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Permeability measurement on ferromagnetic thin films from 50 MHz up to 18 GHz
~H
ELSEVIER
Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
journalof magnetism and magnetic materials
Permeability measurement on ferromagnetic thin films from 50 MHz up to 18 GHz O. Acher
*, J . L . V e r m e u l e n ,
P.M. Jacquart,
J.M. Fontaine,
P. Baclet
CEA / DETN, BP 12, F-91680 Bruy~res le Ch~tel, France
Received 15 December 1993; in revised form 5 March 1994
Abstract
The needs for permeability measurements on ferromagnetic materials at high frequencies are driven by the development of broad-band recording systems. However, measurements above 500 MHz on ferromagnetic films are difficult. Wide band permeability measurements are reported only up to a few GHz. Measurements at higher frequencies can be performed using resonant cavities, as it is done in ferromagnetic resonance, but only at discrete frequencies. In contrast, we present a technique for measuring high frequency permeability of ferromagnetic films over a wide band. It works in a frequency range (50 MHz to 18 GHz or higher) that allows direct observation of the gyromagnetic resonance even on non-saturated samples, and can yield permeability in different directions for anisotropic films. In our technique a surface of about 0.5 dm 2 of the ferromagnetic material has to be wound to obtain proper sample geometry. As a consequence, our technique is restricted to coatings deposited on thin flexible substrates and to thin self supported ribbons produced by rapid solidification. Comparison with another measurement technique working up to 3 GHz, and with calculated gyromagnetic response, yield a satisfactory agreement. The limitations of our method are discussed. Spectroscopic permeability measurements are reported for several alloys.
1. Introduction
T h e needs for permeability m e a s u r e m e n t s on ferromagnetic materials at high frequencies are driven by the d e v e l o p m e n t of b r o a d - b a n d recording systems [1]. However, m e a s u r e m e n t s above 500 M H z on ferromagnetic films are difficult [2]. Wide b a n d permeability m e a s u r e m e n t s are rep o r t e d only up to a few G H z [3,4]. M e a s u r e m e n t s at higher frequencies can be p e r f o r m e d using r e s o n a n t cavities, but at discrete frequencies. F o r
* Corresponding author. Fax: + 33-1-6926 6128.
that reason, ferromagnetic resonance is generally studied by recording permeability as a function of external magnetic field [5], rather than as a function of frequency. This restricts the investigations to saturated samples. In contrast, the high frequency permeability of ferrimagnetics is conveniently m e a s u r e d using reflexion-transmission m e a s u r e m e n t s in a waveguide [6]. Such measurements are c o m m o n l y p e r f o r m e d f r o m a few M H z to over 40 G H z , using coaxial lines or p r o p e r waveguides and n e t w o r k analyzers. T h e coaxial line is particularly convenient to p e r f o r m measurements on a wide frequency range, using a single toroidal sample. This m e t h o d is well known
0304-8853/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0304-8853(94)00323-J
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O. Acher et aL /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
and regarded as precise and reliable [7]. However, this technique is not suitable for materials with permittivity larger than the permeability by several orders of magnitude. This is the case of ferromagnetic materials that are highly conducting and therefore have extremely high permittivities. Total reflexion occurs on a bulk conducting ferromagnetic placed in a waveguide, and this does not allow the determination of its permeability. The present work presents a method to determine the permeability of ferromagnetic films using standard coaxial measurement apparatus. The theoretical background and the experimental procedure are described in a first part. In particular, this method requires that the ferromagnetic layer is wound, so it has to be deposited on a thin flexible substrate such as mylar. Thin ribbons produced by rapid solidification are also well suited for these measurements. In all cases, a surface of 0.5 dm 2 of film is required. Experimental results on a variety of different magnetic thin films are presented in the second part. They are compared to theoretical predictions and to resuits obtained by other measurements techniques. In the third part, the validity and the limitations of the method are discussed, as well as the opportunities it opens up.
Insulator ferromagnetic lamination
(a)
(b) Fig. 1. (a) Sketch of the geometry of a Laminated InsulatorFerromagnetic on Edge (LIFE) composite adapted to coaxial line geometry. The propagation vector k, and E and It fields corresponding to the fundamental mode are also sketched. (b) Micrograph of part of the surface of a wound torus. The torus was made by winding a 0.4 p,m thick amorphous Cobalt-based alloy deposited by magnetron sputtering on 8 ~ m thick mylar.
2. Experimental method In order to benefit from the coaxial measurement abilities, we manufactured our ferromagnetic thin films into samples that appear both as insulating (and therefore with relatively small permittivity) and magnetic for the fundamental mode propagating in the coaxial line. Since the fundamental mode in the coaxial line has nearly radial electric field and concentric magnetic field, it is intuitive that a laminated sample consisting of concentric cylinders of alternated insulating and ferromagnetic materials would behave as an insulator and allows the penetration of the wave in the composite (Fig. la). This sample geometry will be designated as Laminated Insulator-Ferromagnetic on Edge (LIFE). The fact that the propagating wave arrives on the edge of the lamina-
tions and propagates along the laminations allows large penetration of the wave in the material for the fundamental mode. If the insulator thickness is much smaller than the wavelength, and the ferromagnetic thickness much smaller than the skin depth, Wiener's relations [8] confirm this intuitive view. They indicate that the composite has a magnetic susceptibility that is simply that of the ferromagnetic film, multiplied by its volume fraction. Clogston [9] and Rytov [10] treated the case of laminations including skin effects. However, conforming to strictly coaxial Clogston geometry would lead to great difficulties in the fabrication of the samples. For that reason, we slightly departed from this geometry by wounding ribbons of ferromagnetic films deposited on thin
O. Acher et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
flexible insulating substrates into torus suitable for coaxial line measurement [11,12] (Fig. lb). Our samples were therefore spiral-like, rather than a series of concentric cylinders, but we believe that this is of little consequence for finely laminated samples at high frequency, as will be discussed further. If the ferromagnetic film is anisotropic, one can cut two sets of ribbons, one along each anisotropy eigenaxis, and then make two tori. Each torus will yield the permeability along its ribbon direction, since magnetic field in the coaxial line is orthoradial [6,9] and therefore along the ribbon direction. The permeability/zeff of a laminated composite illuminated by a wave with propagation vector and H field in the plane of the composite is given by Rytov [10]. In our experiments, the thickness of the dielectric is in the 3.5 to 15 ~ m range. Since it is much smaller than the wavelength in the composite, Rytov's expression becomes: fi/-t i + fcfc/-~ c [£eff =
1
(1)
+ f c ( C ¢ - 1)
with C¢=
tg X X
(2a)
and "IT
]d.i and /z c are the permeability of the insulating dielectric and of the conducting ferromagnetic respectively, fi and fc the volume fraction of the dielectric and conducting ferromagnetic, e~ and othe thickness and conductivity of the ferromagnetic. F designates the frequency. For a nonmagnetic insulator (/z i = 1) and a small ferromagnetic volume fraction f~, (1) becomes at the first order in f~: /'Left- 1 = f~Cc(/~ c - 1).
