Physica B 248 (1998) 14-24 Surface and interfacial magnetic diffuse scattering Masayasu Takeda *, Yasuo Endoh , Atsushi Kamijo , Jun'ichiro Mizuki Physics Department, Graduate School of Science, Tohoku University, Aramaki Aobaku, Sendai 980-77, Japan Fundamental Research Laboratories, NEC Corporation, 1-1-4 Miyazaki, Kawasaki 216, Japan SPring-8, Japan Atomic Energy Research Institute, SPring-8, Kamigori-cho, Ako-gun, Hyogo 678-12, Japan Abstract We investigated surface and interfacial roughness in the magnetic multilayers by using neutron off-specular diffuse scattering. Single crystals of Fe/Cr multilayers with different interfacial roughnesses between Fe and Cr layers were used as samples. Interfacial roughness appeared around the antiferromagnetic Bragg peak from the antiferromagnetic structure in the profile of the off-specular diffuse scattering. The profile was very sensitive to the interfacial roughness which were modified by substrates, condition of crystal growth and external magnetic fields. This indicates that neutron off-specular diffuse scattering is a promising tools for the investigation of interfacial magnetism. 1998 Elsevier Science B.V. All rights reserved. Keywords: Neutron off-specular diffuse scattering; Surface; Interface; Roughness; Magnetic disorder 1. Introduction ism. Recently it is shown that the resonant X-ray scattering enables the detection of surface magnet- X-ray off-specular diffuse scattering measure- ism, and it is going to the extended to interfacial ments have been widely used for the investigation magnetism hopefully [1]. of surface and interfacial roughness in various Interaction between neutron and magnetic mo- multilayers. In the magnetic multilayers, the inter- ments is much larger than with X-rays, and neutron facial roughness originating from in atomic dis- shows the optical phenomena as well as X-ray and orders is expected to cause magnetic disorders at visible light. Therefore, neutron is potentially an ex- the surface or interfaces as well as the enhancement cellent probe of surface and interfacial magnetism or reduction of magnetic moments. Because of very by using the same technique as X-ray. However, small cross section available to magnetic moments, neutron has not been used for such an investiga- X-rays have not been used for the study of magnet- tion. This is mainly because the luminosity of a ism especially in the surface and interfacial magnet- neutron source is much less than that of X-ray, synchrotron sources. The less intensity makes it difficult to perform experiments with well-col- * Corresponding author. Fax:#81 22 217 6489; e-mail: limated beams which are essential to observe fine takeda@iiyo.phys.tohoku.ac.jp. structures appearing in the profile of off-specular 0921-4526/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 1 9 6 - 3 M. Takeda et al. / Physica B 248 (1998) 14­24 15 diffuse scattering like the Yoneda peak [2]. On the rectangular whose dimensions are typically other hand, neutron has much less absorption cross 30;40 mm , the crystal face being the (1 0 0) plane sections to most of the materials than X-ray. We of bcc-Fe and bcc-Cr atoms. The thickness of Fe found out that the transparency gave new aspects and Cr layers in the Fe/Cr bilayer is designed to of the off-specular diffuse scattering. In this paper obtain the largest GMR effect. The samples are we report the neutron off-specular diffuse scattering named as 1 (N"80 on sapphire), 2 (N"51 on measurements of Fe/Cr multilayers with various MgO), 3 (N"30 on sapphire) and 4 (N"30 on interfacial roughnesses which clearly appears in the MgO). different profiles of off-specular diffuse scattering around the Bragg peaks from antiferromagnetic Fe/Cr bilayers. 2.2. Reflection measurements of the TOP The Fe/Cr multilayer is one of the magnetic spectrometer multilayers which shows a giant magnetoresistance (GMR) effect [3]. The GMR effect is the phenom- Neutron reflection measurements were per- enon that negative resistivity change whose magni- formed on the TOP spectrometer installed at the tude is very large compared with the conventional pulsed neutron source (KENS) at National Labor- bulk magnets is induced by external magnetic atory for High Energy Physics. TOP is a pulsed- fields. The GMR effect is observed in the magnetic polarized neutron time of flight spectrometer with multilayers which consists of alternative magnetic optical polarizer which utilizes wavelength band of and nonmagnetic layers. In the multilayer ferro- 3-18 A> from a solid methane cryogenic moderator. magnetic moments in the magnetic layers are The band was separated into two sub bands, 3-9 A> coupled antiferromagnetically