DSpace at VNU: Magnetic and magnetostrictive properties in amorphous (Tb0.27Dy0.73)(Fe1-xCox)(2) films

Magnetic 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
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JOURNAL OF APPLIED PHYSICS

VOLUME 87, NUMBER 2

15 JANUARY 2000

Magnetic and magnetostrictive properties in amorphous
„Tb0.27Dy0.73…„Fe1؊ x Cox … 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

͑Received 5 May 1999; accepted for publication 16 September 1999͒
Magnetic and magnetostrictive properties have been investigated for amorphous (Tb0.27Dy0.73)
(Fe1Ϫx Cox ) 2 thin films. An increase in the 3d magnetic moment due to the enhancement of T–T
interactions in substituted ͑Fe, Co͒ alloys was found. This leads to stronger R–͑Fe, Co͒ exchange
energies and then to enhancements of R–sublattice magnetization as well as magnetostriction in
these amorphous R͑Fe, Co͒ 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 480ϫ10Ϫ6 developed in
low fields of 0.3 T was observed for films with xϭ0.47 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. ͓S0021-8979͑99͒06624-4͔

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 (Rϭrare 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 RFe2 laves phase compounds of which TbFe2 ͑terfenol͒,
a ferrimagnet with T C ϭ710 K, is probably the best known,4
having ␭ s ϭ1753ϫ10Ϫ6 . The anisotropy can be further decreased 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 ͑Tb0.27Dy0.73͒Fe2 compound, 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 leading to magnetic frustration in the Fe sublattice. In amorphous
a-YFe alloys, this results in a concentrated spin-glass behavior below room temperature. In a-RFe alloys, where R is a
magnetic rare earth, the additional contributions of R–Fe exa͒

Author to whom correspondence should be addressed; electronic mail:


change and local crystalline electric-field interactions lead to
the formation of sperimagnetic structures.5 The ordering
temperatures are above room temperature ͓T C ϭ410 K for
a-Tb0.33Fe0.66 ͑Refs. 6 and 7͔͒. It is, however, still rather low
and is thus detrimental to large magnetostrictions being obtained in such materials at room temperature.
Actually, with a view to obtaining large magnetostrictions 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 temperature is now raised up to 600 K ͑Ref. 7͒ for Tb0.33Co66. Recently, we have studied a-Tbx Co1Ϫx and shown that large
magnetostrictions of b ␥ ,2ϭ300ϫ10Ϫ6 at 300 K are obtained
for xϳ0.33.9
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
(Tϭtransition metal) is approximately the same for TϭFe
and Co. In addition, the T–T interactions tend to be stronger
in ͑FeCo͒- than in either Fe- or Co-based alloys.11 This results in an increase of T C for a given R:T ratio. The stronger
R–FeCo exchange energies should then lead to an enhancement of the R moment at room temperature and thus
the magnetostriction in these amorphous alloys. Recently,
we have studied the magnetostriction in amorphous
(Tb1Ϫx Dyx )(Fe0.45Co0.55) 2.1 thin films. A magnetostriction of
was
obtained
for
amorphous
1020ϫ10Ϫ6
Tb͑Fe0.45Co0.55͒2.1 . 12 Indeed, this is much larger than that
seen in other amorphous films of either TbFe or TbCo.

0021-8979/2000/87(2)/834/6/$17.00
834
© 2000 American Institute of Physics
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Duc et al.