(3)
If e c is much smaller than skin depth, Cc = 1 and (1) reduces to the Wiener relation [8]. For thicker films, skin effect occurs, and it is possible to compute the intrinsic permeability/Xc using relation (2) and (3). The coefficient Cc accounts for
271
skin effect. It can be shown that its module is equal or less than unity. It is also convenient to introduce the apparent permeability I.Lap defined by: /.Lap -- 1 = C c ( / £ c -
1) -
/~ff - 1 -
-
L
(4)
We investigated the high frequency permeability of several ferromagnetic films with different thicknesses and compositions using this method. Cobalt-based amorphous alloys were prepared onto continuously transported mylar films 8 to 12 Ixm thick by dc planar magnetron sputtering. Kerr magnetooptic measurements indicated that the materials had soft properties ( H c < 0.5 Oe), and that their easy and hard axes had a constant orientation over the whole film surface. The magnetic field created by the magnetron was responsible for this orientation. Ribbons were cut in the ferromagnetic-coated mylar sheets, some parallel to the easy axis, and some parallel to the hard axis. Amorphous CoFeNiMoSiB ribbons were prepared by melt spinning. Ribbon thickness was reduced from 20 to about 6 txm by chemical etching, and glued on 8 Ixm thick polyethylene film. Ion Beam Sputtering (IBS) [13] was also used to manufacture microcrystalline CoFeSiB films and pure iron films on 8 txm thick polyethylene substrate. These ribbons were wound and glued into torus. Then the LIFE sample was machined to the desired dimensions with tight tolerances [7] and measured in APC-7 coaxial line with 3 mm inner diameter and 7 mm outer diameter [6,7]. APC-7 measurements yielded values of ]'/'eft with a precision better than 5% for frequencies higher than 500 MHz. The low frequency bound of our measurements could be made lower than 50 MHz, but with some degradation in accuracy. The upper measurement frequency is fixed by the capabilities of the network analyzer used, and also by the cut-on frequency of higher modes in the coaxial line. It would be possible to extend the upper frequency bound by using a proper network analyzer and a coaxial line with smaller diameter. Depending on the insulator, ferromagnetic and
O. Acher et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
272
glue thickness, each sample consisted of about 100 to 250 turns. As a consequence, the composites can be adequately described as finely laminated samples. Torus thickness ranged from 0.7 to 3 mm. Ferromagnetic volume fraction in the torus was deduced from microscopic observations of ferromagnetic, substrate and glue thickness, and also from density measurements. Apparent and intrinsic permeability were deduced from measured composite permeability ]'/'eft using relations (2) to (4), Flexible insulating substrate and glue were considered as a single non-magnetic insulating material. The electrical conductivity occurring in (2) was measured using four point probe. In order to make comparisons with already existing methods, permeability measurements up to 3 GHz were also performed using a single-turn coil susceptometer described elsewhere [3] on 1 cm 2 film samples. Gyromagnetic permeability predicted by the Landau-Lifschitz model [14] was calculated for some samples. In the saturated thin film geometry, when damping parameter/3 is small and anisotropy field is much smaller than saturation magnetization, the per-
meability along hard axis predicted by this model is: B~
uc
1
Ha 1-7,2+j/3v
+ 1
(5)
where F ~'=~-
and
Fr~--~B s ~ s ~ a
.
F is the frequency,/3 is the damping parameter, and 3' is the gyromagnetic ratio. Calculations were performed using experimental values of anisotropy field H a deduced from Kerr measurements, and saturation magnetization B~ measured using a magnetic balance.
3. E x p e r i m e n t a l results
A first concern was to compare experimental results obtained from measurements on LIFE torus with other experimental results or theoretical predictions. Soft amorphous ferromagnetic thin films are convenient for that purpose, be-
0.4 ixm thick amorphous CoZrMoNi on mylar
700
oo
600
(a) LIFE
o • .
~
IJ''J
500
.o,
400
300 25
•
~o
.-
\~
o o Ix"J (b) col
i
L
t ~
200
°o ~
Ix'
(c) calculated
100 0 0.1
1
10
-100 -200 -300
F(GHz) Fig. 2. Intrinsic permeability/z' - j/x" of a 0.4 ixm thick CoNbZr film (a) measured using our coaxial technique on a LIFE sample, (b) measured up to 3 GHz using a single coil technique, (c) calculated using Landau Lifschitz equation.