through adjacent and 11-18 A> by a band selector of disk chopper in nonmagnetic layers. This antiferromagnetic ex- order to avoid frame-overlap of neutrons. Fig. 1a change coupling oscillates with the nonmagnetic shows the schematic representation of experimental layer thickness with a period ranging from 12 to setup for reflection measurements on the TOP 21 A> [4]. The GMR effect only appears in the spectrometer. Unpolarized neutrons were introduc- multilayers with the antiferromagnetic coupling. It ed to neutron polarizers, and outgoing polarized is experimentally concluded that the resistivity neutrons are collimated by a pair of horizontal slits, strongly depends on the alignment of the adjacent s ferromagnetic layer. Since such spin-dependent and s , before the sample. The vertical collima- tion of neutrons are fixed by a pair of vertical slits scattering of conduction electrons cannot be ex- of 20 mm height. The one-dimensional position- pected to occur in the bulk or at the perfect flat sensitive detectors (PSD) were used as a detecting interface between magnetic and nonmagnetic system. An effective length of the PSD is 640 mm layers, the interfacial roughness, the atomic mixing long which can be divided up to 256 positional at the interfaces, has now been considered to be channels. The PSD are horizontally arranged in essential to the GMR effect. three lines in order to detect neutrons of 20 mm height. At each positional channel neutrons are counted according to time of flight from moderator 2. Experimental to the PSD during 50 ms at each pulse. The time channel can be divided into up to 4096 channels. 2.1. Samples The number of positional channels was set to be 64 and that of the time channel 32 in these experi- Single crystals of Fe/Cr multilayers are prepared ments. Fig. 1b graphically explained the way of by molecular beam epitaxy at NEC Corp. [5,6]. A reflection measurements using pulsed neutrons and [Fe (3 nm)/Cr (1 nm)] bilayer is grown N(N"30, the PSD detecting system. The sample plane is 51, 80) times on the seed Cr layer under which Nb aligned vertically, and the scattering vector, Q, is in buffer layer is grown on Al O (1 1 0 2) or MgO the horizontal plane. Incident neutrons hit the (1 0 0) substrates. The shape of the sample is sample with incident angle of . A part of the 16 M. Takeda et al. / Physica B 248 (1998) 14­24 Fig. 1. Schematic representation of (a) the pulsed cold polarized neutron spectrometer TOP and (b) reflectivity measurement using position sensitive detector and TOF method. neutron is reflected with the reflection angle of 2 sample. The analyzer, PG(002), was used only to in the case of specular reflection and hits the corres- reduce background from the incident beams. The ponding positional channel in the vicinity of which beam collimation is defined by four Soller col- intensities of off-specular diffuse scattering are limators as shown in Fig. 2. The sample was set in observed. The rest of neutrons goes through the such a way that the scattering vector, Q, is normal sample and are detected at the center position of to the sample plane in the -2 measurements. the PSD. Hereafter, the direction normal to the sample plane is defined as the z-axis and the sample plane as the xy-plane. Therefore, the -2 scan corresponds to 2.3. Specular and off-specular diffuse scattering the QX scan in the reciprocal space. The measure- measurements on the ¹OPAN spectrometer ments of off-specular diffuse scattering were done by the transverse scan (Q scans for the constant QX) Measurements of detailed profile of off-specular as shown in the inset of Fig. 2. The transverse scan diffuse scattering have been done on a conventional is similar to the rocking scan of the fixed scattering triple-axis spectrometer, TOPAN, installed at angle in the small Q region. Here we assume that JRR-3M in Tokai Establishment, Japanese Atomic there is no anisotropy in the sample plane and Energy Research Institute (JAERI) (Fig. 2). The define Q which indicates the component in the incident wavelength was fixed at 0.24 nm by xy-plane of the scattering vector, i.e. "QP", a PG(002) monochrometer, and the higher-order (Q reflections were removed by a PG filter before the V#Q W. External magnetic fields were applied up to 1 T in the sample plane by an electromagnet. M. Takeda et al. / Physica B 248 (1998) 14­24 17 Fig. 2. Experimental setup of the TOPAN spectrometer in JRR-3M for off-specular diffuse scattering measurement. Inset shows the difference between the ordinary longitudinal scan and the transverse one. 3. Results and 2.7°. The curve was obtained only using the data at the positional channel 51 which was satis- 