Spectroscopic study of the incommensurate phase of ThBr4 via the optical and magnetooptical properties of U4+

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Spectroscopic study of the incommensurate phase of

ThBr4 via the optical and magnetooptical properties of

U4+

B. Briat, P. Delamoye, J.C. Rivoal, S. Hubert, P. Evesque

To cite this version:

Spectroscopic

study

of

the

incommensurate

_phase

of

ThBr4

via

the

_optical

and

_{magnetooptical}

_properties

of U4+

B. Briat

_(*),

P.

_Delamoye

_(+),

J. C. Rivoal

_(*),

S. Hubert

(+)

and P.

_Evesque

_(*)

(*) Laboratoire

_d’Optique

_{Physique, ESPCI, 10,} rue

_Vauquelin,

75231 Paris Cedex 05, France

(+)

Laboratoire de Radiochimie, Institut de _{Physique Nucléaire,} Université de Paris-Sud, B.P. 1, 91406

_Orsay,

France

(Reçu le 19 décembre 1984, accepté le 22 mars ₁₉₈₅₎

Résumé. 2014 U4+ est utilisé pour tester la

phase

incommensurable de

_ThBr4

grace à des mesures

_{d’absorption}

et de dichroisme circulaire

_magnétique.

En dessous de _Tc = 95 _K, la

symétrie

au site de l’ion sonde est

_D2d

ou

_D2;

elle _peut être simulée en faisant varier un

_angle

de

_phase

~ entre

_0(D2d)

et ±

03C0/2(D2).

Le DCM

_présente

sur

l’absorp-tion le

_grand

_avantage de montrer une

_singularité

_{pour les} centres

_D2d.

Nous

_présentons

un modèle _permettant

de

_reproduire

assez fidèlement nos courbes _{d’absorption,} d’effet Zeeman et de DCM. Nous aboutissons à deux conclusions _{importantes : (i)} la _phase est

_probablement

vraiment incommensurable dans la mesure où nous

établis-sons à 80 une limite inférieure du nombre de sites différents ; (ii) _pour un cristal de concentration 2 x

10-4,

nous

établissons l’absence _{d’accrochage} de l’onde incommensurable sur les

_impuretés.

Par ailleurs, le DCM démontre

sans _{ambiguïté que l’état} fondamental de U4+ dans

_ThBr4

est ₀₃₉₃₄ en

_{symétrie D2d.}

Nous déterminons enfin le

fac-teur de Landé de _cinq niveaux _excités, ces mesures étant en bon accord avec les résultats de calculs récents. Abstract. 2014 U4+ is used to

probe

the incommensurate structure

_{of ThBr4}

via _absorption and _magnetic circular

dichroism (MCD)

measurements. Below _Tc = 95

K, the _crystal field

_{experienced by}

U4+ ions is either

_{of D2d}

or

_D2

symmetry. This can be simulated

_{by varying}

a

_{phase angle}

_~ form

_0(D2d)

to

_±

_03C0/2

_(D2).

_{One very} neat

_advantage

of MCD over _absorption is that the

_D2d

centres _{show up very}

_clearly

in the former due to the occurrence of a

deri-vative-like

_singularity.

We _present a model to simulate

_absorption,

Zeeman and MCD

_profiles.

It accounts

satis-factorily

for most of our data and we arrive at the _following main conclusions : (i) it is _probable that the _phase is

truly

incommensurate since the lower limit of the number of sites is found to be _80;

_(ii)

for a low concentration of

U4+ ₍₂ x

10-4),

we found no evidence of a

_pinning

of the incommensurate modulation

_by

the _impurities. MCD

provides also a definite

_{proof that}

the

_ground

state of U4+ in

_ThBr4

is ₀₃₉₃₄ with a

_D2d

_symmetry.

_Finally,

we determine

the Landé factors of five excited states, our

_{findings being}

in fair _agreement with the results of recent _crystal field calculations.

Classification

Physics Abstracts

78.20L - 64. 70K - 78 . 50 - 78.40

1. Introduction.

Seven _{years ago}

_{[1], ThBr4}

was

_only

considered as an

additional suitable host for

spectroscopic

studies on I

tetravalent actinide ions. At room

_temperature,

the

crystal

is

_tetragonal

_{with space group}

_Dl:.

As

for

I

Zr4+

in zircon

_[2,

_3],

each

Th4+

ion is located at a

site

of

_D2d

_symmetry.

Due to the lack of an inversion

I

centre,

absorption

spectra

of

_{doped crystals}

were

expected

to show

_parity

allowed electric

_{dipole origins,}

the location of which was to be

_compared

with the results of

_{crystal-field}

calculations. The situation is

substantially

different since the

_{discovery [4]}

that

ThBr4

is a

_prototype

incommensurate

(INC)

material

below

_Tc

= 95 K and is

probably

so all the

way

down to zero Kelvin. One aim of _present studies is

probably

to

_probe

the INC structure

_by,

_e.g.,

spectro-scopic

means or else to examine the effect of

_impurities

on this structure. Earlier

low-temperature

absorption

and emission

_spectra

_[1]

of

_ThBr4/U4+

have been reexamined and a model has been

_presented

to

explain

the unusual

_line-shapes

encountered

_[5].

Basically,

in the INC

_phase

there is a transverse sinusoidal

_displacement

of the bromide ions

per-pendicular

to the c-axis of the

_crystal

and the

_crystal

field

_{probed by}

U4+

is either

_D2d

or

_D2.

This model

has

_recently

been checked further

_against

site-selective excitation measurements

_[6]

and theoretical calcula-tions

_[7].

All

_experimental

data available

_support

a

continuous distribution of

_{crystal-field strengths}

at the

U4+

sites.

The

_present

_study

has been undertaken with several aims in mind :

(i)

to

_provide

an

_experimental

and

_unambiguous

proof

of the

_long

_{postulated singlet}

character of the

ground

state of U4+ in

_ThBr4.

For that _purpose,

polarized absorption

studies

_{(axial, 7c and a)}

have been

complemented by magnetic

circular dichroism

_(MCD)

measurements. It is well established

_[8]

that MCD can

easily distinguish

between a

diamagnetic

and a

paramagnetic

species.

