DSpace at VNU: Intersublattice exchange coupling in rare earth-iron-based R-Fe-LT intermetallics (LT = light transition elements Ti, V)

Physica B 319 (2002) 17–20

Intersublattice exchange coupling in rare earth–iron-based
R-Fe–LT intermetallics (LT=light transition elements Ti, V)
N.H. Duca,*, N.D. Tana, B.T. Conga, D. Givordb
a

Faculty of Physics, Vietnam National University, 334-Nguyen Trai Road, Thanh Xuan, Hanoi, Viet Nam
b
Laboratoire de Magnetisme Louis N!eel, CNRS, BP-166, 38042 Grenoble Cedex 9, France
Received 8 February 2002

Abstract
The values of the d-sublattice magnetic moment (Md ) and the Gd–Fe exchange coupling parameter (AGdFe ) were
derived for the R(Fe1ÀxTix)2, R(Fe1ÀxTix)3 and RFe12ÀxVx (R=Gd, Lu and Y) compounds. As the Ti(V)
concentration increases, a tendency of Md to decrease is found, whereas AGdFe is enhanced. These behaviours are
discussed in terms of the similar role of the 3d(Fe)–5d(R) and 3d(Fe)–3d(Ti,V) hybridizations on the negative
polarization of both the 5d(R) and 3d(Ti,V) electrons. The arguments are reinforced by the analysis of the magnetic
valence and a linear relationship between AGdFe and Md is presented. r 2002 Elsevier Science B.V. All rights reserved.
Keywords: Rare earth–transition metal compounds; Exchange interactions; Hybridization effects

The understanding of magnetism in rare earth
(R)—heavy transition-metal (HT=Fe,Co) intermetallic compounds has considerably progressed
in the last two decades [1–3]. It has been realized
that the specific magnetic behaviours observed
result not only from the 3d and 4f electrons
independently, but also from their association,
especially from 4f–3d exchange interactions. The
values of the 3d-magnetic moments as well as
the strengths of the 4f–3d interactions depend on
the nature of both the transition metal and the rare

earth element. These physical parameters show
systematic variations as a function of the rareearth concentration [1,4]. These were discussed by
Duc et al. [5] on the basis of the model proposed
by Campbell [6] and reinterpreted by Brooks et al.
[7]. Accordingly, the T-magnetic moment de*Corresponding author. Tel./fax: +84-4-8584438.
E-mail address: (N.H. Duc).

creases whereas the strength of the 4f–3d coupling
increases as the degree of 3d–5d hybridization
increases. The role of the light 3d elements,
LT=Ti, V,y, in establishing the magnetic properties is not understood quantitatively, however. In
the 1:12 system, beside the phase stablising role,
the LT elements have a pronounced influence on
the 4f–3d exchange interaction strength [8,9]. In
Ref. [9], the enhancement of the 4f–3d exchange
coupling associated with the introduction of LT
elements in the compounds was ascribed to the
fact that 5d(R)–3d(LT) hybridization must be
weaker than 5d(R)–3d(Fe,Co) hybridization as
shown by the non-existence of R–LT compounds.
As a consequence, in R–(Fe1ÀxLTx) compounds,
the fraction of electrons which can participate in
3d(R)–3d(Fe) hybridization must increase with x:
In this paper, we discuss systematically the
influence of LT substitution on the d-sublattice
magnetic moments and the 4f(R)–3d(Fe) exchange

0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 1 0 1 - 8

18

N.H. Duc et al. / Physica B 319 (2002) 17–20

interactions in R(Fe1ÀxTix)2 (0XxX0:065),
R(Fe1ÀxTix)3 (0XxX0:10) and RFe12ÀxVx
(0XxX4:0) compounds with R=Gd, Lu and Y.
The compounds were prepared by arc-melting.
Their magnetic properties were investigated by
means of magnetization measurements in the
temperature range from 4.2 to 800 K and in
magnetic fields up to 10 T. The d-sublattice
magnetic moment (Md ) was deduced from the
isotherm magnetization measured at 4.2 K. The
ordering temperature (TC ) was determined from
the thermal variation of magnetization in an
applied field of 0.1 T. Md and TC in various
compounds are collected in Table 1. It is seen that
in all three investigated systems, TC and Md
decrease with increasing x: Similar result was
reported earlier for R(Fe1ÀxVx)12 [8]. In these
three pseudo-binary compounds, the influence of
the LT elements on the magnetic behaviours seems
thus to be similar.
The value of the intersublattice exchange
coupling parameter ART (in the Hamiltonian
Hex ¼ ÀSART SR ST ) was derived in the same way
as in our previous papers [4,5]:
ðART =kB Þ2

