Neutron investigations of magnetic multilayers

Physica B 192 (1993) 122-136 North-Holland

PHYSICAI

SDI: 0921-4526(93)E0119-2

Neutron investigations of magnetic multilayers Ph. Mangin a, C. D u f o u r a and B. R o d m a c q b aLaboratoire de M~tallurgie, Physique et Sciences des Mat~riaux, Universit~ Nancy 1, Vandoeuvre, France bCEA, D~partement de Recherche Fondamentale sur la Mati~re Condens~e, Centre d'Etudes NuclOaires, Grenoble, France Recent low-angle neutron scattering results from magnetic multilayers are reviewed. After a recall of the theory, three sorts of studies are examined: the determination of the magnetization profiles in layers, the magnetic structures resulting from the coupling between magnetic layers through nonmagnetic ones and finally the particular case of rare earth/iron systems.

1. Introduction

During the last few years, the field of multilayers has grown very rapidly in interest. This is due to the improvement of the preparation techniques, the theoretical interest in low-dimension physics and the potential application of these new materials in recording media. Some spectacular effects as the giant magnetoresistance or the coherent coupling between magnetic layers through nonmagnetic ones have been observed. The coupling of dysprosium helix through yttrium was demonstrated by neutron scattering [1,2]. Therefore a large place has been devoted to this field in recent conferences and a lot of review papers have been published. As an example, the report 'Surface, interface and thin film magnetism' [3] provides an extensive overview of the current interest in magnetism of multilayers in the general framework of the twodimensional structures. In fact, from the pioneering works of Mezei i

Correspondence to: Ph. Mangin, Laboratoire de Physique du Solide, Universit6 Nancy 1, BP 239, 54506 Vandoeuvre Cedex, France.

[4] and Sch~irpf [5] on polarization mirrors and supermirrors, neutron technology is one of the first users of nanoscale magnetic multilayers. This is a very good illustration of the sensitivity of neutrons to the magnetic structure of these materials: indeed by interaction with the magnetic moments of thin films and multilayers, the reflected and scattered neutron beams can almost be 100% polarized. In this paper, the recent results obtained on multilayers from low-angle unpolarized and polarized neutron scattering from multilayers are reviewed. In part 2 we recall the basic theoretical background of the method. Starting from the nonmagnetic scattering of neutrons by multilayers we present the theory of polarized neutron scattering in systems where the magnetization is along the quantization axis and, following the recent work of Blundell and Bland [6], in systems where the magnetization is at an angle 0 with this axis. Then we focus on three subjects: the magnetic profile in noninteracting magnetic layers (part 3), the magnetic structure resulting from ferromagnetic, antiferromagnetic and biquadratic interactions between magnetic layers through nonmagnetic ones (part 4) and the

0921-4526/93/$06.00 © 1993- Elsevier Science Publishers B.V. All rights reserved

Ph. Mangin et al. / Neutron investigations of magnetic multilayers

magnetic structure of rare earth/iron multilayers (part 5). High-angle magnetic scattering from superlattices as well as magnetic reflectometry observed near the critical angle of total reflection provide complementary information. They are reviewed by McMorrow [7] and Felcher [8] respectively in these proceedings.

2. Basic theory of low-angle neutron scattering by muitilayered systems

2.1. Nonmagnetic scattering In nonmagnetic materials, neutrons interact with the nuclear potential:

123

sin(/Aqm/2)

f(qm)=(PA--PB)

qm/2

where PA = NAbA (NA is the atomic density) is the scattering amplitude density of element A and ln is the thickness of layer A. The above approximation is a continuous limit in which the inverse of the scattering vector is large compared to the interatomic distance. It tells that the intensity is the product of a function of the geometry of the system (referred to in the following as the shape of the profile) and of the square of the difference between the scattering amplitude densities of the two layers of the unit cell.

2.a-h2

VN(r ) = ~ --~--- bi~(r -

Optical treatment

ri)

i

where b i is the coherent scattering length of element i located at r i (see refs. [9-11]). In the kinematic approximation (weak scattering), the differential cross section is given by

where F(q) is the scattering amplitude and q the scattering vector. Then the reflectivity ~ is written [12] as ~(q)

=

IR(q)l =

where R(q) = (4rr/q)F(q) is the reflectance. In a multilayer made of N one-dimensional cells of period A, F(q) can be expressed as the product of the interference function of the multilayer S(q) and the structure factor of the one-dimensional cell f(q) [12]:

F(q) = S(q)f(q)

sin(NAq / 2 )

with S(q) = sin(Aq/2)

S(q) exhibits sharp peaks at qm values corresponding to the 'Bragg peaks' of the multilayer (Aqm = 2"rrm). If the one-dimensional cell is a bilayer (A, B), the low-angle scattering factor at qm is simply

The above approximation is however no longer valid at very low angles, near the total reflection edge where extinction effects are no longer negligible. These effects can be taken into account by the dynamical theory of neutron diffraction or more simply by considering the multilayer as a stack of homogeneous media with an average potential V(z) and by proceeding as in optics of stratified media [13-16]. Each layer (corresponding to the nominal deposition or to thinner slices) is referred to as a homogeneous medium a ; vacuum is medium 0, and the substrate is medium v. If k0,z is the component of the wave vector along the z direction perpendicular to the plane of the film, its component in medium a is 2 - 4"rrN~b~ k,,z = ~ / k 0,z

Then, following the method introduced by Ab616s for the electromagnetic waves [14], the amplitudes of the waves propagating in medium a and those propagating in medium a + 1 are linked by the relation [ D o I [ P o ] [ e j = [D. with

Ph. Mangin et al. / Neutron investigations o f magnetic multilayers

124

[D~]=

[1 1] k~,~ - k

z ,

[exp(i~,~/ ) [P~] = [6ol--

[Ao] Bo

r,~,,~+ 1 --

0 exp(_ik zl~)] ,

= [ma.a+l][6a+m]

n~=1-6,-i/3~

and finally 60 can be obtained from 6. (medium v is the substrate): = [M][6~].

