geometrical restrictions.
In this context, the S = 1/2 antiferromagnetic zigzag
spin-chain gives rise to one of the most fundamental
model systems for analyzing the interplay of frustration
and magnetism. Recently, In2VO5 has been put for-
ward for consideration as a promising candidate for a
frustrated zigzag spin-chain. Vanadium oxides in gen-
eral are very susceptible to electronic ordering phenom-
ena, see [1, 2, 3], for instance, and the references given
there. To be more specific, the essential structural fea-
ture of In2VO5 is a double chain of corner sharing VO6-
octahedra along the crystallographical b-axis. As indium
realizes the oxidation state In3+, the vanadium ions are
left with a single electron in the 3d shell. This formal
V4+ valence with a 3d1 electronic configuration comes
along with S = 1/2 spins at the vanadium sites, sepa-
rated by non-magnetic oxygen sites. Because of nearest
and next-nearest neighbour V-V interactions of the same
order of magnitude, competence between the intrachain
and interchain exchange coupling is typical for In2VO5.
The compound crystallizes in the simple orthorhombic
space group Pnma, where a unit cell comprises four for-
mula units. Senegas et al. [4] have obtained the lattice
parameters a = 7.232 Å, b = 3.468 Å, and c = 14.82 Å
FIG. 1: (Color online) Schematic structure of the zigzag VO-
chains in In2VO5. The magnetic V sites are surrounded by
distorted O-octahedra, sharing corners along the chains.
by means of single crystal x-ray analysis at room tem-
perature. Figure 1 illustrates the spacial arrangement of
the zigzag VO-chains. The coordination polyhedron of
the magnetic V sites is a distorted O-octahedron with
one strongly elongated VO-bond of length 2.23 Å. This
bond connects two adjacent VO-chains, therefore giving
rise to the characteristical double chain geometry. The
VO-bond in trans-position accordingly is shortened to
1.76 Å. Moreover, the intrachain bond length amounts to
1.81 Å in both directions and the remaining VO-bonds
in the equatorial plane of the coordination polyhedron
have lengths of 2.01 Å and 2.03 Å. All V sites are crys-
tallographically equivalent, as are the intrachain O sites.
Within the zigzag VO-chains we have V-O-V bond an-
gles of 146◦, thus considerable deviations from a straight
line configuration. In contrast, the V-O-V bond angles
between V sites in adjacent chains amount to only 107◦.
Nearest neighbour magnetic sites therefore are located in
different VO-chains, whereas intrachain V sites are next-
nearest neighbours.
Sign and strength of the magnetic coupling constants
in In2VO5 very recently have been analyzed by Volkova
[5] based on a phenomenological theoretical method for
quantitatively estimating the magnetic coupling in low-
dimensional crystalline compounds. The only input into
the calculation is the crystal structure [6]. This crystal
chemical approach results in an antiferromagnetic near-
est neighbour interaction given by the coupling constant
J1 = −0.9mRyd. Competing magnetic interaction along
the zigzag VO-chains is likewise antiferromagnetic, with
coupling constant J2 = −1.6mRyd. Despite two paths
for the nearest neighbour exchange and a single path for
the intrachain exchange, see figure 1, the next-nearest
neighbour magnetic coupling therefore is found to domi-
nate. Furthermore, since the ratio J2/J1 = 1.68 exceeds
the Majumdar-Ghosh point 0.5, the zigzag spin-chains in
In2VO5 are expected to be frustrated.
The following electronic structure results for In2VO5
rely on the scalar-relativistic augmented spherical wave
(ASW) method [7]. The implementation in use particu-
larly accounts for the non-spherical contributions to the
charge density inside the atomic spheres. The structural
http://arxiv.org/abs/0704.1205v2
input for the calculation is taken from Senegas et al. [4].
