MAGNETIC FORM FACTOR OF NpAs2 : A
CRYSTAL FIELD WAVE FUNCTION FOR 5f
ELECTRONS ?
G. Amoretti, A. Blaise, M. Bonnet, J. Boucherle, A. Delapalme, J. Fournier,
F. Vigneron
To cite this version:
G. Amoretti, A. Blaise, M. Bonnet, J. Boucherle, A. Delapalme, et al..
MAGNETIC FORM FACTOR OF NpAs2 : A CRYSTAL FIELD WAVE FUNCTION FOR
5f ELECTRONS ?. Journal de Physique Colloques, 1982, 43 (C7), pp.C7-293-C7-299.
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JOURNAL DE PHYSIQUE
Colloque
C7, supplément
au n°18,
Tome 43,
MAGNETIC FORM FACTOR OF NpAs
décembre
1982
page C7-293
: A CRYSTAL FIELD WAVE FUNCTION FOR
5f ELECTRONS ?
G. Amoretti , A. Blaise , M. Bonnet
J.M. Fournier+ and F. Vigneron
+
DHF/FS, CEN Grenoble,
++
L1,B, CFN Saclay,
8bX, 28041 Grenoble
91191 Gif-sur-Yvetle
**URF/DN, CEN Grenoble,
, J.X. Boucherle
Cedex,
Cedex,
8bX, 68041 Grenoble
, A. Delapalme
,
France
France
Cedex,
France
Résumé.- Les mesures du facteur de forme magnétique du neptunium dans la phase ferromagnétique de NpAs ? (T = 4,2 K, H = 4,6 T) sont analysées avec différentes hypothèses:
valence de l'ion neptunium égale à 3,4 ou 5+, fonction d'onde de l'ion libre (couplage Russell-Saunders et couplage intermédiaire) ou état fondamental de champ cristallin £ a |J,m> . Compte-tenu de la précision expérimentale dont on dispose, il n'est
pas pSssTble de conclure avec certitude quant à la valence de l'ion Np (3+ ou 4+).
Abstract.- Neptunium magnetic form factor measurements in the ferromagnetic phase
of NpAs ? (T = 4.2 K, H = 4.6 T) are analysed under different assumptions : NpJ + ,
Np 4 + or Np 5 + , with a free ion wave-function (Russell-Saunders and intermediate
coupling scheme) or with a Crystal Field Wave function for 5f electrons :m ajj,m>
The experimental results are compatible with either a 3+ or 4+ state.
I. Introduction.- In studies of the electronic structures of actinide metals and
compounds, one of the major problems is related to the determination of the number
of 5f electrons associated with an actinide ion. In order to answer this question,
a polarized neutron study of the neptunium magnetic form factor in NpAs 9 [1] was
undertaken at the ILL.
NpAsp crystalline structure is tetragonal (P4nmm space group) with
a =3.930 (5) A and c = 8.137 (5) S at 4.2 K [2] . With no external magnetic field,
NpAs~ orders at T„ = 52 K in a sine-wave modulated structure and becomes ferromagnetic at T = 1 8 K [3J ; the crystal is strongly anisotropic with the easy-magnetization
direction along ?.
In the present work,the measured (T=4.2 K, ify/c, H=4.6 T) magnetic form factor of
neptunium in NpAsg is compared with theory : different 5f electrons wave functions
are used corresponding to Np 5 + , Np 4 + and Np 3 + and also to different assumptions
(a,b,c : see below) in the treatment of the ionic hamiltonian H . H may be written :
H = Hc + H s o + Hr,£p, where Hc is the Coulomb interaction, H S o the spin-orbit interaction and HCEF the crystal field interaction. In the presence of H c only, the wave
function is characterized by quantum numbers S and L.
In the Russell-Saunders (RS) coupling scheme (assumption a : H = Hc + W s o with
so < < Hc) the appropriate quantumnumber for neptunium ground state wave function is
J = L -S with L and S given by Hund's rules.
H
Assumption b takes into account the strong spin-orbit coupling in the actinide
ions : H = H + H with H ~ H , such that H mixes states of different S and L
into the ground-state J manifold (intermediate coupling scheme).
H r c r with Hrcc « H «H .
