Crystal fields and magnetic properties of NdSn3, NdPb 3 and Ndin3

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Crystal fields and magnetic properties of NdSn3, NdPb 3 and Ndin3

P. Lethuillier, J. Pierre, K. Knorr, W. Drexel

To cite this version:

P. Lethuillier, J. Pierre, K. Knorr, W. Drexel. Crystal fields and magnetic properties of NdSn3, NdPb 3 and Ndin3. Journal de Physique, 1975, 36 (4), pp.329-333. �10.1051/jphys:01975003604032900�.

�jpa-00208258�

CRYSTAL FIELDS AND MAGNETIC PROPERTIES OF NdSn3, NdPb3 ^AND Ndin3 (*)

P. LETHUILLIER and J. PIERRE

Laboratoire de

Magnétisme, C.N.R.S.,

^BP

166,

³⁸⁰⁴²

Grenoble, Cedex,

^France and

K. KNORR

(**)

and W. DREXEL Institut Max-von

Laüe-Paul-Langevin,

BP

156,

³⁸⁰⁴²

Grenoble, Cedex,

^France

(Reçu

^{le 9 décembre}

1974, accepté

^{le 23 décembre}

1974)

Résumé. ²⁰¹⁴ Nous avons réalisé des expériences ^{de diffusion} inélastique ^{des neutrons sur les} composés intermétalliques

NdPb3

^et NdSn3. ^{Nous avons} observé des transitions bien résolues entre niveaux de champ cristallin à différentes températures. Deux schémas de champ ^cristallin

sont possibles pour chaque composé. ^{Des mesures} magnétiques ^{et des}

expériences

de diffraction

neutronique permettent ^{de lever cette} indétermination. Les paramètres ^de champ cristallin obtenus diffèrent beaucoup ^des

prévisions

d’un modèle de charges

ponctuelles.

Abstract. ²⁰¹⁴ Inelastic neutron scattering experiments ^{have been} performed ^on the intermetallic

compounds NdPb3

^and NdSn3. Well resolved transitions between crystal field levels were observed at different temperatures and for each compound, ^{two level schemes were} possible. Magnetic ^measure-

ments and elastic neutron scattering experiments ^were performed ^{to remove this} uncertainty. ^The

experimental

crystal ^field parameters ^deviate considerably ^from

point charge

^estimates.

Classification Physics ^Abstracts 8.524 ^- 8.537 ^- 8.512

1. Introduction. ^- The cubic

compounds RX3

^with

CU3Au

^{structure between rare earths}

(R)

and different metals

(X)

^{such as}

In,

^Sn and Pb have been studied from different

points

^{of view :}

magnetic

structure,

crystalline field, superconducting properties

^{and elec-}

tronic structure. In

particular,

^a great deal of work has been spent ^to determine the

crystalline

^electric

field

(CEF)

levels : the direction and the values of the ordered moments have been determined in the

RIn3 [1-3]

^{and the}

RSn3 [3] compounds. Schottky

anomalies have been observed and

analyzed

ⁱⁿ

specific

^heat measurements on

Celn3, Prln3 [4]

and

Lao.9Pro.1Pb3 [5]. Susceptibility

studies have led to the determination of the

ground

^{state levels}

in

praseodymium compounds [6, 7].

However,

^{the most}

straightforward

^{method to}

determine the level scheme is inelastic ^neutron

scattering.

^We have thus undertaken

experiments

on the two

neodymium compounds, NdSn3

^and

NdPb3,

^{which were}

complemented by magnetization

measurements in

pulsed fields, susceptibility

^and

magnetic

^structure determinations. All these

experi-

ments were

performed

^with

polycrystalline samples.

(*) This ^{work is} part of the thesis of P. Lethuillier.

(**) Present ^{address :} Physikalisches Institut, Frankfurt/M, Germany.

2. Neutron

spectroscopy.

^{- In cubic} symmetry, the J ⁼

2 multiplet

^{of the Nd3+ ion is}

split

^into

one doublet

r6

^{and two} quartets

T8(1)

^and

T8(2).

The level scheme can be described

by

^{two CEF-}

parameters A4 r 4 >

^and

A6 r6 >

^or

equivalently, following Lea,

Leask and Wolf

[8],

^{W and x. The}

transition

probabilities

^are

given by Birgeneau [9].

Inelastic neutron

scattering

^{is a} very direct method for the determination of

crystal

field levels.

Magnetic dipole

transitions between

crystal

field levels occur

with

matching

^neutron energy transfers. The

resulting peaks

^{in the neutron} energy spectrum ^are propor- tional to the _square of the

magnetic dipole

^matrix

elements and to the thermal

population

of the initial CEF-level.