o. Acher et aL /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
cause their gyromagnetic behaviour is rather well understood, and also because their resonance frequency is in the frequency range of our single-coil permeability m e a s u r e m e n t system. Fig. 2 shows the complex permeability of a C o Z r M o N i amorphous film (0.4 ixm thick) along hard axis. Curve (a) is the experimental result obtained from coaxial m e a s u r e m e n t on a L I F E sample according to our method. Curve (b) was obtained by single-coil m e a s u r e m e n t technique up to 3 GHz, and curve (c) from Landau-Lifschitz model, using experimental values of H a and B s, and the damping p a r a m e t e r as the single adjustable parameter. A very good agreement is observed between our method and the other determinations. It should be however mentioned that our method requires the precise determination of the ferromagnetic volume fraction. This value is deduced essentially from density measurements, with an uncertainty of about 10%. Clearly, it would be possible to reduce this uncertainty, for example by measuring the saturation magnetization of the L I F E sample. Single coil measurements also require the knowledge of the volume,
273
and therefore suffer from this same 10% uncertainty, plus the uncertainty related to the apparatus calibration and to finite sample size effects that is much larger, of about 40%. For that reason, experimental curves of Fig. 2 were obtained by adjusting the ferromagnetic volume fraction so that /z' at 100 M H z would be the same for all three determinations. This was possible by changing the ferromagnetic volume fraction from its determination by less than 10% for L I F E measurements and less than 30% for single coil measurement. The same adjustment was performed for Figs. 3 and 4, always by adjusting the volume fraction within the experimental uncertainty. Fig. 3 shows the apparent permeability measured on relatively thick (5 Ixm) amorphous ribbons. Experimental determination on two L I F E samples measured in a coaxial line are given. One torus was obtained by wounding a continuous ribbon. The other torus was made by wounding the ribbon with many electrical discontinuities. A 1 or 2 m m gap was left between 1.5 cm long portions of ribbon. The purpose was to assess the effect of having a spiral-wound torus with electrical continuity between inner conductor and outer
5 pm thick Co-based ribbon 400
300
• • tl'~ (a) LIFE 1 [] l l " j
200
0 0
>., c~
E O_ ¢-
,,}- (b) LIFE 2
r,
O_ t'~
~ (C) coil
~a
100
0.1
/,t,J ~"J
1
10
F(GHz) Fig. 3. apparent permeability of a 5 gm thick Co-based amorphous ribbon (a) measured using our technique on a LIFE sample obtained by wounding a continuous ribbon, (b) measured on a LIFE sample obtained by wounding a discontinuous ribbon (one cut every 1.5 cm), (c) measured using single coil technique up to 1.6 GHz.
274
O. Acher et al. / Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
6 Ixm thick Co-based ribbon 200 (a) LIFE 150
o
•
%%
(b) coil =~ 100 Q.
E ~ 50
(c) calculated "k."
e~ O.
.
.
.
.
~%o
---
c
~c'j
.
0.1 -50
F(GHz) Fig. 4. apparent permeability of a 6 I~m thick Co-based amorphous ribbon (a) measured using our technique on a LIFE sample obtained by wounding a continuous ribbon, (b) measured using single coil technique up to 3 GHz, (c) calculated using Landau-Lifschitz and Rytov equations.
conductor, i n s t e a d of a strictly coaxial geometry as described by Clogston [9]. A good a g r e e m e n t is also o b t a i n e d with single coil m e a s u r e m e n t s .
Fig. 4 c o m p a r e s a p p a r e n t p e r m e a b i l i t y determ i n a t i o n s o n a n o t h e r thick a m o r p h o u s ribbon, o b t a i n e d by coaxial m e a s u r e m e n t s o n a L I F E
0.5 ~tm thick amorphous CoZrMoNi on mylar 600
__
,,
(hard axis)
400 ....... .
.
.
.
.
.
.
.
-"'"""/\,
/
~t~ (easy axis)
.
-~ 200 E
0
o,
4
""i ..... ///,
-200
% /
-400 F(GHz) Fig. 5. Intrinsic permeability/z' - j/x" of a CoNbZr film along hard and easy axis.
O. Acher et aL /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
275
0.5 I~m thick microcrystalline CoFe SiB
't
. - . s
120
G ~
~U.' I
.
as deposited ILl,"
80
.....
P"
after magnetization
.JD (D
E
40
0 ~).1
-40 F(GHz)
Fig. 6. Intrinsic permeability of a 0.5 p,m thick microcrystallineCoFeSiB film, measured before and after magnetization.
sample, by single-coil m e a s u r e m e n t s and from theoretical predictions. Theoretical predictions were obtained from Landau-Lifschitz equations for gyromagnetic resonance that were injected in Rytov's model to take skin effect into account. A very good concordance between experimental re-
250
i
sults and theoretical predictions is observed. The agreement is not so good with single-coil measurements. Inhomogeneities over the length of the melt-spun ribbon may account for differences in electromagnetic properties among different samples.
]
I
Iron thin films deposited ""
=
,,
=
~
100
by I.B.S. under different condil ons
I
i
!
i
I
i
"~,
50 .
0
0
.
.
.
.
. 5
.
.
"'i'".'": 10 F(GHz)
"': . . . . . . 15
20
Fig. 7. Intrinsic permeability (imaginary part) of two iron films less than 0.2 p,m thick deposited by Ion Beam Sputtering under different conditions.
276
O. Acher et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
Fig. 5 represents the intrinsic permeability of CoNbZr along easy and hard axes deduced from coaxial measurements. The film was 0.5 txm thick, its conductivity was 135 ixl~" cm, and corrections due to skin effect brought by factor C c in Eq. (3) were less than 15%. The permeability along hard axis exhibits two resonance peaks at 850 MHz and 1.84 GHz. As expected, the permeability is much larger along the hard axis than along the easy axis, which is consistent with the gyromagnetic origin of the permeability in this frequency range. Permeability along the easy axis would be expected to be unity if the magnetization were uniform and parallel to the ribbon axis. Ripple [15] or inhomogeneities may account for the residual permeability observed here, and also extrinsic effects like stress [16] as discussed in the next section. Fig. 6 shows the permeability measured on a microcrystalline CoFeSiB LIFE torus before and after magnetization along its axis. The permeability is clearly affected by the magnetization. Kerr effect measurements on the film indicate that it does not have good soft magnetic properties, the coercive force is larger than 10 Oe. In contrast, all other materials in Figs. 2-5 have soft properties (He < 1 0 e ) and do not show significant permeability change after magnetization. Fig. 7 shows the intrinsic imaginary permeability of two iron layers deposited using IBS under different conditions. Layer thickness is less than 0.2 Ixm. Permeability levels are small, but unlike most soft amorphous materials, these layers exhibit a very broad gyromagnetic response, with significant magnetic losses above 10 GHz. This makes the high frequency ability and high sensitivity of our measurement process very valuable for studying the effect of deposition conditions and texture on gyromagnetic permeability of Febased layers.
