HAL Id: jpa-00231177
https://hal.archives-ouvertes.fr/jpa-00231177
Submitted on 1 Jan 1975
HAL
is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire
HAL, estdestinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
To cite this version:
C. Sommers, R. de Groot, D. Kaplan, A. Zylbersztejn. Cluster calculations of the elec- tronic d-states in VO2. Journal de Physique Lettres, Edp sciences, 1975, 36 (5), pp.157-160.
�10.1051/jphyslet:01975003605015700�. �jpa-00231177�
CLUSTER CALCULATIONS OF THE ELECTRONIC d-STATES
INVO2
C. SOMMERS
Laboratoire de
Physique
desSolides,
Université ParisXI,
91405Orsay,
FranceR. DE GROOT
(*)
Centre de Calcul
Atomique
etMoléculaire,
91401
Orsay,
FranceD. KAPLAN and A. ZYLBERSZTEJN Laboratoire Central de
Recherches, Thomson-C.S.F.,
91401
Orsay,
FranceRésumé. - Un calcul des états électroniques d de VO2 à partir des premiers principes a été effectué.
On utilise, de manière auto-cohérente, la méthode par diffusion multiple, avec traitement statistique
de l’échange. Un octaèdre
VO86 -
a été utilisé pour représenter la phase tétragonale et un amasV2O12-10
avec des atomes de
vanadium
appariés a été utilisépour
la phase monoclinique. Les résultats obtenus sont en contradiction avec une explication de l’origine de la bande interdite du semiconducteur en terme de séparation de bandes induite par la distorsion.Abstract. - An ab-initio cluster calculation of the electronic d-states in VO2 has been made by using the self-consistent statistical exchange multiple scattering method. A
VO8-6
octaedron wasused to represent the tetragonal
phase, and
aV2O12-10
cluster with pairedvanadium atoms
wasused for the monoclinic phase. Our results are in conflict with an explanation of the semiconducting
gap in terms of simple distortion-induced band splitting.
Vanadium dioxide
(V02) undergoes
a transitionfrom a
high
temperature metallicphase
to a low tem- peraturesemiconducting phase
at 340 K[1].
Thesetwo
phases
have differentcrystallographic
structures.Metallic
V02
has a rutiletetragonal
structure, each vanadium atombeing
located at the center of anoxygen octahedron
(Fig. la).
The low temperaturephase
is a monoclinic distortion of this rutile structureinvolving
apairing
and off axisdisplacement
ofalternate vanadium ions
along
the rutilecr-axis (Fig. 1 b).
As aresult,
thecrystal
unit cell is doubled.Starting
with the work of Adler and Brooks[2],
there have been several theoretical I
descriptions
interms of band models
[3, 4].
Inthese,
theband-gap
of
semi-conducting V02 originates completely
froma modification of the band structure
by
the distortion.In order to
investigate
thevalidity
of suchdescriptions
we have made several cluster calculations of the electronic structure, both in the rutile and distorted
(*) Present address : Laboratory of Chemistry, University of Groningen, Groningen (Holland).
configurations, by using
the self-consistent statisticalexchange multiple scattering
method of Slater and Johnson[5].
This is an ab-initiocalculation,
whichyields
thesplitting
of the vanadium 3d-levels in the distorted structure. Acomplete
detaileddescription
of the calculations will be
given
elsewhere. We present hereonly
the data and results relevant to theproblem
of the metal-insulator transition. We compare the band scheme inferred from our calculation toexperimental
data. Adisagreement
is found which is considered as evidence for theimportance
ofintra-atomic correlations in
inducing
aband-gap.
Our calculations simulate a neutral cell of
V02
in the solid
by surrounding
each atomicspecies
ofthe cluster with
non-overlapping
muffin tinspheres,
and
by enclosing
the cluster with a so-called outer-sphere [5].
Threecomplete
cluster calculations wereperformed, using
a different geometryand/or
adifferent number of atoms in each case. The
quantities
of main interest
coming
out of the calculation are theenergies
of the vanadium d-levels and thecorrespond- ing charge
distributions. The clusters have been chosenArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:01975003605015700
FIG. 1. - Atomic clusters used in the calculations : large spheres represent oxygen atoms and small spheres vanadium atoms.
a) Single octahedron with atoms in the tetragonal phase positions.
b)
Double
. octahedron with vanadiumdisplacements
(0, by, 6z) corresponding to the monoclinic phase.of the d-state
charge residing
in the outersphere region.