The inelastic ^neutron

scattering experiments

^were

performed

^{on the} statistical

chopper

^{time of}

flight

spectrometer ^{IN 7} of the Institut

Laüe-Langevin

at Grenoble. An _array of 10 detectors was located at

scattering angles

between 150 and 200. Several incident neutron

energies

^were

^used,

^{from 10 meV}

up ^to 56 meV. The

samples weighed

^{about 100} g ;

a

typical counting

^{time was one}

day.

^{The resolution}

of the instrument was seven time of

flight

^channels

(full

^{width at half}

maximum).

^All spectra ^{were domi-} nated

by

the elastic line. The error bars were estimated from the scatter of data

points

^between

peaks.

^Neutron

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01975003604032900

330

detected in channels to the left of the elastic

peak gained

energy

by

the de-excitation _{of upper} states,

neutrons

inducing upward

transitions were counted in channels on the

right

^{hand side.}

The first measurement was taken on

NdPb3

^at

6,5 K with incident neutrons of 56 meV. A

peak at

10 to 11 meV

appeared

^{on the neutron} energy loss side

(Fig. 1).

^A measurement on

LaPb3

^{at 80 K but}

otherwise under the same conditions did not show any ^structure other than the elastic line. Thus we

explain

^the

peak

observed for

NdPb3

^{as a transition}

from the

ground

^{state to an excited state at about}

11 meV. The second spectrum ^{was measured at} 120 K in order to observe new transitions from this excited level

(Fig. 1).

^The

original peak

^was

changed

into a shoulder

indicating

^a new, not yet

resolved,

transition in the energy range from about 4 to 9 meV.

Fm. 1. ^- Neutron time of flight spectra ^of NdPb3 ^{at 6.5 and 120 K.}

The incident energy is E. ^{= 56.0 meV.}

A

corresponding

^shoulder

appeared

^on the de-excita- tion

side,

^too. Since this new transition was absent at 6

K,

^it must connect the two excited CEF levels of

Nd3+.

To increase the resolution and to ascertain the

transition,

^{a third} spectrum ^{was measured at} 51 K with the incident neutron energy lowered to 40.0 meV

(Fig. 2a).

^{The two} transitions were now

FIG. 2. ^- Neutron time of flight spectra. The incident _{energy is} Eo ^{= 40.0 meV.} a) NdPb3 : ^{T = 51 K.} b) NdSn3 : ^{T = 10 K.}

c) NdSn3 : ^{T = 51 K.}

resolved,

^with

energies

^of

(10.6

±

0.2)

^{meV and}

(7.6

^±

0.2)

^{meV. A}

hint

^{of the reverse} transitions can

be seen on the de-excitation side of the spectrum.

The fact that the 7.6 meV transition was

already

visible at 51 K where the level at 10.6 meV is still not

substantially populated

^{demands a} sequence of levels as follows :

We searched for the transition between the

ground

state and the first excited level at 3.0 meV. A spectrum taken at low

temperature

^{with an} incident energy of 14.0 meV did not show more than a

slight

^indication

of a

peak

^{around 3 meV. One has to} conclude that the

probability

for this third transition is

significantly

lower than for the other two.

Refering

^to the level scheme

given

^{in ref.}

[8]

^for

Nd3+,

^one finds that five sets of CEF parameters

can

reproduce

the observed

splitting, namely :

The decision between these cases has to be based on

the transition

probabilities [9]. Quite clearly,

^the

solutions

c) d) e)

^{can be ruled out because}

they

demand a very intense transition at 3 meV. The distinction between case

a)

^and

b)

^{is more difficult.}

The situation is best described

by

^a calculation of the theoretical spectra

[13, 14]

^{for both cases}

(Fig. 3).

Both spectra ^{fit the}

experimental

results within the statistical error. There is a small

preference

^{for case}

a),

where the

ground

^{state is the}

r 6

^doublet.

FIG. 3. ^- Theoretical spectra ^of NdPb3 ^and NdSn3 ^{at 51} K, ^with Eo ^{= 40.0 meV.}

The results on

NdSn3

^are very similar and the

interpretation

follows the same scheme. At 10

K,

an excitation

peak

^{at 10.2 meV can} be observed

(Fig. 2b).

^{At 51}

^K,

^a broad maximum

ranging

^{from 7}

to 12 meV is visible

(Fig. 2c).