4. Discussion
Figs. 2 to 4 show clearly that our technique yields results that are in good agreement with other experimental determinations and theoretical predictions. In particular, Fig. 3 shows clearly
that there is no difference between samples made from continuous and electrically discontinuous ribbons. This addresses the objection that our coaxial measurements are performed on spiralwound sample, and not on strictly coaxial geometry. However, one should keep in mind that the equivalence of properties between wound and perfectly concentric torus has a limited range of validity. It is expected no longer to be valid at low frequency, where the wound torus will act as a short. It is also expected not to be valid for thick conducting layers. However, it seems clear that in the frequency range investigated here and for ferromagnetic layers up to several txm thick, the laminated sample can be produced by winding. The validity of the Clogston-Rytov relations may also be questioned. They rely on exact propagation equations in an infinite laminated medium, so they are expected to be much more appropriate than many homogenization laws. However, coaxial measurement relies not only on measurement of propagation constants, but also on measurement of the reflexion-transmission coefficients at the interfaces. It is still a question to what extent permeability and permittivity inferred from exact propagation equations can be used to calculate Fresnel coefficients for inhomogeneous media. However, Figs. 2 and 4 suggest that the permeability of the composites are adequately described by Rytov's model, even when strong skin effect is present as in Fig. 4. Another objection is that gyromagnetic permeability is not a scalar as in the Clogston-Rytov approach, but a tensor, as shown by Polder [17]. In the case of a thin ferromagnetic sheet, it is possible to show that the off diagonal components of Polder's tensor are very small. Systematic comparisons between single-coil and coaxial measurements were performed on several materials produced by magnetron sputtering on mylar over large areas. The single coil technique lacks absolute accuracy, but it is expected to yield resonance frequencies with reasonable accuracy. For the amorphous CoZrMoNi alloy, resonance frequency in coil measurements ranged from 1.2 to 1.4 GHz, and from 1.4 to 1.8 GHz for coaxial measurements. On CoNbZr alloy, resonance frequency ranged from 1.1 to 1.5
O. Acher et aL /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
GHz, coaxial determination lead to frequencies in the 1.2 to 2 G H z range. Some dispersion in the intrinsic characteristics of the film accounts for part of the observed dispersion. In particular, several resonance peaks can be seen, as in Fig. 5. It is believed that magnetostriction also accounts for the observed dispersion, and for the somewhat higher frequencies measured on LIFE. Previous work [16] performed on these two same alloys indicated that a few Newton tensile stress on the amorphous alloys deposited on mylar thin film would shift the resonance frequency up by 1 GHz. In particular, it was shown that the magnetostriction coefficient was higher for CoNbZr than for CoZrMoNi. This may account for the larger dispersion observed on CoNbZr. One should also remember that the gyromagnetic resonance is affected by external magnetic fields, but also by demagnetizing fields. Demagnetizing fields may be due to the macroscopic shape of the sample. It was checked that machining a 3 mm thick torus down to 0.9 mm had no effect on its permeability. For materials that are not very soft, domain structure and orientation can be significantly modified by magnetization, which leads to a change in the gyromagnetic response [14,18]. This is illustrated by Fig. 6. This indicates that the ability of our technique to study gyromagnetic resonance in the absence of an external field is particularly valuable compared to conventional ferromagnetic resonance experiments. It should be extremely helpful to study samples with complicated domain structure. In particular, Fig. 7 shows that the gyromagnetic response of pure iron is very dependent on deposition conditions. Resonance frequency, linewidth and permeability levels change with deposition conditions. Besides it should be underlined that as high frequency permeability levels are expected to be rather small, the good accuracy brought by coaxial measurements on L I F E sample is very valuable for this kind of studies.
5. Conclusion We presented broad-band high frequency (50 M H z - 1 8 GHz) permeability measurements on
277
ferromagnetic thin films on unsaturated samples. This technique is adapted to the study of anisotropic thin films. Its broad-band high frequency low noise ability exceeds by far all already existing permeability measurement techniques on ferromagnetic thin films. It is based on standard commercially available coaxial line measurement apparatus, but it requires that the film is either self-supported or deposited on a thin flexible substrate. Within some limitations connected to the notion itself of intrinsic permeability, the coaxial line measurement technique proves extremely helpful to study the resonance linewidth of materials, the influence of skin effect at high frequency, the effect of remanent magnetization state on permeability. It may open new opportunities for applications of ferromagnetic films and L I F E composites in the microwave region.
Acknowledgments We are thankful to C. Boscher and G. Nouhaut for the deposition of the films, N. Bardy, P. LeGourrierec and C. Couderc for coaxial measurements, and A. Lucas, G. Perrin, E. Capelle, G. Zdrah and J.C. Peuzin for fruitful discussions.
References [1] K. Saito, IEEE Trans. Magn. 26 (1990) 2942. [2] H. Koyama, H. Tsujimoto, and K. Shirae, IEEE Transl. J. Magn. in Japan 2 (1987) 815. [3] J.C. Peuzin and J.G. Gay, Acte des Journ~es d'l~tude sur la Caract6risation Microonde des Mat~riaux Absorbants, Limoges (1991) 75. [4] C.A. Grimes, J. Appl. Phys. 73 (1993) 6989. [5] N. Bloembergen, Phys. Rev. 78 (1950) 572. [6] A.M. Nicholson and G.F. Ross, IEEE Trans. Instrum. Meas. 17 (1968) 395; Hewlett Packard product note no. 8510-3. [7] G. Maz~-Merceur, J.L. Bonnefoy,J. Garat and R. Mittra, in: IEEE URSI/APS Proceedings (1992). [8] M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1959), p. 702. [9] A.M. Clogston, Bell Syst. Tech. J. 30 (1951) 491. [10] S.M. Rytov, Sov. Phys. JETP 2 (1956) 466. [11] O. Acher, P.M. Jacquart and A. Schaal, Patent under issue. [12] O. Acher, J.L. Vermeulen, P.M. Jacquart, J.M. Fontaine
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O. Acher et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
and P. Baclet, in: MMM93 Conference Proceedings, to be published [13] J.L. Vermeulen, O. Acher and F. Ravel, J. de Physique IV, Coll. C3, Suppl. J. de Phys. III (1992) 235. [14] N. Bloembergen, Proc. IRE (1956) 1259, and references therein. [15] H. Hoffmann, G. Heller and K.H. Kammerer, IEEE Trans. Magn. 23 (1987) 2731, and references therein.
[16] O. Acher, J.L. Vermeulen, A. Lucas, Ph. Baclet, J. Kazandjoglou and J.C. Peuzin, J. Appl. Phys. 73 (1993) 6162. [17] D. Polder, Phil. Mag. 40 (1949) 99. [18] O. Acher, J.L. Vermeulen, C. Boscher, P. LeGourrierec, P. Baclet and S. Aoustin, Proc. 8~mes Journ~es Nationales Microondes, Brest (1993).