As there is no reflected wave in medium v, B. = 0. If the amplitude of the incident wave is equal to unity (A 0 = 1) then B 0 is the reflectance R and A. the transmittance T. So from the profile of the average potential, the reflectivity can be easily calculated. Note that the multilayer does not need to be periodic. Alternatively [13,15] the reflectance can be calculated from the reflection coefficient of each individual interface by using the following recurrence relation which takes into account the multiple reflections: r~_l, . + R~_I,~ exp(2ik~,zl~) R ~ - I ' ~ - 1 + r ~ _ l , ~ R ~ _ l , ~ exp(2ik ,~1~)

where R~_ ~,~ is the reflectance of the (a - 1, a) interface, taking into account the multiple reflection in the layers located below this interface. The reflectance of the multilayer is R =RoA which can be calculated by recurrence, with the initial condition R~_ 1,. = r._ a,~. The reflection and transmission coefficients are given by the classical relations

a2 A with6~=~-w-wp~, /3~=~-~-wp~

(h is the neutron wavelength and/x the absorption coefficient). If the reflectivities are small, the reflectance R of a periodic system with a (A, B) bilayer as unit cell can simply be written as

R

w i t h [ M . , . + ~ ] = [ p ~] -1 [Do] -1 [D .+~]

[60] = [ M o , , ] [ M I . z l " ' t M ~ _ ~ , . ] [ 6 . ]

2k~,z t~'~+l - k~,~ + k~+l, ~ This optical method turns finally out to attribute to medium a the complex refraction index

"

[6~] is the columnar matrix containing the amplitudes of the waves propagating in +z (As) and - z (B~) directions. [P~] is the propagation matrix which expresses the phase shift of the waves from one side of a layer to the other side and [D~] is the transmission matrix which expresses the continuities. Then [6~] can be calculated from [6~+1] by

[6a]

k,, ,z - k,~ + l ,z k .z + k~,+l,z '

=

(rA,B +

ra. A

exp(2ik0,~) ) ~ exp(2ik0,~A) U

which is exactly equivalent to the low-angle kinematic approximation. It can be expressed as follows: the reflectivity is proportional to the square of the difference between the refraction indexes of the two layers of the bilayer. 2.2. M a g n e t i c scattering with the m a g n e t i z a t i o n direction a l o n g the q u a n t i z a t i o n axis o f the neutrons

In a classical polarized neutron scattering experiment (more sophisticated analyses are possible) an experimental quantization axis (+, - ) is chosen. The incident and the scattered beams are polarized and analyzed in reference to this axis. In a triple-axis configuration, the (+, - ) axis is vertical, parallel to the rotation axis of the goniometer and corresponds to the x direction in the plane of the multilayers (fig. 1). In scattering processes, the components of the magnetization along the x, y and z directions act differently. M~, which according to fig. 1 is in the direction of the scattering vector, does not act at all: there is no magnetic scattering contribution from the component of the magnetization along the direction of the scattering vector. M x which is along the ( + , - ) quantization axis gives rise (along with the nuclear scattering) to a non spin

Ph. Mangin et al. I Neutron investigations of magnetic multilayers

multilayers the I+ ) and I - } structure factors of the one-dimensional cell are expressed as

H x

Quantization axis

f-+(qm) = (P~ + P B ) z-

/\

,ao

Scattering Incident beam

vector

Fig. 1. Schematic view of low-angle polarized neutron scattering. The scattering vector q is perpendicular to the plane

(x, y) of the sample and M is the component of the magnetization in (x, y). M makes an angle 0 with the field applied along the quantization axis x. The ]+ ) incident neutrons can be scattered l+ ) or 1-). flip scattering. My, which lies in the scattering plane and is perpendicular to the quantization ( + , - ) axis, provides spin flip scattering. Let us at first consider the simple case where in every layer the magnetization is in the direction of the quantization axis x. There is no spin flip scattering and two independent scattering and propagation processes occur. The I+ } incident neutrons are scattered I+} and the I - ) neutrons are scattered I - ) . The ]+} and I - ) neutrons interact with two different potentials V ÷ and V - with corresponding scattering amplitude densities p ÷ or p - : p +(z) = oN(z) + pM~(z),

p - ( z ) = oN(z) - pMx(z),

with pN(Z) = N(z)b(z), pMx(Z)= 0.27N(Z)Mx(z ) where M x is expressed in /~,B/Cm3. Then the formalism developed in the previous section can be reproduced for [~b+] and [~b-] independently. The two (2 x 2) matrix relations can be replaced by one relation between a (4 x 4) matrix with nondiagonal blocks equal to 0:

[ t<11

[¢21J

0 1 , I-tool •

[P;IJ

L o

o

]1

[D~-]

X [[Di+l][D~+I]] [[~;.I] 1 [~2+11J

125

"

Then in the kinematic approximation of periodic

sin(/A qm / 2) qm/2

With nonpolarized neutrons, information can be obtained from I x = 1(1+ + I - ) and from III which is the purely nuclear contribution; this intensity is obtained if a strong enough magnetic field orientates the magnetic moments parallel to the scattering vector (i.e. perpendicular to the plane of the layers). 2.3. Neutron scattering from magnetic multilayers : general case

In the general case, the projection of the magnetization in the reflection plane M~ makes an angle 0~ with the quantization axis (+, - ) . So for each layer, we have to introduce a quantization axis (1', ~)~ along M~. Then [~] can be expressed in the ( + , - ) basis or in the (1', ~)~ basis and the matrix elements can be changed by the simple spin-l/2 rotation matrix. In the (~', ~)~ basis, [q~] is a 4 x 4 matrix with two 2 x 2 blocks [qb~] and [~b2] which as in the previous section propagate independently. However, as the (1', ~)~ basis changes from the ath layer to the (a + 1)th layer, the continuity conditions have to be expressed in the same basis, for example the ( + , - ) one. This is equivalent to the resolution of the coupled Schr6dinger equations proposed by some authors [17]. So, as shown in detail by Blundell and Bland [6] and provided the continuous approximation is valid, the scattered intensities I ÷÷, I - - , I ÷- and I -÷ can be calculated by recurrence from a model with a uniform magnetization in each slice. Note that the method is also valid in materials with strong absorption by using the complex scattering amplitude. Alternatively, a recurrence method (similar to that presented in section 2.1) with four interface reflection coefficients r ++, r +-, r -+ and r - - has been proposed [18]. Finally, in the kinematic limit four scattering amplitude densities can be defined:

P h . M a n g i n et al. / N e u t r o n investigations o f m a g n e t i c multilayers

126

p++

= p N + PMx ,

+ P

p

= PN-- PM x ,

+= RM~ ,

P

= --PM v "

In this approximation, the intensities are proportional to ( p + + - p . ++~+ j ~2 etc. Such formulations are very useful for a qualitative discussion of the data.

