R–Fe R⫽rare earth based alloys offer the possibility to develop very large magnetostriction at room temperature.. The stronger R–FeCo exchange energies should then lead to an enhance-men
Trang 1Magnetic and magnetostrictive properties in amorphous ( Tb 0.27 Dy 0.73 )( Fe 1−x Co x
) 2 films
N H Duc, K Mackay, J Betz, and D Givord
Citation: Journal of Applied Physics 87, 834 (2000); doi: 10.1063/1.371950
View online: http://dx.doi.org/10.1063/1.371950
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/87/2?ver=pdfcov
Published by the AIP Publishing
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Trang 2Magnetic and magnetostrictive properties in amorphous
„ Tb0.27Dy0.73…„ Fe1ⴚxCox…2 films
N H Duca)
Cryogenic Laboratory, Faculty of Physics, National University of Hanoi, 334-Nguyen Trai, Thanh Xuan,
Hanoi, Vietnam
K Mackay, J Betz, and D Givord
Laboratoire de Magne´tisme Louis Ne´el, CNRS, 38042 Grenoble, Cedex 9, France
共Received 5 May 1999; accepted for publication 16 September 1999兲
Magnetic and magnetostrictive properties have been investigated for amorphous (Tb0.27Dy0.73)
(Fe1⫺xCox)2 thin films An increase in the 3d magnetic moment due to the enhancement of T–T
interactions in substituted 共Fe, Co兲 alloys was found This leads to stronger R–共Fe, Co兲 exchange
energies and then to enhancements of R–sublattice magnetization as well as magnetostriction in
these amorphous R共Fe, Co兲 thin films In addition, a well-defined in-plane anisotropy is created by
magnetic-field annealing for the Co-rich films A large magnetostriction of 480⫻10⫺6developed in
low fields of 0.3 T was observed for films with x⫽0.47 after magnetic-field annealing The differing
roles of Fe and Co atoms on the magnetization process have also been discussed © 2000
American Institute of Physics. 关S0021-8979共99兲06624-4兴
I INTRODUCTION
Over the past few years there has been a growing interest
in magnetic thin films with large magnetostriction.1–3 This
interest is motivated by the potential such films show for use
in microsystems actuators
R–Fe (R⫽rare earth) based alloys offer the possibility to
develop very large magnetostriction at room temperature
This is due to the highly aspherical 4 f orbitals remaining
oriented by the strong coupling between R and Fe moments
In order to exploit this property at reasonably low fields, it is
essential to have low macroscopic anisotropy A first route to
low anisotropy is by using cubic compounds in which the
second-order anisotropy constants vanish This is the case for
the RFe2laves phase compounds of which TbFe2共terfenol兲,
a ferrimagnet with T C⫽710 K, is probably the best known,4
having s⫽1753⫻10⫺6 The anisotropy can be further
de-creased by substitution of Tb and Dy in these compounds
This is due to Dy and Tb having opposite signs of the
Steven’s J coefficient and thus their contribution to the
fourth-order anisotropy being of opposite sign This leads to
the magnetostriction, albeit less than in pure TbFe2, being
saturated in much lower fields This is the case for the
terfenol-D material, the crystalline 共Tb0.27Dy0.73兲Fe2
com-pound, which has found many applications as high-power
actuators
An alternative route to low macroscopic anisotropy is by
using amorphous materials In Fe-based amorphous alloys,
both positive and negative exchange interactions exist5
lead-ing to magnetic frustration in the Fe sublattice In amorphous
a-YFe alloys, this results in a concentrated spin-glass
behav-ior below room temperature In a-RFe alloys, where R is a
magnetic rare earth, the additional contributions of R–Fe
ex-change and local crystalline electric-field interactions lead to the formation of sperimagnetic structures.5 The ordering temperatures are above room temperature 关T C⫽410 K for
a-Tb0.33Fe0.66共Refs 6 and 7兲兴 It is, however, still rather low
and is thus detrimental to large magnetostrictions being ob-tained in such materials at room temperature
Actually, with a view to obtaining large magnetostric-tions in the amorphous state, it is interesting to consider the
equivalent a-RCo-based alloys Although crystalline RCo2