J. Appl. Phys., Vol. 87, No. 2, 15 January 2000

835

In the present article, we have studied the influence of
the Fe:Co ratio on the magnetization and magnetostriction of
(Tb0.27Dy0.73)(Fe1Ϫx Cox ) 2 . We will show that the Fe:Co ratio of 50:50 responds approximately to the optimum composition 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 pressure was 10Ϫ2 mbar. A composite target was used allowing a
wide range of alloys to be made in a controllable way without a large cost of materials. The target consisted of 18 segments of about 20°, of different elements ͑here, Tb, Dy, Fe,
Co͒. 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 backscattering spectroscopy ͑RBS͒ and X-ray energy-dispersive spectroscopy ͑XEDS͒ measurements that no Cu and Ag contamination has occurred. The target–substrate distance was 8 cm.
The substrates were glass microscope cover slips with a
nominal thickness of 150 ␮m. Both target and sample holder
were water cooled.
The ratio of the deposition rates of RϭTb, Dy to TϭFe,
Co is 0.85. Thus, for the (Tb0.27Dy0.73)(Fe1Ϫx Cox ) 2 films
made here, the Tb͑Dy͒ and Fe͑Co͒ concentrations could, in
principle, be varied in steps of about 14% and 9%, respectively. 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 sputtering. The typical film thickness was 1.2 ␮m. X-ray ␪ – 2 ␪

diffraction showed the as-deposited samples to be amorphous.
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 induced during the sputtering process and to induce a welldefined uniaxial in-plane anisotropy. Subsequent x-ray ␪ – 2 ␪
diffraction showed no evidence of recrystallization after annealing.
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 deflectometer ͑resolution of 5ϫ10Ϫ8 rad͒, in which the bending of the substrate due to the magnetostriction in the film
was measured. This allows the magnetoelastic coupling coefficient of film ͑b͒ to be directly determined13,14 using
bϭ

␣ h s2
Es
,
L h f 6 ͑ 1ϩ ␯ s ͒

͑1͒

where ␣ is the deflection angle of the sample as a function of
applied field, L is the sample length, and E s and ␯ s 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.

FIG. 1. Hysteresis loops at 4.2 K for several (Tb0.27Dy0.73)(Fe1Ϫx Cox ) 2 thin
films: ͑1͒ Ϫxϭ0, ͑2͒ xϭ0.31, and ͑3͒ Ϫxϭ1.0.

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
␭ϭ

Ϫb ͑ 1ϩ ␯ f ͒
,
Ef

͑2͒

where E f and ␯ s are taken to be 80 GPa and 0.31, respectively.
We measured two coefficients at saturation, b ʈ and bЌ ,
which correspond to the applied field, always in the film
plane, being, respectively, parallel and perpendicular to the
sample length ͑i.e., the measurement direction͒. In addition,
the perpendicular direction corresponds to the easy axis induced after field annealing. The intrinsic material-dependent
parameter b ␥ ,2 ͑or ␭ ␥ ,2͒ is just the difference b ʈ ϪbЌ ͑or ␭ ʈ
Ϫ␭Ќ , respectively͒.
III. EXPERIMENTAL RESULTS
A. Magnetization

Figure 1 presents the hysteresis loops for several asdeposited (Tb0.27Dy0.73)(Fe1Ϫx Cox ) 2 films at 4.2 K. The coercive fields are very large for all samples and the magnetization 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 sperimagnetic systems. The high-field susceptibility ( ␹ hf) is also typical of sperimagnetic systems and is associated with the closing of the cone distribution of R moments as the field is
increased.5
The coercive fields ( ␮ 0 H C ) reach their highest value of
3.4 T for xϭ0. With increasing Co concentration, coercivity
decreases rapidly down to about 0.5 T for 0.67рxр1.0 ͓see

Fig. 2͑a͔͒. The ␹ hf also decreases with increasing Co concentration, to a minimum at xϭ0.47 and then slightly increases
with further increasing x.
In all cases, ␮ 0 H C also decreases with increasing temperature ͓see the inset in Fig. 2͑a͔͒, while the ␹ hf is strongly
enhanced. This is due to the rapid decrease local anisotropy
of the R atoms as the temperature is increased compared to

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836

Duc et al.

J. Appl. Phys., Vol. 87, No. 2, 15 January 2000

FIG. 4. Hysteresis loops for the ͑Tb0.27Dy0.73͒Co2 ͑1͒ as-deposited film and
͑2͒ after annealing along induced easy axis and ͑3͒ hard axis.