Moreover, the

_sign

of the observed features can be correlated with the nature of the

_ground

and excited states;

(ii)

to derive

(via MCD)

the

_{spectroscopic splitting}

factors of the

U4+

excited states for a severe test of the correctness of

_computed

wave

functions;

(iii)

to

_develop

more

_fully

and check further the model outlined

_{previously, by predicting}

the

_profile

of MCD _spectra and

_comparing

with

_experimental

fmdings.

In the next

_{section, §}

2,

we

_present

our model for

the simulation of

_absorption

and MCD

_profiles.

In

§

3 we describe our

_experimental

conditions and the more

_important

results. These data are

finally

discussed

in § 4.

2. Theoretical model.

2.1 ABSORPTION AND MCD. 2.1.1

_D2d

symmetry. - We first

ignore

the existence of an INC

_phase

and establish selection rules for electric

_dipole

transitions in the case of an even electron

configuration

(f2).

Those for a

_D2d

_symmetry

_[9]

are

given

in table Ia where a and n refer to the electric vector of the

_light

beam

_{being perpendicular}

and

parallel

to the

_{tetragonal c(z)}

axis

_{respectively.}

The axial

_(a)

and a _spectra are

expected

to be similar. In

the _presence of a

_magnetic

field B

_along

_z, the

_symmetry

is lowered to

_S4.

Then

_{r l’ F2 -+ F’; T3, F --i. F’}

and

F 5 --* fg

+

_{F’ 4}

where

_primes

are used to

_distinguish

S4

from

_D2d

notations. The new selection rules are

also shown in table

_Ib,

where _{a +} and Q_ stand for

circularly polarized light travelling along

z

_(a

spec-trum)

and are associated with the _{operators mt} =

T-(i/,r2)

(mx

±

_my)

which transform as

_F’(m+)

and

F’(m-).

3

MCD is defined as the difference in

_absorbaoce

DA= A+ - A_

for _{er +} and y_

light.

In

_D2d

(Table Ia),

this can

_only

occur for a

_singlet

- doublet or a

doublet -

_singlet

transition between the

_ground

state

I

go )

and the excited

_state

_{I eo >.}

In the limit where the Zeeman

_splitting

is small

_compared

to both the thermal energy kT and half the

line-width,

the

rigid

shift

approximation

leads to

_{[8] :}

while

_A/E

=

K f Do

for a _zero

magnetic

field.

Table I. - Electric

dipole

transitions

_for

even electron

configurations,

go and eo

(g’

and

_e’)

stand

_for

the

ground

and excited states

_{respectively.}

f

is a normalized

shape

function E is the energy

(in

wave numbers

hereafter); Do

is the

dipole strength

of the

transition;

K is a numerical

factor

_{and PB is}

the

_{Bohr-magneton.}

The

_eo

term

arises from the difference in

_population

_among the

possible

substates

_of

_{I go >}

in

_S4,

_i.e.,

it can be non-zero

_{only when}

_{go j}

=

F..

The

_origin

of the

_At

term _{lies in the energy differences} between the

two

Zeeman

_components.

This term should therefore

_be

observable in

_principle

for all 6 transitions of

U4+.

$0

arises from the

_{possible mixing of}

_{go j or/and ,}

1

eo j

with a

_statue

_{ko j}

located at an _{energy AW}

above it. Since B transforms as

_F’

in

_S4,

_’%0

terms are

expected only

for those

_{representations}

of

_D2d

which

reduce to the same

_{representation}

in

_{S4, namely}

T 1-T 2, r3-r4

and

_r5-r5.

Note that if the

_coupling

arises

_between

_{I eo) and}

_ko),

the transitions

I

go ) --+ I eo > and ! go ) -

ko >

show

_%o

terms of the same absolute

magnitude

but of

opposite sign.

Finally,

the

_peak

to

_{peak magnitude}

of the

derivative-like term in

_{equation (1)}

varies

_{approximately}

as

_1/y

while the two

_{absorption-like}

contributions are

MCD

_parameters

are

_usually

extracted via a moment

analysis

of the data. For further use, we define :

where

E is

the

_barycentre

of the line.

Assuming

first a

non-degenerate

_ground

state and an

isolated s --+ d

transition,

we

_easily

find

₍

AA

_)o

= 0

and

AA > 1

=

± 2 99B

B. Here _we

adopt

the

con-vention

_{F’ 3 Lz}

+ 2

_SJ

_{I F’ 3 >}

_{= g,} the

_plus

or

minus

_{sign depending}

on whether the

_ground

state is

F’

or

_F’

in

_S4

_symmetry.

_Knowledge

of the nature of the

_ground

state and the

_sign

of the

_associated

_{AA >}

would lead to the

_sign

of

_{the g}

factors for the excited doublets

_(D2d)’

We note that the

_relationship

between

(

LBA > 1

and g

does not

_require

the

_rigid

shift

approxi-mation and is

independent

of

_{electron-phonon}

coupling.

If the

_ground

state were a

_doublet,

then OA

_)o

_{would carry the} information

_regarding

the

sign

of

its g

factor and the

_symmetry

of the excited state.

2.1.2

_D2

_symmetry. -

Anticipating

upon our

dis-cussion,

we treat the MCD

_problem

for the case of a

F4 -+ F 5

transition in

_D2d.

This has been done

pre-viously

in the case

of Pr3+

in

_AlLao3

_[10].

_Let

_{s )}

be

a

_{F’ 2}

_ground

state in the _presence of

_B,

_{I p >}

and

q >

the excited states associated with

_{F’ 3}

and

_{F’ 4}

respectively.

Then

Iplm+ Is> I =

Iqlm- Is>

I

(Table

Ib).

For

_convenience,

we take 1 as their common

value. In the absence of

B,

for

_D2

_symmetry,

the

_{r 5}

doublet

_splits

into two

_{singlets separated by}

an

energy 2 Li.

Appropriate

wavefunctions are now of

the form :

where one can take a =

p

=

10

without loss of

generality. Then,

P) and

[ Q )

transform _{as y}

and - ix

_respectively

in

_D2

_symmetry.

When B is

applied,

the Hamiltonian is :

with

_eigenvalues

± A where A =

[A 2

₊

(99B

B)2]1/2.