compounds order below 300 K as Co is merely paramagnetic,8 the amorphous state stabilizes a moment on the Co sublattice due to band narrowing These Co moments are strongly ferromagnetically coupled A sperimagnetic structure occurs as in a-RFe alloys but the ordering tempera-ture is now raised up to 600 K 共Ref 7兲 for Tb0.33Co66
Re-cently, we have studied a-Tb xCo1⫺x and shown that large
magnetostrictions of b␥,2⫽300⫻10⫺6 at 300 K are obtained
for x⬃0.33.9
In general, however, R–Fe exchange energies are larger than the equivalent R–Co interaction energies.10 This arises from the fact the Fe moment is significantly larger than the
Co one, while the R–T intersublattice exchange constant (T⫽transition metal) is approximately the same for T⫽Fe
and Co In addition, the T–T interactions tend to be stronger
in 共FeCo兲- than in either Fe- or Co-based alloys.11 This
re-sults in an increase of T C for a given R:T ratio The stronger R–FeCo exchange energies should then lead to an enhance-ment of the R moenhance-ment at room temperature and thus the magnetostriction in these amorphous alloys Recently,
we have studied the magnetostriction in amorphous (Tb1⫺xDyx)(Fe0.45Co0.55)2.1thin films A magnetostriction of
1020⫻10⫺6 was obtained for amorphous
Tb共Fe0.45Co0.55兲2.1.12 Indeed, this is much larger than that seen in other amorphous films of either TbFe or TbCo
a兲Author to whom correspondence should be addressed; electronic mail:
duc@cryolab.edu.vn
834
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Trang 3In the present article, we have studied the influence of
the Fe:Co ratio on the magnetization and magnetostriction of
(Tb0.27Dy0.73)(Fe1⫺xCox)2 We will show that the Fe:Co
ra-tio of 50:50 responds approximately to the optimum
compo-sition for the giant magnetostriction
II EXPERIMENT
The films were prepared by rf magnetron sputtering The
typical power during sputtering was 300 W and the Ar
pres-sure was 10⫺2mbar A composite target was used allowing a
wide range of alloys to be made in a controllable way
with-out a large cost of materials The target consisted of 18
seg-ments of about 20°, of different eleseg-ments共here, Tb, Dy, Fe,
Co兲 These were made by spark cutting pure element disks
They were then assembled and stuck to a Cu sample holder
using silver paint It was verified by Rutherford
backscatter-ing spectroscopy 共RBS兲 and X-ray energy-dispersive
spec-troscopy共XEDS兲 measurements that no Cu and Ag
contami-nation has occurred The target–substrate distance was 8 cm
The substrates were glass microscope cover slips with a
nominal thickness of 150m Both target and sample holder
were water cooled
The ratio of the deposition rates of R⫽Tb, Dy to T⫽Fe,
Co is 0.85 Thus, for the (Tb0.27Dy0.73)(Fe1⫺xCox)2 films
made here, the Tb共Dy兲 and Fe共Co兲 concentrations could, in
principle, be varied in steps of about 14% and 9%,
respec-tively The resulting composition, contamination, and the
composition homogeneity were measured using XEDS and
RBS analyses The thicknesses were measured mechanically
using an ␣-step and the sample mass was determined from
the mass difference of the substrates before and after
sput-tering The typical film thickness was 1.2m X-ray – 2
diffraction showed the as-deposited samples to be
amor-phous
Samples were annealed at 150° and 250 °C for 1 h under
a magnetic field of 2.2 T in order to relieve any stress
in-duced during the sputtering process and to induce a
well-defined uniaxial in-plane anisotropy Subsequent x-ray– 2
diffraction showed no evidence of recrystallization after
an-nealing
The magnetization measurements were carried out using
a vibrating sample magnetometer in a field of up 8 T from
4.2 to 800 K
The magnetostriction was measured using an optical
de-flectometer 共resolution of 5⫻10⫺8rad兲, in which the
bend-ing of the substrate due to the magnetostriction in the film
was measured This allows the magnetoelastic coupling
co-efficient of film共b兲 to be directly determined13,14
using
b⫽␣
L
h s2
h f
E s
where␣is the deflection angle of the sample as a function of
applied field, L is the sample length, and E s ands are the
Young’s modulus and Poission’s ratio for the substrate
which are taken to be 72 GPa and 0.21, respectively h s and
h f are the thicknesses of the substrate and film, respectively
L was typically of the order of 13 mm.