FIG. 2. ͑a͒ Coercive field ␮ 0 H c as a function of Co concentration at 4.2 K.
Inset shows the temperature dependence of ␮ 0 H c for xϭ0.83. ͑b͒ Coercive field ␮ 0 H c as a function of Co concentration at 300 K: ͑1͒ the asdeposited films, ͑2͒ after annealing at 150 °C, and ͑3͒ after annealing
at 250 °C.

the exchange field. In Fig. 2͑b͒, we present ␮ 0 H C at 300 K
as function of x. All the films are magnetically rather soft at
room temperature and there is a maximum in ␮ 0 H C at x
ϭ0.63.
The spontaneous magnetization values at 4.2 and 300 K
for the as-deposited (Tb0.27Dy0.73)(Fe1Ϫx Cox ) 2 films extrapolated to zero field are shown in Fig. 3. At 4.2 K there is
a maximum at xϭ0.47 while at 300 K, within experimental

errors, the magnetization is independent of the Co concentration. 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 xϭ0.47 reflects that, at low temperature, the enhancement of M 3d is
smaller than the associated increase in the magnetization of
the R sublattice ( ͗ M R͘ ).
Samples were annealed at temperatures between 150 and
250 °C in an applied magnetic field of 2.2 T. The field dependences of the magnetization before and after annealing
are shown in Fig. 4 for xϭ1. For the as-deposited samples,
the magnetization reversal process is progressive and isotropic with a rather large coercive field. This property is often
observed in sperimagnetic systems where domains of correlated 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 2͑b͒ shows the coercive field as a
function of composition before and after annealing. After
annealing at 250 °C, ␮ 0 H C is less than 0.002 T for samples
with xϭ0.0 and 1.0. A slight maximum of ␮ 0 H C around the
middle of the composition range is still observed, however,
with ␮ 0 H C ϳ0.006 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 induced anisotropy suggests that a process of single-ion directional ordering17 has occurred, in which there is a local reorientation of the Tb easy axes along the field direction. The
composition dependence of this uniaxial anisotropy is, however, more complex and will be discussed further in connection with the magnetostriction data. The field annealing also

causes a reduction in ␹ hf , indicating that the cone distribution of the Tb moments is somewhat closed.
B. Magnetostriction

In general, the comparison of b ʈ and bЌ indicates clearly
the anisotropy state of the sample. If the zero-field state is
fully isotropic, then b ʈ ϭϪ2bЌ , and if it is isotropic in the
plane, then b ʈ ϭϪbЌ . 18 For 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. 3. Variation of spontaneous magnetization as a function of x at 4.2 and
300 K for (Tb0.27Dy0.73)(Fe1Ϫx Cox ) 2 thin films.
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J. Appl. Phys., Vol. 87, No. 2, 15 January 2000

FIG. 5. ͑a͒ Magnetostriction for xϭ0.83: ͑1͒ as-deposited film, ͑2͒ annealing at 150 °C, and ͑3͒ 250 °C. ͑b͒ Magnetostriction for xϭ0: ͑1͒ asdeposited film, and ͑3͒ 250 °C.

glecting domain-wall contributions, no magnetostriction is
associated with this process. Thus, bЌ should be zero and
b ʈ ϭb ␥ ,2.
Figure 5 shows the effect of annealing on the magnetostriction for two alloys with xϭ0.83 and xϭ0. For xϭ0.83
͓see Fig. 5͑a͔͒, we see that annealing increases the ratio of b ʈ
to bЌ while b ␥ ,2 rests roughly constant. This is due to the
creation of an in-plane uniaxial anisotropy as seen from magnetization measurements. In addition, we see that this anisotropy is completely induced after annealing at 150 °C and is