C£r
CEF
so
c
Each of these assumptions is considered below : assumptions a and b in part II,
assumption c in part III. A crystal field model is then developed in part IV.
Assumption c introduces the crystal field interaction
Fellowship of C.C.E. Bruxelles, Belgium. On leave from Univ. Parma, Italy.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982742
JOURNAL DE PHYSIQUF,
C7-294
11. Magnetic form f a c t o r o f neptunium : f r e e i o n wave f u n c t i o n
As t h e experimental form f a c t o r
c r i b e d t h e s p a t i a l extension o f t h e
t i o n s t a t e s o f neptunium w i t h i n t h e
c a l c u l a t e d magnetic form f a c t o r may
f
=
<j >
0
+
( f i g . 1 ) seems t o be n e a r l y i s o t r o p i c , we desmagnetization d e n s i t y f o r t h e d i f f e r e n t i o n i z a d i p o l e approximation. I n t h i s approximation, t h e
be w r i t t e n :
c2 < j 2 >
.
The r a d i a l i n t e g r a l s < j.> have been obtained by J.P.
i n a r e l a t i v i s t i c ~ i r a c l ~ o cc ak J c u l a t i o n .
Desclaux and A.J.
Freeman [41
I n t h e RS c o u p l i n g scheme (abunpZLon a)
Experimental r e s u l t s ( p f o b s ) and c a l c u l a t e d magnetic form f a c t o r s (pfcalc)
then compared w i t h i n a least-square method (parameter : pcalc).
are
The r e s u l t s f o r
4+
(c2 = 1.75) and Np3+ (c2 = 2.33) RS f r e e ions are summarized i n
Np5+ (c2 = 1.5), Np
Table I and Fig. I : t h e i o n i z a t i o n s t a t e o f neptunium cannot be c l e a r l y i d e n t i f i e d ,
however t h e 5+ s t a t e seems t o be l e s s probable. This r e s u l t i s t o be compared w i t h
the YSssbauer measurement, which a l s o discounts the presence of a 5+ s t a t e [51.
I
I
I
I
I
Fig.1. Magnetic form f a c t o r
o f p t u n i u m (NpAs2 T=4.2 K ) :
experimental r e s u l t s
4
(4 : h k t = 0, : h k L # 0)
and c a l c u l a t e d p f i n t h e
d i p o l e approximation f o r
Np5+
4+
3+
, NP , NP
.
D ~ ~ ~ ~ R ((% ) u ~ x)
Wave-function
~
~ 5 f+2 : 3 ~ 4
NP4+
!if3 : 4 ~ 9 j 2
N
Free i o n
-
RS
N ~ ~ 5 +f 4 : 5 ~ 4
4
5 f 3 : 83% IgI2
, 15% 2
Np4'
ion
-
5
5 f 4 : 80% I4
,
Free
Np3+
np4+ sf3
9
9
: 0 . 6 0 1 ~,+ f
Hg/2
2
1.50
4.7
0.86
1.45
4.0
0.64
1.30
4.2
0.69
1.475
4.4.
0.77
1.375
3.8
0.56
1.400
4.4
0.77
1.340
3.8
0.58
i n t e r m e d i a t e coupl4ng [51
17%
+
3
H4
9
1 +0.007,9
0.801~,+
9
7 >
C r y s t a l - F i e l d ground s t a t e (R minimum)
N ~ ~ 5 f+4 : 0.90]4,+3>
+
0.4414,-1>
Table I. Wave f u n c t i o n information used i n c a l c u l a t i n g p f : RS s t a t e s , i n t e r m e d i a t e
1~,m> The agreement
c o u p l i n g s t a t e s o r c r y s t a l - f i e l d ground - s t a t e given as2
1
(pfobs)2]1'2 o r
w i t h experiment i s given by R = [i - (pfobs
pfcal c ) /i
2
1
1
x2 = N-P C 7 (ufobs- "fcalc)
.,The 02
sum i s over a l l r e f l e c t ~ o n s (N) and o i s t h e
-
experimentaY u n c e r t a i n t y on
k :,
.
ufobs.