(1)

F,’

states are associated with wavefunctions of the

general form E

_ai

_LSJM;

M = _5, 1 _{or -} 3 _).

The associated

_{eigenfunctions}

are :

where a = 2

AI(A

₊

d )

and b =

gyB

BI(A

+

_L1).

So,

for

_{example, I}

_+!

_{I mj:}

_{I S >}

_{= (1/2}

_{a) (1}

₊

_b)2

and

₍

DA

_o

for

_the

_{Is> --+}

_>

transitions is ± 99B

BIA.

One has the situation of two states mixed

via the

_magnetic

field and

_giving

rise to

_{opposite $0}

terms with an

_absorption

like

_shape.

2.2 INCOMMENSURATE PHASE. - Below

T,

= 95

K,

neutron diffraction

_experiments

_[4]

indicate a

modu-lated structure for

_ThBr4,

with the modulation

wave-vector q.

being

directed

_along

the

_tetragonal

axis :

The _consequences of this structural

_change

_upon

absorption line-shapes

have

_already

been outlined

_by

Delamoye

[5].

We

_provide

here a more

_general

and

quantitative

treatment with the added consideration of the action of a

_magnetic

field.

For the dilution levels used in our

_experiments,

the

U4+

ions _may be treated as isolated

impurities,

ran-domly

distributed

_throughout

the host lattice. Each of them is surrounded

_by

two distorted tetrahedra of Br- ions. Below

_Tc,

each of 8 Br- ions

_{(index i)}

suffers a

displacement

_ui

along

one or the other of two

orthogonal

directions

_{perpendicular}

to the

tetra-gonal

axis. ui can be written as :

where q

is a

_temperature

_{dependent amplitude}

factor

which _may be

taken

as the order _parameter;

(- n/2 ,

cp

7T/2)

is a linear function of the z

coordinate and characterizes a

_given

U"

ion. The

various ((Ji are known from

crystallographic

data. It can be shown

_[5]

that

U4+

ions lie at a site of

_symmetry

D2d (T

=

0)

_or

D2 (T

₌₁₌

0).

We have derived

_formally

the

_{explicit dependence}

of the

_crystal

field

_parameters

_upon the

_{displacements}

of the Br- ions. After tedious

calculations,

one

obtains the

_energies

_A(T)

of the various levels under the

_general

form :

where the coefficients a,

P

and _{y are} all

_{(in principle)}

non-zero in the case of a

_{« high}

_{temperature »}

doublet

while _y = 0 for _a

D2d

singlet. Equation

(2)

_can also

be found

_by

_using

_solely

_symmetry

_arguments. A

comparable approach

was used

_{previously by}

Blinc

et al.

_[11]

to discuss their NMR data. Since

optical

spectroscopy concerns differences _{in energy}

_E(T)

between the

_ground

state and the various excited

We can now _express the

_{inhomogeneous line-shape}

of the

_composite

_absorption

_spectrum,

or the absor-bance at _{energy E} as :

where n is the

_density

of

_spectral

lines at the

frequen-cies

_E(T)

and

_{L[E, E(T)]}

is a normalized

_shape

function

_{corresponding}

to the

_absorption

of

U"

in a

_given

site.

If dN stands for the number of atoms

_absorbing

at

an _energy

_lying

in the _range

d[E(q»]

around

_E(g),

then :

Since the distribution is random

_(dN/dz

=

constant)

and _cp is a linear function of _z, one has n dE =

dT

and :

A/E

will

_present

_{singularities}

whenever n is

maximum,

i.e.,

when

_d[E(cp)]/dcp

= 0. For _a

singlet

H

_singlet

transition,

two

_{singularities}

with

_equal

_intensity

are

predicted for

19

I

=

n/2 (E ,

= E_ =

Eo

₊

v2/2) and

9 = 0

(E

=

Eo).

In the _case of _a

singlet

doublet

transition,

the

_absorption

_profile

also shows two

singularities (cp

= _±

n/2)

_at

Et -

Eo

± VI

+

_v2/2

when k

₌

_{I V2/Vl}

_I

1. A third one is

_predicted

at

E,

=

Eo

₊

(vl)1/2

v2 for sin 9 = :F

Ilk

when

I k

I

> 1. Note

that,

when _present, the extra band at

_E,,

_always

lies outside the interval between

_E,

and

E_.

Furthermore,

upon

increasing

the energy, the

relative intensities of the three bands either increase

or decrease

_{continuously.}

An

_important

result is that

no

_{singularity is expected for}

₉ =

0, i.e.,

for

those

centres at a site

of D2d

_symmetry. The

frequency

sepa-ration between

_E+

and E_ is

_predicted

to _vary with

temperature

since :

where P

is the critical _{exponent of} the _order para-meter.

A _{program has been written} to

_compute

_absorption,

Zeeman effect and MCD

_profiles

for a model

_including

in

_D2d

a

singlet ground

state and two excited

doublets,

one of which

_(or

one of its

_{D2 branches) being}

ther-mally

populated.

The

_following

notations were

adopted :

Ground state

Low

_lying

doublet

Higher

doublet

with

Putting V2 1

= _z2 = 0

corresponds

_to the

problem

of

a

_singlet

--+

_singlet

transition.

The first

_step

is to _compute for all _(p values

_(-

_Tr/2

9

n/2)

the

respective populations Pi

(Boltzmann

distribution)

of the levels at

_Ei

_(i

=

0,

₊ 1 and -

1).

Next,

we assume normalized Lorentzian lines

L(E,

_{E(cp)) =}

(l/ny)/(1

+

X 2)

with X =

(E -

EJ/y.

For a

_singlet

- doublet transition

(D2d

notation),

one

finally

obtains the Zeeman effect and MCD

profiles

from the

_{following relationships :}

Absorption profiles

are found

_{by simply putting}

zi =

Z2 = o.

Figure

1 illustrates the results of such calculations

(dcp

=

n/l(0)

in the _case where the first doublet is

ignored.

One _very neat

_{qualitative advantage of}

MCD

versus

_absorption

is that the

_D2d

centre

_(cp

=

0)

shows

up very

clearly

in

_{the former,}

due to the occurrence

_of

Fig. 1. 2013 Illustration of the simulated

absorption

(doted

line)

and MCD

_(full

_line)

_profiles

in the case of an isolated

s -+ d _transition, as a function of k =

V2/Vi.