accompanied by a reduction in the saturation field. Subsequent annealing at 250 °C simply further reduces the saturation field. For the xϭ0 sample ͓see Fig. 5͑b͔͒, we see a
different behavior. Before annealing, the approach to saturation is rather slow and the ratio of b ʈ to bЌ indicates an
initial anisotropy. After annealing, the saturation field is reduced and this initial anisotropy is destroyed, leaving the
sample almost isotropic. However, b ␥ ,2 ͑measured at 1.8 T͒
actually increases after annealing probably due to the reduction in the saturation field.
These differences are reflected across the whole composition range and the results obtained are summarized in Fig.
6͑a͒. 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 ʈ increases significantly after
annealing while b ␥ ,2 rests virtually unchanged. For the Ferich alloys, we see the opposite effect in that b ␥ ,2 increases
significantly after annealing while b ʈ rests virtually unchanged. The annealing seems to destroy the initial asdeposited anisotropy and does not induce an in-plane
uniaxial anisotropy. These differences in anisotropy are also

837

FIG. 6. ͑a͒ Magnetostriction ␭ ␥ ,2(1.8 T) and ␭ ʈ (0.06 T) for the
(Tb0.27Dy0.73)(Fe1Ϫx Cox ) 2 as-deposited thin films ͑1͒ and ͑1͒, films annealed at 150 °C ͑2 and 2 Ј ͒ and at 250 °C ͑3 and 3 Ј ͒. ͑b͒ Ratio b ʈ /bЌ as a
function of x before and after annealing.

reflected in Fig. 6͑b͒, which shows the ratio of b ʈ to bЌ
before and after annealing. This will be discussed later. The
largest magnetostriction of ␭ ␥ ,2ϭ480ϫ10Ϫ6 and ␭ ʈ ϭ250
ϫ10Ϫ6 is found in the middle of the composition range at
xϭ0.47 and can be obtained in very low applied magnetic
fields of 0.06 T.
IV. DISCUSSION

The magnetic properties of these alloys are rather complex 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 amorphous RT2 alloys and their crystalline counterparts is the
sperimagnetic distribution of R and Fe moments in the amorphous case.12 This sperimagnetic structure arises from the
competition between exchange interactions and random local
anisotropy and leads to the formation of domains of correlated 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 explains 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 molecular 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 xϭ0.47. At room temperature, however, this enhancement of the T sublattice moment is less clear. The mag-

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838

Duc et al.

J. Appl. Phys., Vol. 87, No. 2, 15 January 2000

FIG. 7. Calculated variation of ͗ M R ͘ and M 3d from magnetostriction data
as a function of x.

netostriction 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 magnetostriction of a sperimagnetic system with respect to a collinear
ferrimagnetic one using
␥ ,2
b ␥ ,2ϭ 23 b int
͑ ͗ ␣ z ͘ 2 Ϫ 31 ͒ ,

where ␣ z is the direction cosine for each rare-earth moment
␥ ,2
is the intrinstic
with respect to the field direction and b int
magnetoelastic coupling coefficient ͑i.e., that of the collinear
ferrimagnet͒. Here, we take b ␥int,2ϭ127 MPa, the roomtemperature value of b ␥ ,2 in isotropic polycrystalline crystalline ͑Tb0.27Dy0.73͒Fe2. 20 Assuming a uniform probability distribution of easy axes within a cone, we can deduce the
characteristic sperimagnetic cone angle ͑␪͒. For the films under consideration, this gives values of between 48° and 53°,
which are typical of those reported in the literature.5,21 This
variation in ␪ implies that there is a variation in the average
͑Tb, Dy͒ moment as a function of x. Using M ͑Tb, Dy͒
ϭ7.27 ␮ B ,
the
room-temperature
value
in
͑Tb0.27Dy0.73͒Fe2, 4 we can deduce ͗ M TbDy͘ ϭM ͑TbDy͒͗ ␣ z ͘ , as
a function of x, and this is plotted in Fig. 7. From the measured magnetization data, we can now deduce M 3d as a function of x ͑Fig. 7͒. The values thus determined are in good
agreement with those found for M 3d in ‘‘pure’’ a-TbCo2 and
a-TbFe2 alloys6 at room temperature. This clearly indicates
that there is an enhancement in M 3d for the substituted
a-R͑Fe, Co͒2 alloys and a maximum is reached for xϭ0.47
where there is sufficient Co to ensure good ferromagnetic
T–T coupling as well as sufficient Fe giving the larger magnetic 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 enhancement 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 magnetic 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 ʈ to bЌ is a useful tool
for understanding the role of Co in these alloys ͓Fig. 6͑b͔͒.
For the Fe-rich alloys before annealing, b ʈ /bЌ is large indi-

