Folding CuO2 planes into fullerene-like clusters

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Folding CuO2 planes into fullerene-like clusters

M. Núñez-Regueiro

To cite this version:

M. Núñez-Regueiro. Folding CuO2 planes into fullerene-like clusters. Journal de Physique I, EDP

Sciences, 1994, 4 (2), pp.169-174. �10.1051/jp1:1994129�. �jpa-00246894�

Classification Physics Abstracts

74.10 75.25 74.10W

Short Communication

Folding Cn02 planes into fnllerene-like cInsters

M.D.

Nùfiez-Regueiro(~,*)

and M.

Nùfiez-Regueiro(~,*)

(~)

European Synchroton Radiation Facility, B-P. 220, 38043 Grenoble Cedex, France

(~) Centre de Recherches _sur les Très Basses Températures, Centre National de la Recherche Scientifique, B-P- 166, 38042 Grenoble Cedex 09, France

(Received

26 November1993, accepted 21 December 1993)

Abstract Trie wrapping of graphite planes into fullerenes induces, _among other interesting properties, _{an increase} of trie superconducting temperature in their corresponding intercalation

compounds that has been attributed to the cluster structure. This motivates the search for similar behaviour in other systems. Here _we explore the clusters that _may be obtained by trie folding of Cu02 Planes and study their magnetic and electronic properties. Natural murdochite

minerai _proves that, at least in _an interconnected structure, the Cu02 layers fold into cages, while the BaCu02 Phase _can be viewed _{as a} first step towards their separation within _a cationic

matrix.

Metals made out of dusters have

yielded

remarkable

properties.

In

particular buckyballs iii

and Chevrel

phases

_[2] have

larger superconducting

transition temperatures Te thon

doped layered graphite

_[3] and

molybdenum disulphide

_[4]. In

A3C60 IA

=

K, Rb, Cs)

the

high

Te bas been related _to the

huge

electronic

density

of _states of weak

interacting

^dusters [5, _GI.

Though

it _con be diilicult _{to agree on} the

precise

_reasons for this increase of

Te,

it is

tempting

to

probe

what would

happen

to other

layered

structures wl~en transformed into dusters. A

particularly interesting

_case is tl~e _one of l~igl~ Te _copper oxides. We

study

l~ere the

possible

dustered structures that _con evolve from the

Cu02 Planes.

Using

the fullerene

approach

the _square Cu02 lattice _con

theoretically

be folded

keeping

the

original connectivity.

Euler's formula for dosed

polyhedra,

V E + F

=

2,

where

V,

E and F

are

respectively

the number of vertices,

edges

and

faces, yields

dusters with 8

triangles

and _s squares. We show in

figure

_some

examples

of tl~is

family.

Relevant elements for tl~e

properties

_{of l~igl~} Te cuprates are tl~e _square

Cu02 lattice,

witl~

its

particular

connectivity, and tl~e

quasidegeneracy

of tl~e Cu and O

energies. Doping

simul-

taneously

introduces carriers and frustration _to tl~e

original insulating antiferromagnetic (AF)

lattice.

Conceming

tl~e

magnetic properties

of the

clusters,

tl~e first point to remark is tl~at l~ere

(*)

On leave of absence from CNEA and CONICET, Centro Atômico Bariloche, 8400 Argentina.

170 JOURNAL DE PHYSIQUE I N°2

/~

Jé _,

, ,

/ ₁

/ ,

/ ~

j , 1

/ 1

j ,

(il ^(dl

l'i, ,jl'

/ j ^'

/ ' ,

Î

'

4

1

j

/ '

o

' 1

/ ,

' '

1

Fig. l. Left side: closed _convex polyhedra obtained by folding _{a square}

(s)

lattice with 8 triangles.

la)

octahedron _{s =} 0, 16) cuboctahedron _s

= 6, (c) rhombicuboctahedron _s

= 18. There _is

a Cu _on

each vertex and _an O _at the middle of each edge, conserving the Cu-O loyer connectivity. llight side:

classical AF configuration ^of

Cu~+

_atours

m the

(Cu02)n

clusters

(pro

jected

on a plane perpendicular

to the shown C3

axis); (d)

_n = 6, (e) _{n =} 12,

(f)

_n

= 24, ail spins are on parallel planes.

frustration is induced _even before

doping, just by

the

folding

of the _square

Cu~+

lattice with

triangles.

Let _us consider _a nearest

neighbour (n.n.) Heisenberg

^AF interaction for classical

spins

in _a cluster with _n

magnetic

sites. Due to frustration tl~e

ground

state of _an isolated tri-

angle

bas ail

spins coplanar

and _{an energy} of

Jicos(2x /3)

_per bond. Tl~is reduces tl~e

Inagnetic

energy of the octahedron to E

=

-6Ji (Fig. id).