b is proportional to the magnetostriction via the Young’s modulus (E f) and Poisson’s ratio (f) of the film These cannot be reliably measured for thin films However, for comparison, we also give values of calculated using
⫽⫺b共1⫹f兲
where E f ands are taken to be 80 GPa and 0.31, respec-tively
We measured two coefficients at saturation, b储 and b⬜,
which correspond to the applied field, always in the film plane, being, respectively, parallel and perpendicular to the sample length 共i.e., the measurement direction兲 In addition,
the perpendicular direction corresponds to the easy axis in-duced after field annealing The intrinsic material-dependent
parameter b␥,2共or ␥,2兲 is just the difference b储⫺b⬜ 共or 储
⫺⬜, respectively兲
III EXPERIMENTAL RESULTS
A Magnetization
Figure 1 presents the hysteresis loops for several as-deposited (Tb0.27Dy0.73)(Fe1⫺xCox)2 films at 4.2 K The co-ercive fields are very large for all samples and the magneti-zation does not completely saturate even at 8 T Such large coercive fields are typical of amorphous RT alloys at low
temperatures, where R is a non-S state rare earth They are
related to the strong local anisotropy of the R atoms and their random distribution of easy axes present in such sperimag-netic systems The high-field susceptibility (hf) is also typi-cal of sperimagnetic systems and is associated with the clos-ing of the cone distribution of R moments as the field is increased.5
The coercive fields (0H C) reach their highest value of
3.4 T for x⫽0 With increasing Co concentration, coercivity
decreases rapidly down to about 0.5 T for 0.67⭐x⭐1.0 关see
Fig 2共a兲兴 Thehfalso decreases with increasing Co
concen-tration, to a minimum at x⫽0.47 and then slightly increases
with further increasing x.
In all cases, 0H C also decreases with increasing tem-perature关see the inset in Fig 2共a兲兴, while thehfis strongly enhanced This is due to the rapid decrease local anisotropy
of the R atoms as the temperature is increased compared to
FIG 1 Hysteresis loops at 4.2 K for several (Tb 0.27 Dy 0.73 )(Fe 1⫺xCox) 2 thin films:共1兲 ⫺x⫽0, 共2兲 x⫽0.31, and 共3兲 ⫺x⫽1.0.
835
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Trang 4the exchange field In Fig 2共b兲, we present0H C at 300 K
as function of x All the films are magnetically rather soft at
room temperature and there is a maximum in 0H C at x
⫽0.63
The spontaneous magnetization values at 4.2 and 300 K
for the as-deposited (Tb0.27Dy0.73)(Fe1⫺xCox)2 films
ex-trapolated to zero field are shown in Fig 3 At 4.2 K there is
a maximum at x⫽0.47 while at 300 K, within experimental
errors, the magnetization is independent of the Co
concen-tration This is in contrast with the behavior observed for the
corresponding crystalline alloys where M s always shows a
minimum in the middle of the composition range due to the
enhancement of the 3d magnetic moment ( M 3d) In the
amorphous case, however, an increase in M 3d will close the
R-sperimagnetic cone The maximum in M s at x⫽0.47
re-flects that, at low temperature, the enhancement of M 3d is smaller than the associated increase in the magnetization of the R sublattice (具MR典)
Samples were annealed at temperatures between 150 and
250 °C in an applied magnetic field of 2.2 T The field de-pendences of the magnetization before and after annealing
are shown in Fig 4 for x⫽1 For the as-deposited samples,
the magnetization reversal process is progressive and isotro-pic with a rather large coercive field This property is often observed in sperimagnetic systems where domains of corre-lated moments are formed due to the competition between exchange interactions and random local anisotropy These domains, termed Imry and Ma domains,15,16 are oriented more or less at random in zero field but can be reoriented relatively easily under applied field
After annealing, there are a number of clear differences
in the magnetization process First, the coercive field is strongly reduced Figure 2共b兲 shows the coercive field as a
function of composition before and after annealing After annealing at 250 °C,0H C is less than 0.002 T for samples
with x⫽0.0 and 1.0 A slight maximum of0H Caround the middle of the composition range is still observed, however, with0H C⬃0.006 T only Second, for this sample, there is
now a well-defined easy axis with an increased low-field susceptibility These properties are characteristic of systems which show uniaxial anisotropy This field-annealing in-duced anisotropy suggests that a process of single-ion direc-tional ordering17 has occurred, in which there is a local re-orientation of the Tb easy axes along the field direction The composition dependence of this uniaxial anisotropy is, how-ever, more complex and will be discussed further in connec-tion with the magnetostricconnec-tion data The field annealing also causes a reduction in hf, indicating that the cone distribu-tion of the Tb moments is somewhat closed
B Magnetostriction
In general, the comparison of b储and b⬜indicates clearly
the anisotropy state of the sample If the zero-field state is
fully isotropic, then b储⫽⫺2b⬜, and if it is isotropic in the
plane, then b储⫽⫺b⬜.18For a well-defined in-plane, uniaxial system, magnetization reversal under a field applied along the easy axis, occurs by 180° domain-wall displacement
Ne-FIG 2 共a兲 Coercive field 0H cas a function of Co concentration at 4.2 K.