cating a well-defined initial anisotropy. After annealing,
b ʈ /bЌ ϷϪ2 suggests that the zero-field magnetization state
is isotropic. The as-deposited material is not completely saturated at 1.8 T, while after annealing saturation is achieved at
around 1 T. This leads to the measured increase in (b ʈ
ϪbЌ ) at 1.8 T after annealing. For the as-deposited Co-rich
alloys, b ʈ /bЌ ϷϪ1 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 6͑b͒ shows the variation
of b ʈ /bЌ as a function of Co concentration. It clearly indicates that after annealing the easy axis becomes better defined with increasing Co content. This may be accounted for
as follows. During the annealing process, it is the local internal 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 conveyed to the R sublattice and gives no net anisotropy. However, the strongly ferromagnetically coupled Co sublattice is
well ordered and its molecular field acts to orient the R sublattice in one direction, giving rise to the observed uniaxial
anisotropy. The differing anisotropies seen in the asdeposited 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 counterpart.
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 magnetization of M 0 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 magnetization and magnetostriction. For the case M 0 ϭM max/2, the
relation between magnetostriction and magnetization is
given as18
␭ ͑ H ͒ /␭ maxϭ ͓ 2M ͑ H ͒ /M maxϪ1 ͔ 3/2.

͑3͒

For the rotation of magnetization out of the easy axis, the
magnetostriction is related to magnetization as follows:22
␭ ͑ H ͒ /␭ maxϭ ͓ M ͑ H ͒ /M max͔ 2 .

͑4͒

The results of this analysis are presented in Fig. 8. The
experimental data for the ͑Tb, Dy͒Fe2 film are rather well
described by Eq. ͑3͒. With increasing Co concentration, the
␭/␭ max vs M /M max curves shift towards the line described by
Eq. ͑4͒. This further confirms that Co substitution is advantageous 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 investigated alloys. It is worth reporting here that one has found the
T C value of 440 K for the a-͑Tb0.27Dy0.73)(Fe1Ϫx Cox ) 2 film
with xϭ0.63. Indeed, this T C value is much higher than that
reported for a-͑Tb0.27Dy0.73͒Fe2 (T C ϭ370 K, see also, e.g.,
Ref. 23͒. The larger T C is associated also to the stronger

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Duc et al.

J. Appl. Phys., Vol. 87, No. 2, 15 January 2000

839

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 ͑Contract No.
BRE2-0536͒. The work of one of the authors ͑N. H. D.͒ is
partly supported by the National University of Hanoi within
Project No. QG.99.08.

E. Quandt, J. Alloys Compd. 258, 126 ͑1997͒.
E. Tre´molet de Lacheisserise, K. Mackey, J. Betz, and J. C. Peuzin, J.
Appl. Phys. 275–277, 685 ͑1998͒.
3
N. H. Duc, in Handbook on the Physics and Chemistry of Rare Earths,
edited by K. A. Gschneidner, Jr. and L. Eyring ͑North-Holland, Amsterdam͒, Vol. 28. ͑to be published͒.
4
A. E. Clark, in Ferromagnetic Materials, edited by E. P. Wohlfarth, Vol.
1 ͑North-Holland, Amsterdam, 1980͒, Vol. 1, p. 531.
5
J. M. D. Coey, D. Givord, A. Lie´nard, and J. P. Rebouillat, J. Phys. F 11,