ELSEVIER
Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
journalof magnetism and magnetic materials
Permeability measurement on ferromagnetic thin films from 50 MHz up to 18 GHz O. Acher
*, J . L . V e r m e u l e n ,
P.M. Jacquart,
J.M. Fontaine,
P. Baclet
CEA / DETN, BP 12, F-91680 Bruy~res le Ch~tel, France
Received 15 December 1993; in revised form 5 March 1994
Abstract
The needs for permeability measurements on ferromagnetic materials at high frequencies are driven by the development of broad-band recording systems. However, measurements above 500 MHz on ferromagnetic films are difficult. Wide band permeability measurements are reported only up to a few GHz. Measurements at higher frequencies can be performed using resonant cavities, as it is done in ferromagnetic resonance, but only at discrete frequencies. In contrast, we present a technique for measuring high frequency permeability of ferromagnetic films over a wide band. It works in a frequency range (50 MHz to 18 GHz or higher) that allows direct observation of the gyromagnetic resonance even on non-saturated samples, and can yield permeability in different directions for anisotropic films. In our technique a surface of about 0.5 dm 2 of the ferromagnetic material has to be wound to obtain proper sample geometry. As a consequence, our technique is restricted to coatings deposited on thin flexible substrates and to thin self supported ribbons produced by rapid solidification. Comparison with another measurement technique working up to 3 GHz, and with calculated gyromagnetic response, yield a satisfactory agreement. The limitations of our method are discussed. Spectroscopic permeability measurements are reported for several alloys.
1. Introduction
T h e needs for permeability m e a s u r e m e n t s on ferromagnetic materials at high frequencies are driven by the d e v e l o p m e n t of b r o a d - b a n d recording systems [1]. However, m e a s u r e m e n t s above 500 M H z on ferromagnetic films are difficult [2]. Wide b a n d permeability m e a s u r e m e n t s are rep o r t e d only up to a few G H z [3,4]. M e a s u r e m e n t s at higher frequencies can be p e r f o r m e d using r e s o n a n t cavities, but at discrete frequencies. F o r
* Corresponding author. Fax: + 33-1-6926 6128.
that reason, ferromagnetic resonance is generally studied by recording permeability as a function of external magnetic field [5], rather than as a function of frequency. This restricts the investigations to saturated samples. In contrast, the high frequency permeability of ferrimagnetics is conveniently m e a s u r e d using reflexion-transmission m e a s u r e m e n t s in a waveguide [6]. Such measurements are c o m m o n l y p e r f o r m e d f r o m a few M H z to over 40 G H z , using coaxial lines or p r o p e r waveguides and n e t w o r k analyzers. T h e coaxial line is particularly convenient to p e r f o r m measurements on a wide frequency range, using a single toroidal sample. This m e t h o d is well known
0304-8853/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0304-8853(94)00323-J
270
O. Acher et aL /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
and regarded as precise and reliable [7]. However, this technique is not suitable for materials with permittivity larger than the permeability by several orders of magnitude. This is the case of ferromagnetic materials that are highly conducting and therefore have extremely high permittivities. Total reflexion occurs on a bulk conducting ferromagnetic placed in a waveguide, and this does not allow the determination of its permeability. The present work presents a method to determine the permeability of ferromagnetic films using standard coaxial measurement apparatus. The theoretical background and the experimental procedure are described in a first part. In particular, this method requires that the ferromagnetic layer is wound, so it has to be deposited on a thin flexible substrate such as mylar. Thin ribbons produced by rapid solidification are also well suited for these measurements. In all cases, a surface of 0.5 dm 2 of film is required. Experimental results on a variety of different magnetic thin films are presented in the second part. They are compared to theoretical predictions and to resuits obtained by other measurements techniques. In the third part, the validity and the limitations of the method are discussed, as well as the opportunities it opens up.
Insulator ferromagnetic lamination
(a)
(b) Fig. 1. (a) Sketch of the geometry of a Laminated InsulatorFerromagnetic on Edge (LIFE) composite adapted to coaxial line geometry. The propagation vector k, and E and It fields corresponding to the fundamental mode are also sketched. (b) Micrograph of part of the surface of a wound torus. The torus was made by winding a 0.4 p,m thick amorphous Cobalt-based alloy deposited by magnetron sputtering on 8 ~ m thick mylar.
2. Experimental method In order to benefit from the coaxial measurement abilities, we manufactured our ferromagnetic thin films into samples that appear both as insulating (and therefore with relatively small permittivity) and magnetic for the fundamental mode propagating in the coaxial line. Since the fundamental mode in the coaxial line has nearly radial electric field and concentric magnetic field, it is intuitive that a laminated sample consisting of concentric cylinders of alternated insulating and ferromagnetic materials would behave as an insulator and allows the penetration of the wave in the composite (Fig. la). This sample geometry will be designated as Laminated Insulator-Ferromagnetic on Edge (LIFE). The fact that the propagating wave arrives on the edge of the lamina-
tions and propagates along the laminations allows large penetration of the wave in the material for the fundamental mode. If the insulator thickness is much smaller than the wavelength, and the ferromagnetic thickness much smaller than the skin depth, Wiener's relations [8] confirm this intuitive view. They indicate that the composite has a magnetic susceptibility that is simply that of the ferromagnetic film, multiplied by its volume fraction. Clogston [9] and Rytov [10] treated the case of laminations including skin effects. However, conforming to strictly coaxial Clogston geometry would lead to great difficulties in the fabrication of the samples. For that reason, we slightly departed from this geometry by wounding ribbons of ferromagnetic films deposited on thin
O. Acher et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
flexible insulating substrates into torus suitable for coaxial line measurement [11,12] (Fig. lb). Our samples were therefore spiral-like, rather than a series of concentric cylinders, but we believe that this is of little consequence for finely laminated samples at high frequency, as will be discussed further. If the ferromagnetic film is anisotropic, one can cut two sets of ribbons, one along each anisotropy eigenaxis, and then make two tori. Each torus will yield the permeability along its ribbon direction, since magnetic field in the coaxial line is orthoradial [6,9] and therefore along the ribbon direction. The permeability/zeff of a laminated composite illuminated by a wave with propagation vector and H field in the plane of the composite is given by Rytov [10]. In our experiments, the thickness of the dielectric is in the 3.5 to 15 ~ m range. Since it is much smaller than the wavelength in the composite, Rytov's expression becomes: fi/-t i + fcfc/-~ c [£eff =
1
(1)
+ f c ( C ¢ - 1)
with C¢=
tg X X
(2a)
and "IT
]d.i and /z c are the permeability of the insulating dielectric and of the conducting ferromagnetic respectively, fi and fc the volume fraction of the dielectric and conducting ferromagnetic, e~ and othe thickness and conductivity of the ferromagnetic. F designates the frequency. For a nonmagnetic insulator (/z i = 1) and a small ferromagnetic volume fraction f~, (1) becomes at the first order in f~: /'Left- 1 = f~Cc(/~ c - 1).