---------
As f o r t h e a c t i n i d e i o n s the s p i n - o r b i t i n t e r a c t i o n tfs, does n o t s a t i s f y t h e
<< H ) f o r RS c o u p l i n g scheme, we t r e e d a 5 f e l e c t r o n s wave-function
c o n d i t i o n (tf
l i n ~ f o r Np4+ and Np4+ ions [61 (aadurnpfion bi I n
i n t h e i n t e r ~ f i ? d i a t e ~ c o u ~scheme
t h e t h e o r e t i c a l expression f o r fcalc (fcalc = <j > + c2 <j2>) c2 was considered as
2
O
4
) t o 1.75 ( IgI2)
f o r Np4' and
an a d j u s t a b l e parameter, v a r y i n g from 1.20-( H
3+
9/2
3
5
from 1:50 ( Ha) t o 2.33 ( I,)
for N
~ The
~ b e~s t f.i t ( f i g . 1 1 ) i s obtained f o r Np
.
and c = 2.10.: t h i s value i s i n good agreement w i t h t h e wave f u n c t i o n c a l c u l a t e d
by c h i n and Lam 161 f o r t h e 5 f 4 c o n f i g u r a t i o n (80% 514, 17% 3 ~ 4 ) .
Table I, Figs. I and I1 show t h a t t h e c a l c u l a t i o n s , w i t h and w i t h o u t intermed i a t e coupling, reproduce t h e experimental value w i t h n e a r l y t h e same agreement.
Fig. I shows a l s o t h a t t h e c a l c u l a t e d curves, corresponding t o Np5+,Np4+ o r Np3+,
are w e l l separated f o r o n l y t h e low values o f sinB/A , where no observation can be
obtained : so, w i t h o u t any f u r t h e r i n f o r m a t i o n on t h e 5 f moment, t h e d i p o l e approximation i s n o t a b l e t o g i v e t h e neptunium i o n i z a t i o n s t a t e .
The 5f c a l c u l a t e d moment,^
, i s given i n Table I : i t v a r i e s from 1.30 uB t o
1 . 5 0 ~ These r e s u l t s correspon8"g a s t r o n g r e d u c t i o n o f t h e n e p t u n i u 9 f r e e i g n
and
ma neeic moment : g J i s r e s p e c t i v e l y equal t o 2.4, 3.27 and 3.2 f o r Np , Np
Npg+. T h i s r e d u t t i o i may be explained by t h e c r y s t a l f i e l d i n t e r a c t i o n HCEF t h a t we
have n o t taken i n t o account up t o now.
.
J O U R N I ~ L DE PHYSIQUE
F i .II.R (see Table I ) as a
*on
o f c2 when
= c j > + c2 <j2> The
fcalc
o
arrows i n d i c a t e c2 values f o r
RS c o u p l i n g scheme (Np4+ and ~ p ~
f r e e i o n s ) . For ~ p 4 + , t h e best
f i t ( R minimum) corresponds t o
1.90,which i s o u t s i d e o f t h e
:?l;wed
range (1.20, 1.75) f o r
i n t e r m e d i a t e c o u p l i n g scheme.
.
111. Magnetic form f a c t o r o f neptunium : c r y s t a l f i e l d wave f u n c t i o n f o r 5 f
electrons ?
A f t e r Hc and HSo, t h e n e x t most important i n t e r a c t i o n t o condider i s HCEF. I n a
t e t r a ~ o n a lsystem ( f o r Np As2), t h i s i n t e r a c t i o n i s s p e c i f i e d by 5 parameters
:B :
where 0: a r e the Stevens e q u i v a l e n t operators. I n a l l our c a l c u l a t i o n s i n v o l v i n g the
c r y s t a l f i e l d , we assume H >> H >> H EF and a q u a n t i z a t i o n a x i s p a r a l l e l t o t h e
-f
c a x i s (easy magnetizationCaxis
Np $A!
and t h e d i r e c t i o n of fl i n our p o l a r i z e d
neutron experiment ).
a?
When comparing pfobs and ufcalc
we s y s t e m a t i c a l l y i n v e s t i g a t e t h e p o s s i b l e c r y s -
t a l - f i e l d + exchange ground s t a t e wave f u n c t i o n s o f N
with
~ and
~ +N
~ :~I@+ =
=
c
m m lJ,m>
and
The best f i t between theory and experiment i s obtained f o r ~ p w~i t h +
= 0.90 14,+3> + 0.4414,-1> (See Table I and F i g u r e 111). Ne have then
ucalc = 1 - 3 4 uB.