3. Magnetization profile in ferromagnetic/ nonmagnetic layers 3.1. Introduction In many systems, the multilayers are periodic with a bilayer unit cell composed of a ferromagnetic layer (Fe, Co, Ni, Gd, etc.) and of a nonmagnetic one. In some systems, the magnetic layers interact through the nonmagnetic ones, whereas in other systems they do not. We consider in this section the case where the magnetic layers do not interact and get on to the question of the profile of the magnetization inside the magnetic layers. Is the magnetization uniform or is there an enhancement or a lowering of the magnetization with a possible magnetically dead layer near the interface? How is the profile modified near the Curie temperature? Are the interfaces abrupt or does a magnetic alloy take place at the interface? If there is an alloy, is there a continuous change of the composition from one element to the other or does an intermediate compound take place? These questions are interesting for theoreticians of lowdimensional physics as well as for metallurgists. 3.2. Principle of the method In the particular case where the magnetization is purely along the x direction, the method [19,20] consists in studying the variations of the flipping ratios I++/I - - or the ratios 111/11 as a function of the order m of the low-angle satellites. Indeed, if the magnetization is uniform in the magnetic layers, these ratios do not depend significantly on m. But if for any reason the magnetic profile is different from the chemical

one, the flipping ratios depend strongly on the order of the satellites. The l+ ) and 1- ) neutrons will see very different shapes of scattering amplitude density profiles. For example, let us consider the Fe/Si [21,22] system and assume sharp interfaces between pure iron (2.2pro/atom) and pure silicon. The scattering profile seen by ]+) neutrons is that of fig. 2(a) and that seen by the [ - ) neutrons is that of fig. 2(b): the scattering amplitude density of silicon is unchanged for both polarizations but that of iron is proportional to bFe +Pve and bFe--PFe for I+) and 1-) neutrons respectively. As the shape of the profile is the same for both polarizations, the ]+) scattering is larger than the ] - ) scattering for all the satellites and in the kinematic approximation 1+/I - is independent of the order of the satellite. On the other hand, if we assume that a Fe0.sSi0.5 nonmagnetic alloy, whose scattering amplitude does not change with the neutron polarization, is formed at the interface, the shapes of the scattering amplitude profile seen by the 1+) and ] - ) neutrons are very different (fig. 2(c) and (d)), the one seen by the [ - ) neutrons being strongly affected by the interface. As a consequence, the flipping ratios are then dependent of the peak order. So in general, from the set of flipping ratios, a model of chemical and magnetic profiles can be tested. This method is illustrated below with the examples of Fe/SiO, Ni/SiO [19], F e / G e [23] and Fe / Si [21,22,24] multilayers. 3.3. Application to different systems Fe/SiO and Ni/SiO At first, Sato et al. [19] found that for a Fe(20 .~)/SiO(40 A) multilayer prepared by vacuum evaporation the ratios Iii/I± of the first peak and of the second one have about the same value. They concluded that the Fe atom magnetization does not suffer any reduction at the interface. The measured Iii/I± = 0.987 ratio was found between 0.889, which would have been obtained if a 1 A iron layer presented an enhanced magnetization at the interface and 1.124, which would be obtained if it were a dead layer. For a Ni(63 ,~)/SiO(21/~) multilayer [19], the

127

Ph. Mangin et al. / Neutron investigations of magnetic multilayers Fe/Ge

pr.

a

p+

Psi

p-

PF= PSl

P~.

.......

r"-I

iiiiiii , b

p*

p~

Psi

!

p~ pF= Psi

e ,

p ~ . p =lloy

\,

i +

I"

Sputtered F e / G e multilayers were studied by Majkrzak et al. [23] at high angles by X-ray and neutron scattering (which showed satellites around the n = 1 main peak) and at low angles by polarized neutron scattering. A n impressive diffraction scan obtained from a sample containing 515 bilayers of G e and Fe (A = 108/~) is shown in fig. 3. The flipping ratio changes significantly with the order of the p e a k from 4.2 for the fourth p e a k to 0.3 for the fifth one. T h e model presented by the authors assumes that each bilayer is c o m p o s e d of three distinct regions: a region of pure a m o r p h o u s g e r m a n i u m , one of a r a n d o m F e G e alloy at the interface and one of pure B C C iron. The best fit was obtained for an interface constituted of 10 (1 1 0) atomic planes in which the concentration changes linearly from pure g e r m a n i u m to pure ion. A reduction of iron m o m e n t proportional to the germanium concentration was assumed.

-3

Fe/Si -4

i

-5

~l

Different samples obtained by evaporation in a vacuum c h a m b e r were studied. A factor up to 85 was observed between the flipping ratios of

C

1

==

=

J

~'~

;

I

i+

io s _~

,

| ~

/',

FG 517 , i

105

40 X4 = ,

,

I

d

104 0.16

1.12 TH ETA

1.18

!

2.14

..5

(degrees)

Fig. 2. Scattering amplitude density profiles (p+ and p-) seen by [+) and I - ) neutrons in a Fe(25,~)/Si(95/~) multilayer assuming (a) an abrupt interface between iron and silicon, (b) the presence of an Feo.sSi0.5 amorphous alloy at the interface. 1+ and 1 intensities calculated (neutron wavelength 2.52,~) (c) from profiles (a), (d) from profiles

i03

IBI*

q, t

§

•

>. lO z

•

o

" *

"~."

'o.

..

(b).

• •

•-

f

flipping ratios I + / I - are R~ = 1.17 and R 2 = 1.49 on the first two peaks. F r o m these values, it was concluded that one or two atomic layers of iron present a reduced magnetization at the interface.

o

6°

~

2

0.00

~-I ,

• ON • OFF

-4

-s

k=2.67 b

I 0.08

I

I 0.16

I

"

N

.

:.~;

A •

"...;

".

I

I 0.24

o

(~-')

."

•

..

"

"

i"

I

i 0."2

"

I

:..'.'

I 0.40

I

J

Fig. 3. Low-angle polarized neutron scattering from a Fe/Ge multilayer (A = 108 ,~). The 'ON' ('OFF') data points correspond to l+ ) (I-)) scattering.

128

Ph. Mangin et al. / Neutron investigations of magnetic multilayers

the second and fourth peaks. The data were first fitted using a one-step model. Then a model in which the composition of an interface amorphous alloy Fe/Sil_ x changes linearly between Fe and Si was tested [24]. In this model the magnetic moments of iron atoms were taken as a function of the statistical number of Fe nearest neighbour (nn) of each iron atoms: Fe atoms with less than 6 Fe-nn were considered as nonmagnetic; those whose neighbourhood contained more Fe-nn were assumed to carry a moment related to the number of Fe-nn, according to a law deduced from a study of the FeSi amorphous system. The best fit was obtained for an interface thickness of 20/~. Recently, the interest in Fe/Si multilayers was renewed because of the discovery of an antiferromagnetic coupling between the ferromagnetic iron layers. These results were interpreted as a consequence of the formation of the Fe/Si alloy at the interface: when the nominal silicon thickness is small, no pure silicon separates the iron layers and the coupling through the alloy is antiferromagnetic [25,26].