3.1. Reflectivities measured on the TOP spectrometer fied with specular condition. Total reflection occurs at 0.018 A>\ . Antiferromagnetic Bragg peak from Fig. 3 is the specular reflectivity curves of the antiferromagnetic structure of Fe/Cr bilayer sample 1 measured by the TOP spectrometer in the with twice the lattice spacing of the bilayer of 4 nm absence of magnetic fields at room temperature. In appears at 0.07 A>\ and the Bragg peak from the order to cover the wide Q range, both subbands of Fe/Cr bilayer itself at 0.13 A>\ . Hereafter, we neutrons were used in the fixed incident angle of 1.1 name the former the peak and the latter the first peak. Fig. 4a and b show the positional channel dependence of intensities obtained in the measure- ments by integration over the TOF channels corre- sponding to 3-9 A> and 11-18 A>, respectively. The peak at channels 32 and 33 in the spectrum are due to the direct beam, which did not pass through the sample and transmitted neutrons which underwent small refraction. The reflected beam under the specular condition was detected at positional chan- nel 51, however, this main peak has an additional small peak at channel 45. The additional peak and the other intense peak at channel 57 were also visible in Fig. 4b. As shown in Fig. 5 contour map of intensities of reflected neutrons in which the hori- zontal axis is the number of position channel of the Fig. 3. Specular reflectivity of Fe/Cr multilayer sample 1 in the PSD (scattering angle) and the vertical axis is the absence of magnetic fields measured on TOP. number of time channel (wavelength of neutrons) 18 M. Takeda et al. / Physica B 248 (1998) 14­24 Fig. 4. The positional channel dependence of integrated inten- Fig. 6. Schematic representation of the wavelength - scattering sities of neutron over TOF channel. The positional channel angle window for the experiments in Fig. 5. corresponds to the scattering angle. peaks, especially the peak, are widely spread along the line of constant QX. The angle-wavelength window of Fig. 4a and b are schematically dis- played in Fig. 6. It is obvious that the extra reflec- tion at channel 57 is the foot of diffuse scattering around the peak. Such large magnetic diffuse scattering suggests that there exists an in-plane magnetic disorder at the interfaces between the Fe layers and the Cr layers. 3.2. The profile of off-specular diffuse scattering Fig. 5. Contour map of reflected intensities of sample 1. The The -2 scan, Q horizontal axis is related to the scattering angle and the vertical X scan, of sample 1 is displayed in Fig. 7a, and the profile of off-specular diffuse one to the wavelength of neutrons. Two broad Bragg peaks are observed centered at (51, 16) and (51, 31) points. scattering around the and the first peaks are shown in Fig. 7b and c as a function of Q , respec- tively. These data were taken in the absence of helps to explain the origin of these extra peaks. The external magnetic fields. The profile of the Q data on the vertical straight line, P scan "51 seems to be composed of sharp specular central (2 "2.7°), correspond to the specular reflectivi- component and additional broad off-specular dif- ties. The peak at (51, 16) is the peak and that at fuse scattering. Intense off-specular diffuse scatter- (51, 2) is the first peak. The map shows that the ing is clearly observed at the peak. On the other M. Takeda et al. / Physica B 248 (1998) 14­24 19 the profile of off-specular diffuse scattering outside the scan range of conventional X-ray off-specular reflection measurements gives us new information of multilayers. However, what information? From the contour map in Fig. 5, intensities of the diffuse scattering extend along the constant QX direction. Such a distribution of off-specular diffuse scattering indicates that the interfacial roughness has coher- ency from the bottom to the top layer [7]. Are the intensities also signals from the interfacial rough- ness in the multilayers? In order to answer the questions, we have measured the off-specular dif- fuse scattering of various Fe/Cr multilayers with different interfacial roughness. Figs. 8-10 are the results of the QX and Q scans of sample 2-4 in several external magnetic fields. Intensities from different samples in these figures cannot be directly compared with each other be- cause the dimensions of samples are not always the same. Sample 2 in Fig. 8 is a multilayer consisting of 51 Fe/Cr bilayers grown on MgO(1 0 0) substra- te. The and the first peak appear more sharply than sample 1 in the QX scans. This indicates that sample 1 has more fluctuated lattice spacing of bilayers than sample 2. When the fluctuation is large, the