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Measurement of saturation magnetostriction using novel strained substrate techniques and the control of the magnetic anisotropy
Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
Measurement of saturation magnetostriction using novel strained substrate techniques and the control of the magnetic anisotropy M. Ali*, R. Watts Department of Physics, University of Shezeld, Shezeld S3 7RH, UK Received 10 September 1998; received in revised form 5 March 1999
Abstract A simple new technique is described for the measurement of saturation magnetostriction in thin "lms deposited onto rigid substrates. The method is based on mechanically introducing a small curvature in the substrate either during the deposition (strained growth) or post-deposition. The strain-induced anisotropy is measured using the magneto-optical Kerr e!ect. Quanti"cation of the "lm strain is obtained using optical interference and stylus measurements; coupled with mechanical "nite-element modelling, this allows the saturation magnetostriction to be determined. No information about the mechanical properties of the substrate is required, and providing that the Young's modulus of the "lm is known accurately, the values of magnetostriction obtained are accurate and absolute. It is envisaged that the technique could be applied to a wide variety of "lms deposited onto commercially important substrates. Here, it is applied to amorphous "lms based on the METGLAS威 2605SC composition deposited onto glass and silicon substrates. A high degree of control is also demonstrated in tailoring the anisotropy "eld, by the technique of substrate straining. 1999 Elsevier Science B.V. All rights reserved. PACS: 75.80.#q; 75.30.Gw; 75.50.Kj Keywords: Magnetostriction; Anisotropy; Magneto-optics; Amorphous systems; Stress annealing
1. Introduction Magnetostrictive materials in the form of thin "lms are becoming increasingly important for the development of sensors and actuators. Their incor-
* Corresponding author. Tel.: #44-(0)114-222-3592; fax: #44-(0)114-272-8079. E-mail address: [email protected] (M. Ali) Current address: Cornell University Medical College, 1300 York Avenue, New York, NY10021, USA.
poration into microelectromechanical systems [1] allows the production of a new range of devices which, unlike conventional piezoelectric and piezoresistive materials, can be remotely addressed and activated. In addition, these materials o!er the possibility of self-test for safety critical systems and potential high sensitivity. It is therefore commercially and technologically important that one can investigate the magnetostriction constant of a material on a variety of substrates. Magnetostriction can be determined using either the magnetostrictive [2] or inverse
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 3 6 1 - 3
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M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
magnetostrictive [3] e!ects. In the former case, the mechanical de#ection of a cantilever system can be measured as the "lm magnetisation is rotated. The latter relies on measuring the induced change in anisotropy "eld as a mechanical stress is applied. Magnetostriction is often investigated on #exible substrates in which a mechanical load can be applied to produce stress. However, in many cases, the magnetic properties of the "lms can vary dramatically with the substrate. We have found that thin "lms grown simultaneously on Corning威 glass and Kapton威 (polyimide substrate) are di!erent magnetically. A further problem with measurement systems in which a known load is applied, is in the calculation of the stress, particularly for the case of multilayer systems. In such cases the stress in the magnetic layers is dependent on the structure. It is usually assumed that the strain is uniform throughout the thickness of the magnetic material. Here, a novel new technique for measuring magnetostriction is described for thin "lms. It is based on mechanically introducing a small curvature into the substrate either during deposition (strained growth), thermal processing (stress annealing) or during the measurement, combined with the magneto-optical Kerr e!ect (MOKE) to determine the stress-induced anisotropy. Quanti"cation of the stress in the magnetic layer gives the ability to accurately determine absolute values of magnetostriction. The technique described is based on a similar method which was "rst described by Becker and Kersten [4] applied to nickel wires, and then by others to ribbon-based materials [5}7]. Thin "lms di!er from their bulk counterparts not only in their thickness, but because of surface, substrate and possible texturing e!ects, which may in#uence the magnetic properties and hence the magnetostriction. It is therefore important that one should obtain the maximum magnetic information from such "lms in order to understand them fully. We have described in Ref. [8] how substrate straining techniques can be used to deliberately introduce a uniaxial anisotropy. A high degree of controllability is demonstrated here in tailoring the anisotropy "eld (H ) of thin "lms, by stress annealing.
2. Experimental The samples were grown using RF magnetron sputtering onto Corning威 glass and silicon substrates. The base pressure of the sputtering system was approximately 2;10\ mbar. The substrates were mounted on a water-cooled platter using a picture frame holder such that the sample was only held in place under its own weight in the sputter-up chamber. The target material was melt}spun ribbon METGLAS威 2605SC of composition Fe Si B C supplied by Allied Signal Corporation, with the "lms displaying a similar composition. Growth using 4 mTorr of Ar pressure and a power of 75 W was found to be optimal for the production of amorphous, magnetically soft "lms. All "lms deposited were 500 nm in thickness unless otherwise stated. The magnetic properties of the "lms were determined using MOKE, with both point hysteresis loop measurements and domain imaging. Since MOKE is sensitive only to the penetration depth of the light (typically 20 nm), bulk measurements of the samples were also made using an inductive magnetometer. Similar results were obtained in both cases, although steps in the MOKE hysteresis loops were sometimes observed due to domain walls moving across the laser spot (diameter &100 lm). Magneto-optic interrogation of the magnetisation is particularly convenient for this study because it can give a measure of the local anisotropy "eld, instead of an average over a large area. For the case of a non-uniform stress distribution, the stress and anisotropy distributions can then be correlated. The as-grown samples display the radial anisotropy distribution observed previously [8], which has been attributed to the stray magnetic "eld from the magnetron sputtering source. Annealing the samples at 4003C for 60 min in a low vacuum (10\ mbar) was found to be su$cient to destroy the as-grown radial anisotropy and to give complete stress relief, but not hot enough to cause crystallisation of the "lm, as determined using h}2h X-ray di!raction. An e!ective method of applying a controlled amount of stress to a "lm is by mechanically clamping the substrate/"lm over a knife edge at its two
M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
87
two-dimensional information in a single measurement, whereas the stylus measurement gave a quick and accurate measurement of the curvature in a given direction. The results of the two techniques were in good agreement. Fig. 1b represents a region of the substrate/"lm which has been mechanically clamped over the knife edge, inducing a circular arc. The radius of curvature, R, can be determined quickly and accurately from the variation of de#ection, >, with lateral position, X, from the stylus measurements
R"
X #H. 2
Substituting H"R!> leads to X#4> R" . 8>
Fig. 1. (a) Schematic of the experimental method for the introduction of mechanical strain into the "lm/substrate. (b) Illustrative pro"le of the radius of curvature from which the radius is calculated using a stylus method. Finite element model of a glass slide clamped tightly over a knife edge. The slide has dimensions of 76 mm;26 mm;0.4 mm. (c) and (d) show the magnitude of the strain in the top surface of the slide along the x- and y-axis, respectively, (e) shows the de#ection of the slide.
