Chemical bonding in transition metal magnetic molecules and clusters

Journal of Molecular

93 (1983)

Structure,

93

93-110

THEOCHEM Elsevier Science

CHEMICAL

Publishers

BONDING

B.V., Amsterdam

- Printed

IN TRANSITION

in The Netherlands

METAL

MAGNETIC

MOLECULES

AND

CLUSTERS

J. KELLER Facultad 04510

Universidad

de Quimica,

D.F. and Seminar

M&xico,

CH-8093

National

Aut6noma

fiir Theoretische

de Me'xico",

Physik,

ETH,

Ziirich, Switzerland

ABSTRACT The chemical bonding among transition metal atoms in molecules and clusters is strongly dependent on a balance between bonding energy and intraatomic exchange energies. Molecules and clusters may be magnetic either because of the degeneracy of the uppermost occupied levels or because there is a ground state where one or more of the atoms build a localized moment. We will show strong evidence of the contribution of the d electrons to the bonding and then, because intraatomic exchange is so strong, of the competition between atomic magnetic moments and chemical bonding. The main examples will be Fe, Ni, MO, Nb and Ir molecules and clusters. The cluster calculations are for groups of atoms in condensed matter boundary conditions. Multiple scattering and local density techniques are used.

INTRODUCTION When

two hydrogen

situation

atoms

in the singlet

as if one of the atoms ed spin direction,

lap for distances distances, within each

sponding cleus.

4 a.u.

of a given

spin having

description

than

are found, 0166-1280/83/$03.00

ceases

2 a.u.,

second

to have

most

where

some

of its wave

0 1983 Elsevier Science

function

equal

B.V.

cen-

corre-

hydrogen

moments,

for internuclear

spins

Publishers

is given DODS with

deformation

the second

UHF and HF calculations

over

intermediate

model

magnetic

fix _

spin,

significant

At this

a small

localized

for both

system

the opposite

spins

lobe around

the

full symmetrization,

a good description

to be significant

then the DODS,

picture

a laboratory

with

(ref.1).

and with

of almost

we could

before with

for different

nucleus

to an incipient

This

begin

and 2 a.u.,

orbitals

the parent

spin densities, smaller

clouds

4 a.u. or smaller

between

around

state,

say up, and the other

the different

electron

tered

overall

each other

had an electron

The electronic

say down.

approach

molecular

nu-

or

distances orbitals

lead to the same

94

result.

Chemical

bonding

the intraatomic

has appeared

(self) electronic

the indistinguishability DODS equivalent Chemical

spin electrons remember

that

change. change

For an atom with

rise to the well

ic multiplicity spins will sultant

which

hand,as

to very strong

highly

intraatomic

electrons

will

either

the intraatomic

normal

bond

or there

as a special bitals.

orbital

Ce, where

ally taken

for granted

that

states

atomic

overlap

allow,

orbitals

atom-

a re-

give rise

the question where bonding

is open on

some of the because

to be overcorned by a

between

of this

or liquids

adyacent energy

second

not entering

atoms is

possibility

of the rare

to think

like moment

ex-

as many

of the states

and then too little

solids

atomic

intraatomic

of the maximum

into chemical

example

to

ex-

be obtained.

forces,

it is customary

case of core

A localized

But we have

state

is too large

well known

in the molecules,

beyond

rules

to find situations

not enter

of

considered.

intraatomic

electrons

simply

will

exchange

is not enough

from bonding.A

is found atoms

Hund

localized

exchange

for that type of atomic gained

known

moment

or not is it possible

valence

valence

because

if two paired

orbital. against

as the degeneracy

spin magnetic

On the other

is stronger

works

in case of spin

be unpaired

atomic

whether

several

Of course,

the two complementary

molecular

process

fully overcomed

be symmetrically

learned

a bonding

the bonding

gives

should

as we have

occupy

exchange.

of the electrons,

descriptions

bonding

and it has

earth

of the f electrons

into the valence

of the 4f electrons

(this may not be the case

or-

is usu-

in some instances

(ref.2)). But of course

most

cases

with

s or p atomic

keep

a localized

atomic

much more

localized

their

we know that with

orbitals

these

localized

be intermediate.

are known

magnetic

series

of atoms

Atoms

to show little

moment.

ndx orbitals

bonding

tendency

The transition

deserve

special

metals

to with

attention

give rise to magnetic

as

materials

spin moments.