For a correct representation of the crystal potential in
voids of the In2VO5 structure the physical spheres have
to be complemented by additional augmentation spheres
at carefully selected interstitial sites. It turns out that it
is sufficient to dispose 84 additional spheres from 15 crys-
tallographically inequivalent classes in order to keep the
linear overlap of the physical spheres below 15% and the
overlap of any pair of spheres below 20%. Since we have
32 physical spheres, the unit cell entering the calculation
thus comprises 116 augmentation spheres in total. The
basis set taken into account in the secular matrix con-
sists of In 5s, 5p, 4d, V 4s, 4p, 3d, and O 2s, 2p states,
as well as states of the additional augmentation spheres.
During the course of the band structure calculation the
Brillouin zone is sampled with an increasing number of
up to 56 k-points in the irreducible wedge, which ensures
convergence of the results with respect to the fineness of
the k-space grid. For the exchange-correlation functional
the Vosko-Wilk-Nusair parametrization is used. As long
as the augmentation spheres are selected carefully and
the crystal structure is not altered, the ASW method is
highly reliable for the comparison of magnetic energies.
We start the discussion of the electronic structure of
In2VO5 by addressing results of a spin-degenerate band
structure calculation. They allow us to study general is-
sues concerning the anisotropy of the electronic states,
the chemical bonding, and hybridization effects. After-
wards we will investigate the magnetic coupling by spin-
polarized calculations for various spin patterns. Figure
2 shows the band structure for the spin-degenerate case
along selected high symmetry lines in the first Brillouin
zone of the simple orthorhombic lattice, where the high
symmetry points are defined by the standard reciprocal
lattice vectors Γ = (0, 0, 0), X = (1
, 0, 0), S = (1
, 0),
Y = (0, 1
, 0), Z = (0, 0, 1
), U = (1
, 0, 1
), R = (1
and T = (0, 1
). In the vicinity of the Fermi energy, we
have several electronic bands revealing little dispersion
throughout the first Brillouin zone. Because these bands
originate from the V 3d states, they are responsible for
a remarkable peak in the V 3d density of states (DOS),
compare the DOS curves in figure 2. In the energy range
shown, we have almost only contributions from the V 3d
and O 2p states. Fully occupied In 4d bands give rise to
a pronounced structure around −15 eV, with respect to
the Fermi level.
The gross features of the partial V 3d and O 2p DOS
are typical for compounds based on VO6-octahedra. As
to be expected from a molecular orbital picture, we can
identify two groups of bands in the energy ranges from
−8.5 eV to −2.8 eV and from −0.2 eV to 4.2 eV. Inter-
action between V 3d and O 2p atomic orbitals leads to
bonding and antibonding molecular states. The bonding
bands are fully occupied, whereas the antibonding bands
cross the Fermi level and cause In2VO5 to be a metal at
room temperature. Even though the bonding and anti-
bonding states are dominated by oxygen and vanadium
contributions, respectively, non-vanishing admixtures of
ZTRUZΓYSXΓ
-8 -6 -4 -2 0 2 4
(E - EF) (eV)
FIG. 2: (Color online) Band structure and partial V 3d and
O 2p DOS (per atom), as resulting from a spin-degenerate
calculation.
intrachain coupling interchain coupling energy gain
fe fe 12mRyd
fe af 10mRyd
af fe 4mRyd
TABLE I: Comparison of the energy gain (per V site) due to
the exchange coupling for various spin patterns.
the other states are present in figure 2. They trace back
to significant VO-hybridization, particularly between or-
bitals mediating σ-type overlap.
For investigating the magnetic coupling in In2VO5, we
have to consider the following three spin patterns, since
nearest and next-nearest neighbour exchange interaction
is relevant. First, we assume the magnetic coupling to
be ferromagnetic both along the VO-chains and between
neighbouring chains. Afterwards, we assume either the
intrachain or the interchain coupling to be antiferromag-
netic, while keeping the other coupling ferromagnetic. In
-1 0 1 2 3 4 5
(E - E ) (eV)
V 3d spin-majority, fe
-1 0 1 2 3 4 5
(E - EF) (eV)
V 3d spin-minority, fe
FIG. 3: (Color online) Partial V 3d spin-majority (top) and
spin-minority (bottom) DOS (per atom) for ferromagnetic in-
trachain coupling.
each case, spin-polarized band structure calculations re-
sult in a lowering of the total energy as compared to the
spin-degenerate solution. Values for the energy gain per
magnetic site are summarized in table I. The largest en-
ergy gain of 12mRyd is obtained when both the nearest
and next-nearest neighbour exchange interaction is ferro-
magnetic. With respect to this value, intrachain and in-
terchain antiferromagnetic coupling raises the energy by
2mRyd and 8mRyd, respectively. The magnetic ground
state of In2VO5 hence is found to be ferromagnetic, i.e.
the room temperature crystal structure of Senegas et al.