extreme points, as illustrated in Fig. 1a. The strain in the "lm depends directly on the radius of curvature of the samples which was determined by optical interferometry, and stylus measurements. The optical measurement had the advantage of giving
A good approximation, when X<>, is that R"X/8>. Assuming that the central surface of the slide remains unstrained, the tensile strain in the top surface is t/2R, where t is the thickness of the substrate; it is assumed that the thickness of the "lm is much smaller than that of the substrate. We know that a beam or cantilever does not bend into a circular arc, and it has been shown [9,10] that the de#ection (>) is proportional to the cube of length (X), and not to the square (X) as for the circular arc (Fig. 1b). The strain induced by the clamping process was investigated by three methods; Newton's rings, stylus measurements and also numerically. The investigation/measurements of the radius of curvature carried out by the Newton's rings and stylus measurements, revealed that a circular arc does exist over a small region of the substrate, above the knife edge. This is shown in Fig. 2a, where a typical Newton's rings interference pattern is shown for a substrate/"lm under a tensile strain of 707 ppm. Fig. 2b is a plot of the square of the lateral position (X) versus the de#ection (>); this indicates that the curve, indeed, is circular over a distance of 5 mm. The strain-induced anisotropy is measured using MOKE, which has a laser spot size of &100 lm in diameter, and therefore the strain is constant within the sampling area of the laser. This ensures that the measured strain and also the strain-induced anisotropy can be directly
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M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
Fig. 2. (a) Newton's ring interference pattern obtained from a glass substrate/"lm which has been mechanical strained. The image has been enlarged and the scale of the image is shown. The x-axis corresponds to the length, and the z-axis is the width of the sample. The y-axis is perpendicular to the page which corresponds to the de#ection. (b) The square of the lateral position (X) is plotted against the de#ection from which the radius of curvature is determined for the above image (R"X/nj).
correlated. The substrates used in this study were found to produce a circular arc over a length scale which was always much greater than the diameter of the laser spot (100 lm). Films which are deposited on substrates which are too #exible (or liable to distort) may be studied in this way by laying the "lm and substrate on top of a more rigid material, for example, a glass slide.
The strain in the "lm was also numerically modelled using the ANSYS威 "nite-element modelling package. This shows that the strain is not constant over the entire slide, but can vary greatly between the central region above the knife edge, to near the clamping ends. Fig. 1c shows the variation of strain with position for the top surface of a glass slide clamped rigidly over such a knife edge. The
M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
strain can be seen to be almost uniaxial in the x-direction over the majority of the area of the slide, but with some edge e!ects near the clamps and close to the edges on either side of the knife edge. Since the techniques used to measure both the mechanical strain (stylus and interferometric) and the magnetic anisotropy probe the local properties, it can be concluded that provided the same area is measured in both cases, reliable results can be obtained. The strain was introduced into the samples in three di!erent ways: by straining the substrate during the deposition, stress annealing, and during the measurement. In the "rst and second cases, the curved substrate becomes the zero strain state for the "lm. When the substrate is released, it returns elastically to its original #at shape, straining the "lm in the process. Inducing a strain during the measurement allows a range of strains to be introduced. Measuring the resulting variation of magnetic anisotropy allows the accurate calculation of magnetostriction.
3. Results and analysis Magnetostriction implies that a change in the magnetisation induces a strain. On application of an external stress, the resulting strain changes the magnetic anisotropy. The saturation magnetostriction constant j , is determined from the variation of the stress-induced magnetic anisotropy "eld, H , with the applied stress, p, from the well-known expression [11] k M H (1) j" , 3 e>
p"e>
where M is the saturation magnetisation, e the measured strain, and > the Young's modulus.
The saturation magnetisation of the material used in this study is assumed to be that of the melt}spun METGLAS威 ribbon used as the target, with k M "1.61 T [12]. The stress calculated de pends upon the Young's modulus of the "lm. Unfortunately, such values are not readily available for such amorphous sputtered "lms and we assume the same value of 160 GPa [12] as for the target
89
ribbon. It should be noted that the strain state and structure of the ribbon and "lm are likely to be di!erent, with the possibility of di!erent mechanical properties. However, evidence from the de#ection of METGLAS威 thin "lm membranes under pressure indicate similar values, and further work will give more accurate, quantitative values. In the present case, the uncertainty in the Young's modulus gives a large systematic error ($40 GPa) which is much greater than the random errors in the measurement of strain and anisotropy. 3.1. Strained growth Samples were produced by straining the substrate during the growth process, and releasing it afterwards to introduce a strain into the "lm. The substrate curvature was veri"ed pre- and post-deposition by interferometric and stylus measurements. Such a treatment could be used as a simple method for the introduction of a controlled uniaxial anisotropy for device fabrication. A disadvantage of the strained growth technique is that the strain-induced anisotropy will be added to the intrinsic growth anisotropy [8]. However, since the growth anisotropy is assumed to be constant, it can be subtracted to quantify the magnetostriction measurement. Fig. 3 shows hysteresis loops and domain images obtained from a sample grown on a strained substrate. The hysteresis loops indicate that the "lm exhibits a well-de"ned uniaxial anisotropy, with no observable opening of the hard axis loop. The domain images con"rm the well-de"ned uniaxial anisotropy, with 1803 domain walls running parallel to the easy axis. Reverse domain spikes appear at the edges to reduce the demagnetising e!ect. Subtraction of the intrinsic anisotropy (shown in the inset) yields a magnetostriction constant of 30.4$ 7.5 ppm, in good agreement with the bulk data [12]. The error in this measurement is dominated by that of the Young's modulus. Further samples grown with varying strains give similar values. 3.2. Stress annealing Stress annealing is an alternative way to introduce a uniaxial anisotropy. The advantage of stress
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M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
Fig. 4. Stress annealing. (a) Hysteresis loops (i) for an as-cast "lm (open squares), (ii) the "lm placed under an external strain of 507 ppm (solid triangle), (iii) after stress annealing (solid circles), and (iv) upon removal of the strain (open diamond). (b) MOKE domain image at remanence.