^{It is}

explained by

^a

second transition at 8.2 meV of about the same

intensity as

^{the first one. We} conclude that the _sequence of levels is 0

meV, (10.2 - 8.2)

^{= 2}

meV,

^{10.2 meV.}

The transition at 2.0 meV could not be detected.

These results exclude all but two sets of CEF _para- meters,

namely x = 0.24,

W = 0.123 meV and

x = 0.48,

^{W = 0.166}

meV,

^which

again

^{fit the}

experimental

data with about the same

quality (Fig. 3b).

^{For both}

compounds,

^the

question

^remains

as to whether the _sequence of levels is

r 6’ T8(1), rà2)

or

râ1), r 6’ râ2).

^{In order to remove this}

uncertainty,

we

performed magnetic

measurements and elastic neutron diffraction studies.

3.

Magnetic susceptibility (Fig. 4).

^{- We have}

studied the

magnetic susceptibility

^{of these}

compounds using

^a translation balance in a

magnetic

^{field of}

7

kOe,

^{over the} temperature range from 1.6 K to 300 K. Above 50

K,

^a Curie-Weiss behaviour is observed for both

compounds,

the effective moments

FIG. 4. ^- Reciprocal susceptibility ^versus temperature ^for NdSn3

and NdPb3. The continuous curves have been calculated for _respec-

tively : ^{W =} 1.43 ; ^{x =} 0.24 and W ⁼ 1.26 ; ^{x = 0.13.}

are in close agreement with that of the free

tripositive

Nd ion.

NdSn3

^{shows a} maximum of the _suscep-

tibility

^{at 4.6}

K,

ⁱⁿ

good

agreement with Tsuchida and Wallace

[10], indicating

^{the onset} of antiferro-

magnetism ;

^this

compound

^{shows a} minimum of the

susceptibility

^{at 3 K. Below 50}

K,

^{in the}

paramagnetic domain,

^the

susceptibility

x deviates

slightly

^from

Curie-Weiss behaviour.

NdPb3

orders antiferroma-

gnetically

^{at 2.6 K and as for}

NdSn3,

x deviates

slightly

^{from a} Curie-Weiss behaviour at low tempe-

rature. We have calculated the

crystal

^field

suscepti- bility

for the three

crystallographic ’axes 100 j, 111 >, 110 >

^{and found it}

weakly anisotropic.

For both

compounds,

^the agreement between the calculated and measured values of the

susceptibility

is

good

for the different sets of W and x : it is

slightly

better when

r 6

is the lowest level.

332

4. Elastic neutron diffraction. ^- In a

previous study,

we had

performed

^{a neutron} diffraction

experiment

on

NdSn3 [3].

^The

magnetic

^{cell was found}

quadratic (a,

^{a, 2}

a)

^{and the}

magnetic

moment, which ^{is in} the basal

plane,

^{reaches 1.5} +

0.311B

^{at 1.3 K. We}

performed

similar work on

NdPb3

^{at the reactor}

Siloe

(Neutron

Diffraction

Laboratory, C.E.N.,

^Gre-

noble).

^This

compound

^{has the same}

magnetic

^struc-

ture as

NdSn3

^{and the}

magnetic

^{moment reaches}

1.4 ±

0.411B

^{at 1.3 K}

[11].

^{In order} to account for these neutron diffraction

results,

^we have calculated the

magnetic

^{moment at} 1.3 K. For this _purpose we

diagonalize

the Hamiltonian

where the

exchange

^field

Hm

is taken from

Jz)

is the thermal _average of the

magnetization

and C is the Curie constant at low temperature. ^The

magnetization

^and

ground

^state energy ^are found

by

a self-consistent method. The

anisotropy

energy between the

principal

^{axes is weak}

(AE

¹

K)

^for

the different sets of W and x. For

NdSn3,

^{the solution}

W ⁼ 0.123 meV

(1.43 K),

^{x = 0.24}

(r6 lowest) gives

^a moment Il ⁼

1.62,u,

^{close to the}

experimental

value

(1.5

^{± 0.3}

I1B).

The other solution will lead to a moment Il ⁼ 2.47 _IUB-

For

NdPb3,

_Ilexp ^{= 1.4} +

0.4’UB.

The solution W ⁼ 0.109 meV

(1.26 K),

^{x = 0.13}

(r6 lowest) gives

^a moment p ⁼

1.39 ,uB.

The other solution

gives

^a moment Il ⁼

2.26 y/a. Quite clearly,

^{for both}

compounds,

^the

r 6

level is lowest and the CEF

parameters

^{are : for}

NdSn3 : W

^{= 1.43}

K ;

^{x = 0.24} and for

NdPb3 : W

^{= 1.26}

K ; x

^{= 0.13 .}

We

give

the level scheme in

figure

^5.