We chose

the associated

_.ae1

term.

_As

_{I k}

_I

increases from

_0,

this term moves from the centre of the

_spectrum

towards one of the ends since

_E,

is

_hardly

distinguisha-ble from

_{Eo when}

_{I k I >}

3. We note

_that,

_irrespective

of the value and

_sign

_{of vi}

and

_v’,

_{AA >1}

is

_always

2 _z2

i.e.,

the value found in the case of one centre in

D2d

symmetry.

Without loss of

_generality,

we can

_always

state that _vi > 0 and so

only change

the

_sign

_{of v2}

to simulate all

_possible

situations.

_{Only slight}

modifi-cations in

equations (6), (7)

are _{necessary in order} to

compute

profiles

for the hot bands associated with doublet -

_singlet

transitions

_(D2d

_{nomenclature).}

3.

_ExperimentaL

3.1

_EQUIPMENT.

-

Absorption

and MCD data have been taken on five

_{crystals separated}

from different

lingots,

of thickness t

ranging

from 0.54 to 2.6 mm

and concentration

_c(U/Th)

of the order of 10-

3-10-4.

All

_quantitative

data will be

_given

for a

crystal

of

t = 0.54 mm and

chemically

determined c = 2 x

10-4.

A

_spectral

band _pass of 0.3

A

was found to be

appro-priate

to

_get

all the details of the a, n and MCD

spectra.

ThBr4/U4+

crystals prepared

as described in

_[12]

are sensitive to moisture and are

_{highly birefringent.}

Special

care was

_required

for MCD measurements since a

slight

misorientation of the

crystal, especially

when combined with a defective surface leads to a

significant depolarization

of the

_light

beam and thus to an

_important

reduction of the MCD

_signal

_(or

even

artefacts).

Data were taken on

platelets

cleaved

perpendicularly

to the

_{tetragonal axis,}

checked under the

_{polarizing microscope}

and

_{freshly polished}

under

a stream of

_dry

hot air. We verified the absence of

stray

signal

in zero field and corrected the data for the rate of

_{depolarization}

as measured

_by

_placing

an

optically

active

_sample

(camphorquinone

in

_dioxane)

before and after the

_{crystal investigated.}

MCD

spectra were taken with standard

_equipment,

_i.e.,

a

photoelastic

modulator

_[13]

and a

phase

sensitive

detector. Measurements at 4.2 K and below

_(pumped

helium)

were made with a

superconducting

_magnet

(2.5

T or 5

_T).

All

_quantitative

data are normalized

to 1 T. Less care was

_required

to obtain reliable axial

a and 7c

absorption

_spectra

over a wide _range of

temperatures.

3.2 MAIN MULTS. -

_Figure

2 shows a _{summary of} our

_{polarized absorption}

and MCD

_spectra

in the

14 200-22 100 cm-1

_spectral

_range.

_Quite

noticeable is the fact that a number of

sharp

features occur on the

top of a

_poorly

defined broad band structure. This

occurs

_especially

around 17 350 cm-1.

_Up

to 2.5

_T,

the

_height

of MCD

_peaks

was found to _vary

_linearly

with the

_{applied magnetic}

field.

The 6 and axial

_spectra

were found to be

_identical,

thus

_{demonstrating}

the electric

_dipole

character of transitions. More detailed data for selected

_spectral

Fig.

2. - Schematic view of _our MCD and

polarized

absorption spectra. All scales are

_arbitrary.

T = 2.1 K.

ranges are shown in

_{subsequent figures}

and will now

be

_briefly

commented upon.

The

_strongest

axial

_absorption

is found in this

region

and extends over more than a hundred

wave-numbers. The extreme bands a

_{and P}

are

_separated

by

92

_{cm - 1,}

with an unresolved shoulder on the blue side of a. Additional features occur such as band 6

and a

quite intringuing dip

_y.

The associated MCD was

_reproduced

for three

different

_samples

where in one case the

_{positive bump}

around

_{band P}

was

_replaced

_by

a

_{dip going}

to AA = 0.

At both 4.2 K and 1.7

_{K, (}

AA

_o

was

_{found to}

be

strictly

zero, a result inconsistent with a

paramagnetic

ground

state in

_D2d.

We

_always

observed two

_sharp

_peaks

a

and P

(Ea -

Eo

= 30

cm-1)

in the axial

_spectrum

while the

additional features marked

_by

arrows were found to

depend

upon the

sample,

and are

_clearly

seen in the MCD _spectrum.

The

_sharp

features shown in

_figure

5b are

_reasonably

well isolated from the broad bands which appear

on each side in

_figure

5a. The

_spacing

between lines

a

and fi

in the axial

_spectrum

is 13

cm - ’

with a relative

intensity

Ia/lp ’"

4-5,

depending

upon the

sample.

The

Fig. 3. - Axial

absorption

(- - -) and MCD

_(-)

in the 14 580-14 730 cm-1 1

Fig.

4. - Axial

absorption

(- - -) and MCD

_(-)

in the 15 390-15 450 cm -I spectral range (arb. scales) at 2.1 K.

Fig.

5. -

a) Axial _{(- - -)} and n _{(- - -)}

_absorption

spectra

at 2.1 K in the 15 800-16 400 cm-’

_spectral

_{range; b) sharp} lines around 16 010 cm-1 with the

_accompanying

MCD spectrum

(-).

Note that the 7r spectrum is

approxi-mately twice as intense as the a _spectrum.

shape

of band a _suggests that it covers two compo-nents. Under a 4.2 T

_longitudinal

_field,

_only

this line

shows a noticeable

splitting.

The MCD

_profile

for this

_region

was found to _vary

only slightly

from

_sample

to

_sample,

the

_peak

corres-ponding

to

_{band P eventually becoming}

more intense

than that around 16 007

cm - 1

(Fig. 5b).

We note that the

_negative

part

of the MCD becomes less

negative (~ 10 %)

upon

cooling

the

crystal

from

4.2 K to 1.7

K,

in contrast to what we found

during

the same

experiment

for the 14 580-14 730

cm-1

region

(slight

increase in DA at all

_energies).