4. Magnetic coupling through nonmagnetic layers 4. i. Introduction One of the more interesting findings in solid state physics during the last few years is the observation of antiferromagnetic coupling between ferromagnetic layers through chromium or through nonmagnetic layers [27], which leads to the so-called giant magnetoresistance effect [28,29]. It was shown later that the coupling was in fact an oscillatory function of the thickness of the nonmagnetic layer and that it could be either ferromagnetic or antiferromagnetic [30-32], which was explained by modified RKKY coupling [33,34]. More recently [35] it has been suggested that biquadratic coupling could take place for thicknesses of the nonmagnetic spacer corresponding to the transition from antiferromagnetic to ferromagnetic coupling. A lot of techniques can indirectly provide information on the magnetic structure of such

systems but neutron scattering is the natural tool for the investigation of long-range magnetic order in magnetic materials, especially when noncollinear structures are present. For the magnetic systems considered here, the interface is usually very abrupt, since most of the constitutive elements are not mutually soluble. Thus in this part we will suppose that the magnetic layers are magnetically homogeneous and consider any possible magnetic profile inside the layers as a second-order effect.

4.2. The ideal case of an isotropic antiferromagnetic multilayer The configuration of the magnetic moments in an ideal isotropic antiferromagnetic multilayer with moments lying in the plane of the film is shown in fig. 4. The magnetic moments are alternatively at +0 and - 0 from the field direction. They exhibit a net ferromagnetic component M scos0 in the x direction and an antiferromagnetic component M s sin 0 in the.y direction. The I ÷÷, I - - and I + intensities expected from the kinematic approximation are reported in table 1. The non spin flip contribution, due to both the nuclear and the ferromagnetic scattering is observed at the position of the chemical Bragg peaks q], q2, etc. of the multilayer. The spin flip contribution, which is due to the transverse component of the magnetization (along y), has a period twice that of the chemical cell, which appears in between the chemical Bragg peaks at q]/2, q3/2, etc. As far as the system has no in-plane aniso-

t 14 1

x

Mcx+l I~a !

-Y v

Fig. 4. Orientations of the spontaneous magnetizations of two successive layers in antiferromagnetically coupled multilayers submitted to a field H. The angles 0~ = 0 and 0~ + ~ = - O are equal and opposite.

Ph. Mangin et al. / Neutron investigations of magnetic multilayers

129

Table 1 Polarized neutron intensities expected from a multilayered system in which the magnetizations of the successive layers make alternatively the angle +0 and - 0 with the quantization axis (fig. 4). Note that the non spin flip scattering is at q~, the position of the nuclear peak and the spin flip scattering at q,~2-

ql qln

I +÷

1

I +-

y(ANb + NmPm COSO)2 0

T(ANb-NmPm COSO)2 0

0 fl(Nmp m sin 0) 2

tropy, cos 0 and the net magnetization are proportional to the external field. Then, up to the saturation field Hsat, beyond which the spontaneous magnetizations of all the layers are parallel, I - - as well as I +- decrease with the field in a parabolic way, whereas I ++ increases. The difference (I ++ - I - - ) increases linearly. Above Hsa t, I ++, I - are constant and I +- is 0. The factors 7 and /3 can in principle be calculated but, as they depend on both interface roughness and sample imperfections, it is better to extract information which is independent of these constants. This is the case for the main parameters, which are the magnetization of the magnetic layers and the value of the angle 0:

the saturation and that, in scattering experiments with nonpolarized neutrons, the intensity of the antiferromagnetic peak decreases as 1 - ( M / M s ) 2 (fig. 5), in agreement with the above description. Recent results [39] indicate that the intensity at ql/2 is purely spin flip above an anisotropy field of about 400 Oe, which means that below this field domains are present. Above this field, the system follows the evolution given in table 1.

== -_=

PNi = A P ( b / 4 p N i ) [ ( I ÷+ - I - - ) n s a /(I++)n=O] ,

cos 0 = [(I++ - I - - ) 1 4 / ( 1 ++ - I--)n~a,] " I

A test of the validity of the model is obtained by checking that the following relation holds whatever the angle O:

0.0

r

0.1

0.2

0.3

.4

(A~,)

.5

0.3 ,0

[(I++ - I - - ) / ( i

++

-- /--)Hsat

]2

x 0.2

"

+ [(I+-)/(I+-)n=o] = 1.

If the sample is not magnetically isotropic in the plane, the system is no more symmetric, domains can appear and the intensities at ql/2 and ql are distributed among spin flip and non spin flip processes. The q1/2 peak remains however proportional to the square of the antiferromagnetic order parameter. A p p l i c a t i o n to N i / A g m u l t i l a y e r s

It has been shown [36-39] in N i ( l l A ) / A g ( l l / ~ , ) multilayers that, except at low fields, the magnetization increases linearly with the field up to

"~

%,

0.5

,

b

o.o

x

,

0.0

I

,

1.0

,

q 4~;...

o.o

2.0 3.0 H (kOe)

Fig. 5. (a) Low-angle neutron scattering from a Ag/Ni • . -1 antlferromagneUc sample. The peak at ql = 0.37 .~ is the nuclear peak, that at qw2 = 0 . 1 8 5 / ~ 1 is the surstructure antiferromagnetic one. (b) Field dependence of the intensity of the antiferromagnetic peak• It is compared to the field dependence of 1 - ( M / M s ) 2. Above 400Oe this peak is purely spin flip•

130

Ph. Mangin et al. t Neutron investigations of magnetic multilayers

First measurements carried out at different temperatures show that the anisotropy field decreases with increasing temperature.