The _same

happens

with the cuboctal~edron

(Fig. le) altl~ougl~

_{squares are now} present,

tl~ey

ail sl~are eacl~ of their

edges

with _a

triangle,

and tl~e total energy of the 24 bond cluster _{is E}

=

-12Ji

Wl~en two types ^of bonds _appear,

a lower bound for tl~e energy of the entire cluster is

given by,

Eb _"

24Jicos(2x/3) nssJ2,

_nss

being

tl~e number of

edges

between two squares and

J2

_an

eventually

^{diflerent AF} constant between tl~e

spins coupled by

^tl~ese s-s

edges.

A solution _con be obtained

by inspection:

ail

spins

_{are m}

parallel planes,

tl~e

angles

tl~at minimize tl~e energy within _a

triangle

_are conserved but the

spins

on either end of _{any s-s} bond _are

precisely antiparallel, avoiding

interference and

lowering

the energy down to Eb. The

ground

state

configuration

has _{a zero}

global magnetic

moment and is tl~e _saine for ail AF

Ji

and J2. For

J2

_"

Ji,

E

= -36Ji for the 24 Cu atom cluster

(Fig. lf), yielding

_{an average energy} ^of

-l~.75Ji

_Per bond. Tl~e _average frustration

decreases _as tl~e number of _squares increases. An

analogous

result bas been found for

undoped c60 Iii.

àe<e»z~cy 3

-

a~

àig

_- 2

2

^'

^'lu

Q 'lu '2g

~

-

1 _e,

-

~

t~~

+

e,

ÎÎ

~2g ^~

'2u

'

1g ^{~ ~} lu ^~

'2g

~ ~u^~

~2u

ilJ

-i

- ---

Z tz~

+

e,

'lu 'zg

a~

'lu

'

~lg

ja) (bj

Fig. 2. MO _energy levels for the

(Cu02)n

clusters. The IiIling is discussed in the text.

(a)

_n

= 6,

(b)

n = 12. 6

= Ecu go is taken equal to the Cu-O hopping term t. The _same structure is obtained for degenerate ^Cu-O levels, 6

= 0. Larger values of 6 increase the energy splitting without modifying

the general features of trie spectra.

All

superconducting

_copper oxides _are obtained from

insulating

matrices in which two elec- trons _are transferred from _a "reservoir"

loyer,

_C,g.

(Lasr)O,

to each formula unit in the

plane

to

satisfy

tl~e Cu~+ and O~~ valencies.

Considering

tl~en tl~at 13 electrons tilt the 7 orbitals

(derived

from _one

d~2-~2

^{and six}

p)

of tl~e

Cu02 loyer,

_a metallic behaviour _is obtained for _a small on-site Coulomb interaction U. The

splitting

of tl~e spectra _m tl~e

large

U liInit for _one

electron _per orbital

filling

accounts for tl~e

insulating

properties of tl~e

undoped

system and the O character of hale

doping.

The essential features of the relevant bonds _con be described in terms of _a

tight binding

model with two parameters: ^the

quasidegenerate

_energy for Cu and O

loyer

atoms and _an effective

hopping

between them [8].

For weak

interacting

dusters molecular orbital

(MO)

calculations

give

_a

good

^first

approacl~

to their electronic _structure. Let _us consider

only

tl~e

3d~2-~2

^{orbitals of tl~e Cu atoms}

(Ecu)

and the

02p orbitals(eo)

directed to their _n-n- Cu atoms, the other 4n

02p

orbitals _are taken

172 JOURNAL DE PHYSIQUE I N°2

as

non-bonding,

6

= Ecu go in units of tl~e Cu-O

l~opping

t,

assuming

_no

changes

with respect

to tl~e

plane. Figure

2 shows that within this

approximation

the _saine

l~appens

wl~en

(13n)

electrons _are introduced in tl~e

(Cu02)1"~

duster. For tl~e _n

= 6

in

₌

12)

_case, when each MO is

doubly occupied,

tl~e HOMO _{is a}

partially

^filled un

(t2g)

^{level. For}

large

U

splitting,

tl~e Fermi level lies _m tl~e _gap between the

non-bonding

O levels and tl~e eg

(t2u

+

eg)

^LUMO

antibonding

level. Tl~e l~igl~

degeneracy

of the

non-bonding

O levels cl~aracteristic of higl~ T~

cuprates is conserved.

We bave

ignored

tl~e curvature of _our duster in tl~e calculation and taken tl~e Cu-d and

O-p

levels _as in tl~e

layered

materials.

However,

tl~e

non-planarity

will force _new

l~ybridizations

or level

mixings.

If tl~e _square

planar

coordination of tl~e Cu atom is conserved to gain tl~e energy of the

d~2-~2

^dz2

^spitting,

^{tl~e O} atoms will

l~ybridize

into a

sp~ configuration

to introduce the _necessary curvature _as shown

graphically

ⁱⁿ

figure

3 for the

(Cu02)12

duster.