(3)
If e c is much smaller than skin depth, Cc = 1 and (1) reduces to the Wiener relation [8]. For thicker films, skin effect occurs, and it is possible to compute the intrinsic permeability/Xc using relation (2) and (3). The coefficient Cc accounts for
271
skin effect. It can be shown that its module is equal or less than unity. It is also convenient to introduce the apparent permeability I.Lap defined by: /.Lap -- 1 = C c ( / £ c -
1) -
/~ff - 1 -
-
L
(4)
We investigated the high frequency permeability of several ferromagnetic films with different thicknesses and compositions using this method. Cobalt-based amorphous alloys were prepared onto continuously transported mylar films 8 to 12 Ixm thick by dc planar magnetron sputtering. Kerr magnetooptic measurements indicated that the materials had soft properties ( H c < 0.5 Oe), and that their easy and hard axes had a constant orientation over the whole film surface. The magnetic field created by the magnetron was responsible for this orientation. Ribbons were cut in the ferromagnetic-coated mylar sheets, some parallel to the easy axis, and some parallel to the hard axis. Amorphous CoFeNiMoSiB ribbons were prepared by melt spinning. Ribbon thickness was reduced from 20 to about 6 txm by chemical etching, and glued on 8 Ixm thick polyethylene film. Ion Beam Sputtering (IBS) [13] was also used to manufacture microcrystalline CoFeSiB films and pure iron films on 8 txm thick polyethylene substrate. These ribbons were wound and glued into torus. Then the LIFE sample was machined to the desired dimensions with tight tolerances [7] and measured in APC-7 coaxial line with 3 mm inner diameter and 7 mm outer diameter [6,7]. APC-7 measurements yielded values of ]'/'eft with a precision better than 5% for frequencies higher than 500 MHz. The low frequency bound of our measurements could be made lower than 50 MHz, but with some degradation in accuracy. The upper measurement frequency is fixed by the capabilities of the network analyzer used, and also by the cut-on frequency of higher modes in the coaxial line. It would be possible to extend the upper frequency bound by using a proper network analyzer and a coaxial line with smaller diameter. Depending on the insulator, ferromagnetic and
O. Acher et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
272
glue thickness, each sample consisted of about 100 to 250 turns. As a consequence, the composites can be adequately described as finely laminated samples. Torus thickness ranged from 0.7 to 3 mm. Ferromagnetic volume fraction in the torus was deduced from microscopic observations of ferromagnetic, substrate and glue thickness, and also from density measurements. Apparent and intrinsic permeability were deduced from measured composite permeability ]'/'eft using relations (2) to (4), Flexible insulating substrate and glue were considered as a single non-magnetic insulating material. The electrical conductivity occurring in (2) was measured using four point probe. In order to make comparisons with already existing methods, permeability measurements up to 3 GHz were also performed using a single-turn coil susceptometer described elsewhere [3] on 1 cm 2 film samples. Gyromagnetic permeability predicted by the Landau-Lifschitz model [14] was calculated for some samples. In the saturated thin film geometry, when damping parameter/3 is small and anisotropy field is much smaller than saturation magnetization, the per-
meability along hard axis predicted by this model is: B~
uc
1
Ha 1-7,2+j/3v
+ 1
(5)
where F ~'=~-
and
Fr~--~B s ~ s ~ a
.
F is the frequency,/3 is the damping parameter, and 3' is the gyromagnetic ratio. Calculations were performed using experimental values of anisotropy field H a deduced from Kerr measurements, and saturation magnetization B~ measured using a magnetic balance.
3. E x p e r i m e n t a l results
A first concern was to compare experimental results obtained from measurements on LIFE torus with other experimental results or theoretical predictions. Soft amorphous ferromagnetic thin films are convenient for that purpose, be-
0.4 ixm thick amorphous CoZrMoNi on mylar
700
oo
600
(a) LIFE
o • .
~
IJ''J
500
.o,
400
300 25
•
~o
.-
\~
o o Ix"J (b) col
i
L
t ~
200
°o ~
Ix'
(c) calculated
100 0 0.1
1
10
-100 -200 -300
F(GHz) Fig. 2. Intrinsic permeability/z' - j/x" of a 0.4 ixm thick CoNbZr film (a) measured using our coaxial technique on a LIFE sample, (b) measured up to 3 GHz using a single coil technique, (c) calculated using Landau Lifschitz equation.
