Interpretation of the optical absorption spectrum and of the paramagnetic susceptibility of neodymium oxisulfide

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Interpretation of the optical absorption spectrum and of

the paramagnetic susceptibility of neodymium oxisulfide

L. Beaury, P. Caro

To cite this version:

Interpretation

of the

_{optical absorption}

_spectrum

and of

the

paramagnetic susceptibility

of

_neodymium

oxisulfide

L.

_Beaury

and P. Caro

Eléments de Transition dans les Solides

_(*),

C.N.R.S., 1

_place

A. _Briand, 92195 Meudon _Cedex, France

(Reçu

le 10

_juillet

1989, révisé le 23 octobre 1989,

accepté

le 25 octobre

₁₉₈₉₎

Résumé. 2014 Le

spectre

d’absorption

optique

de

_{l’oxysulfure}

de

_néodyme

a été

_{ajusté ;}

la déviation

quadratique

moyenne est de _10,7

cm-1

pour 65 niveaux Stark

assignés,

avec un Hamiltonien comprenant 14

_paramètres

ion-libre et six

_paramètres

de

_champ

cristallin, la

_{symétrie ponctuelle}

étant

_C3v.

Les

_{susceptibilités}

_{paramagnétiques (moyenne,}

_parallèle

et

_{perpendiculaire}

à l’axe d’ordre trois de la

_structure)

ont été mesurées de 4,2 K à 200 K environ, et

_comparées

avec les valeurs _{obtenues par}

_{l’application}

de la formule de Van Vleck aux 18 doublets de Kramers

d’énergies

les

_plus

basses. Nous donnons

également

les valeurs de la constante de

_couplage

spin-orbite 03B6

en fonction du

_paramètre

de Slater

_F2

_{pour six}

_composés

couvrant la totalité de la série

néphélauxétique

du

_néodyme.

Abstract. 2014 The

_{optical absorption}

_spectrum of

_neodymium

oxisulfide has been fitted ; the mean

quadratic

deviation is 10.7

cm-1

for

65

_assigned

Stark levels with a Hamiltonian

_involving

14 free-ion _parameters and six

_C3v

_crystal

field _parameters. The

_paramagnetic

_{susceptibilities}

_(mean,

parallel

and

_{perpendicular}

to the

_trigonal

axis in the

_structure)

have been measured from 4.2 K to

about 200 K, and

_compared

with the values derived from the wave vectors and

_energies

of the 18 lowest Kramers doublets

_through

the

_application

of the Van Vleck formula. We also

_give

the values of the

_{spin-orbit coupling}

constant 03B6 versus the Slater _parameter

_F2

for six

_compounds

spanning

the whole of the

_{neodymium nephelautic}

series.

Classification

Physics

Abstracts

71.70C - 71.70E - 75.20

1. Introduction.

The energy level sequence of

Nd 3,

(4f3)

in

_neodymium

oxisulfide has

_already

been

_reported

by

Souillat et al.

_[1].

In the

_present

work,

we

_interpret

the

_absorption

_spectrum

_taking

into

account the

_C3,

_crystal

field Hamiltonian written in

_Wybourne’s

formalism

_[2]

_together

with the electrostatic and

_spin-orbit

interactions. The calculation is

_performed

on the basis of the

364

SLJM)

kets in the

_{configuration, including}

J

_mixing.

Two and

_three-body

_operators

(with

Tree’s and Judd’s

_parameters)

are also used to take into account the interactions with the other

_{configurations}

_(in

_particular

_4f26p,

4f25f

and

_{4p54f ) ;}

_they

are

_absolutely

_necessary

to

_get

the correct

_position

of the

_barycenters

of several excited levels.

(*)

UPR 210.

The wave vectors obtained from the

_{interpretation}

of the

_{optical absorption}

data have been

tested for their

_ability

to

_reproduce

the mean,

parallel

and

perpendicular paramagnetic

susceptibility

measured versus

_temperature

on a

_{single crystal.}

2.

Crystallographic

background.

The rare-earth oxisulfides

_T202S

have a

_hexagonal

structure ;

neodymium,

oxygen and sulfur have the

_following

coordinates :

Faucher et al.