The fact that a molecule course,

will

necessarily

to be found,

as in the well

gen molecule

with

x level with

two unpaired

It is clear

presents

indicates

known

the uppermost

that

a magnetic

that a localized example

occupied

moment magnetic

does not, of moment

of the paramagnetic orbital

being

is oxy-

a degenerate

spin electrons.

it is necessary

to consider

a balance

between

95

exchange

splitting

of the levels

to a sequential

filling

plain

this more

carefully.

netic

if the spin

where

not divergent.

produce magnetic destroy change

field

much more

tained

by pairing

be gained

moment

intraatomic ation

exchange

between

these

approach

of filling

of a given field

orbitals,

to be larger

will ex -

spin

and more ob-

a permanent is for the

than

the separ-

without

level

between

d and s electrons

degeneracy

with more with

will

being

of six Ni atoms

have

in energy of the

obtained

even

difference

Ry of the u

of that Ae=0.075

character

org Ry of the

(ref.3).

in a cluster

calculation

1 the symmetrized embedded

but a new fea-

split

been

The

of increasing

1). The stricking

half

(spa).

the separation

in the Ae=O.O4

is also observed In figure

in order

orbitals

would

(see table

3dZ 2 predominant

nickel.

spin per atom

than

dis -

is paramagnetic

give this result;

state

is seen

at the interatomic

material

up the levels

Ae is larger

4s character

This behavior

the case of two and six nickel

so the molecular

splitting

the paramagnetic

for a cluster

direction

the intraatomic

is then needed

of one electron

in doing

appears:

romagnetic

What

energy

we could

a very minute

than the one that was

in the crystalline

(as in 02 for example)

u u orbital

because

The Ni 2 molecule

calculations.

and the energy

bital

state

by the external

ideas with

a net magnetization

then

configuration

subbands.

cluster

levels

Let us ex-

not be ferromag-

in the field

in molecular

appear.

splitting

the Ni atoms have

ture

orbitals.

all the orbitals

produced

then

tance

simplest

electrons

of the levels shift

corresponding

if at low temperature

by this process

atoms

energy

that

the electrons

will

Let us clarify

with

some

than the effect

will

lying

like Ni will

in the non magnetic

order

cooperatively

state

of the non magnetic

This means

aligning

energy

magnetic

A metal

of metal

the existing will

up of the lowest

suceptibility

a Ni piece

and the ground

molecular

for fer orbitals

in a ferromagnetic

Ni me-

dium. The exchange nant

Ni

the T

4s

splitting

origin

ation

is Ae=0.025

of predominant

lg er than in the Ni per atom,

largest

exchange

of the lowest

lying A

Ry whereas

3d character

states of predomi lg. the exchange splitting of

is Ae=0.05

Ry. That

it is smallmagnetis-

calculation comes from the reduced 2 0.56 spa instead of 1.0 spa in Ni2, but the splitting

of the more

localized

3d levels

is clear.

96

TABLE

1

Orbital

energies

and population

analysis

(electrons/region-orbital)

of the Ni

molecule in the cellular spin polarized calculations. 2 electrons, the degeneracy factor is included.

Valence

state

2 x Ni cells

e$Ry)

S

P

region d

outer region

interstitial region

og(4)

-0.385

0.2165

0.0652

0.6342

0.0286

0.0555

agW

-0.341

0.4514

0.0956

0.3749

0.0678

0.0103

0.0124

0.0335

II"(+) -0.340

-

1.9403

0.0138

6gW

-0.320

-

1.9455

0.0158

0.0387

6uC-t) -0.310

-

1.9657

0.0100

0.0243

0.0226

0.2968

0.0991

0.1675

0.0065

1.9642

0.0259

0.0034

0.0047

0.9285

0.0100

0.0211

cJgW

-0.295

0.4140

ng(z.) -0.291 OuW

-

-0.290

nu(+)

0.0357

-0.267

-

.pg(J) -0.252

0.1815

&g(s)

-0.244

-

au(+)

-0.232

-

ouW

-0.215

iIgO)

-0.212

(+) majority

spin

(G) minority

spin

energy=-6026.8420

The Ae is again

Reference

larger,

0.0748

0.1243

1.9288

0.0225

0.0487

1.9574

0.0136

0.0290

0.0027

0.8809

0.0182

0.0340

0.2296

17.3641

0.4177

0.6253

Ry

even

for the reduced

of the cluster

3 contains

the surface

0.0176

0.6183

1.3633

the separation

1.9286

0.0011 -

0.0642

total

Total

0.0188

0.0350

energy

levels

also a discussion

Ni2 cluster

and interstitial

magnetisation, near the Fermi

of the effect

than energy.

of hydrogen

in the Ni6 bulk-like

cluster. There

are three

principal

cases

to consider

in general:

Ae
normal case of covalent molecules, Ae=AE bonding' as bonding' in the transition metals where localized magnetic moments can or

not appear, localized special

as in the rare earth metals where a bonding' moment is very common and can be treated as a

and Ae>AE

magnetic

case of core

electrons.

on

97 electrons

I

Symmetrized

Ni,orbiials

histogram

6Ni

H 1

______-F;1____ ;

l&=dA DODS

Hydrogen

0.1

,

0.3

’

0.2

’

0.4

0.5

,

0.7

,

’

0.6

’

0.8

100

0.9 ,!/Ry

Molecule

111

I

2.5

50

P’

4.0 3.0

0

1.0 0”

spa seq. 1.0 0.8

spins

0.6

+:+gj)____\:* 0.4

CT”

t

per

H atom

0.2

0 l--L__ 0

1.0

2.0

3.0

4.0

5.0

dhh

+I----@----,+ t II

Fig. 1

BONDING

IN CONDENSED

MATTER

Let us now study which

has

a particular we have

the chemical

to be defined

computational

chosen

bonding

method

a two steps approach:

the difference

"single

site"

sidered should uum

to correspond distinguish

first

ing renormalized

compute

with

the main finite

volume

the electronic

structure

by first

and, afterwards,

computing

structure

We could

inside

field

is con-

is because

an atom

a renormalized

and,

of the

we

from vac-

charge

and the actual

of an atom

the crystal

This

of the atomic

material.

calculation

is described

configuration

of taking

of

to do that

of a material

bonding.

result

of the embedding

say Cu + in NaCl,

the atom

inside

electronic

the process

to a given

nature

In order

the electronic

to the chemical

between

into a material

the chemical

between

atom and the actual

metals

it is as independent

as posible.

not as in free space but as it appears second,

in solid transition

in such a way that

be-

effect

of

for example

a ionic material, Cu+ atomic

splitting

ion

of the Cu+

98

atomic

energy

levels

The result matter

of bringing

is not only,

of the charge, which

resonant

energies trated 3

above

above

levels

we show:

by the niobium

of the Nb metal

of states

where

tronic

q

NT(E)

site atomic

being

density

the free electron

Bessel

The second

shift

the interstitial

single

site density

seen. The resonant

going

through

in the density

practically

of states

the effect

r/2 and

of elec-

corresponds

(an integral

of the chemical

any suitable

it by the single

to

over

method

bonding

the final

site density

den-

of states

MSRl m 5

can be mathematically

free electronic called

with

and dividing

1 N;;m(E) 1,m

As this ratio

have

above

of states

density

step is to compute

sity of states q

2 and

functions).

can be done computing

N(E)

is illus-

in Figs.

- 2 anl/aE) 71

~(N;(E) 1

spherical

This

for

on the free electron

are clearly

of the d band

This

will

states

energy.

The single Nap

band.

for energies

band

levels

of the crystal

niobium

produced

resonant

in condensed

renormalization

of the atomic

and the corresponding

defined

The center

states.

the Fermi

shifts

the s, p and d bands

3 as a well

volume

free electron

metal

in Fig. 2 as the d-phase

d band appears

and Cl- ions.

potential

of the conduction

potential

potential

in Fig.

change

the average

the phase

+

into a finite

that will mix with

the bottom

Na

the selfconsistent

in the case of the transition

where

waves

an atom

of course,

but also a qualitative

for energies

become

due to the embedding

waves

described

by the different

it the multiple

scattering

atoms ratios

as the scattering of the material

of

we

MSR. They are given

by (ref.5) MSRi1 ,(E)

3

q

Im GIi'(E)/Im

In order

to keep

minology

it is convenient

as much

momentum

and azimuthal

In Fig. 4 we show these lysed

G+" o,iicE) as possible to compute

quantum results

per s, p and d bands.

number

the traditional

chemical

ter-

the MSR per atom,

band angular

for all energies

of interest.

for the example

It is apparent

of Nb metal

ana-

that the d band has been

rI I N(E)stotes/Ry-at0837

I

I

I

I

.6

.8

1.0

1.2

Nb phase shifts V,,, = 1.669 Ry

cl

I

I

.2

.4

0

1 .6

1 .8

I

I

1.0

1.2 E/Rv

.2

.4

E/Ry

-1

Fig. 2

N(E)22 t 20 -

Fig. 5

I8 I6 14 12 IO 864-

0

.2

Fig. 3

.4

.6

.8

1.0

1.2 E/R

1

I

0

3.6

Fig. 6

5.0

6.4

Rlro_laIbohrsl

100 splitted

into bonding

the Fermi

energy

The two peaks

the d band. regions

correspond

a result

and antibonding

Ef. This would

for energies

produce

in each of the bonding

to the splitting

of the cubic

symmetry

We can see, furthermore,

that

below

and above

a deep at the middle

of

and antibonding

subbands as and t g 2g in the insert of Fig. 4.