These features

suggest

the existence of an

_impurity

line in this

_region.

This is further

_supported

_by

the presence of a

_strong

7c band

_(Fig.

_5b)

which no theoretical calculation can

reasonably

account for and whose

_{overall intensity,}

as

compared

to that of the axial _spectrum, is

_greatly

dependent

upon the

sample.

It has in fact

recently

been established

_[14]

that

U3 +

is

_responsible

for these features if

_ThCl4

is

_{intentionally doped}

with this ion. Note that the _stray n band has a

_two-peak

structure with

_{Eo, -}

_Ea,

= 7.5

cm -1

and intensities of ratio

-

0.97.

- 17 335-17 390

cm-1 (Fig.

6).

The features in this

_region

have been

_reproduced

for several

_crystals

with no noticeable

_spurious

effects. No 7r line is seen within several hundred

wavenumbers on each side. The axial

_spectrum

(Fig. 6a)

shows three well resolved lines with

_{Ey -}

_E.

=

32.5

cm - 1

and

_{Ey - Eo}

= 20.5

cm - 1.

Our most

impor-tant result is

_again

that A and AA _vary

_by

no more

than about

_{3 %}

between 4.2 K and 2.1

_{K, (}

AA

_>0

being

zero.

_Actually,

as will be seen

in §

4,

these _very

clear-cut data demonstrate that the

_ground

state

_of

U4+ in

_ThBr4

is

_T4

_(D2d)

and that the host has an

incommensurate structure.

_{Furthermore, sillce (}

AA

_>0

=

0,

we know that we are

_dealing

with a

_complete

set of excited states,

i.e.,

no noticeable

mixing

(via

B)

occurs with states outside this

_spectral

_range. The

Zeeman

_spectrum

under 4.2 T

_(Fig.

_6b)

is

_perfectly

consistent with the MCD.

_Only

line a shows a

mea-surable

_splitting

₍₂₎

_{(1 g}

_I

=

1.3)

or

_{displacement,}

the

barycentre

of the

_split

lines

_{(see arrow) being}

at an

energy

slightly higher

than that of the zero field

components.

Similarly,

the A,

term is also

_displaced

towards

_{high energies}

while

_{only %o}

terms of

_opposite

sign

are seen for

bands P

and _y, with a continuum

between them. The difference in

_{absorption profiles}

between

_figures

6a and 6b results from the fact that

Fig. 6. - a) Axial

(- - -)

and MCD

spectra

through

the 17 335-17 390 cm - 1

_spectral

_range at 2.1 K;

b)

transmission spectra in zero field

( )

and under a 4.2 T _longitudinal field

_{(- - -).}

the Zeeman

_experiment

was

performed by simply

recording

the

_light

transmitted

by

the

_sample.

- 19 300-19 600 cm-1

(Figs. 7-8).

The dominant feature of the axial

_spectrum

_(Fig.

₇₎

is a three level

_{reasonably sharp}

structure at low

energy

(see inset)

with a less intense and broader

vibrational _counterpart

_roughly

50

cm- 1

towards

higher energies.

The low _temperature

_(1.7

_K)

n

spec-trum shows also weak lines in this

_region,

the

_sharpest

occurring

at 19 311 cm-1.

The

_energies

of the axial lines are such that

Ea -

Ey =

31.8 cm -1 and

_{Ea -}

_{Eo =}

7.8

cm -1.

The

band P

is

_{substantially}

broader than the two others and its

_intensity

is

_{greatly dependent}

_upon the

U4+

concentration of the

_sample.

The MCD associated to these bands is weak and does not

_change

appre-ciably

upon

cooling

from 4.2 K to 1.7 K.

An

_important

result in that

_region

is the occurrence

of a

disymmetrical

hot band at 19 311

_(inset

of

_Fig.

_7).

Fig. 7. - Axial

(- - - at 2.1 _K, ... at 4.1 K)

absorption,

n

_absorption

_(black 1.2 _K) and MCD at 2.1 K

_(full

line in the _inset) in the 19 400 cm-1 _region.

Fig.

8. -

a) Cold band - hot band behaviour of

_absorption

in the 19 240-19 400 cm-1

_spectral

_range.

_T/K

= 20

(-),

30 _(...) and 40 _{(- - -). b) Temperature dependence} at

T 4.2 K of the hot band

_peaking

around 19 310 cm - 1.

It is observed at 4.2 K but shows no measurable MCD and

_nearly

vanishes at 2.1 K. The hot band-cold band behaviour is further illustrated in

_figure

8a at

_higher

temperatures.

It is clear that the hot band increases

at the expanse of the cold band when T

_increases,

the former

_becoming

less and less

_symmetrical.

We made

a detailed

_study

of the T

_{dependence of}

A

_>0

for the hot band at

_{T %}

4.2 K. The zero order moment

was found to _vary as

_{exp(- WlkT)}

with W =

(9.8

_±

0.2) cm- 1,

as shown in

figure

8b. In the frame of a

D2d

model,

this

_finding

demonstrates that a level lies 10

cm-1

above the

_ground

state, both

_having

the same

degeneracy

d. This

spacing

was found

inde-pendently

from fluorescence measurements

_[6].

It is also

_tempting

to _{presume that the hot} 6 band at 19 311

em -1

_(intensity

₁₁₎

and the cold n line at 19 321

cm-1

₍₁₀₎

reach the same excited state. A

_glance

at table I shows however that this

_possibility

is excluded in

_D2d

with either d = 1 or d = 2. We

cannot

_explain

either the hot band

_profile

with a

one-site

_picture.

These failures

_provided

a stimulus to

find another

_type

of

_explanation.

We note

_finally

that

1,110

can be obtained

easily

from the zero order

moments of the two bands. We found 1.45 at 4.2

_K,

in excellent

_agreement

with the value obtained at 20 K

_(1.40)

- 19 950-22 050

cm-1

(Fig. 9).

Absorption

features in these

_regions

are

signifi-cantly

broader than those

_encoyntered

so far. We

assign

two electronic a

origins

at 19 966 and

21 866

cm-1.

Some

_plausible

vibrational

assignments

Fig. 9. - Axial

absorption

(- - -) x

absorption (black)

and MCD

_(-)

in the 19 500-20 150 cm- I _(a) and 21750-22 050 cm -1 1

are sketched on the

figure by

reference to the Raman

data

_[15].