Fig. 3. Strained growth (a) MOKE loops obtained along the easy (dashed) and hard (solid) axes of magnetisation for a sample deposited while the top surface of the substrate was held under a strain of 562 ppm. The inset shows loops taken in the same directions for an unstrained sample. Comparison gives a straininduced anisotropy of 5863 A/m. (b) MOKE domain image at remanence and at a "eld of 70 A/m applied along the easy axis.
annealing is that it destroys the intrinsic growth anisotropy (radial anisotropy in this case), generally improves the magnetic properties, and provides the means of tailoring the anisotropy "eld (H ). The problem associated with strained growth is the separation of the substrate from the watercooled platter. In the vacuum used, there is almost no heat transfer through the residual gas. All transfer of heat is by direct contact conduction or radiation. Too large a separation would cause the "lms to become magnetically hard because of the increased temperature. This puts an upper limit on the induced strain. Stress annealing is immune to such a problem. Fig. 4 represents the hard axis
hysteresis loops taken (i) from an as-cast "lm, (ii) the "lm placed under a tensile strain, (iii) after stress annealing, and (iv) upon removal of the external strain. The intrinsic growth anisotropy (i) competes with that of the stress-induced anisotropy (ii), since removal of the external mechanical strain after stress annealing creates a stress-induced anisotropy (iv) with a higher anisotropy "eld. Stress annealing minimises the two dominant anisotropies, leaving only a small material intrinsic anisotropy as shown in Fig. 4 (iii). Domain images con"rm a uniaxial anisotropy with 1803 domain walls upon removal of the external mechanical strain. A value of 29.1$7.3 ppm is obtained for the magnetostriction constant. Similar values were obtained for other samples using this method. The most bene"cial advantage of stress annealing, is that it provides the ability to tailor in a speci"c anisotropy "eld. This is very important for the fabrication of devices where it is necessary to control the anisotropy "eld, and hence the permeability. Fig. 5 shows that the induced anisotropy varies linearly with strain on both glass and silicon
M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
91
Fig. 5. (a) Induced-anisotropy "eld by stress annealing for "lms grown on Corning glass. Domain images 25 mm;15 mm at remanence. (b) Induced-anisotropy "eld by stress annealing for "lms grown on silicon. Domain images 5 mm;15 mm at remanence. In both cases each point was obtained from independent samples.
Fig. 6. (a) Hysteresis loops for a METGLAS威 "lm as a function of strain. All loops taken perpendicular to the direction of tensile strain. (b) Corresponding variation of anisotropy "eld with strain, from which a magnetostriction constant of 32.0$ 7.7 ppm is determined.
substrates, as expected from Eq. (1). In each case, each point was obtained from independently grown samples which were then stress annealed. The linearity is due to the strain-induced anisotropy which scales linearly being the dominant anisotropy. Fig. 5 demonstrates the high level of control which can be achieved in inducing a speci"c anisotropy "eld and the reproducibility of the magnetic samples. The magnitude of this induced anisotropy is much larger than an anisotropy induced by "eld annealing [13]. Domain images have been included to indicate the uniaxial anisotropy. The simplicity of the technique provides the means to induce an
in-plane transverse or longitudinal uniaxial anisotropy. 3.3. Strain during measurement Quanti"cation of the magnetostriction is more conveniently achieved by measuring the variation of the anisotropy "eld as a function of the strain applied during the measurement. In this way, several independent measurements of magnetostriction can be made from a single sample, increasing the con"dence in the result. It also eliminates the need to take account of the growth induced and/or
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M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
intrinsic anisotropy. Annealing of the sample prior to the measurements can e!ectively destroy the as-grown anisotropy, making this term quite small. Fig. 6a shows the variation of hard-axis MH loop with induced strain for a "lm grown on a standard microscope slide. The induced anisotropy varies linearly with strain, as expected. The gradient of the graph of anisotropy versus strain gives a measurement of magnetostriction using Eq. (1), while the intercept corresponds to the intrinsic anisotropy (for annealed samples, this term is usually smaller). From the gradient of the graph shown in Fig. 6b, the magnetostriction constant is calculated to be 32.0$7.7 ppm. Similar measurements carried out on METGLAS威 "lms grown on silicon and Corning威 glass substrates are represented in Fig. 7. The magnetostriction values calculated from the "rst two graphs in Fig. 7 are shown in Table 1. Again, the uncertainty in the Young's modulus of the METGLAS威 "lm dominates the error (25%). Repeating these measurements with di!erent samples gave values of j which varied by less than 5%, indicating that the random errors in the measurement are small. The quantity j > and its asso ciated error have been included in Table 1 to indicate how the uncertainty in the Young's modulus (> ) dominates the error. For systems in
which the Young's modulus of the "lm is well known, values of j which are quantitatively accu rate to within 5% should be possible. Fig. 7 also shows the technique applied to an FeCo thin "lm deposited on glass; as expected the anisotropy "eld varies linearly with strain. The magnetostriction constant is calculated to be 72.1$2 ppm, in good agreement with the quoted [14] value of 75 ppm for the bulk material from which the thin "lm was grown. A detailed study on magnetostrictive soft FeCo thin "lms, including magnetostriction measurements, will be the subject of another paper [15]. The variation of anisotropy "eld with strain also shows the potential of such materials for sensor applications. Since the anisotropy "eld varies by nearly two orders of magnitude over a modest range of strains, the sensitivity of such devices is expected to be high. Further work is underway to integrate these materials into micromachined sensors. The magnetostriction measurements have been gathered in Table 1, including values determined
Fig. 7. Variation of anisotropy "eld with strain. All loops taken perpendicular to the direction of tensile strain. METGLAS威 on silicon j "30.6$7.3 ppm, METGLAS威 on Corning威 glass j "31.2$7.5 ppm and FeCo on microscope slide glass j "72.1$1.3 ppm.