2707 ͑1981͒.
6
P. Hansen, G. Much, M. Rosenkranz, and K. Witter, J. Phys. 66, 756
͑1989͒.
7
K. Lee and N. Heiman, AIP Conf. Proc. 18, 108 ͑1973͒.
8
R. Lemaire R., Cobalt ͑Engl. Ed.͒ 1968, 33.
9
J. Betz, Thesis, University Joseph Fourier of Grenoble ͑1997͒.
10
J. P. Liu, F. R. de Boer, P. F. de Chaˆtel, R. Coehoorn, and K. H. J.
Buschow, J. Magn. Magn. Mater. 134, 159 ͑1994͒.
11
J. P. Gavigan, D. Givord, H. S. Li, and J. Voiron, Physica B 149, 345
͑1988͒.
12
N. H. Duc, K. Mackay, J. Betz, and D. Givord, J. Appl. Phys. 79, 973
͑1996͒.
13
E. Tre´molet de Lacheisserise and J. C. Peuzin, J. Magn. Magn. Mater.
136, 189 ͑1994͒.
14
J. Betz, E. du Tre´molet de Lacheisserise, and L. T. Baczewski, Appl.
Phys. Lett. 68, 132 ͑1996͒.
15
Y. Imry and S. Ma, Phys. Rev. Lett. 35, 1399 ͑1975͒.
16
B. Boucher, A. Lie´nard, J. P. Rebouillat, and J. Schweizer, J. Phys. F 9,
1421 ͑1979͒.

17
L. Ne´el, Compte Rendu 273, 1468 ͑1953͒; J. Phys. Radium 15, 225
͑1954͒.
18
F. Schatz, M. Hirscher, M. Schnell, G. Flik, and H. Kro¨muller, J. Appl.
Phys. 76, 5380 ͑1994͒.
19
R. Alben, J. I. Bundrik, and G. S. Cargill, Metallic Glasses ͑American
Society for Metals, Metals Park, OH, 1978͒, Chap. 12.
20
The values given in Ref. 4 are for somewhat textured samples. Here, we
calculate b ␥ ,2 for an isotropic polycrystalline sample of Tb0.27Dy0.73Fe2,
using single-crystal data. b ␥ ,2ϭ3G␭ S with 1/(2G)ϭ2/5S ␥ ϩ3/5S ⑀ and ␭ S
ϭ0.6␭ 111 . E. du Tre´molet de Lacheisserise ͑private communication͒.
21
P. Hansen, in Ferromagnetic Materials, edited by K. H. J. Buschow
͑North-Holland, Amsterdam, 1991͒, Vol. 6, p. 289.
22
S. Chikazumi, Physics of Magnetism ͑Willey, New York, 1964͒.
23
K. Ried, M. Schnell, F. Schatz, M. Hirscher, B. Ludescher, W. Sigle, and
H. Kro¨muller, Phys. Status Solidi A 167, 195 ͑1998͒.
1
2

FIG. 8. Experimental and theoretical relations between normalized magnetostriction and magnetization for amorphous (Tb0.27Dy0.73)(Fe1Ϫx Cox ) 2 thin
films.

R–FeCo exchange energies. This is one of the reasons why
the room-temperature magnetostriction was enhanced in

amorphous ͑Tb, Dy͒͑Fe, Co͒ films.
V. CONCLUDING REMARKS

In conclusion, we would like to point out that
larger magnetostrictions are obtained in amorphous
͑Tb, Dy͒͑Fe, Co͒ films as compared to their parent amorphous films of either ͑Tb, Dy͒Fe or ͑Tb, Dy͒Co. This has
been explained in terms of an increase in the ferromagnetic
coupling strength within the ͑Fe, Co͒ 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 magnetostriction. In this study, we have shown that Co substitution, coupled with the effects of annealing, results in an enhancement 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 magnetostriction of ␭ ␥ ,2ϭ1020ϫ10Ϫ6 at 1.8 T with ␭ ʈ ϭ585ϫ10Ϫ6
at 0.1 T in amorphous Tb͑Fe0.55Co0.45͒2. 12

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