_[3]

have refined the u and v values at 4 K from neutron

_powder

diffraction

data. Two methods have been used : a conventional

(integrated intensities)

and a

_profil

refinement method. The initial u and v values are those of

_Ce202S

found

_by

Zachariasen

_[4].

These values of u and v are _{very close} to those found for

_H0202S

_by

_{Rossat-Mignod}

_[5]

and

_by

Boucherle et al.

_[6]

and for

_La202S

_by

Morosin and Newman

_[7].

The

_parameters

of the

_hexagonal

lattice

_[3]

are a = 3.946

Â

and _c = 6.780

Â.

The space group is

P3m

_[8].and

the

_point

_symmetry

of the two rare-earth ions in the

crystallographic

lattice is

_{~3 y.}

3.

_Optical

_spectrum.

A first

_fitting

has been made

_by

Souillat et al.

_{[1] ;}

_they

obtain first the free-ion

_{parameters :}

E’=

4 939

cm-’,

Ez =

24.36

cm-l,

E3 =

480.2

cm-l

1

(Racah’s parameters)

then the

_crystal

field

_parameters

_{by fitting only}

17 Stark

levels,

the mean

_quadratic

deviation

being

3.5

cm- 1.

The

_experimental

_{energy levels}

_{(Stark components)}

are

_given

in table

1 ;

we have tried to

assign

most of them but some Stark

_components

(for

_example

those of

4Gll/2

and

2K15/2)

are _{very mixed.}

Table I. 2013

Experimental

and calculated _energy

levels,

computed

values

_of

_g1 and

Table 1

_(continued).

(*)

Not

assigned.

Remark : when g, = 0,

gp is in absolute value.

For the

_fitting,

the initial values chosen for

_{El, E2, E3, ,}

and the

_Bq

are those of Souillat

[1] ;

we have added Tree’s

parameters

a,

8,

y and Judd’s

parameters

T2, T3, T4,

T6, T7,

T8.

We find

_again

the

_difficulty

of the

2H

_{(2 11/2}

level.

_Fitting

of this level was also bad for

Souillat,

and this has been described

_by

_many

authors,

especially

Minhas et al.

_[9]

and

Chang

[10]

as well as

_{Rossat-Mignot et}

al.

_[11]

for the

_conjugated

ion

Er3 +

in

Er202S,

and discussed

_by

Faucher et al.

_[12].

Finally,

we obtain a mean

_quadratic

deviation of 10.7

cm-1

for

65

_assigned

levels with the

parameters

given

in table

II ;

the

_assignment

_{of these 65 energy levels is}

_given

in table 1 with the

_experimental

values.

Of course, we do not know the irreducible

_{representations}

_{of the double group}

Table II. - Free-ion and

_{crystal field}

_parameters

_{for Nd 3,}

in

_Nd202S

at 4.2 K

_{(corresponding}

to calculation in Tab.

_I).

The

_ground

state is of

_(SI

+

_{S3 ),}

_symmetry

in the

_computation

in

_agreement

with the

magnetic susceptibility

simulation below. We could

_expect

from

_{polarized light absorption}

to

recognize

levels of

symmetry

(SI

+

_S3)

or

_Dj/2

and check our

_computation.

This would have

considerably improved

the

_quality

of our

_fitting

and hence _{the accuracy of} our wave vectors

especially

the

_ground

state ones which were used for the simulation of

_paramagnetic

data.

Unfortunately

our

_{single crystals}

were too small to be

_effectively

used in «

polarized

»

_spectra

absorption

experiment

at

_liquid

helium

_temperature.

The Slater

_parameters

_Fk

derived from the Racah

_parameters

Ek

are

_given

in table III and

compared

with

_previous

results we have obtained on other

_compounds.

In this

table,

we _span

the whole

_{neodymium nephelauxetic}

series

_[19].

_F2

decreases as we _{go from the} fluoride to the

oxisulfide ;

F4

and

_F6

do not

_change

too much. There is a clear decrease of

C

which _appears to be correlated with the decrease of

_F2

_{(Fig. 1).}

This

_experimental

evidence

may be

important

for theoretical considerations about the factors which affect the free ion

parameters

in solids. The values

of e

and

_F2

for

_Nd202S

_give

a

_point

which is

_exactly

on the

straight

line’ =

_f

(F2)-On the other

hand,

the

_crystal

field

_parameters

have been

_computed,

from the structural data

_only,

_through

a mixed « covalo-electrostatic model »

_by

Garcia and Faucher

(20) ;

their

Table III. - Slater’s

parameters

and

spin-orbit coupling

constant

_(at

the

_fixed

value

y =750

cm- 1).