from the gradients of the two graphs shown in Fig. 5, where "lms were grown on glass and silicon substrates, and then stress annealed to induce different anisotropy "elds. The two magnetostriction constants obtained are in good agreement considering that each point on the graph was obtained from independently grown samples. It is apparent from Table 1 that the substrate has little or no in#uence on the value of the magnetostriction constant. This conclusion is con"rmed by magnetostriction measurements carried out by Mattingley [16], where METGLAS威 "lms grown on Kapton威 under similar growth conditions also gave similar values for j , even though the "lms were magneti cally much harder (coercive "elds &1500 A/m). The much higher coercive "elds are due to the
M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
93
Table 1 Magnetostriction constants determined for METGLAS威 thin "lms Method
j > (MPa)
j (ppm)
H (A/m)
Strained growth Stress annealing (i) Single measurement (ii) Corning glass (Fig. 4) (iii) Silicon (Fig. 4)
5.1$0.3
30.4$7.5
60
4.9$0.3 5.0$0.1 5.2$0.2
29.1$7.3 29.7$7.1 30.9$7.4
18 18 18
Strain during measurement (i) Microscope slide (ii) Corning glass (iii) Silicon
5.4$0.1 5.1$0.2 5.2$0.2
32.0$7.7 30.6$7.3 31.2$7.5
20 52 18
stresses introduced by the Kapton威 substrate. Experiments [5] have shown the saturation magnetostriction does depend upon stress for nearly zero magnetostrictive materials, and therefore the linear dependence between the anisotropy "eld and stress becomes non-linear. The nonlinearity is small and can only be seen in materials possessing nearly zero magnetostriction. The random stresses from the substrate do have a small e!ect on the value of j , but can be con sidered to be negligible in highly magnetostrictive materials.
4. Conclusions A new, simple technique for the measurement of magnetostriction in thin "lms deposited onto fairly rigid thick substrates has been described. It has been applied to amorphous METGLAS威 "lms sputter deposited onto microscope slides, Corning威 glass, and silicon substrates. For these systems, the error in the measurement of magnetostriction is determined almost entirely by the uncertainty in the Young's modulus. The technique has also been applied to an FeCo "lm deposited by sputtering onto a microscope slide. In both the METGLAS威 and FeCo cases the values obtained are in good agreement with expected values. The technique can be applied to a wide variety of di!erent "lm/substrate combinations. If the Young's modulus of the "lm is known to a good accuracy, then the error in the value of j obtained
can be less than 5%, which compares well with other methods [3,17]. Such precise quantitative values could be used to provide sample standards for use with other techniques. The technique is not limited by "lm thickness, since the magneto-optical Kerr e!ect can comfortably monitor the magnetisation down to a "lm thickness of 10 nm. It overcomes the problem of non-uniform stresses by correlating the local stress with that of the local anisotropy "eld. No mechanical properties of the substrate are required, simplifying the calculation of j . There is no special preparation of samples required, and the equipment needed to implement the technique is inexpensive and commonly available. Since magnetostriction is a fundamental physical property of magnetic materials, it is vital for high precision devices (such as magnetic information storage systems) that accurate quanti"cation of its e!ects can be obtained. The values of magnetostriction obtained in this study have been very reproducible from the three di!erent methods used to strain the magnetic "lms. We have found that the substrates have no signi"cant in#uence on j , and the magnetic softness (coercive "elds) which is presumed to be caused by residual strains, also has little in#uence. These experiments also show that in these strongly magnetostrictive materials j is independent of strain for the applied strains and also the residual strains caused by the substrate. The technique of stress annealing to tailor the anisotropy "eld has been demonstrated to a high
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M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
degree of precision on silicon and Corning威 glass substrates. It provides an excellent means of inducing a given anisotropy "eld in thin "lm-based sensors. It also provides the means of inducing a well-de"ned uniaxial domain structure, which simpli"es the understanding of the magnetic process for device applications. Acknowledgements We are grateful to the Engineering and Physical Sciences Research Council (UK) for the "nancial support of this work under grant GR/K55905 and for the studentship for M. Ali. We wish to acknowledge and thank M.D. Cooke for providing the soft FeCo "lm. We also wish to thank Prof. G.A. Gehring and J.E.L. Bishop for their valuable discussions. References [1] M.R.J. Gibbs, R. Watts, W.J. Karl, A.L. Powell, R.B. Yates, Sensors Actuators A 59 (1997) 229.