No MCD could be measured in the 19 950-20150 cm-1 range. The MCD at

_higher

energy

(21 850-22 050

cm-’)

has an overall

S-shape

with (

AA

_>0

0. A few weak n lines were seen in

that

_region

for the more concentrated

_crystals.

- Other features

(Fig. 10).

The

_sharpest

band in the 7c

_{spectrum of U4+}

occurs

around 14 369 cm-1 with two

_{singularities separated}

by

3.25

cm-1.

The low energy

peak

is about

3 %

more intense that the

_high-energy

one. This band is

accompanied by

a Q hot band at 14 359

cm - 1

_having

the same

profile

and

_temperature

behaviour as that found at 19 311

cm-1.

Note that the 10

cm-1

_spacing

is met for the second time in these

_experiments.

A

similar situation occurs at a somewhat

_higher

_energy. A hot 7c band is seen at 14 609

cm- I

on the foot of a

residual

_(~

2

_%)

Q cold _spectrum

peaking

around

14 620

cm -1.

Finally,

a much weaker line with two

_{singularities}

was observed around 15 212

cm-1

(Fig. 10).

It occurs

on the blue foot of an intense and

_highly

structured

broad band. On the basis of this

_{experiment only,}

it is

_{clearly impossible}

to locate

_precisely

an

_origin

for the latter. -

Summary.

Anticipating

the fact

_{(§ 4)}

that all

_sharp

_absorption

structures with two

_(n)

or

_{two/three «(1) singularities}

actually

cover

_only

one electronic

_origin

in

_D2d,

we have summarized our results for energy,

polariza-tion and

_{dipole strengths}

in the first three columns of table II. The

_{figures quoted}

are sometimes

_slightly

different from those

_{published previously}

_[7],

due to the use of several

_{spectrometers.}

Fig. 10. - Most

important features in the n _spectra at 2.1 K

(-)

and 4.2 K _{(- - -).}

In view of the arguments

developed

so

far,

it should

be realized that an accurate

_numbering

of these

origins

has been

_long

and difficult. Some of the

_assignments

(marked by

an

_asterisk)

could

_only

be

_firmly

esta-blished via fluorescence and site selective excitation

experiments

[6].

3. 3 ROLE OF IMPURITIES. -

The presence of

impuri-ties in our

_crystals

was most

_clearly

demonstrated

by

MCD

_experiments.

For

_example,

all the features marked

_by

arrows on

figure

11 are

_spurious

on the

basis of their

_sample

_{dependence. Actually, only}

the two

_peak

structure around 15 400

cm-1

was

retained as

_belonging

to

U4 +

in the 15 100-15 500

cm - 1

region.

The rest of the MCD

_spectrum

shows some

low

_temperature

_dependence

which

_requires

further

investigation.

For

_example,

the term around

Table II. -

Experimental

(e)

and theoretical

_(t

_{from Ref}

_[7])

results in the

_{investigated spectral}

range.

Fig.

11. - Role of

impurities in the 15 100-15 500 cm - 1

spectral

range. MCD

experiments (full

lines) were run on

two different

_samples

with a different band pass for _(a)

and _{(b) (0.3 A} and 0.6 A

_{respectively).}

The absorbance is shown in dotted lines.

15 335 cm-1 becomes less

_symmetrical

_upon

_cooling

from 4.2 K to 1.8

_K,

this

_implying

that the

responsible

impurity

is

_{paramagnetic.}

A

_large

number of weak

_sharp

lines were observed

in

_absorption

for the more concentrated

_crystals

on

the red foot of the _strongest a

band, i.e.,

between

14 350 and 14 550

cm-’.

These are shown with mode-rate resolution in

figure

12a with the associated MCD

(Fig. 12b).

Under the

_appropriate

resolution

_(0.6

_{cm -1),}

the MCD shows a wealth of fine structure

_(Fig.

_12c).

This was examined in detail as a function of T for the

strongest lines in the 14 430-14 450 _{cm-1 range}

I

(Fig. 12d).

We found four

_absorption

_components,

I

each

_being

associated with a combination of an

_A,

term and a

_eo

term. We conclude therefore that _these lines are associated with a

paramagnetic impurity.

Fig.

12. - Role of

impurities

in the 14 350-14 600 cm--’* range. a and b : A and AA at moderate resolution; c and d :

AA at _high resolution.

In view of their

sharpness,

it has to be an actinide or

lanthanide

_ion,

most

_likely

U3+.

Four n lines in the

region

13 710-13 725

cm-1

_{probably belong}

to the

same

_species.

4. Discussion.

4.1 SPECTROSCOPIC ASSIGNMENTS.

4.1.1 Historical. - The

structure of the

_ground

multiplet

of U4+

in

_D2d

_symmetry

_(zircon

and

_ThBr4

hosts)

has

_long

been uncertain due to the lack of conclusive

_experiments.

Calculations can

_produce

either a

_singlet

or a doublet

ground

state for the f2

configuration. Actually,

it was

precisely

to

_firmly

establish this characteristic that the

present

work was

undertaken.

In 1975

_[3],

Zeeman and MCD data on

_ZrSi04/U4+

proved unambiguously

that the

_ground

state is

_T4

for that host. At _present, the

_{accepted picture}

for

ThBr4/U4+

is also

_{r 4}

lowest

_D2d.

Our _arguments for this choice can be summarized as follows :

(i)

our Zeeman effect

experiments

have shown that

the

_splitting

is

_{substantially}

different on the various

lines which have been examined

_carefully.

This

neces-sarily implies

a

singlet ground

state since doublet H

doublet transitions are forbidden for non-Kramers

ions in

_D2d.

Due to the use of

linearly polarized light

however,

we lack one crucial

_piece

of

_information,

i.e.,

the

_respective

circular

_polarization

of the

_split

components;

(ii)

the choice of

_{r 4}

rests

_essentially

_upon a

precise

numbering

of the Q and n electronic

_origins.

In the 14 000-22 200

cm-1

_{region investigated}

here,

we

should find those

_crystal

field levels

_originating

from the

_strongly

mixed free ion terms

_{3Po, lD29 lG4, 3p,}

11 6

and

_3P2.