Application to G d / Y multilayers A very similar study has been performed on the G d / Y system [40] by following the evolution of the high-angle satellites of the first ( 0 0 0 2 ) Bragg peak. Two sets of satellites have been observed: those corresponding to the chemical modulation (non spin flip), and those (spin flip) at intermediate positions due to the antiferromagnetic structure. As in Ni/Ag, the intensity of these peaks decreases with increasing field or temperature. 4.3. Ferromagnetic coupling In Gd/Y [40] as well as in the Fe-, Co- or Ni-based multilayers mentioned above, the coupling varies in strength and sign with the thickness of the spacer layer, and thus becomes ferromagnetic for specific thicknesses. The ferromagnetic coupling is often difficult to evidence since it does not lead to any extra scattering peak. It can be checked from the difference between I +÷ and I - - intensities but, since it is necessary to apply an external field to align the domains, the possibility of no coupling (or even weak antiferromagnetic coupling overcome by the field) cannot be eliminated. With the same restrictions, one can also measure the qc+ and qc critical scattering vectors of total reflections: their relative positions are related to the difference between the average positions are related to the difference between the average potentials experienced by the I+) and I - ) neutrons. Another possibility is, provided the magnetic ordering temperature is not too high, to deduce the ferromagnetic contribution from the difference in intensities of the chemical Bragg peak above and well below T~. In some favourable cases the chemical contrast ANb between the layers can be very small and almost all the intensity of the chemical Bragg peak is thus of magnetic origin. A more straightforward possibility to demonstrate the ferromagnetic coupling is to prepare

samples in which, keeping the thickness of the magnetic layers constant, one alternates the thicknesses of the spacer layer, one leading to antiferromagnetic coupling and the other one to the ferromagnetic coupling. Thus, if the coupling is really ferromagnetic, one has in zero field the spin configuration depicted in fig. 6. The magnetic unit cell is twice the chemical one and supplementary diffraction peaks will be observed. Such stackings have been prepared to prove ferromagnetic coupling in G d / Y [41] and Ni/Ag [42] systems.

4.4. Application to other coupled systems Co / Cu The Co/Cu system was the first one in which neutron scattering experiments were carried out in order to check antiferromagnetic coupling [43]. The diffraction pattern showed the occurrence of a supplementary low-angle diffraction peak corresponding to twice the chemical periodicity. The behavior of both antiferromagnetic and chemical peaks as a function of applied field led the authors to the conclusion that the superstructure peak was purely magnetic, and that the magnetic moment carried by the Co atoms was identical to the bulk value. Fe l Cr Giant magnetoresistance effects and antiferromagnetic coupling were first observed in the Fe/Cr system. The neutron scattering experiments were performed by different groups. First measurements by Barthdldmy et al. [44] showed in Fe(30/~)/Cr(15/~) samples the occurrence of

i

i

Ag F

I A

Fig. 6. Magnetic structure of an Ag/Ni sample in which the thickness of the silver layers produce alternatively ferromagnetic and antiferromagnetic coupling between Ni layers. The one-dimension magnetic cell A has been checked by neutron diffraction.

131

Ph. Mangin et al. / Neutron investigations of magnetic multilayers

an antiferromagnetic peak which disappeared under a 8 kOe applied field. Similar results were obtained by Parkin et al. on Fe(32 ]~)/Cr(10 A) and on F e ( 2 0 / ~ ) / C r ( 1 0 & ) samples [45]. The antiferromagnetic structure was inferred from a polarization analysis of this diffraction peak. At low fields 50% of the intensity was found to be spin flip, this contribution increasing with increasing field up to 1 kOe. At this field all the domains were aligned, the magnetic moments being at 90 ° from the applied field. Increasing the field up to 4 kOe led to a decrease of this angle down to 45 ° . Hosoito et al. [46,47] followed the intensities I + and I - of the nuclear and antiferromagnetic peaks as a function of field and temperature. They showed that a 0.5p~ moment, oriented in the field direction was to be attributed to the chromium atoms. As in the above-mentioned work, the transverse component was evidenced by spin flip scattering. The polarization analysis suggested a multidomain structure below 1 kOe. In a recent work, Loewenhaupt et al. [48] studied the effect of annealing on the ferromagnetic and antiferromagnetic components, by measuring the critical q value of total reflection for the two spin polarizations (ferromagnetic c o m p o n e n t ) and the intensity of the Bragg peaks (antiferromagnetic component). The ferromagnetic moment was found to reach 2/zB for high enough fields. The saturation field was observed to decrease with annealing, as a consequence of interface mixing. The authors were not able to observe the antiferromagnetic component. It was suggested that, because of diffuse scattering in the y direction, all the intensity was not integrated by the detector.

whereas samples with Ru thicknesses of 10 and 20/~ were essentially ferromagnetic. The difference between ferromagnetic and antiferromagnetic samples is shown in fig. 7. From the shift in qc values for J+) and J - ) neutrons, a magnetic moment of 1.8ixB per Co atom was deduced for ferromagnetic samples in low fields and for antiferromagnetic ones under the saturating field, whereas much smaller values were obtained in the antiferromagnetic state. This was attributed to diffuse scattering resulting from the limited lateral extension of the antiferromagnetic domains.

l 10 °

a R° R"

10 "I

calculated R*

>,

~

- - calculated R"

10~

10 .3

10 .4 0.00

10 °

0.O2

0.04

J

,

~ 1 1 ~

q(Aq)

0.06

0.08

•

i

.

•

1 o" ~

I~

0.10

R°

b

Calculated R"

10"2

10.~i

~

-"o~c~~

o

Co/Ru

The C o / R u system has been studied by Huang et al. [49] on samples prepared by high vacuum D C magnetron sputtering with Co layers 30 ]k thick and Ru layers 6, 10, 16 and 20 A thick. The ferromagnetic and antiferromagnetic components were analyzed as in ref. [48] under a 80 Oe applied field. Ru thicknesses of 6 and 16 ~ were found to lead to antiferromagnetic coupling,

10 .4

o.oo

J

o,o2

0.04

q(]-l)

0.06

I o.oe

O.lO

Fig. 7. Reflectivitiesfrom Co(30/~)/Ru(16 A) (a) and from Co(30/~)/Ru(10/~) (b) multilayers. The peak in (a) corresponds to an antiferromagnetic surstructure. In (b) the peak is that of the chemical modulations, and there is no antiferromagnetic peak. The proof of the ferromagnetic coupling is provided by the total-reflection shifts between R + and R-.