into a e

as shown

subband

the e

is hybridised

with

g the s states

in the bonding

The p band

gion.

is spectrally

in between

lated,

large

and will

the Fermi a magnetic width

excluded

the bonding

The bonding-antibonding overcome

energy

were

but not

region

in the antibonding

and appears,

and antibonding

splitting,

more

the intraatomic

state will

appear

because

iso-

regions.

than

5 eV, is very

exchange

in one of the bonding

almost

re-

splitting.

But if

or antibonding

Ae is of the order

subbands

of the

of a subband.

In Fig. netic

5 we present

nickel

bonding

for both

splitting splitting

the e

antibonding

occurs

spins where

is very

change g Because

the corresponding

large

for the d band

EF would bringing

which

and that the ex-

of magnitude

as the width

is the one at the Fermi

be at the last antibonding the majority

for ferromag

it is seen that the bonding-anti

is of the same order subband

analysis

d-antibonding

subband subband

of

level.

a splitting of t

character 2g

below

the Fermi

level

To understand densed

matter

by X0

).

the magnetisation

it is important

spin susceptibility given

(ref. 3 and4

(ref.6

of the transition

to analyse

X of that atom.

metals

the enhanced

The spin

in con-

paramagnetic

susceptibility

is

)

x= 1 - N(EF)I where

X0 is the free electron

the electronic to the number

density

of electrons

netic

field,

which

is a weighted

and I is the

change

atoms,

that

can be easily

(atomic)

with

is of the order

splitting

at the Fermi

exchange

sum of the exchange

the spin of one electron metal

spin susceptibility,

of states

ei=EF.

N(EF),

aligned

to the magintegral

energy

gained

atoms

is

by aligning

of I, for transition

of 0.04 Ry (it is one half

metal

to

that

enhancement

The value

Ae) for the molecular

0.03 Ry for the transition

proportional

energy

of the ex-

case and it decreases in condensed

matter,

up to then a

101 density cause

of states

a magnetic

the result integral

near N(EF)=33 instability.

of a bonding

BONDING

is seldom

IN TRANSITION

multiple

we will

particularly atomics.

Before

the density

tion

functional

into a combination potential

the numerical

function

which

will

t;le particular nique

we have

of cells

The cellular calibrated found

The best

say however

sults

in poor

thermochemical around

equa-

of comput-

and eigenfunctions

for a

known

methods

aids.

The construction

can be divided of the

or analytical

of a trial

construction

be used to solve mathematical

in our case

scattering

as scatterers

number

data because

within

or planar

the method

and one big enclousing

cells

very large

interstitial

are accomodated volumes

is assumed

for the col-

the cluster

have

has been method

been

molecules

found

outer

that

there

cell within

in general,

to be constant,

so far.

(cluster)

like spectroscopic assumes

and

It is fair to

and this partitioning where

The tech-

partitioning

(CMS-XeB)

of applications.

properties

for

(ref.8).

of the method

linear with

space

solution

technique

and solids,

wave

equation

form of the potential.

scattering

limitations

of large

the SchrBdinger

is the cellular

multiple

considered

the potential

SchrBdinger a series

and,

agreement

each atom

of the elec-

suitable

the atomic

case,

the calculation

that

diverges,

for a large

The calculation

internuclear

remember

expansion

multiple

which

are in di-

multicenter

for molecules

suitable

atoms

at each atom the potential

chosen used

we should

that we need

metal

and methods metal

case the resulting

This means

(ref.?') and the numerical lection

allows

of two numerical

where

ideas

was Ni2 a-S the solid

in one of the appropiated

for molecules,

and the use of

of transition

transition

into the subject

potential.