[4] is incompatible with antiferromagnetism within the
VO-chains as well as between the chains.
We next study the effects of the intrachain magnetic
coupling on the electronic structure of ferromagnetically
coupled VO-chains. Partial V 3d spin-majority and spin-
minority densities of states for ferromagnetic and anti-
ferromagnetic exchange along the chains are shown in
figures 3 and 4. The width of the spin-majority bands in
-1 0 1 2 3 4 5
(E - E ) (eV)
V 3d spin-majority, af
-1 0 1 2 3 4 5
(E - EF) (eV)
V 3d spin-minority, af
FIG. 4: (Color online) Partial V 3d spin-majority (top) and
spin-minority (bottom) DOS (per atom) for antiferromagnetic
intrachain coupling.
figure 3 amounts to 4.8 eV. It therefore is about 0.4 eV
larger than for the spin-degenerate bands, see figure 2,
whereas the width of the spin-minority bands hardly al-
ters. In contrast, the spin-majority and spin-minority
band widths are rather similar in figure 4. While for fer-
romagnetic intrachain coupling the spin-minority group
of states is observed at higher energies, leaving only V
3d spin-majority states occupied, both spin components
contribute at the Fermi level for antiferromagnetic cou-
pling. As a consequence, the local V magnetic moment
accumulates to only 0.71µB in the latter case. Oxygen
magnetic moments are neglectible. On the contrary, the
ferromagnetic coupling results in magnetic moments of
0.92µB for the V and 0.05µB for the intrachain O sites,
which sum up to 4µB per unit cell. Due to a strong spin
splitting of nearly 0.8 eV, see figure 3, a large number of
occupied states is shifted to lower energies, paving the
way for the ferromagnetic ground state.
In conclusion, electronic structure calculations using
density functional theory indicate that the experimental
room-temperature crystal structure of the zigzag spin-
chain compound In2VO5 is incompatible with both an-
tiferromagnetic intrachain and interchain coupling. Fer-
romagnetism is stabilized instead, which contradicts the
crystal chemical estimates by Volkova [5]. This discrep-
ancy probably traces back to hybridization between the
V 3d and O 2p states, as reflected by remarkable oxygen
magnetic moments. Nevertheless, the antiferromagnetic
coupling likewise comes along with energy gain as com-
pared to the non-magnetic solution. Because of narrow
V 3d bands at the Fermi energy, see figure 2, electronic
correlations beyond the local density approximation can
play a role and further stabilize antiferromagnetic inter-
action. However, this seems not to be the case here, as
recent experiments point at a transition from ferromag-
netic to antiferromagnetic exchange at low temperature,
accompanied by structural alterations [8]. Since strong
coupling of the electronic system to the crystal lattice is
typical for transition metal oxides [9], slight changes in
the crystal structure may induce relevant modifications
of the magnetic exchange. A large variety of phase tran-
sitions is known for compounds with octahedrally coor-
dinated transition metal atoms. The vanadium and tita-
nium Magnéli phases, for example, are subject to metal-
insulator transitions accompanied by distinct structural
alterations [10, 11]. A low temperature structural phase
transition in In2VO5 therefore still could cause an anti-
ferromagnetic ground state with frustrated zigzag spin-
chains. In order to solve this question, a detailed inves-
tigation of the In2VO5 crystal structure is required.
Acknowledgement
Valuable discussions with L.M. Volkova are gratefully
acknowledged. This work was supported by the Deutsche
Forschungsgemeinschaft (SFB 484).
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