[2] M. Weber, R. Koch, K.H. Rieder, Phys. Rev. Lett. 73 (8) (1994) 1166. [3] K. Narita, J. Yamasaki, H. Fukunaga, IEEE Trans. Magn. MAG-16 (2) (1980) 435. [4] R. Becker, M. Kersten, Z. Phys. 64 (1930) 64. [5] H.K. Lachowicz, A. Siemko, IEEE Trans. Magn. MAG-25 (5) (1989) 3605. [6] M.L. Spano, K.B. Hathaway, H.T. Savage, J. Appl. Phys. 53 (3) (1982) 2667. [7] T.H. O'Dell, Phys. Stat. Sol. (a) 68 (1981) 221. [8] M. Ali, R. Watts, W.J. Karl, M.R.J. Gibbs, J. Magn. Magn. Mater. 190 (1998) 199. [9] G. Joos, Theoretical Physics, Third ed., Blackie, London, 1958, pp. 176 (Chapter 8). [10] R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics, Vol. 2, Addison-Wesley, Reading, MA, 1964, pp. 38}10 (Chapter 8). [11] B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, Reading, MA, 1972, p. 274 (Chapter 8). [12] Allied Signal Corporation data sheet, 1995. [13] A.P. Thomas. Ph.D. Thesis, University of Bath, 1991. [14] Telcon data sheet FeCo, 1998. [15] M.D. Cooke, L.C. Wang, R. Watts, G.A. Gehring, W.M. Rainforth, G.P. Heydon, R. Zuberek, H. Szymczak, to be published. [16] A.D. Mattingley, C. Shearwood, M.R.J. Gibbs, IEEE Trans. Magn. MAG-30 (6) (1994) 4806. [17] J. Wenda, H. Jankowski, A. Kulak, Thin Solid Films 148 (1987) 1.
Measurement of saturation magnetostriction using novel strained substrate techniques and the control of the magnetic anisotropy M. Ali*, R. Watts Department of Physics, University of Shezeld, Shezeld S3 7RH, UK Received 10 September 1998; received in revised form 5 March 1999
Abstract A simple new technique is described for the measurement of saturation magnetostriction in thin "lms deposited onto rigid substrates. The method is based on mechanically introducing a small curvature in the substrate either during the deposition (strained growth) or post-deposition. The strain-induced anisotropy is measured using the magneto-optical Kerr e!ect. Quanti"cation of the "lm strain is obtained using optical interference and stylus measurements; coupled with mechanical "nite-element modelling, this allows the saturation magnetostriction to be determined. No information about the mechanical properties of the substrate is required, and providing that the Young's modulus of the "lm is known accurately, the values of magnetostriction obtained are accurate and absolute. It is envisaged that the technique could be applied to a wide variety of "lms deposited onto commercially important substrates. Here, it is applied to amorphous "lms based on the METGLAS威 2605SC composition deposited onto glass and silicon substrates. A high degree of control is also demonstrated in tailoring the anisotropy "eld, by the technique of substrate straining. 1999 Elsevier Science B.V. All rights reserved. PACS: 75.80.#q; 75.30.Gw; 75.50.Kj Keywords: Magnetostriction; Anisotropy; Magneto-optics; Amorphous systems; Stress annealing
1. Introduction Magnetostrictive materials in the form of thin "lms are becoming increasingly important for the development of sensors and actuators. Their incor-
* Corresponding author. Tel.: #44-(0)114-222-3592; fax: #44-(0)114-272-8079. E-mail address: [email protected] (M. Ali) Current address: Cornell University Medical College, 1300 York Avenue, New York, NY10021, USA.
poration into microelectromechanical systems [1] allows the production of a new range of devices which, unlike conventional piezoelectric and piezoresistive materials, can be remotely addressed and activated. In addition, these materials o!er the possibility of self-test for safety critical systems and potential high sensitivity. It is therefore commercially and technologically important that one can investigate the magnetostriction constant of a material on a variety of substrates. Magnetostriction can be determined using either the magnetostrictive [2] or inverse
0304-8853/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 9 ) 0 0 3 6 1 - 3
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M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
magnetostrictive [3] e!ects. In the former case, the mechanical de#ection of a cantilever system can be measured as the "lm magnetisation is rotated. The latter relies on measuring the induced change in anisotropy "eld as a mechanical stress is applied. Magnetostriction is often investigated on #exible substrates in which a mechanical load can be applied to produce stress. However, in many cases, the magnetic properties of the "lms can vary dramatically with the substrate. We have found that thin "lms grown simultaneously on Corning威 glass and Kapton威 (polyimide substrate) are di!erent magnetically. A further problem with measurement systems in which a known load is applied, is in the calculation of the stress, particularly for the case of multilayer systems. In such cases the stress in the magnetic layers is dependent on the structure. It is usually assumed that the strain is uniform throughout the thickness of the magnetic material. Here, a novel new technique for measuring magnetostriction is described for thin "lms. It is based on mechanically introducing a small curvature into the substrate either during deposition (strained growth), thermal processing (stress annealing) or during the measurement, combined with the magneto-optical Kerr e!ect (MOKE) to determine the stress-induced anisotropy. Quanti"cation of the stress in the magnetic layer gives the ability to accurately determine absolute values of magnetostriction. The technique described is based on a similar method which was "rst described by Becker and Kersten [4] applied to nickel wires, and then by others to ribbon-based materials [5}7]. Thin "lms di!er from their bulk counterparts not only in their thickness, but because of surface, substrate and possible texturing e!ects, which may in#uence the magnetic properties and hence the magnetostriction. It is therefore important that one should obtain the maximum magnetic information from such "lms in order to understand them fully. We have described in Ref. [8] how substrate straining techniques can be used to deliberately introduce a uniaxial anisotropy. A high degree of controllability is demonstrated here in tailoring the anisotropy "eld (H ) of thin "lms, by stress annealing.