o. Acher et aL /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
cause their gyromagnetic behaviour is rather well understood, and also because their resonance frequency is in the frequency range of our single-coil permeability m e a s u r e m e n t system. Fig. 2 shows the complex permeability of a C o Z r M o N i amorphous film (0.4 ixm thick) along hard axis. Curve (a) is the experimental result obtained from coaxial m e a s u r e m e n t on a L I F E sample according to our method. Curve (b) was obtained by single-coil m e a s u r e m e n t technique up to 3 GHz, and curve (c) from Landau-Lifschitz model, using experimental values of H a and B s, and the damping p a r a m e t e r as the single adjustable parameter. A very good agreement is observed between our method and the other determinations. It should be however mentioned that our method requires the precise determination of the ferromagnetic volume fraction. This value is deduced essentially from density measurements, with an uncertainty of about 10%. Clearly, it would be possible to reduce this uncertainty, for example by measuring the saturation magnetization of the L I F E sample. Single coil measurements also require the knowledge of the volume,
273
and therefore suffer from this same 10% uncertainty, plus the uncertainty related to the apparatus calibration and to finite sample size effects that is much larger, of about 40%. For that reason, experimental curves of Fig. 2 were obtained by adjusting the ferromagnetic volume fraction so that /z' at 100 M H z would be the same for all three determinations. This was possible by changing the ferromagnetic volume fraction from its determination by less than 10% for L I F E measurements and less than 30% for single coil measurement. The same adjustment was performed for Figs. 3 and 4, always by adjusting the volume fraction within the experimental uncertainty. Fig. 3 shows the apparent permeability measured on relatively thick (5 Ixm) amorphous ribbons. Experimental determination on two L I F E samples measured in a coaxial line are given. One torus was obtained by wounding a continuous ribbon. The other torus was made by wounding the ribbon with many electrical discontinuities. A 1 or 2 m m gap was left between 1.5 cm long portions of ribbon. The purpose was to assess the effect of having a spiral-wound torus with electrical continuity between inner conductor and outer
5 pm thick Co-based ribbon 400
300
• • tl'~ (a) LIFE 1 [] l l " j
200
0 0
>., c~
E O_ ¢-
,,}- (b) LIFE 2
r,
O_ t'~
~ (C) coil
~a
100
0.1
/,t,J ~"J
1
10
F(GHz) Fig. 3. apparent permeability of a 5 gm thick Co-based amorphous ribbon (a) measured using our technique on a LIFE sample obtained by wounding a continuous ribbon, (b) measured on a LIFE sample obtained by wounding a discontinuous ribbon (one cut every 1.5 cm), (c) measured using single coil technique up to 1.6 GHz.
274
O. Acher et al. / Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
6 Ixm thick Co-based ribbon 200 (a) LIFE 150
o
•
%%
(b) coil =~ 100 Q.
E ~ 50
(c) calculated "k."
e~ O.
.
.
.
.
~%o
---
c
~c'j
.
0.1 -50
F(GHz) Fig. 4. apparent permeability of a 6 I~m thick Co-based amorphous ribbon (a) measured using our technique on a LIFE sample obtained by wounding a continuous ribbon, (b) measured using single coil technique up to 3 GHz, (c) calculated using Landau-Lifschitz and Rytov equations.
conductor, i n s t e a d of a strictly coaxial geometry as described by Clogston [9]. A good a g r e e m e n t is also o b t a i n e d with single coil m e a s u r e m e n t s .
Fig. 4 c o m p a r e s a p p a r e n t p e r m e a b i l i t y determ i n a t i o n s o n a n o t h e r thick a m o r p h o u s ribbon, o b t a i n e d by coaxial m e a s u r e m e n t s o n a L I F E
0.5 ~tm thick amorphous CoZrMoNi on mylar 600
__
,,
(hard axis)
400 ....... .
.
.
.
.
.
.
.
-"'"""/\,
/
~t~ (easy axis)
.
-~ 200 E
0
o,
4
""i ..... ///,
-200
% /
-400 F(GHz) Fig. 5. Intrinsic permeability/z' - j/x" of a CoNbZr film along hard and easy axis.
O. Acher et aL /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
275
0.5 I~m thick microcrystalline CoFe SiB
't
. - . s
120
G ~
~U.' I
.
as deposited ILl,"
80
.....
P"
after magnetization
.JD (D
E
40
0 ~).1
-40 F(GHz)
Fig. 6. Intrinsic permeability of a 0.5 p,m thick microcrystallineCoFeSiB film, measured before and after magnetization.
sample, by single-coil m e a s u r e m e n t s and from theoretical predictions. Theoretical predictions were obtained from Landau-Lifschitz equations for gyromagnetic resonance that were injected in Rytov's model to take skin effect into account. A very good concordance between experimental re-
250
i
sults and theoretical predictions is observed. The agreement is not so good with single-coil measurements. Inhomogeneities over the length of the melt-spun ribbon may account for differences in electromagnetic properties among different samples.
]
I
Iron thin films deposited ""
=
,,
=
~
100
by I.B.S. under different condil ons
I
i
!
i
I
i
"~,
50 .
0
0
.
.
.
.
. 5
.
.
"'i'".'": 10 F(GHz)
"': . . . . . . 15
20
Fig. 7. Intrinsic permeability (imaginary part) of two iron films less than 0.2 p,m thick deposited by Ion Beam Sputtering under different conditions.
276
O. Acher et al. /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
Fig. 5 represents the intrinsic permeability of CoNbZr along easy and hard axes deduced from coaxial measurements. The film was 0.5 txm thick, its conductivity was 135 ixl~" cm, and corrections due to skin effect brought by factor C c in Eq. (3) were less than 15%. The permeability along hard axis exhibits two resonance peaks at 850 MHz and 1.84 GHz. As expected, the permeability is much larger along the hard axis than along the easy axis, which is consistent with the gyromagnetic origin of the permeability in this frequency range. Permeability along the easy axis would be expected to be unity if the magnetization were uniform and parallel to the ribbon axis. Ripple [15] or inhomogeneities may account for the residual permeability observed here, and also extrinsic effects like stress [16] as discussed in the next section. Fig. 6 shows the permeability measured on a microcrystalline CoFeSiB LIFE torus before and after magnetization along its axis. The permeability is clearly affected by the magnetization. Kerr effect measurements on the film indicate that it does not have good soft magnetic properties, the coercive force is larger than 10 Oe. In contrast, all other materials in Figs. 2-5 have soft properties (He < 1 0 e ) and do not show significant permeability change after magnetization. Fig. 7 shows the intrinsic imaginary permeability of two iron layers deposited using IBS under different conditions. Layer thickness is less than 0.2 Ixm. Permeability levels are small, but unlike most soft amorphous materials, these layers exhibit a very broad gyromagnetic response, with significant magnetic losses above 10 GHz. This makes the high frequency ability and high sensitivity of our measurement process very valuable for studying the effect of deposition conditions and texture on gyromagnetic permeability of Febased layers.