The exchange

but the density

l=O,l.

above

these

between

to find the eigenvalues

molecular

second

a case where

but in every

is

MOLECULES

presented

example

will

of states

in N(E).

with

in the study

theory

be solved.

ing techniques

DIATOMIC

bonding

entering

potential

should

given

present

suited:

density

peak

for Nl(E)

techniques

The introductory

distance.

tronic

large

METAL

or greater

for s and p electrons

of the ideas

scattering

bonding

large

very

As a new example

large,

This,

or antibonding

I can be very

of states

electrons/Ry-atom

is a cell which

results

and this

a volume

re-

data or

all in

is our

average

102

41114.45

.&0.72p

Nblr ET[WI 4,,,4,55 2L$&l

5.0

@-

4d-5d bonding 6.5

Fig. 7

7.0 RN,,, [bohrs1

41114.63 I

’ 5.0

I

I

6.0

R [bohrs]

Fig. 8

Ferromagnetic Iron

\

P Mognetizatton

Fig. 9

103 Thus

being

made.

large

numerical

for open molecules oversimplification

of the eigenvalues estimated titial

within

region

each cell

course

i is taken

linear

or planar

molecules

approximation

local

exchange

ecules

bonding

like character dominate

with

interesting

or molecules

where

are the homonuclear

diatomic

clear

NbIr.

interesting

index

6 can be considered.

either netic

into double

in a large moment.

change

we have

put together

ground total

state energy

character figuration paired being

example

orbital f-like

where

s-

character we will heteronu-

a nominal

will

bond

of the

result

of the mag

between

unpaired)

above,

with

the pairing

orbitals

illustrated

mol-

intraatomic

ex -

and bonding

and the suitability

to study

this

of

effect

be shown.

In the homonuclear were

metal

The examples

the competition

mentioned

molecules

Mo2 and the magnetic

to remain

the case

to be studied

molecular

or in cancelation

was well

the single

metai

of examples

molecular

corre-

are used.

is a case where

transfer

the electrons

the electrons)

the techniques, could

occupied

charge

In particular

(forcing

(pairing

NbIr

makes

Transition

orbitals.

refer

Mo2 is a very

is used almost

d- and probably

molecular

is of

and for large

transition

of a simple

and,

is even more

potentials

however.

within

that non-local

and this

series

can be that

in the bonding

electrons

known

case of diatomic suited

Vi(r)

functional

delocalization

unsuitable

of error

the description

approximation

it is well

is well

are a very

because

density

over-

the inters-

source

the potential

symmetric part,

a

shifting

functions

avoid

Another

in practice

and correlation

For the particular the CMS-Xa6method

as they will

the density

the local

the one associated

lation, particule when

Moreover

within

a corresponding

potential.

important

this resultsin

and the wave

to be spherically

is the most

incomplete.

exclusively

cells

constant

in the fact that

Vi(r)

with

energies

the atomic

of high

is to be found

although

to higher

or cluster

Mo2 molecule

of this

configuration

for different

molecular

trial

orbital

It was

such that

found

was

found

the 16u remains

in spite empty

atoms

of the MO metal.

by minimazing

The

the

of the CT, 71 and 6

are to be expected

molybdenum.

that

two molybdenum

distance

accupations

which

5s' 4d5 of atomic

spins.

(ref.9)

at the internuclear

from the con-

The atom has

six non-

of the energy

and 20 g

double

eigenvalues

occupied,

104 with

the result

remains

true

that the molecule

for a large

3.6 and 9.0 a.u. one advantage auxiliar these

in which

as the occupation

orbitals

below. below

will

The fact that an auxiliar the Fermi

completely because

level

the total

occupied

is a good

restrained

energy

energy

effective

potential this

Another

and energy

corrections

important

feature

moleculat

orbitals

restricted seing

can easily

the uppermost

of each atomic

be followed

or spin-unrestricted

in Fig.6,

double

type

either

level

count-

selfconsist

occupations. and in NbIr,

orbital within

of calculations.

occupied

to the the spin-

For Mo2, as

has a weakly

20

ing character

from

5.0 a.u.

interatomic

g distance on, whereas

1U

the one which

contributes

most

is always

g being

two regions

atomic

bond

gives

5s predominates,

would

be the equilibrium could

where

gins at somewhat strong

bond

state

g defined series remain

occupied

metal

contribute distances

The bond

orbitals,of

orbital.The

5s atomic

and the atomic of bonding

energy

of the molecule

interatomic

a.u..

order

a.u.

orbital

if only

which

a single But fur-

directly,

to produce

be-

a very

by the num-

symmetry,as

the

by a non contributing contributes

of MO does

and antibonding

orbitals,

diatomics. more

inter-

minimum

is not given

the correct

d-band

the

split

states,

mostly

to

into a well

three

of which

empty.