2. Experimental The samples were grown using RF magnetron sputtering onto Corning威 glass and silicon substrates. The base pressure of the sputtering system was approximately 2;10\ mbar. The substrates were mounted on a water-cooled platter using a picture frame holder such that the sample was only held in place under its own weight in the sputter-up chamber. The target material was melt}spun ribbon METGLAS威 2605SC of composition Fe Si B C supplied by Allied Signal Corporation, with the "lms displaying a similar composition. Growth using 4 mTorr of Ar pressure and a power of 75 W was found to be optimal for the production of amorphous, magnetically soft "lms. All "lms deposited were 500 nm in thickness unless otherwise stated. The magnetic properties of the "lms were determined using MOKE, with both point hysteresis loop measurements and domain imaging. Since MOKE is sensitive only to the penetration depth of the light (typically 20 nm), bulk measurements of the samples were also made using an inductive magnetometer. Similar results were obtained in both cases, although steps in the MOKE hysteresis loops were sometimes observed due to domain walls moving across the laser spot (diameter &100 lm). Magneto-optic interrogation of the magnetisation is particularly convenient for this study because it can give a measure of the local anisotropy "eld, instead of an average over a large area. For the case of a non-uniform stress distribution, the stress and anisotropy distributions can then be correlated. The as-grown samples display the radial anisotropy distribution observed previously [8], which has been attributed to the stray magnetic "eld from the magnetron sputtering source. Annealing the samples at 4003C for 60 min in a low vacuum (10\ mbar) was found to be su$cient to destroy the as-grown radial anisotropy and to give complete stress relief, but not hot enough to cause crystallisation of the "lm, as determined using h}2h X-ray di!raction. An e!ective method of applying a controlled amount of stress to a "lm is by mechanically clamping the substrate/"lm over a knife edge at its two
M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
87
two-dimensional information in a single measurement, whereas the stylus measurement gave a quick and accurate measurement of the curvature in a given direction. The results of the two techniques were in good agreement. Fig. 1b represents a region of the substrate/"lm which has been mechanically clamped over the knife edge, inducing a circular arc. The radius of curvature, R, can be determined quickly and accurately from the variation of de#ection, >, with lateral position, X, from the stylus measurements
R"
X #H. 2
Substituting H"R!> leads to X#4> R" . 8>
Fig. 1. (a) Schematic of the experimental method for the introduction of mechanical strain into the "lm/substrate. (b) Illustrative pro"le of the radius of curvature from which the radius is calculated using a stylus method. Finite element model of a glass slide clamped tightly over a knife edge. The slide has dimensions of 76 mm;26 mm;0.4 mm. (c) and (d) show the magnitude of the strain in the top surface of the slide along the x- and y-axis, respectively, (e) shows the de#ection of the slide.
extreme points, as illustrated in Fig. 1a. The strain in the "lm depends directly on the radius of curvature of the samples which was determined by optical interferometry, and stylus measurements. The optical measurement had the advantage of giving
A good approximation, when X<>, is that R"X/8>. Assuming that the central surface of the slide remains unstrained, the tensile strain in the top surface is t/2R, where t is the thickness of the substrate; it is assumed that the thickness of the "lm is much smaller than that of the substrate. We know that a beam or cantilever does not bend into a circular arc, and it has been shown [9,10] that the de#ection (>) is proportional to the cube of length (X), and not to the square (X) as for the circular arc (Fig. 1b). The strain induced by the clamping process was investigated by three methods; Newton's rings, stylus measurements and also numerically. The investigation/measurements of the radius of curvature carried out by the Newton's rings and stylus measurements, revealed that a circular arc does exist over a small region of the substrate, above the knife edge. This is shown in Fig. 2a, where a typical Newton's rings interference pattern is shown for a substrate/"lm under a tensile strain of 707 ppm. Fig. 2b is a plot of the square of the lateral position (X) versus the de#ection (>); this indicates that the curve, indeed, is circular over a distance of 5 mm. The strain-induced anisotropy is measured using MOKE, which has a laser spot size of &100 lm in diameter, and therefore the strain is constant within the sampling area of the laser. This ensures that the measured strain and also the strain-induced anisotropy can be directly
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Fig. 2. (a) Newton's ring interference pattern obtained from a glass substrate/"lm which has been mechanical strained. The image has been enlarged and the scale of the image is shown. The x-axis corresponds to the length, and the z-axis is the width of the sample. The y-axis is perpendicular to the page which corresponds to the de#ection. (b) The square of the lateral position (X) is plotted against the de#ection from which the radius of curvature is determined for the above image (R"X/nj).
correlated. The substrates used in this study were found to produce a circular arc over a length scale which was always much greater than the diameter of the laser spot (100 lm). Films which are deposited on substrates which are too #exible (or liable to distort) may be studied in this way by laying the "lm and substrate on top of a more rigid material, for example, a glass slide.
The strain in the "lm was also numerically modelled using the ANSYS威 "nite-element modelling package. This shows that the strain is not constant over the entire slide, but can vary greatly between the central region above the knife edge, to near the clamping ends. Fig. 1c shows the variation of strain with position for the top surface of a glass slide clamped rigidly over such a knife edge. The
M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
strain can be seen to be almost uniaxial in the x-direction over the majority of the area of the slide, but with some edge e!ects near the clamps and close to the edges on either side of the knife edge. Since the techniques used to measure both the mechanical strain (stylus and interferometric) and the magnetic anisotropy probe the local properties, it can be concluded that provided the same area is measured in both cases, reliable results can be obtained. The strain was introduced into the samples in three di!erent ways: by straining the substrate during the deposition, stress annealing, and during the measurement. In the "rst and second cases, the curved substrate becomes the zero strain state for the "lm. When the substrate is released, it returns elastically to its original #at shape, straining the "lm in the process. Inducing a strain during the measurement allows a range of strains to be introduced. Measuring the resulting variation of magnetic anisotropy allows the accurate calculation of magnetostriction.
3. Results and analysis Magnetostriction implies that a change in the magnetisation induces a strain. On application of an external stress, the resulting strain changes the magnetic anisotropy. The saturation magnetostriction constant j , is determined from the variation of the stress-induced magnetic anisotropy "eld, H , with the applied stress, p, from the well-known expression [11] k M H (1) j" , 3 e>
p"e>
where M is the saturation magnetisation, e the measured strain, and > the Young's modulus.