4. Discussion
Figs. 2 to 4 show clearly that our technique yields results that are in good agreement with other experimental determinations and theoretical predictions. In particular, Fig. 3 shows clearly
that there is no difference between samples made from continuous and electrically discontinuous ribbons. This addresses the objection that our coaxial measurements are performed on spiralwound sample, and not on strictly coaxial geometry. However, one should keep in mind that the equivalence of properties between wound and perfectly concentric torus has a limited range of validity. It is expected no longer to be valid at low frequency, where the wound torus will act as a short. It is also expected not to be valid for thick conducting layers. However, it seems clear that in the frequency range investigated here and for ferromagnetic layers up to several txm thick, the laminated sample can be produced by winding. The validity of the Clogston-Rytov relations may also be questioned. They rely on exact propagation equations in an infinite laminated medium, so they are expected to be much more appropriate than many homogenization laws. However, coaxial measurement relies not only on measurement of propagation constants, but also on measurement of the reflexion-transmission coefficients at the interfaces. It is still a question to what extent permeability and permittivity inferred from exact propagation equations can be used to calculate Fresnel coefficients for inhomogeneous media. However, Figs. 2 and 4 suggest that the permeability of the composites are adequately described by Rytov's model, even when strong skin effect is present as in Fig. 4. Another objection is that gyromagnetic permeability is not a scalar as in the Clogston-Rytov approach, but a tensor, as shown by Polder [17]. In the case of a thin ferromagnetic sheet, it is possible to show that the off diagonal components of Polder's tensor are very small. Systematic comparisons between single-coil and coaxial measurements were performed on several materials produced by magnetron sputtering on mylar over large areas. The single coil technique lacks absolute accuracy, but it is expected to yield resonance frequencies with reasonable accuracy. For the amorphous CoZrMoNi alloy, resonance frequency in coil measurements ranged from 1.2 to 1.4 GHz, and from 1.4 to 1.8 GHz for coaxial measurements. On CoNbZr alloy, resonance frequency ranged from 1.1 to 1.5
O. Acher et aL /Journal of Magnetism and Magnetic Materials 136 (1994) 269-278
GHz, coaxial determination lead to frequencies in the 1.2 to 2 G H z range. Some dispersion in the intrinsic characteristics of the film accounts for part of the observed dispersion. In particular, several resonance peaks can be seen, as in Fig. 5. It is believed that magnetostriction also accounts for the observed dispersion, and for the somewhat higher frequencies measured on LIFE. Previous work [16] performed on these two same alloys indicated that a few Newton tensile stress on the amorphous alloys deposited on mylar thin film would shift the resonance frequency up by 1 GHz. In particular, it was shown that the magnetostriction coefficient was higher for CoNbZr than for CoZrMoNi. This may account for the larger dispersion observed on CoNbZr. One should also remember that the gyromagnetic resonance is affected by external magnetic fields, but also by demagnetizing fields. Demagnetizing fields may be due to the macroscopic shape of the sample. It was checked that machining a 3 mm thick torus down to 0.9 mm had no effect on its permeability. For materials that are not very soft, domain structure and orientation can be significantly modified by magnetization, which leads to a change in the gyromagnetic response [14,18]. This is illustrated by Fig. 6. This indicates that the ability of our technique to study gyromagnetic resonance in the absence of an external field is particularly valuable compared to conventional ferromagnetic resonance experiments. It should be extremely helpful to study samples with complicated domain structure. In particular, Fig. 7 shows that the gyromagnetic response of pure iron is very dependent on deposition conditions. Resonance frequency, linewidth and permeability levels change with deposition conditions. Besides it should be underlined that as high frequency permeability levels are expected to be rather small, the good accuracy brought by coaxial measurements on L I F E sample is very valuable for this kind of studies.
5. Conclusion We presented broad-band high frequency (50 M H z - 1 8 GHz) permeability measurements on
277
ferromagnetic thin films on unsaturated samples. This technique is adapted to the study of anisotropic thin films. Its broad-band high frequency low noise ability exceeds by far all already existing permeability measurement techniques on ferromagnetic thin films. It is based on standard commercially available coaxial line measurement apparatus, but it requires that the film is either self-supported or deposited on a thin flexible substrate. Within some limitations connected to the notion itself of intrinsic permeability, the coaxial line measurement technique proves extremely helpful to study the resonance linewidth of materials, the influence of skin effect at high frequency, the effect of remanent magnetization state on permeability. It may open new opportunities for applications of ferromagnetic films and L I F E composites in the microwave region.
Acknowledgments We are thankful to C. Boscher and G. Nouhaut for the deposition of the films, N. Bardy, P. LeGourrierec and C. Couderc for coaxial measurements, and A. Lucas, G. Perrin, E. Capelle, G. Zdrah and J.C. Peuzin for fruitful discussions.
References [1] K. Saito, IEEE Trans. Magn. 26 (1990) 2942. [2] H. Koyama, H. Tsujimoto, and K. Shirae, IEEE Transl. J. Magn. in Japan 2 (1987) 815. [3] J.C. Peuzin and J.G. Gay, Acte des Journ~es d'l~tude sur la Caract6risation Microonde des Mat~riaux Absorbants, Limoges (1991) 75. [4] C.A. Grimes, J. Appl. Phys. 73 (1993) 6989. [5] N. Bloembergen, Phys. Rev. 78 (1950) 572. [6] A.M. Nicholson and G.F. Ross, IEEE Trans. Instrum. Meas. 17 (1968) 395; Hewlett Packard product note no. 8510-3. [7] G. Maz~-Merceur, J.L. Bonnefoy,J. Garat and R. Mittra, in: IEEE URSI/APS Proceedings (1992). [8] M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1959), p. 702. [9] A.M. Clogston, Bell Syst. Tech. J. 30 (1951) 491. [10] S.M. Rytov, Sov. Phys. JETP 2 (1956) 466. [11] O. Acher, P.M. Jacquart and A. Schaal, Patent under issue. [12] O. Acher, J.L. Vermeulen, P.M. Jacquart, J.M. Fontaine
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and P. Baclet, in: MMM93 Conference Proceedings, to be published [13] J.L. Vermeulen, O. Acher and F. Ravel, J. de Physique IV, Coll. C3, Suppl. J. de Phys. III (1992) 235. [14] N. Bloembergen, Proc. IRE (1956) 1259, and references therein. [15] H. Hoffmann, G. Heller and K.H. Kammerer, IEEE Trans. Magn. 23 (1987) 2731, and references therein.
[16] O. Acher, J.L. Vermeulen, A. Lucas, Ph. Baclet, J. Kazandjoglou and J.C. Peuzin, J. Appl. Phys. 73 (1993) 6162. [17] D. Polder, Phil. Mag. 40 (1949) 99. [18] O. Acher, J.L. Vermeulen, C. Boscher, P. LeGourrierec, P. Baclet and S. Aoustin, Proc. 8~mes Journ~es Nationales Microondes, Brest (1993).