Fig.

1. -

Values of C as a function of

_F2

for the

_compounds

listed in table III

_(for

Nd 3, :

_LaCl3,

we have taken the values of Ref.

_[16]).

The error

_rectangles

are indicated.

B6 =

473. In absolute

value,

these results are of the same

_magnitude

as ours ; the

sign

of

B 0 2

is inverted but the absolute value is weak. 4.

_Magnetic

_{susceptibility.}

4.1 EXPERIMENTAL DATA. - The measurements of the

_{paramagnetic susceptibility}

have been made on two sets of

_{apparatus :}

- a Foner

_magnetometer

which

_gives

a better

_precision

between 100 K and 300

K,

but it is necessary to have

_{large single crystals}

_(at

last 10

_{mg) ;}

-

a

_Faraday

balance whose

sensitivity

is at the best between 4 K and 100

K ;

with this

The

_{single crystals}

we have used

_{weighed barely}

_{1 mg ;} so, the measurements were

extremely

difficult and not _very accurate.

_{Nevertheless,}

some main features emerge :

- at low

temperatures,

the

_{parallel susceptibility}

yll is

larger

than the

perpendicular

susceptibility

X 1 that is :

1 /X

il «.-

1 IX 1

. The boundaries are :

- from 90

K,

the

_anisotropy

is zero

_(X

_p --- _X,

).

This last

point

has

permitted

_us to correct

our values. The measurements of the mean

_{susceptibility}

_{X m} on

_powder

are

_{unambiguous :}

between 100 K and 200

K,

we must _{have X m} =

X_L = X II ; we have noted a little shift between the curves : the

_{experimental points}

in

_figure

2 take this into account.

Fig.

2. -

Paramagnetic

susceptibility

of

_Nd202S

parallel

(circles)

and

_{perpendicular}

_(triangles)

to the

C3

axis measured from 4.2 K to 200 K. The curves show values

_computed

from the wave vectors of the

18 lowest Kramers doublets with the _parameters

_given

in table II.

The measured

_powder

_{susceptibility}

from 4 K to 200 K of our

_sample

is shown in

_figure

3. We have also

_represented

the values obtained from the measurements on

_single

_crystal

,

together

with the

_experimental

data of

Quezel

_[21].

These three series

of values are in

_good

_agreement.

4.2 COMPUTED VALUES. - The

parameters

of table II

_give

the

_eigenvalues

and the

eigenfunctions

that we feed into the Van Vleck formula

_{[22] ;}

the

_magnetic

_{susceptibility}

Fig.

3. - Inverse

mean

_{susceptibility}

of

_{Nd202S : 1)}

computed

values,

2)

our

_experimental

measure-ments,

3)

experimental

measurements of Quezel.

with

where N is the

_Avogadro

_number,

_k,

the Boltzmann constant

_{and Q ,}

the Bohr

_magneton.

The

wave

_{functions .pi}

_{and tpj}

are

_{eigenfunctions}

of the

Hamiltonian,

_{unperturbed by}

the

_magnetic

field,

corresponding

to the

_eigenvalues

_Ei(’),

_£/°),

..., u is a unit vector ;

according

to its

direction,

one finds the

_{perpendicular susceptibility}

_(here

_{X,, = Xy = X,)}

and the

_parallel

susceptibility

(X,

= XII).

To

_perform

the

calculation,

we used the wave vectors of the lowest 18 Kramers doublets

(that

is

_419/2@

_4111/2’

_{4113/2) ; it is}

sufficient to cover the thermal

_population

effect well above 1000 K. We have

_applied

this method before to

_{A-Nd203 [14] NdAI03 [18], NdF3 [15],}

NdCl3

and NdOCI

_[23].