Inset shows the temperature dependence of 0H c for x⫽0.83 共b兲
Coer-cive field 0H c as a function of Co concentration at 300 K: 共1兲 the
as-deposited films, 共2兲 after annealing at 150 °C, and 共3兲 after annealing
at 250 °C.
FIG 3 Variation of spontaneous magnetization as a function of x at 4.2 and
300 K for (Tb 0.27 Dy 0.73 )(Fe 1⫺xCox) 2 thin films.
FIG 4 Hysteresis loops for the 共Tb 0.27 Dy 0.73 兲Co 2 共1兲 as-deposited film and 共2兲 after annealing along induced easy axis and 共3兲 hard axis.
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Trang 5glecting domain-wall contributions, no magnetostriction is
associated with this process Thus, b⬜ should be zero and
b储⫽b␥,2.
Figure 5 shows the effect of annealing on the
magneto-striction for two alloys with x ⫽0.83 and x⫽0 For x⫽0.83
关see Fig 5共a兲兴, we see that annealing increases the ratio of b储
to b⬜ while b␥,2 rests roughly constant This is due to the
creation of an in-plane uniaxial anisotropy as seen from
mag-netization measurements In addition, we see that this
anisot-ropy is completely induced after annealing at 150 °C and is
accompanied by a reduction in the saturation field
Subse-quent annealing at 250 °C simply further reduces the
satura-tion field For the x⫽0 sample 关see Fig 5共b兲兴, we see a
different behavior Before annealing, the approach to
satura-tion is rather slow and the ratio of b储 to b⬜ indicates an
initial anisotropy After annealing, the saturation field is
re-duced and this initial anisotropy is destroyed, leaving the
sample almost isotropic However, b␥,2共measured at 1.8 T兲
actually increases after annealing probably due to the
reduc-tion in the saturareduc-tion field
These differences are reflected across the whole
compo-sition range and the results obtained are summarized in Fig
6共a兲 As outlined above, it is clear that the annealing affects
very differently the Fe-rich alloys compared to the Co-rich
ones For the Co-rich alloys, b储 increases significantly after
annealing while b␥,2 rests virtually unchanged For the
Fe-rich alloys, we see the opposite effect in that b␥,2increases
significantly after annealing while b储 rests virtually
un-changed The annealing seems to destroy the initial
as-deposited anisotropy and does not induce an in-plane
uniaxial anisotropy These differences in anisotropy are also
reflected in Fig 6共b兲, which shows the ratio of b储 to b⬜
before and after annealing This will be discussed later The largest magnetostriction of ␥,2⫽480⫻10⫺6 and 储⫽250
⫻10⫺6 is found in the middle of the composition range at
x⫽0.47 and can be obtained in very low applied magnetic
fields of 0.06 T
IV DISCUSSION
The magnetic properties of these alloys are rather com-plex but it is important to attempt to understand them in order to better optimize the magnetostrictive properties of such alloys with respect to potential applications One of the main differences between the magnetic properties of amor-phous RT2 alloys and their crystalline counterparts is the sperimagnetic distribution of R and Fe moments in the amor-phous case.12 This sperimagnetic structure arises from the competition between exchange interactions and random local anisotropy and leads to the formation of domains of corre-lated moments These domains are oriented more or less at random in zero field and the macroscopic anisotropy energy, which determines the coercive field, is an average of the random local anisotropy over the volume of each domain.19
At low temperature, these domains are small and this ex-plains the large coercive fields found in these alloys The sperimagnetic cone, within which the Tb and Dy moments lie, can be somewhat closed due to an increase in the mo-lecular field of the T sublattice acting on them and this could
account for the maximum seen in M s and the minimum in
hf for x⫽0.47 At room temperature, however, this
en-hancement of the T sublattice moment is less clear The
mag-FIG 5. 共a兲 Magnetostriction for x⫽0.83: 共1兲 as-deposited film, 共2兲
anneal-ing at 150 °C, and 共3兲 250 °C 共b兲 Magnetostriction for x⫽0: 共1兲
as-deposited film, and 共3兲 250 °C.