The second atomic

to a local

of the 10~ is in fact counteracted

2ag molecular the 2a

smaller

R=5.2

of the 5s and 4d atomic

in the noble

bond

to the bonding,there

At around

the 4d orbitals

at R=4.0

ber of double bonding

rise

distance

like

be formed,

ther bonding,

bonding.

a hybridization

distance

where

of strong

example

molecule,

shows

chosen,

that of the NbIr heteronuclear

an interesting

is

between

are to be made,

for different

This

sum of the

to avoid

of the Mo2 calculation

is the fact that the contribution

not being

for the difference

density,

empty

approximation.

by the direct

different

A detailed

remains

of the method

as corrections

and to account

energy.

orbital

particle

is not given

eigenvalues,

ing of interactions,

ency makes

example

to

in the NbIr molecule

molecular

to the single

This points

in the calculation

the total

be given

between

of the different

are just parameters

of this possibility

This result

distances

were made.

can be used as such to minimize

example

diamagnetic.

of interatomic

calculations

of the method:

molecular

is then

interval

balance

between

di-

the intra-

atomic

exchange

bonding tering

pairing

-1.84.

have

a magnetic

d-d bonding

as a result ecular total

energy

observed tional

occupation

pation

largely

configuration different

of almost

In this obtain

if the different

conditions atoms

MATERIALS

they present

giant

limiting

moments

1) Isolated

formation

atoms

configurations

were

with

2) By simple

to find an optimum was found

fracoccu-

functionals orbitals

limit

to

for

of H2 and

for homonuclear

SPACE APPROACH

wave

calculations

functions

can be used matter

to

boundary

act on a group

of

state

in it (ref.12-18). Iron, nickel

alloy

are chosen

of highly

localized

to itinerant

carried

computed

eight

as examples

moment,

ferromagnetism

as

of the tran and of

out as follows: self consistently

or ten conduction

in the range

superposition

was built

atoms

are

respectively.

were

with magnetization

potential

cases moment

where

(see the discussion

cluster

a ferromagnetic

from localized

density

of the way the condensed

iron in palladium

The calculations

tal:

we show how

for the one electron

to promote

of the

ref.11)

FROM A REAL

understanding

and the dilute

sition

(NbIr

the mol-

Fractional

the local

the separate

split

two minima

s-s bonding

had to be made.

is used

of the two

In Fig.7

distance,

very

would

the variation

within

approximation

alone

are largely

mainly

section

more

they

corresponds

is analyzed).

FERROMAGNETIC

which

interaction,

spins

to

The

5.395 a.u. with

bonding.

exclusive

state

coupled.

The d bands

shows

interatomic

calculations

in ref. 1 andlowhere

He2 molecules

a.u..

Fig.8'

scat-

per atom and the Ir atom

nevertheless

d-d chemical

the Nb-Ir

local,

spins

multiple

the ground

distance

at r=5.95

are presented.

with

one,

t3.41

the s-s bonding

in energy,

of the strong

orbitals

showed

antiferromagnetic

equilibrium

a molecule

and the chemical

the cellular

calculation being

overcoming

do not match

magnetization

In effect

moment

The computed

stabilized

atoms

exchange

to the two atoms

Nb atom with

strong

atomic

of electrons.

statistical

correspond

with

favouring

from

of atomic

and analyzed occupation

for the following

for a number

electrons

0.0 - 3.0 spins charge

respectively, per atom

densities

in the single

occupation,

(spa).

a crystalline

site approximation

of the s, p and d levels. final

of

per atom

Consistency in the crys-

106 iron:

3d~4.362~+2.178~)4s~0.364r+0.402~)4p(0.396~+0.3~5~),

nickel:

3d(4.454~+3.894~)4s(O.369f+0.369C)4p(O.457~+o.457~),

palladium: These

4d(4.350~+4.350~)5s(O.4ZO~tO.420~)5p(o.23o~to.23o~).

values,

lations,

not far from more

are subsequently

the atoms

to construct

the cluster

used

is corrected cluster

in an occupation

for a finite

potential

calcu-

description

for the region

The magnetization

self consistency

cellular cluster

is used to obtain

of

outside

of the atoms

analysis

after

the

one electron

Green's

in a condensed electron

function

matter-like

tech-

boundary

and spin densities

as well

poas

energies.

We now discuss

the main

results:

Iron. A preliminary

study

Garritz

led to establish

1978 refJ4)

from a ferromagnetic showed

that the energy is 60 times

netization

relative

moment

required larger

state

of T

to demagnetize

without

temperature

~1000

C

to reverse

This substantiated moments

magnetic

in the its mag

the model

material

moments

rather

(see studies

in

by You et al 1980

Fig.9

therein).

OK and

one iron atom

1979, refl7and

cited

and

shows

this energy-

per atom relationship.

1980 ref.15)

analysis

computed

u=2.22!JB with

(Amador,

cell with

6.63 d-electrons

8 nearest

correlates

experimentally

spins,

density

calculation

of electronic

Ry-atom.