The result of the calculation is shown in

_figure

2 for the

_parallel

and

_{perpendicular}

susceptibilities

and in

_figure

3 for the mean

_{susceptibility.}

The

_agreement

is

_good

for the mean

_{susceptibility.}

For the

_computation

_{corresponding}

to the measurements on

_{single crystal,}

the

_agreement

is far from

being perfect

but,

on account of the small dimensions of the

_single

_crystal,

one can consider that the

_agreement

is

_{satisfactory.}

Indeed,

the behaviour at low

temperatures

is

_{reproduced :}

The

_anisotropy

diminishes when the

temperature

increases,

it is non zero as we have found

have

_reported

this error in

_figure

_{2 ;}

we can see that the

computed anisotropy

is of the same

order as the

_{possible experimental}

one.

In table IV we have

reported

the

composition

of the

4I9/2,

wave vectors,

retaining only

the kets

_1419/2’

_{M) ;}

indeed,

owing

to

_J-mixing

there are also kets with other values of

J,

but in very small

percentage

(each

level

_being

a Kramers

doublet,

we

_{give only}

one vector :

the other is the

_{conjugate :}

We remark that the Stark

_ground

state is of

_{(Si +83)}

_symmetry

that is

_involving

_only

the kets with M = ±

_3/2,

± 9/2. In this case we have shown

(Ref. [24],

_p.

33)

that the

perpendicular

susceptibility

is

_independent

of

_temperature

at low

_{temperatures.}

Table IV. -

Composition

of

4jg/2

wave vectors.

The

_{paramagnetic susceptibility anisotropy depends only}

on the value of the

B6

_parameter

(as

in the

_A-Nd203

case

[14]).

From the

_sign

and value obtained from the simulation of

optical

data

_{(Table II),}

one _may

_expect

a

_{slightly larger anisotropy}

with

1IX-L ::. 11XI,

in contrast

with what is observed for the

_isomorphous

oxide

_A-Nd203

where

_1/Xl

>

11X,

with a

_large

negative

value of

_{B 0 2 (B6}

= - 836

_cm-1).

The

_experimental

_magnetic

data

_suggest

a value of

B 0 2

much closer to zero than the small

positive

«

_optical

» value. Nevertheless it is clear that the

B 0 2value

for the oxisulfide structure

is small. It even seems that it

_{changes sign}

_along

the rare-earth series

_{[25] becoming slightly}

negative

(for

example

from

_optical

data

_{B 0 2 = +124cm-1}

1 for

Eu 3+ :

_{Y202S [26]}

and

B 0 2

= - 210

cm - 1

for

_{Gd3 + : Y202S [27]).}

The value of

_{B 0 2is}

_extremely

sensitive to small

_changes

in the electrostatic conditions at the

site

_[20].

Our

_optical

overall

_{fitting gives}

a

Bô value

which is

_mostly

weighed

for excited states.

phonon density

of states. The Raman

_spectrum

of

_{Nd202S [29]}

shows the four

_frequencies

expected :

102, 192,

388 and 417

cm’ 1.

The 102

cm-1

1 libration

_{is therefore very close} to the energy difference between the

ground

Stark level and the second excited Stark level. Under those conditions the

_{B 0 2}

value used in the

_computation

_{may be} overestimated due to the

neglect

of the

_{electron-phonon}

contribution to

_ground

state

_eigenvalues.

Moreover if a simulation of the

_ground

state _{energy levels is done}

_{varying only}

Bô

from + 200 to - 200

cm-1,

the lower two

_ground

state levels cross. This is a situation of

potential crossing

of

_crystal

field levels

_[30].

5.

_{Magnetic splitting}

factors.

To our

_knowledge,

the

_experimental

values have not been measured.

The oxisulfide

_Nd202S

has a three fold axis

_parallel

to Oz. The axes Ox and

Oy

are

_equivalent,

we have :

The

_computed

values

are

_reported

in table I. For the Stark levels of

_(SI

+

_S3)

_symmetry,

9 1 = 0 and gp is

only given

in absolute value.

Acknowledgments.

The authors thank Dr. M. Guittard from the « Laboratoire de Chimie Minérale de la Faculté

de Pharmacie » in Paris for

_growing

the

_{single crystals}

used in this

_study,

and Dr. M. Drillon from the « Ecole

Européenne

des Hautes Etudes des Industries

Chimiques

de

Strasbourg »

for

_permission

to use his

_equipment

and for measurement of the mean

_{susceptibility}

and also

the check of the

_parallel

and

_{perpendicular susceptibility}

values.

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