The saturation magnetisation of the material used in this study is assumed to be that of the melt}spun METGLAS威 ribbon used as the target, with k M "1.61 T [12]. The stress calculated de pends upon the Young's modulus of the "lm. Unfortunately, such values are not readily available for such amorphous sputtered "lms and we assume the same value of 160 GPa [12] as for the target
89
ribbon. It should be noted that the strain state and structure of the ribbon and "lm are likely to be di!erent, with the possibility of di!erent mechanical properties. However, evidence from the de#ection of METGLAS威 thin "lm membranes under pressure indicate similar values, and further work will give more accurate, quantitative values. In the present case, the uncertainty in the Young's modulus gives a large systematic error ($40 GPa) which is much greater than the random errors in the measurement of strain and anisotropy. 3.1. Strained growth Samples were produced by straining the substrate during the growth process, and releasing it afterwards to introduce a strain into the "lm. The substrate curvature was veri"ed pre- and post-deposition by interferometric and stylus measurements. Such a treatment could be used as a simple method for the introduction of a controlled uniaxial anisotropy for device fabrication. A disadvantage of the strained growth technique is that the strain-induced anisotropy will be added to the intrinsic growth anisotropy [8]. However, since the growth anisotropy is assumed to be constant, it can be subtracted to quantify the magnetostriction measurement. Fig. 3 shows hysteresis loops and domain images obtained from a sample grown on a strained substrate. The hysteresis loops indicate that the "lm exhibits a well-de"ned uniaxial anisotropy, with no observable opening of the hard axis loop. The domain images con"rm the well-de"ned uniaxial anisotropy, with 1803 domain walls running parallel to the easy axis. Reverse domain spikes appear at the edges to reduce the demagnetising e!ect. Subtraction of the intrinsic anisotropy (shown in the inset) yields a magnetostriction constant of 30.4$ 7.5 ppm, in good agreement with the bulk data [12]. The error in this measurement is dominated by that of the Young's modulus. Further samples grown with varying strains give similar values. 3.2. Stress annealing Stress annealing is an alternative way to introduce a uniaxial anisotropy. The advantage of stress
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M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
Fig. 4. Stress annealing. (a) Hysteresis loops (i) for an as-cast "lm (open squares), (ii) the "lm placed under an external strain of 507 ppm (solid triangle), (iii) after stress annealing (solid circles), and (iv) upon removal of the strain (open diamond). (b) MOKE domain image at remanence.
Fig. 3. Strained growth (a) MOKE loops obtained along the easy (dashed) and hard (solid) axes of magnetisation for a sample deposited while the top surface of the substrate was held under a strain of 562 ppm. The inset shows loops taken in the same directions for an unstrained sample. Comparison gives a straininduced anisotropy of 5863 A/m. (b) MOKE domain image at remanence and at a "eld of 70 A/m applied along the easy axis.
annealing is that it destroys the intrinsic growth anisotropy (radial anisotropy in this case), generally improves the magnetic properties, and provides the means of tailoring the anisotropy "eld (H ). The problem associated with strained growth is the separation of the substrate from the watercooled platter. In the vacuum used, there is almost no heat transfer through the residual gas. All transfer of heat is by direct contact conduction or radiation. Too large a separation would cause the "lms to become magnetically hard because of the increased temperature. This puts an upper limit on the induced strain. Stress annealing is immune to such a problem. Fig. 4 represents the hard axis
hysteresis loops taken (i) from an as-cast "lm, (ii) the "lm placed under a tensile strain, (iii) after stress annealing, and (iv) upon removal of the external strain. The intrinsic growth anisotropy (i) competes with that of the stress-induced anisotropy (ii), since removal of the external mechanical strain after stress annealing creates a stress-induced anisotropy (iv) with a higher anisotropy "eld. Stress annealing minimises the two dominant anisotropies, leaving only a small material intrinsic anisotropy as shown in Fig. 4 (iii). Domain images con"rm a uniaxial anisotropy with 1803 domain walls upon removal of the external mechanical strain. A value of 29.1$7.3 ppm is obtained for the magnetostriction constant. Similar values were obtained for other samples using this method. The most bene"cial advantage of stress annealing, is that it provides the ability to tailor in a speci"c anisotropy "eld. This is very important for the fabrication of devices where it is necessary to control the anisotropy "eld, and hence the permeability. Fig. 5 shows that the induced anisotropy varies linearly with strain on both glass and silicon
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91
Fig. 5. (a) Induced-anisotropy "eld by stress annealing for "lms grown on Corning glass. Domain images 25 mm;15 mm at remanence. (b) Induced-anisotropy "eld by stress annealing for "lms grown on silicon. Domain images 5 mm;15 mm at remanence. In both cases each point was obtained from independent samples.
Fig. 6. (a) Hysteresis loops for a METGLAS威 "lm as a function of strain. All loops taken perpendicular to the direction of tensile strain. (b) Corresponding variation of anisotropy "eld with strain, from which a magnetostriction constant of 32.0$ 7.7 ppm is determined.