¼ 9ðTC À TR ÞðTC À TT Þ=4ZRT ZTR GR GT ;

ð1Þ

where TC is the Curie temperature, TR and TT
represent the contribution to TC due to R–R and
T–T interactions, respectively. GR is the de Gennes
factor ðgR À 1Þ2 JðJ þ 1Þ for rare-earth atoms. GT ;
the corresponding factor for the transition metal,
GT ¼ p2eff =4: peff is the T-effective paramagnetic
moment, obtained by assuming that the ratio
between peff and the spontaneous moment (i.e.
Md ) equals about 2 [4,5]. For these three series of
compounds, TR was determined from TC of the
RNi2 compounds (TC ðGdNi2 Þ ¼ 75 K) and TT was
taken as the Curie temperatures of the corresponding Lu (or Y) compounds. Finally, ZRT (respectively, ZTR ) is the number of TðRÞ neighbours of
one R ðTÞ atom. The value of ZRT and ZTR is given
in Ref. [4]. On the basis of Eq. (1), the Gd–Fe
exchange-coupling parameter was evaluated for all
investigated compounds. The obtained results are
listed in Table 1. AGdFe strongly increases with
increasing Ti(V) concentration.

Table 1
The values of the d-sublattice magnetic moment Md (in mB/at),
Curie temperature TC (in K), contribution of the 3d–3d
interactions to ordering temperature TT (in K) and Gd–Fe
exchange parameter AGdFe (in 10À23 J) for Gd(Fe1ÀxTix)2,
Gd(Fe1ÀxTix)3 and GdFe12ÀxVx compounds
TC

TT

AGdFe

Compounds

Md

R(Fe1ÀxTix)2
x ¼ 0:0
0.015
0.030
0.045
0.050
0.065

1.5
1.4
1.35
1.32
1.30
1.26

780
775
768
760
755
750

495
490
485
480
475
470

16.2
17.6
17.2
18.3
18.6
19.3

R(Fe1ÀxTix)3
x ¼ 0:0
0.025
0.050
0.075
0.10

1.75
1.64
1.51
1.37
1.20

712
705

697
670
660

505
502
496
489
485

12.1
12.7
14.1
17.9
18.5

R(Fe12ÀxVx)
x ¼ 0:0
1.0
2.0
2.5
3.0
3.5
4.0

2.07a
1.85
1.60
1.45
1.30

1.15
0.90

768a
682.5
597.5
555
512.5
476
427.5

670a
579
488
442.5
397
351
306

11.3
12.4
13.0
14.5
16.2
18.8
22.5

a

Data extrapolated for the hypothetical compounds.

We suggest that the above behaviours can be
understood in terms of hybridization between the
various d-states in the compounds. Let us discuss
first the value of the 3d moment, Md ; in these
systems on the basis of the magnetic valence model
[10,11]. In this approach, the magnetic moment of
an alloy is not considered in terms of magnetic and
non-magnetic atoms, but rather in terms of the
magnetic moment averaged over all atoms present
in the alloy. The mean magnetic moment (M) is
then expressed as
m
M ¼ Zm þ 2Nsp
;

ð2Þ

m
where Zm is the magnetic valence, 2Nsp
is the
number of s, p electrons in the spin-up state band.
m
The value of Nsp
usually ranges from 0.3 to 0.45mB
[10]. At present, as mentioned below, we use
m
Nsp
¼0:45:

N.H. Duc et al. / Physica B 319 (2002) 17–20

Zm ¼ 2Ndm ð1 À yÞ À ZFe ð1 À yÞ
À ðy0 ZR þ y00 ZLT Þ:

ð3Þ

The calculated (mean) magnetic moment is
presented in Fig. 1 as a function of Zm for the
compounds of R(Fe1ÀxTix)2, R(Fe1ÀxTix)3 and
RFe12ÀxVx (R=Gd, Lu and Y). The continuous
line in Fig. 2 was obtained with Nsp ¼ 0:45:
Qualitative agreement is found between the
experimental and calculated values. Both the
calculated and experimental mean magnetic-moment shows a similar reduction with increasing R
and LT (Ti,V) concentration. This finding stresses

Magnetic moment (µB/at)

2.0

1.5

1.0

Gd(Fe,Ti) 2
Y(Fe,Ti) 2
Gd(Fe,Ti) 3

0.5

Y(Fe,Ti) 3
Lu,Y(Fe,V)12
0.0
-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Magnetic valence (Z m )

Fig. 1. Magnetic moment as a function of the magnetic valence
in the pseudo-binary R(Fe1ÀxTix)2, Gd(Fe1ÀxTix)3 and
R(Fe12ÀxVx) systems.

25
Gd(Fe,Ti) 3

20

Gd(Fe,V)12

-23

J)

Gd(Fe,Ti) 2

AGdFe (10

In this model of the magnetic valence, the Gd–
Fe–LT can be considered as alloys of the transition
metals Fe with Gd and LT elements. In this case,
not only the transfer of the rare earth 5d,6s(Gd)
electrons, but also the contribution of the 3d(LT)
electrons to the 3d(Fe) band can reduce the
average magnetic moment. Redenoting the
Gd–Fe–LT intermetallics as Gdy0 Fe1ÀyLTy00
(y ¼ y0 þ y00 ), Zm is then determined by the
chemical values ZFe ð¼ 8Þ; ZGd ð¼ 3Þ; ZTi ð¼ 4Þ and
ZV ð¼ 5Þ [10,11] of the corresponding Fe, Gd, Ti
and V elements, respectively, in the alloys and by
the number of the d electrons in the spin-up state
band (Ndm ), which is 5 per atom for a strong
ferromagnet

19

15

10

5
0.0

0.2

0.4

(R and LT) concentration
Fig. 2. AGdFe as a function of the R- and (Ti,V) concentration
in the binary Gd–Fe and pseudo-binary Gd(Fe1ÀxTix)2,
Gd(Fe1ÀxTix)3 and Gd(Fe12ÀxVx) systems.

the related contributions of the 5d(R) and the
3d(LT) electrons on the magnetic properties of the
Gd–Fe–LT alloys. Both the 5d(R) and 3d(LT)
electrons are found to be negatively polarized with
respect to the 3d(Fe) ones. This is in agreement
with Campbell’s model [5] treating the rare earth
in R–M (M=Fe, Co or Ni) compounds as light
transition elements. In a recent work, Chelkowska
et al. [12] have calculated the electronic structure
for the Gd(Al1ÀxLTx)2 (LT=V,Ti) and found that
a ferromagnetic coupling between 5d(R) and
3d(LT) moments is favoured. 3d(Fe)–3d(LT)
coupling must then be antiferromagnetic as
observed here.
Whereas the variation of the magnetic moments
in the compounds was discussed above in terms of

a global model in which all electrons are included,
the understanding of exchange interactions in
these systems requires that the role of the various
electrons is discussed separately. The non-existence of compounds between the rare earth and LT
elements, such as Ti and V, suggests that in R(Fe–
LT) compounds, the 5d states hybridize more with
the 3d-Fe states than with the 3d-LT states. In a
given series of R(Fe1ÀxLTx) compounds, as x
increases, more electrons can participate in
5d–3d(Fe) hybridization, thus leading to the
observed increase in R–Fe coupling [8,9]. Actually,