I n t h e case o f Np4+, the lower value o f R (Table I ) i s obtained w i t h
9
9
1
7
+ ->
+ 0.80 IT,9 + 7>
+ 0.00 17,9 - P>,
l e a d i n g t o pcalc = 1 . 4 0 ~ ~ .
2
2
]cp> = 0.60
I-,
From [I]
we know t h a t NpAsp presents a s t r o n g magnetic a n i s o t r o p y w i t h
as the
easy a x i s . The c a l c u l a t e d Iw must reproduce t h i s p r o p e r t y
; any a (4,?3>+ b14,+1>
i s convenient f o r m a g n e t o c r y s t a l l i n e anisotropy. I n the case of
9
9
0
I
0
7
a17, t 7 > + a/;?, k2> + +I+,
t2>, n a g n e t o c r y s t a l l i n e a n i s o t r o p y i s o n l y obtained f o r
+
-
.
1.75
NPAS2
%
6 y + !62 = 0, a c o n d i t i o n
whxch i s n o t f u l f i l l e d w i t h
a =0.60,8 =0.80 and y = 0 .
4+
However, i n t h e case o f Np ,
a n i s o t r o p i c exchange i n t e r a c t i o n s may e x p l a i n t h e
s t r o n g magnetic a n i s o t r o p y .
So, w i t h i n a c r y s t a l - f i e l d
model a p p l i e d t o an a c t i n i d e
ion, i t i s again n o t p o s s i b l e
t o decide between 3+ and 4+
Np s t a t e s .
g
1.25
1.00
The most d i r e c t method
t o t e s t CEF model c o u l d be
t o measure t h e CEF energy
' t r a n s i t i o n s w i t h neutron
I spectroscopy : u n f o r t u n a t e l y
these measurements a r e n o t
p r e s e n t l y p o s s i b l e due t o
t h e low s i z e o f t h e a v a i l a b l e
1 Np As2 c r y s t a l s .
-
0.75
0.50
0.25
Fig.111. Magnetic form f a c t o r
o f neptunium (Np As2 T=4.2 K) :
experimental r e s u l t s
and
calculated p f (0) f o r ~ p 3 +
( c r y s t a l - f i e l d wave f u n c t i o n :
0.9014,+3> + 0.4414,-1>)
(4)
0.00
-0.25
-
0.00
I\!.
0.20
O.LO
0.60
0.80
SIN(THETA l/Un ( A - 1 I
1.00
C r y s t a l f i e l d model.
A t e n t a t i v e approach t o f i n d t h e c r y s t a l f i e l d parameter ,:B
and then t h e CEF
energy l e v e l s and eigenstates, has been c a r r i e d o u t i n terms o f an e l e c t r o s t a t i c
model which takes i n t o account the c h a r a c t e r i s t i c l a y e r s t r u c t u r e o f t h i s compound
[TI.
I n f a c t , an accurate a n a l y s i s o f t h e CEF c o n t r i b u t i o n s f o r t h e NpAs2 c r y s t a l
s t r u c t u r e (anti-Fe2As) suggests t h a t t h e most i m p o r t a n t c o n t r i b u t i o n t o t h e Npc e n t r a l i o n comes from t h e i o n s i n the nearest c r y s t a l plahes.
T h i s type o f s t r u c t u r e , which i s s c h e m a t i c a l l y
shown i n t h e f i g u r e , i s composed of sheets o f
c a t i o n s and anions, which a r e stacked i n t h e
f o l l o w i n g sequence along t h e c - a x i s :
-X-M-
Y - Y - M - X -
( I n t h e case o f Np Asg, M E Np, X E AsI,
Y 5 AsII).
The M and Y atoms a r e v e r y close, so t h a t
t h e s t r u c t u r e can be described as composed of
M - Y - Y - M l a y e r s , separated from each other
by a simple sheet of X atoms. The atoms i n the
l a y e r s a r e c h a r a c t e r i z e d by p r e v a l e n t l y i o n i c
mutual coup1 i n g [81.