multilayer is expected to have rather rough interfaces. If the roughness is not of magnetic origin, such roughness can be quantitatively meas- ured using the conventional X-ray technique. In Fe/Cr multilayers the peak is pure magnetic Bragg peak. Thus, the neutron seems to be power- Fig. 7. The QX (a) and the Q dependencies of reflected intensities ful tool for studying magnetic interfacial roughness, of neutrons in sample 1 around the antiferromagnetic Bragg magnetic disorders at the interface, in the multi- peak (b) and the Bragg peak of Fe/Cr bilayer (c). layers. However, in the small Q region we could not observe the obvious difference in the profile around the hand, around the first peak, broad off-specular dif- peaks between these two samples. This is due to the fact that TOPAN has much less fuse scattering did not appear. Two sharp peaks at experimental resolution than the X-ray spectrom- $0.0015 A>\ are the satellite peaks which are eters. Thus, we concentrate on the extra intensities caused by double diffraction [7]. It is noted that, which were observed in the transverse scan outside compared to X-ray scattering experiments, we can the scan limits of X-rays even though the diffuse still observe the significant intensities where the scattering around the first peak shows the different incident angle to the sample or the grazing angle of aspects of the profile as seen in Fig. 7c and 8c. the sample to the detector is beyond zero. At both On the contrary for the data in the small limits only intensity dips centered at $0.001 A>\ Q in Fig. 7b and at $0.004 A>\ in Fig. 7c appear. region, the clear difference of off-specular diffuse scattering appear outside the limits. In sample 2 This is because the neutron has much smaller ab- large off-specular diffuse scattering was not sorption cross section than X-ray. It is clear that observed around either the nor the first peak. Less 20 M. Takeda et al. / Physica B 248 (1998) 14­24 Fig. 8. The QX (a) and the Q scans, (b) and (c), for sample 2. This scan is exactly the same as in Fig. 7. Fig. 9. The magnetic field dependence of the QX (a) and the Q scans, (b) and (c), for sample 3. Data in 0 T are plotterd by solid circles and that in the field of 0.7 T by open circles. number of bilayers and a narrower Bragg peak in the QX scan suggest that sample 2 should have superlattice, even though syntheses are done in the magnetically smoother interfaces than sample 1. At same manner. Figs. 10 and 11 show the data of the first glance this leads to the conclusion that the samples 3 and 4 which have different substrates, rougher interface is accompanied by intense Al off-specular diffuse scattering. However, between O (1 1 0 2) and MgO (1 0 0), and have been prepared simultaneously under the same growth these two samples there are the other factors be- run. The effect of the difference of substrates on MR sides the interfacial roughness which may cause the ratio and magnetization has been carefully investi- difference of off-specular diffuse scattering. These gated and the clear substrate dependence was two samples have not been synthesized under observed in Fe/Cr multilayers [6]. No abrupt or exactly the same conditions. It is known that the discontinuous change of the profiles was observed different growth runs do not always give the same by applying external magnetic fields. Therefore, thickness of layers and quality of crystals in the these figures show the data in antiferromagnetic M. Takeda et al. / Physica B 248 (1998) 14­24 21 In zero field, clear off-specular diffuse scattering appears around the 1/2 peak outside the limits (Fig. 9b and Fig. 10b), and a rather weak scattering was observed around the first peak (Fig. 9c) and Fig. 10c). When the magnetic fields were applied in the multilayers, the diffuse scattering around the peak was drastically suppressed in both samples, while the scattering is enhanced in the case of the first peak. The magnetic diffuse scattering around the peak disappears in the ferromagnetic state, however, a sharp peak remains at the Bragg peak position (Q "0) even in this state. The sharp com- ponent originates from the intensity of the specular reflectivity curve. If the multilayers could have complete antiferromagnetic structures in zero external filed, the first peak would contain no mag- netic information. The X-ray diffraction measure- ments of the Fe(2 0 0) and Cr(2 0 0) Bragg peaks of samples 3 and 4 revealed that a high-quality single crystal in the Fe/Cr multilayers was obtained and that the disorder on the atomic scale is negligible in the bulk Fe and Cr layers [6]. Therefore, the off- specular diffuse scattering observed around the 1st