Tl~is will

change

6 and t, ^and _con

modify

the eventual

superconducting properties.

On the other l~and a neutral duster will bave 24 unsatisfied

Osp~

lobules tl~at will render tl~e molecule

extremely

reactive.

Cl~arging completely

tl~e duster introduces _an important Coulomb _energy tl~at will _most

probably

l~inder tl~e existence of _an isolated

duster,

tl~ougl~ its observation in _a

compound

is

possible.

,

'

Fig. 3. If the square planar Cu

(o)

coordination _is conserved, the O

(~)

hybridize

sp~,

as schema- tized for _a Cu atom and its four _n-n- O. The

(Cu02)12

cluster is blown _up from the cuboctahedral

(Fig. lb)

to the rhombicuboctahedral (Fig. lc) shape, with _now O atours _on the vertices and Cu

atoms _m the center of any square sharing edges with triangles.

One _way of

stabilizing

this type ^of

tetrahedrically

coordinated dusters is

by interconnecting

tl~em witl~ _common faces _as it is

actually

done in

murdochite, PbCu608Cl

_[9],

figure

4a. Each

Cu atom is _common to two cages, wl~ile tl~e O _are sl~ared

by

tl~ree dusters. Tl~e fourtl~ fuit

sp~

lobule

points

towards tl~e Pb~+ _{ion in tl~e cubic} "interstitial" sites, and tl~e Cl~ ion is

in tl~e center of eacl~ cage.

Althougl~ PbCU608CI

_proves tl~at

Cu02 loyers

_con be folded in

tl~e way we suggest, ^tl~e

change

of tl~e Cu-O

connectivity

alters

completely

tl~eir

properties

and

superconductivity

bas net been observed. It is necessary ^to look for _{new structures} witl~

separate dusters l~eld

togetl~er differently,

_e-g-

by

tl~e interaction witl~ _a suitable cationic environment. A step in sucl~ direction is

BaCu02,

_as

separated (Cu02)12

dusters _are present

m its

complex

structure

[loi, figure 4b,

tl~ougl~ ^stabilized

by

tl~e addition of 6 Cu atoms in the empty square faces of tl~e rhombicuboctal~edron. Tl~e

resulting charge

_is compensated

by

Ba atoms

placed

_{on top} of each of the O

triangles.

The dusters _are

separated by planar

Six.membered

rings

m tl~e

il11)

and

equivalent

directions, and

by

disordered _arrays of _atoms

o

o cmJ cura o

a) f

.,,

o

b)

Fig. 4.

(a)

Schematic _view of the interconnected

(Cu02)12

cluster structure _m natural murdochite minerai, PbCu608Cl. For clanty only one of the Cl~ (dotted circle) and of the Pb~+ _ions

(hatched circle)

_are shown. The bold fines mdicate

Cu(O)~O(~)

_n-n- bonds. (b) Projection along the

(001)

direction of the BaCu02 unit cell. In the center the

Cu6(Cu02)12

cluster. Seven sites with occupancy lower than

1/3

_are omitted for clarity. Dotted circles represent Ba _ions.

in the

(100)

and

equivalent

directions. The

connectivity

of the

planes

_{is agoni} lest and witl~ it

probably

tl~eir

interesting

properties.

Considering

tl~ese

examples,

diflerent

possible

structures witl~ cotions around tl~e

(Cu02)1(~

clusters _con be

proposed.

Even if

superconductivity

^faits to appear, tl~e searcl~ for tl~ese _new materials will l~elp

clarifying

the

hypothesis

^{used for} higl~ Te cuprates.

Acknowledgements.

We _are

grateful

to A.F.

Hebard,

C.M. Varma and M.

Avignon

for encouragement and discus-

sions,

and J-L- Hodeau for

pointing

eut tl~e murdochite structure.

References

iii

Hebard A.F, et al., Nature 350

(1991)

600;

Hebard A.F., Phys. Today 45

(1993)

26.

[2] ^{Matthias B-T- et} ai., Science175 (1972) 1465.

[3] Hannay N-B- et ai., Phys. Rev. Lett. 14 (1965) 255.

174 JOURNAL DE PHYSIQUE I N°2

[4] Somoano R-B- and Rembaum A., Phys. Rev. Lett. 27

(1971)

402.

[5] Varma C.M. et ai., Science 254

(1991)

989;

Schluter M. et al., Phys. Rev. Lett. 68

(1992)

526.

[GI Friedel J., J. Pbys. Il France 2

(1992)

959.

(7]Cofsey D. and Trugman S-A-, Phys. ^Rev. Lett. 69

(1992)

176.

[8] Mattheiss L.F., Phys. Rev. Lett. 58

(1987)

1028.

[9] Medunic Z. et al., Mat. Res. Bull. 28

(1993)

741 and references therein.

[loi

Paulus E-F- et ai., Sol. Sta. Ch. 90

(1991)

17.