5.

Magnetization

measurements

(Fig. 6).

^-

Finally, experiments

^{on the three}

compounds NdIn3, NdPb3

and

NdSn3

^were

performed

^{at 1.35 K in}

pulsed

^fields

up ^to 260 kOe in order to overcome the antiferroma-

gnetic exchange

field and

align

^{the moments. The}

samples

^are

powders,

^{and the}

eddy

^{currents do not}

significantly perturb

^the measurements. The magne- tization of

Ndln3

^increases

slowly

^and

linearly

^above

160

kOe,

where its value is about 1.55 _,uB, close to the moment of the

r 6

level. The

magnetization

^of

NdPb3

^and

NdSn3

^do not saturate. For the three

compounds,

^the

magnetization

^{in the}

highest

^field

is below

2,uB,

far from the free ion value

(gJ

⁼

3.27 IUB)’

This is in

qualitative

agreement with the behaviour of a

r 6 ground

^{level in a field.}

FIG. 5. ^- Crystal field level scheme for NdSn3 ^and NdPb3’

FIG. 6. ^- Magnetization ^{curves of} Ndln3, NdSn3 ^and NdPb3.

6. Discussion. ^- In the

following,

^{we will}

analyze

the CEF parameters ^{for these}

neodymium compounds.

In the two isoelectronic

compounds NdSn3

^and

NdPb3,

^{the two} parameters

A2 r4 )

^and

Ag ( r6 ) keep

^{the same}

negative sign (Table I).

^{In a}

point charge ^model,

where all the

neighbouring

^atoms

are taken into account, the CEF parameters ^{can be} written as :

TABLE 1

CEF parameters determined

experimentally

If we first

analyze

^the fourth order term

alone,

^the

experimental

values lead to a small or

negative charge

on Sn or

Pb,

^{if we assume a trivalent rare} earth ion

(Table II).

^{This is in} agreement ^{with the}

assumptions

of Bucher et al.

[12]

^who

analyze

the effective

charges

in relation to

electronegativity. However,

^{with such}

charges,

the calculated sixth order term is smaller than observed

by

^{one order of}

magnitude.

^This

excessive value of the sixth order term has been

TABLE II

CEF parameters Ag r4 ), Ag r6 ) (K)

^calculated

for NdSn3 from a point charge model, assuming

trivalent

neodymium

^and

given charges ZM for

^the

Sn atoms.

observed in a number of intermetallic

compounds :

in the cubic Laves

phases TbAl2

^and

NdAl2

^com-

pounds [13],

^{in the} cubic CsCI

type phases

^between

Ho and Er and the different metals

Cu, Ag,

^{Zn and}

Rh

[14, 15]

^{and in the cubic}

AuCu3 type TmAl3 compound [16].

^In all these

compounds,

^a

point charge ^model,

^{where the rare} earth has a

positive charge

^{and the}

alloyed

metal has no

charge, gives

the correct

sign

^for

A2 ,4)

^and

Ag r6 )

^{but the}

calculated order of

magnitude

^for

Ag ,6 )

^{is then}

generally

much smaller than the

experimental

^value.

Dixon and

Dupree [17, 18] analyze

^{the results}

obtained

by

Williams et al.

[19]

in solid solutions of

heavy

^{rare earths in a} f.c.c. matrix

(Ag, Au) by taking

into account the d- and f-like character of the conduc- tion electrons. In the

LaSn3 compound,

band calcula- tions

[20, 21]

have shown that conduction electrons have a

large

d character in the

vicinity

^{of the Fermi}

level. It is

possible

that the influence of the d-electrons

aspherical

distribution _may

explain

^the

negative sign

^of

A04 r4 >

encountered in

NdSn3

^and

NdPb3 ;

the

large

^{value of}

A06 ,6 )

may then arise from an

exchange-type

interaction with the conduction band.

A

peculiar

^case is that of some

compounds

^with

praseodymium :

ⁱⁿ

Prln3 [6], PrSn3

^and

PrPb3 [7],

the fourth order term is

positive;

^{on the} contrary,

a

study

^{of the}

magnetic properties

^{of the}

RIn3

^com-

pounds

^with

heavy

^{rare earths}

[22]

^{has shown}

that,

most

probably,

^the

A04 ( r4 >

parameter ^is

negative,

as in

NdPb3

^and

NdSn3.

^{The case of}

Ndln3

^{is still}

uncertain and must await a new determination.

References

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