peak is considered to indicate the existence of atomic disorder at the interface. The enhancement of diffuse scattering around the first peak in the external magnetic fields suggests that the magnetic coherent disorder of ferromagnetic moments at the interface is induced by the magnetic fields. At the end of this section it is emphasized that the Q scan extends to the region outside the scan range of X-ray measurement and which makes the difference Fig. 10. The same measurements plotted in Fig. 9 for sample 4. of samples evident. state of ferromagnetic Fe layers in the absence of external magnetic fields (solid circles) and in the 4. Discussion forced ferromagnetic one induced by external mag- netic fields (open circles). The intensities of the Various kind of physical surfaces can be de- peaks decrease with increasing fields, and disappear scribed as a self-affine surface defined by Mandel- in the ferromagnetic state. This is due to the fact brot in terms of the fractional Brownian motion that the antiferromagnetic alignment of the Fe [8]. The reflection of X-ray and neutron from such layers goes to ferromagnetic one through the cant- surfaces is treated based on the self-affine surface ing state. On the other hand, intensities of the first model [9] and the theory has been extended to the peak increases with increasing magnetic fields. The multilayers with interfacial roughness [10-13]. For increase results from the ferromagnetic component the multilayer system correlation between rough- of the Fe layers induced by the magnetic fields. It ness at each interface from bottom to top layer has should be noted that there is no clear difference to be taken into consideration. The coherent inter- between two samples in the profile of QX scans. facial roughness and roughness without correlation 22 M. Takeda et al. / Physica B 248 (1998) 14­24 Fig. 11. Sketch of correlated and uncorrelated interfacial roughness and intensity distribution from the roughness in the reciprocal lattice. between interfaces coexist in real multilayers. These the case of measurements of nonmagnetic multi- two kind of roughnesses are highly correlated and layers using X-rays provided that the magnetic the relation is not simple. Although there is present- disorder at the interface is treated as a height distri- ly no complete theory for interfacial roughness, it bution of homogeneous media with magnetic scat- has been confirmed experimentally that intensities tering length from the average smooth interface. from the coherent roughness come together in the This approximation ignores the fluctuation of di- profile of the transverse scan at the Bragg points as rection of magnetic moments at the interfaces. It is schematically sketched in Fig. 11. On the other not unique but one of the reasonable starting hand, X-ray and neutron reflected at the interfacial points of the quantitative analysis at the first stage. with incoherent roughness are diffusely scattered in Here we have done the preliminary fitting by the all-the directions in the reciprocal space with no following trial function, structures. The diffuse scattering around the first peak with- I I exp(!Q X ) out external magnetic fields can be attributed to the (QX, Q )"2 Q coherent atomic disorder at the interface. The X atomic disorder at the interface may cause the 1 Q ; exp magnetic disorder at the interface. Hence, we have 2 ! (2 2 speculated that magnetic diffuse scattering around the peak mainly originates from the magnetic 2 (Q 1 disorder at the interfaces. # X )K m(m!) 1#(Q The off-specular magnetic diffuse scattering can K /m) be quantitatively analyzed by the same way as in #background, (1) M. Takeda et al. / Physica B 248 (1998) 14­24 23 where I is the reflectivity of the multilayer with perfect surface and interfaces, the rms error of roughness, the lateral correlation length, is related to the experimental resolution. The function is the slightly modified one appearing in Ref. [7]. It assumes that the vertical displacement of interface from its average smooth interface has the exponen- tial correlation function with respect to the lateral separation of two points on the interface. The first term is the specular reflection with experimental resolution and the second one expresses the off- specular diffuse scattering. In the actual measure- ments by using X-rays, there is unreachable regions in the reciprocal space where either they are shadowed by the sample or total reflection occurs. The original function of Eq. (1) can satisfactorily fit the experimental data of ¼/C multilayers within the limits. As mentioned in Section 3.2, the shadow effect is not so effective in the case of neutrons. The formulae describing the off-specular diffuse scatter- ing seem to explicitly restrict the Q region concern- ing the shadow. The attenuation of reflected intensities should be accounted for the calculated profile as well as experimental resolution. There- fore, we neglected the other corrections except the resolution effect on the sharp specular component in the fitting. Fig. 12 shows two examples of Fig. 12. Fits for the data of Q scans of sample 3 (a) and 4 (b) by the fitting where the experimental data of sample a model function (see text). 