Thisgives
us confidence that the calculatedenergies
of the d-levels describecorrectly
the meanpositions
of thecorresponding
energy bands in the actual solid.To simulate the metallic
phase
we chose the basicVO6-
octahedron of the rutile structure(Fig. la).
This
configuration
hasD2h
symmetry. The energy of each d-level and thecorresponding charge
distribu-tion are
given
in table I. Theordering
of the d-levels is such that thedxZ
state is the lastoccupied
one(containing
oneelectron).
The emptyd,,2- y2
anddyz
levels follow in order of
increasing
energy. We find that the orthorhombicsplitting
is small( ~
0.05eV),
the lowest three d-levelsbeing
almostdegenerate.
This group of levelsgives
rise in thecrystal
to the
partially occupied
lowest d-bands. Our calcula- tions show that there is a sizable fraction( ~
6%)
of the total
charge
contribution of these levels resid-ing
in the oxygenspheres.
This tends to support nbonding
via the oxygens as theorigin
of the band- width[6].
Our results are consistent with thesimplified
band scheme discussed
by Goodenough [6] :
a 7r*band
originates
from thed.,z
anddyz levels,
and itoverlaps
adil
~~ bandoriginating
from thed_,2 - y 2
level
(this dll
band should be narrower, due to anunfavorable symmetry with respect to yr
bonding).
In order for the system to become
semiconducting,
two
distinguishable changes
in the band structureare
required : (i)
araising
of the n* bands above theTABLE I
Energy
levels andcharge
distributionsfor
the two clustersof figure
1.Energies
are measuredrelative to the last
filled
level. Thecharge
distributionsfor
thedifferent
clusterregions
aregiven,
aswell as the symmetry
of
the main componentsof
thewavefunctions for
the atomicspheres.
Fermi energy, thus
leaving
thedjj
bandhalf-filled,
and(ii)
asplitting
of thed
band. It has been surmisedby Goodenough [6]
that the firstrequirement
ismainly
fulfilledthrough
theshortening
of one V-0distance
by
thedistortion,
thusdestabilizing
the 7r*orbitals. This is achieved
by
adisplacement
of thevanadiums
perpendicular
to the rutilecr-axis.
Thesplitting
of thed band
can then result from formation of V-Vpairs, through
alternatedisplacements along
this axis
[6].
Given theseconsiderations,
we have made several cluster calculations in order to inves-tigate separately
thechanges
in the energy levelsproduced by
each component of the distortion.In the low temperature
phase
ofV02
all atoms aredisplaced
from theiroriginal
rutilepositions,
and thebasic octahedron loses all its symmetry elements
[4].
We have
approximated
the oxygenpositions by
anoctahedron of
D2h
symmetry,according
to thefollowing procedure : (i)
its center of symmetry is taken at thebarycenter
of the real oxygenpositions;
(ii)
the symmetry axes are theoriginal
rutile axes(Fig. la) ; (iii)
the coordinates of the two oxygenslying
on the z axis are obtainedby averaging
the true zcoordinates; (iiii)
a similaraveraging
is done for the four oxygenslying
in the xyplane.
The vanadiumatom in
semiconducting V02
has coordinates bx = 0.016A, by = 0.155 A,
bz = 0.113A
withrespect to the center of the octahedron. As a first step,
we have made a
V06 -
cluster calculation with thevanadium
atom at(0, 0, bz),
in order toinvestigate
the effect of the off
cr-axis displacement (C2v
sym-metry).
This resulted in areordering
of the d-levelsso that now
dx Z _ y2
is the last filledlevel,
thedxz
and
dyz
statesbeing
located 0.21 eV and 0.26 eV abovein energy.
In order to include the effect of
pairing
one needsa
larger
clustercontaining
two vanadium atoms.We have taken a
V 20~Õ-
cluster with twoadjoining
octahedra
along
thecr-axis (Fig. 16).
The vanadium in one octahedron is at(0, 5~, bz)
whereas the other is in thesymmetric position
with respect to the center of symmetry of the cluster(Fig. 16).
The small ~x component has beenneglected
so as to preserveC2h
symmetry. The last filled level now contains twoelectrons.
Considering
itscharge
distributiongiven
in table
I,
we see that it is notsimply
a vanadiumd-state but rather an admixture of vanadium d- wavefunctions
(mainly dx2 - y2)
and oxygen s and pwavefunctions. This level
corresponds
to a covalentbond between the two vanadiums in the
pair,
obtainedthrough
admixture of wavefunctions on the oxy- gens[7].
