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
Trang 1Intersublattice 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(Fe1xTix)2, R(Fe1xTix)3 and RFe12xVx (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 AGdFeand Mdis 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)
inter-metallic 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
rare-earth 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-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 proper-ties 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–(Fe1xLTx) 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
*Corresponding author Tel./fax: +84-4-8584438.
E-mail address: duc@netnam.org.vn (N.H Duc).
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
Trang 2interactions in R(Fe1xTix)2 (0XxX0:065),
R(Fe1xTix)3 (0XxX0:10) and RFe12xVx
(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(Fe1xVx)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
Hex¼ SARTSRST) was derived in the same way
as in our previous papers [4,5]:
ðART=kBÞ2
¼ 9ðTC TRÞðTC TTÞ=4ZRTZTRGRGT; ð1Þ
where TC is the Curie temperature, TR and TT
represent the contribution to TCdue to R–R and
T–T interactions, respectively GRis the de Gennes
factor ðgR 1Þ2JðJ þ 1Þ for rare-earth atoms GT;
the corresponding factor for the transition metal,
GT¼ p2
eff=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
RNi2compounds (TCðGdNi2Þ ¼ 75 K) and TTwas
taken as the Curie temperatures of the
correspond-ing Lu (or Y) compounds Finally, ZRT
(respec-tively, ZTR) is the number of TðRÞ neighbours of
one R ðTÞ atom The value of ZRTand ZTRis 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
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
where Zm is the magnetic valence, 2Nspm is the number of s, p electrons in the spin-up state band The value of Nspm usually ranges from 0.3 to 0.45mB
[10] At present, as mentioned below, we use
Nm¼0:45:
Table 1 The values of the d-sublattice magnetic moment Md(in m B /at), Curie temperature T C (in K), contribution of the 3d–3d interactions to ordering temperature T T (in K) and Gd–Fe exchange parameter A GdFe (in 1023J) for Gd(Fe 1x Ti x ) 2 , Gd(Fe 1x Ti x ) 3 and GdFe 12x V x compounds
R(Fe 1x Ti x ) 2
R(Fe 1x Ti x ) 3
R(Fe 12x V x )
x ¼ 0:0 2.07 a 768 a 670 a 11.3
a
Data extrapolated for the hypothetical compounds.
Trang 3In 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 Gdy 0Fe1yLTy 00
(y ¼ y0þ y00), Zm is then determined by the
chemical values ZFeð¼ 8Þ; ZGdð¼ 3Þ; ZTið¼ 4Þ and
ZVð¼ 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
Zm¼ 2Ndmð1 yÞ ZFeð1 yÞ
The calculated (mean) magnetic moment is
presented in Fig 1 as a function of Zm for the
compounds of R(Fe1xTix)2, R(Fe1xTix)3 and
RFe12xVx (R=Gd, Lu and Y) The continuous
line in Fig 2 was obtained with Nsp¼ 0:45:
Qualitative agreement is found between the
experimental and calculated values Both the
calculated and experimental mean
magnetic-mo-ment shows a similar reduction with increasing R
and LT (Ti,V) concentration This finding stresses
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(Al1xLTx)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-exis-tence 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(Fe1xLTx) 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,
0.0
0.5
1.0
1.5
2.0
Magnetic valence (Z m )
Gd(Fe ,Ti) Y(Fe ,Ti) Gd(Fe ,Ti) Y(Fe ,Ti) Lu,Y(Fe ,V)
2 2 3 3 12
Fig 1 Magnetic moment as a function of the magnetic valence
in the pseudo-binary R(Fe 1x Ti x ) 2 , Gd(Fe 1x Ti x ) 3 and
R(Fe V ) systems.
5 10 15 20 25
(R and LT) concentration
A Gd
Gd(Fe ,Ti) Gd(Fe ,Ti)
2 3
Fig 2 A GdFe as a function of the R- and (Ti,V) concentration
in the binary Gd–Fe and pseudo-binary Gd(Fe 1x Ti x ) 2 , Gd(Fe 1x Ti x ) 3 and Gd(Fe 12x V x ) systems.
Trang 4the variation of AGdFe obtained for these three
investigated Gd–Fe–Ti(V) systems follows a
com-mon law when described in the relation with
R- and LT concentration, i.e in the relation with
y ¼ ðy0þ y00Þ (see Fig 2) The influence of
introdu-cing 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 Rstates
This work was partly supported by the State
Programme of Fundamental Research of Vietnam,
under project 420.301
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5 10 15 20 25
Gd(Fe,Ti) Gd(Fe,Ti) Gd(Fe,V) 12
2 3
Fig 3 Relationship between A GdFe and M d in in the pseudo-binary R(Fe 1x Ti x ) 2 , Gd(Fe 1x Ti x ) 3 and R(Fe 12x V x ) systems.