FIG 6 共a兲 Magnetostriction ␥,2(1.8 T) and 储 (0.06 T) for the (Tb 0.27 Dy 0.73 )(Fe 1⫺xCox) 2 as-deposited thin films 共1兲 and 共1兲, films
an-nealed at 150 °C 共2 and 2 ⬘ 兲 and at 250 °C 共3 and 3 ⬘兲 共b兲 Ratio b储/b⬜as a
function of x before and after annealing.
837
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Trang 6netostriction is, on the other hand, much more sensitive to
changes in the R–sublattice magnetization and we will now
discuss this effect
Assuming that the R moments have the same value as in
the crystalline laves phase, we can estimate the
magnetostric-tion of a sperimagnetic system with respect to a collinear
ferrimagnetic one using
b␥,2⫽3bint␥,2共具␣z典2⫺1兲,
where␣z is the direction cosine for each rare-earth moment
with respect to the field direction and bint␥,2is the intrinstic
magnetoelastic coupling coefficient共i.e., that of the collinear
ferrimagnet兲 Here, we take bint ␥,2⫽127 MPa, the
room-temperature value of b␥,2in isotropic polycrystalline
crystal-line共Tb0.27Dy0.73兲Fe2.20Assuming a uniform probability
dis-tribution of easy axes within a cone, we can deduce the
characteristic sperimagnetic cone angle共兲 For the films
un-der consiun-deration, this gives values of between 48° and 53°,
which are typical of those reported in the literature.5,21 This
variation inimplies that there is a variation in the average
共Tb, Dy兲 moment as a function of x Using M共Tb, Dy兲
共Tb0.27Dy0.73兲Fe2,4we can deduce具MTbDy典⫽M共TbDy兲具␣z典, as
a function of x, and this is plotted in Fig 7 From the
mea-sured magnetization data, we can now deduce M 3das a
func-tion of x 共Fig 7兲 The values thus determined are in good
agreement with those found for M 3d in ‘‘pure’’ a-TbCo2and
a-TbFe2alloys6 at room temperature This clearly indicates
that there is an enhancement in M 3d for the substituted
a-R共Fe, Co兲2 alloys and a maximum is reached for x⫽0.47
where there is sufficient Co to ensure good ferromagnetic
T–T coupling as well as sufficient Fe giving the larger
mag-netic moment We have, of course, neglected the variation in
ordering temperature, and hence, the intrinsic R-moment
value at room temperature associated with such an
enhance-ment of the T–T interactions However, this simple analysis
illustrates the importance of considering the influence of the
sperimagnetic structure on the magnetostriction and the
mag-netic properties of such alloys
An intriguing aspect in this study is the variation of the
anisotropy state as a function of T composition, before and
after annealing The comparison of b储 to b⬜ is a useful tool
for understanding the role of Co in these alloys 关Fig 6共b兲兴
For the Fe-rich alloys before annealing, b储/b⬜is large
indi-cating a well-defined initial anisotropy After annealing,
b储/b⬜⬇⫺2 suggests that the zero-field magnetization state
is isotropic The as-deposited material is not completely satu-rated at 1.8 T, while after annealing saturation is achieved at
around 1 T This leads to the measured increase in (b储
⫺b⬜) at 1.8 T after annealing For the as-deposited Co-rich
alloys, b储/b⬜⬇⫺1 indicates that the film is isotropic in the
plane After annealing at 250 °C, this ratio is significantly increased showing that a well-defined in-plane anisotropy direction has been induced Figure 6共b兲 shows the variation
of b储/b⬜ as a function of Co concentration It clearly
indi-cates that after annealing the easy axis becomes better de-fined with increasing Co content This may be accounted for
as follows During the annealing process, it is the local in-ternal molecular field that is responsible for the reorientation
of the R moments The external field merely saturates the material in a given direction For the Fe-rich alloys, the sperimagnetic nature of the Fe-sublattice distribution is con-veyed to the R sublattice and gives no net anisotropy How-ever, the strongly ferromagnetically coupled Co sublattice is well ordered and its molecular field acts to orient the R sub-lattice in one direction, giving rise to the observed uniaxial anisotropy The differing anisotropies seen in the as-deposited state are more difficult to account for precisely, but