3 in Fig. 9b and of 4 in Fig. 10b are plotted by open circles, and the results of the best fits are drawn by dashed-dotted lines. Whole profile of in the Q sample 3 cannot be simulated by using Eq. (1), region beyond the scan limits of X-ray measurements. while the fit for sample 4 is excellent, considering the simple model. The main difference of these two profiles is the peaks which appear at 5. Conclusions Q "$0.0075 A>\ in sample 3 but not in sample 4. At the Q , kG is parallel to the kD (1 0 0) We performed the specular and off-specular dif- which satisfies the Bragg condition of the first peak, fuse scattering measurements of various Fe/Cr i.e. kD (1 0 0)!kG (1 0 0)"Q (1 0 0), or kD is paral- multilayers using both pulsed and monochromatic lel to the kG (1 0 0). These peaks may be understood neutrons. In the multilayers it is found that the by the double diffraction in the multilayers diffuse scattering around the Bragg peak from anti- like resonant peak appearing in the diffuse scatter- ferromagnetic Fe/Cr bilayers is widely distributed ing [7]. In this case, however, this is a new along the direction normal to specular direction in feature because a detector is at the opposite side of the reciprocal lattice. The TOF spectrometer, TOP, reflection plane, and neutrons are detected after could make useful contour maps of the intensity going through the samples. Anyway, the present distribution in the wavelength of neutrons and the preliminary fittings suggest that Eq. (1) is a good scattering angle plane. The profiles of the diffuse model function of magnetic interfacial roughness scattering have been measured as a function of the 24 M. Takeda et al. / Physica B 248 (1998) 14­24 Q on the conventional triple-axis spectrometer, work was supported by a Grant-in-Aid for Scient- TOPAN, in the various external magnetic fields. In ific Research (A) (No. 03240102 and No. 05402011) the measurements the diffuse scattering was still and (C) (No. 06640463) from the Ministry of Educa- detectable with a unique profile even under the tion, Science, Sports and Culture. condition that the incident angle exceeded zero degree due to the small absorption cross section. The extra diffuse intensity was associated with the References antiferromagnetic Bragg peak, and the profile has been proved to vary with the external magnetic [1] S. Ferrer, P. Fajardo, F. de Bergevin, J. Alvarez, X. Tor- fields. The profiles were also very sensitive to the relles, H.A. van der Vegt, V.H. Etgens, Phys. Rev. Lett. 77 (1996) 747. interfacial roughness. Therefore it is concluded that [2] Y. Yoneda, Phys. Rev. 131 (1963) 2010. the diffuse scattering is related to magnetic disorder [3] M.N. Baibich, J.M. Broto, A. Fert, F. Nguyen Van Dau, at the interface. In order to quantitatively analyze F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, J. the diffuse intensities the more sophisticated fitting Chazelas, Phys. Rev. Lett. 61 (1988) 2472. function is necessary. Finally, it should be empha- [4] S.S.P. parkin, N. More, K.P. Roche, Phys. Rev. Lett. 64 (1990) 2304. sized that although the origin of extra off-specular [5] A. Kamijo, J. Magn. Magn. Mater. 126 (1993) 59. diffuse scattering reported here has not been fully [6] A. Kamijo, S. Yamamoto, Mater. Sci. Eng. B 31 (1995) 169. understood, it can be a very powerful tool to inves- [7] D.E. Savage, J. Kleiner, N. Schimke, Y.-H. Phang, T. tigate the magnetic disorder at the interfaces in the Jankowski, J. Jacobs, R. Kariotis, M.G. Lagally, J. Appl. magnetic multilayers. Phys. 69 (1991) 1411. [8] H.-O. Peitgen, D. Saupe, The Science of Fractal Images, Springer, New York, 1988. [9] S.K. Sinha, E.B. Sirota, S. Garoff, H.B. Stanley, Phys. Rev. Acknowledgements B 38 (1988) 2297. [10] S.K. Sinha, Physica B 173 (1991) 25. We are indebted to Mr. H. Yasuda for the collab- [11] J.B. Kortright, J. Appl. Phys. 70 (1991) 3620. [12] D.E. Savage, Y.-H. Phang, J.J. Rownd, J.F. MaacKay, oration. We also thank Mr. M. Onodera and Mr. M.G. Lasgally, J. Appl. Phys. 74 (1993) 6158. K. Nemoto for valuable technical assistance. This [13] D.G. Stearns, J. Appl. Phys 71 (1992) 4286.