C7-298
JOURNAL DE PHYSIQUE
Moreover, the basal planes of the unit c e l l s , which are b u i l t up with X atoms
e s s e n t i a l l y covalently bonded, can provide a good screen from the outer ions, without
contributing substantially t o the crystal f i e l d .
This "layer" model i s supported also from the r e s u l t s f o r the e l e c t r i c a l r e s i s t i v i t y in similar Uranium compounds (UP2,UAsz,USb ) , where the conduction i s three
times higherin the basal plane than in the perpen%iculardirection [91.
The hypothesis underlying the application of the e l e c t r o s t a t i c approximation
being precisely defined in the framework of the "layer" model, i t was then possible
to study the behaviour of the energy levels f o r the CEF-splitted ground multiplet
of Npn++, as a function of the charge of the As ions in the layer.
The principal r e s u l t s of t h i s approach a r e the following :
7
1 N
h3 con~igwiatcon: When a wavefunction of the type a l ' p9 + 6 l *1p + - 7
'
i s the ground s t a t e , i t i s always too rich in I?;>
component, t o account f o r the low
value of the saturation moment us, which cannot be obtained in a selfconsistent way,
when the molecular f i e l d i s considered.
However, a c l e a r tendency t o a decreasing of p i s shown as the charge of the
As-ions in the s i t e s of type I1 approach the charac2eristic ionic value of -3, in
the interval (-2,-3).
This situation corresponds in f a c t t o a quasi-cubic CEF-Hamiltonian, with a
ground s t a t e made up principally from the r -doublet of cubic symmetry, which would
lead t o us = 1.33 PB ( i n RR-coupling schemes.
Moreover, the ground s t a t e which provides the best f i t to the neutron form
factor, in the hypothesis Np4+, i s of the T6-type rather than of the rg type.
2 ) NP3+ d4 condLgwu&Lon : The ground mu1 t i p l e t of the f 4 configuration (RS scheme)
i s spliL into 5 s i n g l e t s and 2 doublets by the tetragonal CEF-Hamiltonian.
The quoted e l e c t r o s t a t i c model shows t h a t a r t doublet i s clearljf the groudd
s t a t e f o r the value -3 of the ionic charge of the ~ l ~ ~ - i oThe
n scorresponding eigenfunction i s of the type :
al+3> + b / i l >
with coefficients a and b in good agreement with those found from the magnetic form
factor analysis, and also accounting f o r the saturation moment value.
3 ) N 5',
con igigunation : The energy-levels scheme obtained from the CEF electroc
statyc mogel isdnever consistent with a ground s t a t e of the type : al?3> + bl+l> ,
whlch on the other hand could f i t the experimental form factor in the Np5+ hypothesis.
This argues agaihst the choice of the 5+ charge s t a t e .
Yl+
V. Discussion and conclusion
The polarized neutrons measurements on NpAs2 have been analyzed, assuming localized 5f electrons with different possible neptunium ionization s t a t e s . This analysis,
e i t h e r w i t h a f r e e ion o r w i t h CEF- wave functions, did not enable a choice t o be
made between the 3+ and 4+ charge s t a t e s . The CEF analysis hhs been supplemented by
an e l e c t r o s t a t i c model.
Although the Np3+ hypothesis i s more a t t r a c t i v e from the point of view of a
crystal-field interpretation of the ground-state-properties of NpAs2, the possibility
of an Np4+ ion, as supported from Mossbauer spectroscopy [5land structural considerations[lO], cannot be disregardered.
For Np4+, the e l e c t r o s t a t i c model seems t o be too rough t o completely account
for the low ps value, suggesting the presence of more involved physical effects ( i n
agreement w i t h the complex magnetic behaviour of t h i s compound in the ordered phases).
More experimental information i s needed t o obtain information on the nature (CEF O r
exchange) of the anisotropy. In particular, magnetization in high f i e l d s and polarized neutrons measurements on a single crystal o f NpAs2, in the temperature range
around TN, would be useful.
Moreover w i t h more accurate experimental data, i t would be i n t e r e s t i n g t o take i n t o
account i n t e r m e d i a t e coup1 i n g e f f e c t s together w i t h CEF.
Acknol edgments
We would l i k e t o thank Dr F. Tasset o f the I n s t i t u t Laue Langevin f o r h i s
appreciated h e l p d u r i n g experiment.
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