it has often been noted that Fe-based RT compounds have a different anisotropy state compared to their Co-based coun-terpart
We can further illustrate this variation in anisotropy by associating the field dependence of the magnetostriction with different types of magnetization processes For a system of randomly oriented spin and random distribution of domain walls, the magnetization process takes place in two steps.22 First, the motion of 180° domain walls leads to a
magnetiza-tion of M0 without any contribution to magnetostriction In the second step, the spins rotate into the direction of the applied magnetic field leading to the change of both
magne-tization and magnetostriction For the case M0⫽M max/2, the relation between magnetostriction and magnetization is given as18
For the rotation of magnetization out of the easy axis, the magnetostriction is related to magnetization as follows:22
The results of this analysis are presented in Fig 8 The experimental data for the 共Tb, Dy兲Fe2 film are rather well described by Eq 共3兲 With increasing Co concentration, the
/maxvs M / Mmaxcurves shift towards the line described by
Eq 共4兲 This further confirms that Co substitution is
advan-tageous to the creation of a well-defined easy axis in this system
Finally, the room-temperature magnetostriction is strongly influenced by the Curie temperature of the investi-gated alloys It is worth reporting here that one has found the
T C value of 440 K for the a-共Tb0.27Dy0.73)(Fe1⫺xCox)2 film
with x ⫽0.63 Indeed, this T Cvalue is much higher than that
reported for a-共Tb0.27Dy0.73兲Fe2(T C⫽370 K, see also, e.g.,
Ref 23兲 The larger T C is associated also to the stronger
FIG 7 Calculated variation of具M R典and M 3dfrom magnetostriction data
as a function of x.
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Trang 7R–FeCo exchange energies This is one of the reasons why
the room-temperature magnetostriction was enhanced in
amorphous共Tb, Dy兲共Fe, Co兲 films
V CONCLUDING REMARKS
In conclusion, we would like to point out that
larger magnetostrictions are obtained in amorphous
共Tb, Dy兲共Fe, Co兲 films as compared to their parent
amor-phous films of either 共Tb, Dy兲Fe or 共Tb, Dy兲Co This has
been explained in terms of an increase in the ferromagnetic
coupling strength within the共Fe, Co兲 sublattice In addition,
a well-defined uniaxial anisotropy can be induced by
magnetic-field annealing for Co-rich films
It is well known that the substitution of Dy for Tb gives
rise to the increase of the magnetostriction at low magnetic
fields, through the reduction of the saturation field However,
it is also accompanied by a reduction in the saturation
mag-netostriction In this study, we have shown that Co
substitu-tion, coupled with the effects of annealing, results in an
en-hancement of both the low-field and saturation
magnetostriction Thus, we can expect a further enhancement
of the magnetostriction in these alloys by increasing the Tb
concentration Indeed, we have obtained a giant
magneto-striction of␥,2⫽1020⫻10⫺6 at 1.8 T with储⫽585⫻10⫺6
at 0.1 T in amorphous Tb共Fe0.55Co0.45兲2.12
ACKNOWLEDGMENTS
The authors thank Dr E du Tre´molet de Lacheisserrie for helpful discussions This work was carried out as part of the E C funded ‘‘MAGNIFIT’’ project 共Contract No
BRE2-0536兲 The work of one of the authors 共N H D.兲 is
partly supported by the National University of Hanoi within Project No QG.99.08
1E Quandt, J Alloys Compd 258, 126共1997兲.
2 E Tre´molet de Lacheisserise, K Mackey, J Betz, and J C Peuzin, J.
Appl Phys 275 – 277, 685共1998兲.
3N H Duc, in Handbook on the Physics and Chemistry of Rare Earths,
edited by K A Gschneidner, Jr and L Eyring 共North-Holland,
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FIG 8 Experimental and theoretical relations between normalized
magne-tostriction and magnetization for amorphous (Tb 0.27 Dy 0.73 )(Fe 1⫺xCox) 2 thin
films.
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