_Altogether,

one _{expects 7,}

_{2, 5,}

5 and 7 levels of

_{ri ... r5}

_symmetry

_{respectively.}

With the

help

of table

la,

one can

easily predict

the number of 6

and n lines

_{expected, according}

to the nature of the

ground

state in

_D2d

_(cf.

Table

_III).

_{Experimentally}

(Table II)

we found 8 J lines and 7 n lines and this

strongly

suggests that

_T4

is indeed the

_ground

state. This

_assignment

is further

_{supported by}

the

obser-vance of a n band with two

_{singularities}

associated

with

_3Po(T1)

around 14 400

cm-1.

In no case can the

lowest state be

_r5

_(too

_{many J} lines

_predicted)

or

T3 (too

few).

Table III. - Number

of predicted

a and ’It lines

4.1.2 New

_information.

(i)

Nature of the

_ground

state. - A

definite

_proof

of the

_ground

state

_{being T4}

for U4+ in

_ThBr4

is

provided by

the _present MCD

data,

as will be demon-strated now. Within the

_assumption

of a

_D2d

_model,

T5

is excluded because none of the observed features

in the

_spectra

show the

_eo/kT

behaviour observed

previously

for all

_paramagnetic

_systems.

For

_example,

the AA associated to band y in

figure

6 has indeed

the

_shape

of the

_{corresponding absorption}

_component

but

_DA/A

does not _vary within the limits of

experi-mental errors

_(~

1

_%)

between 4.2 K and 2.1 K.

All calculations made so far

_predict

a

_fairly

well

isolated

_D2a

doublet with almost pure

3p1

parentage

around 17 300

cm-1.

With our

convention, g

is

cer-tainly positive

for that state since the

_{Mj =}

+ 1.

Zeeman

_component

transforms as

_{F’ 3}

in

_S4

_symmetry.

Then,

for a centre in

_D2d

_symmetry,

the

_Â1

_parameter

associated with the transition should be

_positive

or

negative according

to whether the

_ground

state is

F2

or

_{T i}

in

_{S4 (§ 2). Actually,}

the _argument

applies

as well to the first order

moment (

AA >I

if the

inte-gration

is carried over the features associated to all

D2

and

_D2d

centres in the

_{corresponding region.}

The

only assumption

is that the distortion is

_sufficiently

small to act as a

perturbation,

i.e.,

it does not mix

_3P1

with any other level. This turns out to be the case since

DA

_)o

is found to be zero. From our results in

figure

6,

it is clear that both

_{the A,}

term at _{low energy}

and

AA >,

over the entire band are

positive.

We

therefore conclude that the

_ground

state is

_{F’ 2}

in

_S4,

i.e.,

T3

or

_T4

in

_D2d.

It has to be

_F4

since

_T3

can be

firmly

ruled out on the basis of the lack of any noti-ceable 1t

_{absorption (F3 -+ T2}

of

_{3p 1)}

in this

_region

and the

_large

number of observed n

_components

in

the whole

_spectrum,

as

_compared

to

_only

2

_predicted

(Table III)

in this situation. The lack of 1t

_absorption

also rules out the

_possibility

of

_C2

_symmetry

in the low

_temperature

_phase.

(ii) Testing

of wavefunctions. - With

a

_{r 4 ground}

state for

_D2d,

Q and n transitions are allowed towards

excited states of

_symmetry

_{r 5}

and

_{7B respectively.}

One therefore arrives at the

_assignments

shown in table II

which contains also the results of most recent

_crystal

field calculation

_{[7] (energies and g factors).}

As can be

seen, the

computed

energies

match those observed

fairly

well.

MCD also

_provides

a

_powerful

means to test the

wavefunctions. g

factors were determined

experimen-tally

from first order moments. As shown in table

_II,

not

_only

does the calculation account for the actual

sign of g

for 5

bands,

but its

magnitude

is also

reaso-nably

well

_reproduced.

The

_uncertainty

on

experi-mental data is estimated to be about 10

_%.

g

unfortunately

could not be measured for the

bands at 19 966

cm-1

and 20 360

cm-1

_{(Fig. 9a)}

because the absorbance in these

_regions

was too low

on the

investigated samples.

It should be remembered

that AA is

grossly

proportional

to the maximum

absorbance,

this

_{being typically}

10-2

at 19 966

cm-’

and

10- 3

at 20 360

cm-1

for a

_crystal

of thickness

0.54 mm and of concentration

_U/Th

= 2 x

10-’.

The

Á1

coefficient measured for the band at 15 420 cm-1

(Fig.

4)

is not

_reported

in table II. It is unreliable since we

have

demonstrated that

sample

_dependent

(impurity)

features occur in that

region.

4. 2 INCOMMENSURATE MODEL. -

The model

_presented

in detail at the

_beginning

of this _paper

_provides

a nice

understanding

of most of the unusual features observed in

_absorption

and MCD

_experiments.

Hereafter,

we

shall use some now well established facts in our

_fitting

procedure.

Of course the

_ground

state is

_{singlet r 4}

in

D2a.

Furthermore,

fluorescence

_experiments

[7]

can

only

be understood if the next

_higher

level is

_F5(D2d)

at 78

_cm-1,

the

_splitting

of its two

_D2

branches

implying vi

= 69

cm-’

and v’

= 2

cm-1.

In the

following,

we shall use v 1 to characterize the excited state of the transition considered.

4.2.1

_Absorption

and MCD

_profiles.

- First,

we

select the

_{3p 1}

_region

around 17 360

cm - 1

since it is

_fairly

well isolated and no

spurious

effects were

observed. Our simulated curves

_(for

_v2/vl

=

4.3)

_are shown on

_figure

13. A

comparison

with

figure

6 indi-cates that the overall

_{experimental profiles}

are well

reproduced. Clearly,

as shown

_by

the Zeeman and

MCD curves, it is not the a band which

splits

under B

but the

_component

associated with the site at _cp = 0

and located

_{slightly higher}

in energy than a. The

relative intensities of the three

_absorption

singula-rities are well

_reproduced

if we take a due account of the intense

_{absorption background}

illustrated in

figure

2.