132

Ph. Mangin et al. / Neutron investigations of magnetic multilayers

4.5. Biquadratic coupling

3

T = 12K _

It has been recently observed in some systems that, in regions where very small thickness variations can lead to either ferromagnetic or antiferromagnetic coupling, another kind of arrangement could be stabilized, in which the magnetic moments tend to align at 90 ° to each other. Such structures have been observed in F e / C r / F e [35], F e / A I / F e [50,51] and C o / C u / C o [52] trilayers prepared by molecular beam epitaxy. The evolution of the magnetization with applied field has been phenomenologically accounted for by considering in the coupling energy a supplementary biquadratic constant B in addition to the usual bilinear A one [53]. With the notations of fig. 4, the total interaction energy can thus be written

2.5

2 ca

1.5

0.5

0

I

I 200

g

I

I

I 600

400

I 800

I

1000

H (Oe) 1

T = 12K[

r~ II

0.8

v

L~ 0.6 '7:

g

.--2_ o.~

as _~

E = - A cos 20 - B cos 40 - H cos 0 .

0.2

i i

0 200

B = 0 corresponds to the case of a usual antiferromagnet, with 0 = 90 ° in zero field and a linear variation of the magnetization with the applied field. For 0 < B < A/4, 0 is still equal to 90 ° in zero field but the magnetization does not vary anymore linearly with the field. For B > A / 4, the equilibrium configuration in zero field corresponds to a canted state. In this case the difference (I ++ - I - - ) is no more zero in zero field. In NiFe/Ag multilayers [54], both magnetization and polarized neutron results obtained on samples with Ag thicknesses corresponding to the maximum of the antiferromagnetic coupling can be very well accounted for by such a model (fig. 8). With decreasing temperature, the equilibrium magnetic configuration in zero field changes from antiparallel alignment above 100 K to a canted state in which at 12 K the magnetic moments in successive layers are at 140° from each other. Since in this case the thickness of the Ag spacer does not correspond to the transition zone between ferromagnetic and antiferromagnetic regions, other effects, such as the fact that the magnetic layer is an alloy, could be responsible for such a magnetic configuration. Canted structures have recently been observed

400

600

800

1000

H (Oe) Fig. 8. Field dependence of the I++, 1- and I + intensities scattered from a N i s t F e t g ( l l / ~ ) / A g ( 1 2 / k ) sample. The evolutions of the intensities and the fact that at zero field 1 +÷ is different from 1 - - demonstrates the occurrence of a biquadratic contribution to the magnetic coupling.

in neutron scattering experiments by Andrieux et al. [55] on F e / I r superlattices.

5. Rare earth/Fe systems

5.1. Introduction In R E / F e multilayers, both elements are magnetic but with very different magnetic parameters: Fe is a 3d-ferromagnet with a high Curie temperature. The rare earths interact ferromagnetically via the conduction electrons, and most of them exhibit strong magnetocrystalline anisotropy; their ordering temperatures are below room temperature and they exhibit a lot of different magnetic structures. The magnetic coupling between iron and rare earth layers is a

Ph. Mangin et al. / Neutron investigations of magnetic multilayers

direct exchange at the interface: it is antiferromagnetic for heavy rare earths (Gd, Tb, Er, D y , . . . ) and ferromagnetic for light ones (Nd, T m , . . . ) . As these systems are candidates for magnetic recording, a lot of work using different techniques has been devoted to their magnetic structure. The polarized neutron scattering provides information on the M x and My profiles, in complement to the magnetization measurements which give the sum of the magnetizations of both layers in the +x direction (that of the magnetic field) and M6ssbauer spectroscopy which gives information on the iron hyperfine field distribution.

133

H

Aligned-Gd

Twisted

5.2. The in-plane quasi-isotropic G d / F e system

Because Gd is an isotropic S-ion, the Fe/Gd system was very early modelized. From calculations taking into account the positive exchange between iron moments and between gadolinium magnetic moments and the negative exchange at the interface, it was shown that three magnetic states could be stabilized [56] namely alignedGd, aligned-Fe and twisted states (fig. 9). The aligned-Gd state occurs at low field when the magnetization of gadolinium layers is larger than the magnetization of iron layers. Gadolinium moments are simply in the field direction and the iron moments are antiparallel to this direction. The Fe-aligned state occurs at low field when the magnetization of iron is larger than that of gadolinium. The iron moments are oriented in the field direction and the gadolinium moments are antiparallel. The twisted state appears when a large enough field destabilizes the aligned states, which can be easily done near the compensation temperature. In this phase, the magnetic moments of both layers are rather perpendicular to the field direction at the interface where they are blocked antiparallel and rotate towards the field direction (as in a domain wall) from the interface to the center of the layers. The phase diagram of a Fe/Gd sample is pictured in fig. 10 [57]. The low-angle neutron scattering data obtained on a Fe(42/~)/Gd(84/~) as a function of temperature under a 1 kOe field, i.e., in follow-

Aligned-Fe

Fig. 9. Schematic drawing of spin configurations in alignedGd (top), twisted (middle) and aligned-Fe (bottom) states.

.

.

.

.

i

.

.

.

.

i

.

.

.

Twisted

•~. O 2

~" 0

.

t

,

,

~

I

,

,

~

100

,

1

200

Ahgned Fe] ~ '~

r "~

!

300

T(K)

Fig. 10. Critical field H* of transition between the aligned and twisted state determined by magnetization measurements as a function of temperature for a Gd(84,~)/Fe(42,~) sample.

134

Ph. Mangin et al. / Neutron investigations of magnetic multilayers •

== 1.5

I--

•

I++

. . . .

i

. . . .

i

,

•

I+

i

. . . .

I

,

A v

E .~ 0 . 5

, ~

,

,

,

,

,

,

,

i

0 100

200

,

I

300

T(K)

Fig. 11. Thermal dependence of the first low-angle Bragg peak intensities (1 ~+, I and 1 ÷-) from Gd(84~)/ Fe(42/~). The applied field was 1 kOe, which means that the horizontal line of fig. 10 was followed. 1÷- goes through a maximum in the twisted state. Because the direction of iron moments are inversed between Fe and Gd aligned states, the I ++ and 1-- intensities are reversed at low and high temperatures.