The exchange

becomes

ed model

should

adquires

a higher

for T>Tc.

magnetic

effective

a moment moment

susceptibility

at the Fermi

integral

magnetically not be used

moment

is 1=0.034

unstable

which

(1123) found (Busch

same occupation

energy

always

N(EF)

Ry/state,

showing

of a cubic

measurements

iron shows

for this material.

per atom

magnetization

p=2.59uB

value

A spin restricted,

for paramagnetic states

and Pisanty

The reversed

per atom.

from paramagnetic

et al 1974 ref.19)

Keller

the atom at the center

neighbors,

well with

de Teresa,

a (selfconsistent)

in the same enviroment;

terial

Keller

transition

than that required

by Hubbard

the references

A subsequent

atom,

a Curie

iron as a disordered

of atoms

the same direction ref.18and

1977 ref.lZand

to its neighbors.

used for paramagnetic than a collection

(Keller

to a paramagnetic

bulk metal

both

structure

calculation.

tential total

band

to be the initial

a boundary

in the calculation.

3) A self consistent nique

taken

detailed

for

a large

~40 states/

then the ma-

that the spin restrict In the model

of our

107 example,

as shown

paramagnetic nant

xLM with

Nickel. spin

susceptibility

contribution

. . blllty ment

in Fig.io,

should

A/CT-Tc),

q

the Busch

The cluster

cluster

come

method

"itinerant"

behavior

of 3 smaller AE

-0.24

kG

trons/Ry-atom

Iron

solved

slightly shows.

-75.0

kG).

energy

then

enhance

spins which

elec-

together

with

a large moment

magnetization

of the

moment

of the Fe atom.increases

energy

change

of -0.061

the cluster.

No study

due to their

high

spin

because

iron atom.

of further

susceptibility

interaction,

giant moments

of circa

only(flq.\I)

to be exothervalue). Where is given

In effect

to M=3.32pB

atoms

the with

neighbouring

neighbourg

should

When (ref.161

The answer

of 0.16 v,B for a total

was made

and exchange

from?

from Mo=2.2pB

Ry. The palladium

moment

found

to experimental come

is di-

atom.

it bonds

a

of the iron d-band

of Fe in Pd is however

energy

impurity

of calculations

splitting

equal

suscep-

but with

of the guest

in a series

as the smaller

a magnetic

give a spin

if a magnetic

the moment

in palladium

estabilization

shows

The den-

X 10-4emu/mol).

does

field

is computed

Ry/atom.

and NC(EF)=15

is a paramagnetic

Ry (practically

in Pd alloy

is N+(EF)=8

to be

metal

But the solution

by the increased

energy

-0.28

fixed, Curie

overcome

is found

The binding

to

is a factor

to thermally

nucleus

and minority

mic AEs=-0.057

magnetic

the enviroment

. The estimated

Palladium

adquired

the extra

the energy

of 1=0.030 Ry/electron -4 X 10 emu/m01 (X(exp)=l.lO

to the host

Fe adquire

because

keeping

required

by

EP=".14 is the origin of the

This

of the experimental

in it, it will

the iron atom

in good agree

energy

P is 774 K(Tc(exp)=631K)

spin susceptibility,

iron was embedded

suscepti-

The ferro-

integral

of X-1.76

moments

a divergent

than AE

at the nickel

for majority

in Palladium.

very high

smaller

at the Fermi

an enhancement tibility

field

instead

sity of states

the domi-

1 showed

nickel

of one atom,

slightly

(experimental

Ry/atom

enhanced

calculation.

in total

calculation.

than the temperature

The hyperfine

P' -37.661

is lower

q(AER/3R)(stl)

Tc

then

and Tcz1040aK

(ref.4

of ferromagnetic

the magnetization

temperature

emu/K-m01

calculation

calculation

only

a Pauli

X low6 emu/mol,

for a spin restricted

spin restricted

is AER=0.0128

giving

from the localized

A=1.14

Ry than the

reverse

Xp=46

~11.7

et al experiments.

susceptibility

magnetic

N(EF)

the

of 5.2 uB for shells

respond'to

in effect

an

which

this

the dilute

10 uB per iron atom.

large iron

108

lo?, 5-

,60 50 40

4-

30

3-

m

2-

(0

l-

0

Ol234-

AJL =__ --.b

-1 -t

-1 -2 -3 -1

I - ---

32l-

_..___

-u2/

Ol-

1

-04

-40

4-

-0.3

-02

-pj

E,

0.1

-05

234. -0.4

-Q3

-02

-o+

Ef

o;c

92

Erny

Fiq.lOa

Fig. 10. Density of electronic states computed for ferromagnetic iron and the corresponding multiple scattering ratios. The top drawings show Fe in ferromagnetic Fe. The middle drawing, a Fe atom with the magnetization reversed with respect to the ferromagnetic iron environments. Thebottom drawing shows a symmetry analysis of the d band of the previous cases.