During

the

_preliminary

work of

_{Delamoye [5]}

the reasonable

_assumption

was made that

_vi(-

_q)

was

_probably

_larger

than

V2/2(-

?12 )

and this led to the conclusion that

_only

two

_{singularities}

should be observed in both the (1 and the a

_spectra.

It is thus

striking

to see that a

good

_agreement

between

predic-tion and observation occurs

_precisely

for a band for

which

₍₂

_VI/V2)

> 2.

_Actually,

we know

_nothing

of the

coefficients

_{of il}

_{and 112}

and there _may occur the

Fig. 13.

- Simulation of the MCD

(-),

axial

_absorption

in zero field

(- - -)

and axial

absorption

under a 4.2 T field

(... ). The value

_{of g}

for the excited state is 1.28. T = 1.8 K, v 1 = 10.25,

unusual situation where the latter is much

_bigger

than the former. This is not

_{really surprising}

_since,

in the

case of a

singlet

- doublet transition

[5],

the odd

(VII

v3...)

and even

_(V2"’)

terms do not arise via the

same _process,

i.e.,

we do not

_merely

have a

Taylor

expansion.

The features in the 16 000 cm-1

_{region (Fig. 5)}

were

simulatedwith vi

= 6.5 cm-1 and

V2/V 1 -

3

(y

=== 1

em -1).

The

_agreement

was found to be

satisfactory

for the MCD while the calculated value

_I.II,

is smaller

(- 3)

than that found

_{experimentally}

_(4-5).

This failure is

quite certainly

related to the _presence of a

spurious

very strong 7c line and a

positive Co

residual

contribu-tion in the 16 007-16 015 cm-1

region (Fig. 5).

Both

are

_{tentatively assigned}

to a

_{r 7 --+}

_F6

transition

(allowed

7r and

a)

of U3 +

_(possibly

of

_charge

transfer

character).

Apart

from the weak

_bumps

shown

_by

arrows in

figure

4,

the

_absorption

_spectrum in the 15 400

crn -I

region

is

_fairly

well

_reproduced

_{with vi}

= 15

cm-1,

v2 = - 6

cm-’

and

y = 0.6

cm-’.

The MCD data

are not

and

this is due to the mentioned presence of

presumably paramagenetic impurities giving

a

rela-tively

large

MCD. The

_sharp

line at 14 370

cm-’

(Fig. 10)

is well

_reproduced

_{with v2}

= - 7.5

cm-’.

Note that this

_figure

_{actually corresponds}

to the difference in _v2 coefficients for the excited state and the

_ground

state. The

_{negative sign}

is

_{imposed by}

the fact that the low energy

component

is

_{approximately}

3

_%

more intense than the

_high

_energy one.

The

_profile

and T

_dependence

of hot bands

(e.g.,

Fig. 8)

is also

_{produced by}

our

_calculation,

as shown in

_figure

14. Curve a

(y

= 0.8

crn-’)

is similar to _our

experimental

spectrum

(Fig.

7)

while b shows the red shift and red

broadening

of the line under

_heating.

We now consider the 19 300

cm-’

_region

_{(Fig. 7).}

No value of

_V2/V,

could

_possibly

_reproduce

the

absorption

(3

bands)

and MCD

_spectra.

_Regarding

Fig.

14. - Simulation of the hot bands :

(a)

proper

profile

at 4.2 K of the band at 19 311 cm -1 1

(y = 0.8cm-1) ;

(b)

temperature

dependence

of the

_profile

_(we used y = 7 cm - I

to save _{computing time).}

the

_former,

it is clear from

_figure

1 that band a would

be much _stronger than

_{band y if fl}

was a « normal »

third band.

_Regarding

the

_latter,

we do observe the

expected

opposite %o

terms for a

and y

but the

plau-sible

_Al

term around 19 352 cm- I

_(arrow)

is

surpri-singly

small. Such a result is

_only

obtainable when the half band width is

_larger

than _v,, a

_quite

unrealistic

situation.

_Actually,

calculations

_(Table

_II)

indicate

that

_{the g}

factor should be close to zero and it is

therefore

_likely

that the whole MCD can

_hardly

be

attributed to

_only

U4+ .

Note that « extra » bands are

also found in a few

_regions

of the infra-red

spectrum

of

_ThBr4/U4+.

Difficulties also arise in the 14 650 cm-1

_region

(Fig. 3).

The model accounts for the

_respective

inten-sities of bands a

and fl by placing

_Eo

at 14 650

cm - 1

where a

disymmetrical Â1

term seems _{to occur,} and

choosing vi

= 46

cm - 1, V 2

= 5

cm - 1.

This

interpre-tation is further

_{supported by}

the fact

_(Fig.

₁₅₎

that the

_a-fl

_splitting

_(~

order _parameter

_q)

is

expe-rimentally

found to _vary as

_{(T -}

Tc)1/3

for

_T

40

_K,

as does the

frequency

of the Raman soft mode

_[15].

Note that an

_exactly

similar result was obtained for

the

_{a-fl spacing}

in

_figure

8. This

_1/3

_figure

is

_quite

reliable since it was obtained

_{by taking}

a _proper

account of the variation of the bandwidth with

tempe-rature. No reliable measurement of the

splitting

between bands a

_{and P}

at

_temperatures

near

_T,,,

= 95 K

could be made because of the vibrational

_broadening

of the lines upon

heating.

The

_{(Tc - T)I/3}

behaviour

of q

far below

_Tc

is not

_presently

understood.

Returning

to

_figure

_3,

our model

_certainly

fails to account for the additional

bumps

and the

_{dip y}

in the

_absorption

_spectrum,

as well as for some of the

MCD structures.

4.2.2 Role

_of

_vibrations.

- One

possible

issue to the

puzzling questions

raised for the above two

_regions

is to consider the role of

vibrations,

which we have

ignored

so far in our discussion. As encountered for dn ions at a field of

_D2d

_symmetry

_[16],

electronic states are

_{generally coupled}

to several vibrational

modes. This

_obviously

occurs in

_figure

7 where the

absorption

features around 19

_400-19

450

cm-1

bear

a

_striking

resemblance to the three-bands

_origin.

Fig. 15. 2013 Plot of the

splitting

between bands cx

_{and p}