Those of D y / F e [60] obtained from 22 K to r o o m t e m p e r a t u r e are shown in fig. 12. At 22 K both average magnetizations of iron and of the rare earth are in the field direction, except at the interface where the average magnetization of the rare earth is opposite to that of iron (as expected from the antiferromagnetic coupling). In the core of the rare earth layers and because of the larger perpendicular anisotropy, the average magnetization is considerably reduced c o m p a r e d to 1 0 . 7 ~ B / a t o m found in bulk dysprosium. At room t e m p e r a t u r e most of the dysprosium is no more magnetic but some rare earth atoms re2

300<

•

o -2 -4 -6

ing line (a) of fig. 10 are shown in fig. 11 [58]. An inversion of the I ++ and I - - intensities occurs near the compensation temperature, which indicates that in the aligned states the roles of Fe and Gd are reversed. A m a x i m u m of spin flip scattering in the twisted phase is observed at the compensation t e m p e r a t u r e , which proves that the magnetizations are essentially perpendicular to the quantization axis (along the y direction) at this temperature. Surface effects have been evidenced theoretically by Lepage and Camley [59] and experimentally from low-angle neutron scattering by L o e w e n h a u p t et al. [48]: the nature of the top layer plays a role in the magnetic structure of neighbouring layers close to the surface and can lead to a twisted surface state. 5.3. A n i s o t r o p i c rare e a r t h / F e systems

-8

Z

150K

-W

o I

"i -6

2 0

-2 4

221<

0 -2

In D y / F e , E r / F e , T b / F e and N d / F e multilayers, the weaker exchange between rare earth magnetic m o m e n t s and the larger rare earth anisotropy, do not permit the occurrence of a simple aligned or twisted phase. In the absence of a coherent perpendicular component, neutron scattering provides the average M x profiles.

-4 -6 Fe layer

Dy

layer

Fig. 12. Thermal dependence of the magnetic profiles in a Dy(60 ~)/Fe(40 ~k) multilayer as determined from polarized neutron scattering. The unit of the vertical scale is p.B/atom.

Ph. Mangin et al. / Neutron investigations of magnetic multilayers

main coupled antiparallel to iron. Such a behaviour has been observed by low-angle polarized neutron scattering in some Tb/Fe [61] and Er/Fe samples [62]. Information about the possible reorientation of Nd magnetic moments from perpendicular to the film to parallel to the film have been recently obtained by Hosoito et al. [63]. From magnetization measurements and polarized neutron scattering, they showed that the spin reorientation occurs both in the Fe and Nd layers and that the origin of the perpendicular anisotropy could be attributed to the Nd atoms near the interface.

6. Conclusion Neutron scattering has been known for a long time to be a unique tool for the determination of magnetic structures in bulk magnetic materials in which very tricky magnetic structures have been resolved. It is now clear from the above examples that this technique has an important role to play in the determination of the magnetic structures of multilayered materials where unexpected effects have been recently observed; this is all the more true since the structures are non-collinear as in twisted phases or in systems exhibiting a biquadratic coupling. In these more complex structures the information provided by polarized neutron is really conclusive. Finally in the examples presented here, the systems were composed of a lot of individual layers (above fifty) and the studies were focused on low-angle scattering. This is in fact one of the possibilities offered by the neutrons to study the layered systems. When the number of layer is small, as in spin valves [64], the reflectometry is better suited [8-65]. On the other hand, measurements can be performed at high angles when the thin layer (some hundreds of ~ ) is in epitaxy on a substrate and is finally a single crystal [7].

Acknowledgements The authors wish to thank G. Marchal (Nancy) for his contribution in the study of some

135

of the systems presented in this review and to M. Hennion (LLB), J.J. Rhyne (MURR), R. Erwin (NIST) and C. Vettier (ILL) for their active participation and their precious advices in the neutron scattering experiments. Some of the experiments were supported by NATO Collaborative Research Grant No. 550/87.

References [1] M.B. Salamon, S. Sinha, J.J. Rhyne, J.E. Cunningham, R.W. Erwin, J. Borchers and C.P. Flynn, Phys. Rev. Lett. 56 (1986) 259. [2] R.W. Erwin, J.J. Rhyne, M. Salamon, J. Borchers, S. Sinha, R. Du, J.E. Cunningham and C. Flynn, Phys. Rev. B 35 (1987) 6808. [3] L.M. Falicov, D.T. Pierce, S.D. Bader, R. Gronsky, K.B. Hathaway, H.J. Hopster, D.N. Lambeth, S.S.P. Parkin, G. Prinz, M.B. Salamon, I.K. Schuller and R.H. Victoria, in: Materials Reports on Surface, Interface and Thin-Film Magnetism, J. Mater. Res. 5 (1990) 1299. [4] F. Mezei, Commun. Phys. 1 (1976) 81. [5] O. Sch/irpf, Physica B 156&157 (1989) 631. [6] S.J. Blundell and J.A.C. Bland, Phys. Rev. B 46 (1992) 3391. [7] D. McMorrow, Physica B 192 (1993) 150. [8] G. Felcher, Physica B 192 (1993) 137. [9] W. Gavin Williams, Polarized Neutrons (Clarendon Press, Oxford, 1988). [10] S. Lovesey, Theory of Neutron Scattering from Condensed Matter (Clarendon Press, Oxford, 1984). [11] V.F. Sears, Neutron Optics (Clarendon Press, Oxford, 1988). [12] V.F. Sears, Acta Cryst. A 39 (1983) 601. [13] J. Underwood and T. Barbee, Appl. Opt. 20 (1981) 3027. [14] F. Ab~lds, Ann. Phys. (France) 12 (1950) 596. [15] L.G. Paratt, Phys. Rev. 95 (1954) 359. [16] M. Piecuch and L. Nevot, in: Metallic Multilayers, eds. A. Chamberod and J. Hillairet, Mater. Sci. Forum 59-60 (1990) 93. [17] G.P. Felcher, R.O. Hilleke, R.K. Crawford, J. Hanmann, R. Kleb and G. Ostowsksi, Rev. Sci. Instr. 58 (1987) 609. [18] S. Blundell and J.A.C. Bland, J. Magn. Magn. Mater. (in press). [19] M. Sato, K. Abe, Y. Endoh and J. Hayter, J. Phys. C 13 (1980) 3563. [20] Y. Endoh, J. de Phys. C 7 (1982) 159. [21] C. Dufour, A. Bruson, B. George, G. Marchal, Ph. Mangin, C. Vettier, J.J. Rhyne and R.W. Erwin, Solid State Commun. 69 (1989) 963. [22] C. Dufour, Thesis, Nancy University, France (1990).