It willgive
rise to the valence band in thesemiconductor.
Starting
0.5 eVhigher
up in the energy we find a group ofclosely spaced
d-levelscorresponding essentially
to vanadium d-states. These willgive
rise to the conduction band.Comparing
the above twocalculations, namely
distorted
VO~-(C2v)
andV20i~-(C2h)’
we see thatboth components of the distortion have
comparable
effects in
creating
a bandsplitting,
thusconfirming Goodenough’s qualitative description [6].
The ques- tion now arises as to whether themagnitude
of thesplitting
can account for theband-gap.
Our calculationgives
a d-levelsplitting
of 0.5eV,
and this would be the trueband-gap only
in the limit of zero bandwidth.Optical
measurements[8, 9]
in the metallicphase
indicate a bandwidth of order one to two electron- volts
[10],
in agreement with the band calculations of Caruthers et al.[11].
InGoodenough’s descrip-
tion
[6]
thiscorresponds
to the n* bandwidth. Sincewe found a
comparable
admixture of oxygen wave-functions with the vanadium d-states in both struc-
tures, we expect a
comparable
bandwidth for the bandoriginating
from the empty d-levels. Thereforeone would expect this band and the valence band to either
overlap,
or at most beseparated by
aband-gap appreciably
smaller than the calculated level separa- tion of 0.5 eV.Experimentally,
an activation energyE6
= 0.45 ± 0.05 eV for theconductivity
above room temperature has beenreported
forgood quality
sam-ples by
several authors[12-14],
and recent thermo-electric power measurements
(*)
show that this iseffectively
due to excitation ofcarriers,
asopposed
to an activated
mobility.
From these results onededuces an energy gap for carrier excitation
lying
between 2
E6
= 0.9 eV and 0.7eV, depending
onassumptions
of the temperaturedependence
of thegap
[15].
We thus find a definitedisagreement
with themuch smaller value inferred from the cluster calcula- tion
by taking
into account bandwidths.It therefore appears necessary to consider the intra-atomic electron
repulsion
asresponsible
foropening
the gap. This is corroboratedby : (i)
estima-tions of the intra-atomic correlation energy U
[16] (*)
which
yield
values of a fewelectron-volts; (ii)
theobservation of localized moments on vanadium sites in the
insulating phase
ofV,-.,Cr,,02 alloys [17],
for which the
pairing
ispartially suppressed.
We wish to thank Professor J. W. D.
Connolly
for a copy of his MST computer program.
BUCHY et al. Private communication.
(*) SOMMERS, C. and DE GROOT, R., Unpublished.
References [1] MORIN, F. J., Phys. Rev. Lett. 3 (1959) 34.
[2] ADLER, D. and BROOKS, H., Phys. Rev. 155 (1967) 826.
[3] HEARN, C. J., J. Phys. C 5 (1972) 1317.
[4] CARUTHERS, E. and KLEINMAN, L., Phys. Rev. B 7 (1973) 3760.
[5] SLATER, J. C. and JOHNSON, K. H., Phys. Rev. B 5 (1972) 844.
[6] GOODENOUGH, J. B., J. Sol. Stat. Chem. 3 (1971) 490.
[7] In the rutile VO8-6 (D2h) cluster calculation, we find an oxygen s and p level lying not far above the vanadium d-levels (Table I). Covalent bonding presumably occurs by admix-
ture with this state. Note the large amount of intersphere
Phys. (1968)
[9] FAN, J. C. C., Techn. Rep. N° HP-28, Division of Engineering
and Applied Physics, Harvard University, Cambridge,
Massachussetts.
[10] PAUL, W., Mat. Res. Bull. 5 (1970) 691.
[11] CARUTHERS, E., KLEINMAN, L. and ZHANG, H. I., Phys. Rev.
B 7 (1973) 3753.
[14] BORISOV, S., KORETSKAYA, T., MOKEROV, G., RAKOV, A. V. and SOLOV’EV, S. G., Sov. Phys. Solid State 12 (1971) 1763.
[15] ZYLBERSZTEJN, A. and MOTT, N. F., Submitted to Phys. Rev. B.
[16] HYLAND, G. J., Phil. Mag. 20 (1969) 837.
[17] POUGET, J. P., LAUNOIS, H., RICE, T. M., DERNIER, P., GOSSARD, A., VILLENEUVE, G. and HAGENMULLER, P., Phys. Rev.
B 10 (1974) 1801.