N.H. Duc et al. / Physica B 319 (2002) 17–20

the variation of AGdFe obtained for these three
investigated Gd–Fe–Ti(V) systems follows a common law when described in the relation with
R- and LT concentration, i.e. in the relation with
y ¼ ðy0 þ y00 Þ (see Fig. 2). The influence of introducing LT elements in R–Fe compounds has two
complementary effects. On the one hand, 3d(LT)
electrons hybridize with 3d(Fe) electrons, on the
other hand, each LT atom introduced in the lattice
replaces the Fe atom and thus 3d–5d hybridization
per Fe atom is favoured. A consequence of this
hybridization is that more spin-down 3d(Ti,V)electrons appear in the lattice. The present
enhancement of the Gd–Fe exchange coupling
may be related to the increased number of
negatively polarized spins around the magnetic R
atoms.
The variation of AGdFe as a function of Md is

presented in Fig. 3 for the pseudo-binary Gd–Fe–
LT compounds. An almost linear decrease of
AGdFe is observed with increasing Md : This
behaviour is a result of the influence of the same
hybridization effects on the d-sublattice magnetic
moment and 4f–3d exchange [13].
In concluding, we would like to point out that,
the nature of LT elements plays an important role
in establishing the magnetic properties of the
pseudo-binary R–Fe–LT. Unlike remarks in the
literature ([7] and references therein) suggesting
that 4f–5d exchange is important, the mechanism
of R–Fe exchange interactions must be understood
on the basis of the global spin polarization induced
by hybridization between d Fe, LT and R states.
This work was partly supported by the State
Programme of Fundamental Research of Vietnam,
under project 420.301.

References
[1] J.J.M. Franse, R.J. Radvanski, in: K.H.J. Buschow (Ed.),
Handbook of Magnetic Materials, Vol. 7, Elsevier Science,
Amsterdam, 1993, p. 307.

25

20

AGdFe (10 -23 J)

20

15

Gd(Fe,Ti)2

10

Gd(Fe,Ti)3
Gd(Fe,V)12

5
0.5

1.0

1.5

2.0

M d (µ B/at)
Fig. 3. Relationship between AGdFe and Md in in the pseudobinary R(Fe1ÀxTix)2, Gd(Fe1ÀxTix)3 and R(Fe12ÀxVx) systems.

[2] H.S. Lee, J.M.D. Coey, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Vol. 6, Elsevier Science,
Amsterdam, 1991, p. 1.
[3] N.H. Duc, P.E. Brommer, in: K.H.J. Buschow (Ed.),
Handbook of Magnetic Materials, Vol. 12, Elsevier
Science, Amsterdam, 1999, p. 259.
[4] N.H. Duc, in: K.A. Gschneidner Jr., L. Eyring (Eds.),
Handbook on the Physics and Chemistry of Rare Earths,

Vol. 24, Elsevier Science, Amsterdam, 1997, p. 338.
[5] N.H. Duc, T.D. Hien, D. Givord, J.J.M. Franse, F.R. de
Boer, J. Magn. Magn. Mater. 124 (1993) 305.
[6] I.A. Campbell, J. Phys. F 2 (1972) L47.
[7] M.S.S. Brooks, B. Johansson, in: K.H.J. Buschow (Ed.),
Handbook of Magnetic Materials, Vol. 7, Elsevier Science,
Amsterdam, 1993.
[8] X.P. Zhong, F.R. de Boer, D.B. de Mooij, K.H.J.
Buschow, J. Less-Common Metals 163 (1990) 305.
[9] N.H. Duc, M.M. Tan, N.D. Tan, D. Givord, J. Teillet,
J. Magn. Magn. Mater. 177–181 (1998) 1107.
[10] A.R. Williams, V.L. Moruzzi, A.P. Malozemoff, K.
Terakura, IEEE Trans. Magn. 19 (1983) 1983.
[11] J.P. Gavigan, D. Givord, H.S. Li, J. Voiron, Physica B 149
(1988) 345;
J.P. Gavigan, D. Givord, H.S. Li, J. Voiron, Physica B 158
(1996) 719.
[12] G. Chelkowska, H. Ufer, G. Borstel, M. Neumann,
J. Magn. Magn. Mater. 157–158 (1996) 719.
[13] N.H. Duc, Phys. Stat. Sol. (b) 175 (1993) K63.