Fig. 11 shotis a comparison of the computed states for Fe in Pd with those of Fe in ferromagnetic iron and aband structure density of states.

Fiq.lOb

109

- 0.8

-0.4

-0.6

-0.2

0

0.2

E

Fig. 11 A histogram which presents a comparison of the states of the substitutional Fe in Pd (full lines) with those of pure metallic iron (broken lines) and Duff and Das (continuous state density).

CONCLUSION We have bonding densed

presented

in transition matter:

ante between found

a useful

tool

metal

magnetic

the contribution

bonding

density

some of the main

theory

for these

studies.

molecules

of nd and

and intraatomic

functional

features

of the chemical and clusters

in con-

(n+l)s electrons, forces.

the balWe also have

scattering

techniques

exchange

and multiple

AKNOWLEDGEMENTS The literature

quoted

at the end of this

to some of our own publications rected other

to this

papers

in this

paper

field.

to find the connections

provides

The reader with

a guide is di-

the studies

of

groups.

REFERENCES 1 2 3 4

A. Garritz, J.L. Ggzquez, M. Castro and J. Keller, Int. J. of Quantum Chem., xv, 731 (1979). J. Keller, C. Castro and C. Amador, Physica a, 129-133 (1980) J. Keller, M. Castro and A.L. dePaoli, 0, 00 (1982). J. Keller, M. Castro, J. Magn. Mat., 15-18, 856-8 (1980).

110 5

A. Pisanty, E. Orgaz. Ma. de1 C. de Teresa and J. Keller, Physica, 102B, 78-80 (1980). J. Keller, M. Castro, C. Amador and E. Orgaz, Hyperfine Interactions? 8, 483 (19811, and Proceeding of the Second International Topical Meeting on Muon Spin Rotation, Vancouver, 1980 North Holland, Brewer J., Editor. Methods for Large Molecules and Local6 J. Keller, Computational ized States in Solids, Edited by F. Herman, A.D. McLean and R.K. Nesbet, 341-56, Plenum Press, 1973 and J. Physique, 33, e, 241 (1972). 5, 15-23 (1979). J. Keller, Hyperfine Interactions, 7 J. Keller, Int. Journal of Quantum Chem.: E, 583-604 (1975). 2, 00 M. Castro, J. Keller and P. Rius, Hyperfine Interactions, (1982). J. Keller, 1972 XVIII Conference on Magnetism and Magnetic Materials, AIP Conf. Proc., lo, 514 (1973). 8 J. Keller and R. Evans, J. Phys. C. Solid St. Phys., cc, 31333145 (1971). 9 M. Castro, J. Keller and P. Mareca, Intern. J. of Quant. Chem.: Quantum Chem. Symposium, 15, 429-435 (1981). 10 M. Castro, J. Keller and O.N. Ventura, J. Chem. Phys., 00, 000 (1982). 11 J. Keller, M. Castro and P. Mareca, Int..J. Quant. Chem., 00,OO (1982). 12 J. Keller, Computers in Chemical Education and Research, Edited by E.V. Lude?ia, N. Sabelli and A.C. Wahl, Plenum Press, 225, 1975. 13 J. Keller, Rev. Sot. Quim. Mex., s, 56 (1982). J. Keller and Ma. de1 C. de Teresa Proceedings of the Intern. Conf. on the Electronic and Magnetic Properties of Liquid Metals published by the University Press, Mgxico 1976 J. Keller Ed. 14 J. Keller and A. Garritz, Int. Conf. Physics of'Transition Metals, Toronto, 1977. Inst. Phys. Conf. Ser., 39, 372 (1978). 15 C. Amador, C. de Teresa, J. Keller and A. Pisanty, Ins. Phys. Conf. Ser., 55, 225-228 (1981). 16 A. Rodriguez and J. Keller, J. Phys. F: Metal Phys., 11, 14231433 (1981). 17 J. Hubard, Phys. Rev., g, 2626 (1979). J. Hubard, Phys. Rev., E, 4584 (1979). 18 M. V. You, V. Heine, A.J. Holden and P.J. Lin-Chung, Phys. Rev. Lett. *, 1282 (1980). 19 G. Busch, H.J. Guntherodt, H.U. Kiinzi, H.A. Meier, L. Schlapbach C4-329 (1974). and 87. Keller, J. Physique, 2, i'r Permanent

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