136

Ph. Mangin et al. / Neutron investigations of magnetic multilayers

[23] C.F. Majkrzak, J.D. Axe and P. B6ni, J. Appl. Phys. 57 (1985) 3657. [24] C. Dufour, A. Bruson, G. Marchal, B. George and Ph. Mangin, J. Magn. Magn. Mater. 93 (1991) 545. [25] E.E. Fullerton, J.E. Mattson, S.R. Lee, C.H. Sowers, Y.Y. Huang, G. Felcher and S.D. Bader, J. Magn. Magn. Mat. 117 (1992) L301. [26] J.F. Anker, C.F. Majkrzak and H. Homma, J. Appl. Phys., in press. [27] P. Griinberg, R. Schreiber, Y. Pang, M.B. Brodsky and H. Sowers, Phys. Rev. Lett. 57 (1986) 2442. [28] G. Binash, P. Griinberg, F. Saurenbach and W. Zinn, Phys. Rev. B 39 (1989) 482. [29] M.N. Baibich, J.M. Broto, A. Fert, F. Petroff, P. Etienne, G. Creuzet, A. Friedrich and J. Chazelas, Phys. Rev. Lett. 61 (1988) 2472. [30] S.S.P. Parkin, N. More and K.P. Roche, Phys. Rev. Lett. 64 (1990) 2304. [31] D.H. Mosca, F. Petroff, A. Fert, P.A. Schroeder, W.P. Pratt and R. Loloee, J. Magn. Magn. Mater. 94 (1991) L1; S.S.P. Parkin, Z.G. Li and D.J. Smith, Appl. Phys. Lett. 58 (1991) 2710. [32] C.A. dos Santos, B. Rodmacq, M. Vaezzadeh and B. George, Appl. Phys. Lett. 59 (1991) 126. [33] P. Bruno and C. Chappert, Phys. Rev. Lett. 67 (1991) 1602. [34] R. Coehoorn, Phys. Rev. B. 44 (1991) 9331. [35] M. R/ihrig, R. Sch~ifer, A. Hubert, R. Mosler, J.A. Wolf, S. Demokritov and P. Gr/Jnberg, Phys. Stat. Sol. A 125 (1991) 635. [36] B. Rodmacq, Ph. Mangin and Chr. Vettier, Europhys. Lett. 15 (1991) 503. [37] B. Rodmacq, Ph. Mangin, M. Hennion and R.W. Erwin Physica B 180-181 (1992) 477. [38] B. Rodmacq, B. George, M. Vaezzadeh, M. Gerl and Ph. Mangin, J. Phys.: Condens. Matter 4 (1992) 4527. [39] B. Rodmacq, K. Dumesnil, M. Vergnat, Ph. Mangin and M. Hennion, to be published. [40] C.F. Majkrzak, J.W. Cable, J. Kwo, M. Hong, D.B. McWhan, Y. Yafet, J.W. Waszczak and C. Vettier, Phys. Rev. Lett. 56 (1986) 2700. [41] C.F. Majkrzak, J. Kwo, M. Hong, Y. Yafet, D. Gibbs, C.L. Chien and J. Bohr, Adv. Phys. 40 (1991) 99. [42] B. Rodmacq, P. Burlet, Ph. Mangin and M. Hennion, in: Proceedings of the MRS spring meeting, San Francisco, April 1993 (to appear in Mat. Res. Soc. Symp. Proc.). [43] A. Cebollada, J.L. Martinez, J.M. Gallego, J.J. de Miguel, R. Miranda, S. Ferrer, F. Batallan, G. FiUion and J.P. Rebouillat, Phys. Rev. B 39 (1989) 9726.

[44] A. Barth616my, A. Fert, M.N. Baibich, S. Hadjoudj, F. Petroff, P. Etienne, R. Cabanel, R. Lequien, F. Nguyen van Dau and G. Creuzet, J. Appl. Phys. 67 (1990) 5908. [45] S.S.P. Parkin, A. Mansour and G.P. Felcher, Appl. Phys. Lett. 58 (1991) 1473. [46] N. Hosoito, S. Araki, K. Mibu and T. Shinjo, J. Phys. Soc. Japan 59 (1990) 1925. [47] N. Hosoito, K. Mibu, S. Araki, T. Shinjo, S. Itoh and Y. Endoh, J. Phys. Soc. Japan 61 (1992) 300. [48] L. Loewenhaupt, W. Hahn, Y. Huang, G.P. Felcher and S.S.P. Parkin, to be published. [49] Y.Y. Huang, G.P. Felcher and S.S.P. Parkin, J. Magn. Magn. Mater. 99 (1991) L31. [50] A. Fuss, S. Demokritov, P. Griinberg and W. Zinn, J. Magn. Magn. Mater. 103 (1992) L221. [51] C.J. Gutierrez, J.J. Krebs, M.E. Filipkowski and G.A. Prinz, J. Magn. Magn. Mater. 116 (1992) L305. [52] B. Heinrich, J.F. Cochran, M. Kowalewski, J. Kirschner, Z. Celinski, A.S. Arrott and K. Myrtle, Phys. Rev. B 44 (1991) 9348. [53] J.C. Slonczewski, Phys. Rev. Lett. 67 (1991) 3172. [54] B. Rodmacq, K. Dumesnil, Ph. Mangin and M. Hennion, Phys. Rev. B 48 (1993) 3556. [55] S. Andrieux, M. Hennion and M. Piecuch, in: Proceedings of the MRS spring meeting, San Francisco, April 1993 (to appear in Mat. Res. Soc. Symp. Proc.). [56] R.E. Camley, Phys. Rev. B 37 (1988) 3413. [57] K. Cherifi, C. Dufour, Ph. Bauer, G. Marchal and Ph. Mangin, Phys. Rev. Rapid Commun. 44 (1991) 7733. [58] C. Dufour, K. Cherifi, G. Marchal, Ph. Mangin and M. Hennion, Phys. Rev. B 47 (1993) 14572. [59] J.G. LePage and R.E. Camley, Phys. Rev. Lett. 65 (1990) 1152. [60] N. Hosoito, K. Yoden, K. Mibu, T. Shinjo and Y. Endoh, J. Phys. Soc. Japan 58 (1989) 1775. [61] C. Dufour, M. Vergnat, K. Cherifi, G. Marchal, Ph. Mangin and C. Vettier, Physica B 180-181 (1992) 489. [62] C. Dufour, M. Vergnat, G. Marchal, Ph. Mangin, M. Hennion and C. Vettier, to appear in J. Magn. Magn. Mater. [63] N. Hosoito, K. Mibu, T. Shinjo and Y. Endoh, J. Phys. Soc. Japan 61 (1992) 2477. [64] B. Dieny, V.S. Speriosu, S.S.P. Parkin, B.A. Gurney, D.R. Wilhoit and D. Mauri, Phys. Rev. B 43 (1991) 1297. [65] N.M. Harwood, S. Messolaras, R.J. Stewart, J. Penfold and R.C. Ward, Phil. Mag. B 58 (1988) 217.