substrates, as expected from Eq. (1). In each case, each point was obtained from independently grown samples which were then stress annealed. The linearity is due to the strain-induced anisotropy which scales linearly being the dominant anisotropy. Fig. 5 demonstrates the high level of control which can be achieved in inducing a speci"c anisotropy "eld and the reproducibility of the magnetic samples. The magnitude of this induced anisotropy is much larger than an anisotropy induced by "eld annealing [13]. Domain images have been included to indicate the uniaxial anisotropy. The simplicity of the technique provides the means to induce an
in-plane transverse or longitudinal uniaxial anisotropy. 3.3. Strain during measurement Quanti"cation of the magnetostriction is more conveniently achieved by measuring the variation of the anisotropy "eld as a function of the strain applied during the measurement. In this way, several independent measurements of magnetostriction can be made from a single sample, increasing the con"dence in the result. It also eliminates the need to take account of the growth induced and/or
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M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
intrinsic anisotropy. Annealing of the sample prior to the measurements can e!ectively destroy the as-grown anisotropy, making this term quite small. Fig. 6a shows the variation of hard-axis MH loop with induced strain for a "lm grown on a standard microscope slide. The induced anisotropy varies linearly with strain, as expected. The gradient of the graph of anisotropy versus strain gives a measurement of magnetostriction using Eq. (1), while the intercept corresponds to the intrinsic anisotropy (for annealed samples, this term is usually smaller). From the gradient of the graph shown in Fig. 6b, the magnetostriction constant is calculated to be 32.0$7.7 ppm. Similar measurements carried out on METGLAS威 "lms grown on silicon and Corning威 glass substrates are represented in Fig. 7. The magnetostriction values calculated from the "rst two graphs in Fig. 7 are shown in Table 1. Again, the uncertainty in the Young's modulus of the METGLAS威 "lm dominates the error (25%). Repeating these measurements with di!erent samples gave values of j which varied by less than 5%, indicating that the random errors in the measurement are small. The quantity j > and its asso ciated error have been included in Table 1 to indicate how the uncertainty in the Young's modulus (> ) dominates the error. For systems in
which the Young's modulus of the "lm is well known, values of j which are quantitatively accu rate to within 5% should be possible. Fig. 7 also shows the technique applied to an FeCo thin "lm deposited on glass; as expected the anisotropy "eld varies linearly with strain. The magnetostriction constant is calculated to be 72.1$2 ppm, in good agreement with the quoted [14] value of 75 ppm for the bulk material from which the thin "lm was grown. A detailed study on magnetostrictive soft FeCo thin "lms, including magnetostriction measurements, will be the subject of another paper [15]. The variation of anisotropy "eld with strain also shows the potential of such materials for sensor applications. Since the anisotropy "eld varies by nearly two orders of magnitude over a modest range of strains, the sensitivity of such devices is expected to be high. Further work is underway to integrate these materials into micromachined sensors. The magnetostriction measurements have been gathered in Table 1, including values determined
Fig. 7. Variation of anisotropy "eld with strain. All loops taken perpendicular to the direction of tensile strain. METGLAS威 on silicon j "30.6$7.3 ppm, METGLAS威 on Corning威 glass j "31.2$7.5 ppm and FeCo on microscope slide glass j "72.1$1.3 ppm.
from the gradients of the two graphs shown in Fig. 5, where "lms were grown on glass and silicon substrates, and then stress annealed to induce different anisotropy "elds. The two magnetostriction constants obtained are in good agreement considering that each point on the graph was obtained from independently grown samples. It is apparent from Table 1 that the substrate has little or no in#uence on the value of the magnetostriction constant. This conclusion is con"rmed by magnetostriction measurements carried out by Mattingley [16], where METGLAS威 "lms grown on Kapton威 under similar growth conditions also gave similar values for j , even though the "lms were magneti cally much harder (coercive "elds &1500 A/m). The much higher coercive "elds are due to the
M. Ali, R. Watts / Journal of Magnetism and Magnetic Materials 202 (1999) 85}94
93
Table 1 Magnetostriction constants determined for METGLAS威 thin "lms Method
j > (MPa)
j (ppm)
H (A/m)
Strained growth Stress annealing (i) Single measurement (ii) Corning glass (Fig. 4) (iii) Silicon (Fig. 4)
5.1$0.3
30.4$7.5
60
4.9$0.3 5.0$0.1 5.2$0.2
29.1$7.3 29.7$7.1 30.9$7.4
18 18 18
Strain during measurement (i) Microscope slide (ii) Corning glass (iii) Silicon
5.4$0.1 5.1$0.2 5.2$0.2
32.0$7.7 30.6$7.3 31.2$7.5
20 52 18
stresses introduced by the Kapton威 substrate. Experiments [5] have shown the saturation magnetostriction does depend upon stress for nearly zero magnetostrictive materials, and therefore the linear dependence between the anisotropy "eld and stress becomes non-linear. The nonlinearity is small and can only be seen in materials possessing nearly zero magnetostriction. The random stresses from the substrate do have a small e!ect on the value of j , but can be con sidered to be negligible in highly magnetostrictive materials.
4. Conclusions A new, simple technique for the measurement of magnetostriction in thin "lms deposited onto fairly rigid thick substrates has been described. It has been applied to amorphous METGLAS威 "lms sputter deposited onto microscope slides, Corning威 glass, and silicon substrates. For these systems, the error in the measurement of magnetostriction is determined almost entirely by the uncertainty in the Young's modulus. The technique has also been applied to an FeCo "lm deposited by sputtering onto a microscope slide. In both the METGLAS威 and FeCo cases the values obtained are in good agreement with expected values. The technique can be applied to a wide variety of di!erent "lm/substrate combinations. If the Young's modulus of the "lm is known to a good accuracy, then the error in the value of j obtained
can be less than 5%, which compares well with other methods [3,17]. Such precise quantitative values could be used to provide sample standards for use with other techniques. The technique is not limited by "lm thickness, since the magneto-optical Kerr e!ect can comfortably monitor the magnetisation down to a "lm thickness of 10 nm. It overcomes the problem of non-uniform stresses by correlating the local stress with that of the local anisotropy "eld. No mechanical properties of the substrate are required, simplifying the calculation of j . There is no special preparation of samples required, and the equipment needed to implement the technique is inexpensive and commonly available. Since magnetostriction is a fundamental physical property of magnetic materials, it is vital for high precision devices (such as magnetic information storage systems) that accurate quanti"cation of its e!ects can be obtained. The values of magnetostriction obtained in this study have been very reproducible from the three di!erent methods used to strain the magnetic "lms. We have found that the substrates have no signi"cant in#uence on j , and the magnetic softness (coercive "elds) which is presumed to be caused by residual strains, also has little in#uence. These experiments also show that in these strongly magnetostrictive materials j is independent of strain for the applied strains and also the residual strains caused by the substrate. The technique of stress annealing to tailor the anisotropy "eld has been demonstrated to a high
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degree of precision on silicon and Corning威 glass substrates. It provides an excellent means of inducing a given anisotropy "eld in thin "lm-based sensors. It also provides the means of inducing a well-de"ned uniaxial domain structure, which simpli"es the understanding of the magnetic process for device applications. Acknowledgements We are grateful to the Engineering and Physical Sciences Research Council (UK) for the "nancial support of this work under grant GR/K55905 and for the studentship for M. Ali. We wish to acknowledge and thank M.D. Cooke for providing the soft FeCo "lm. We also wish to thank Prof. G.A. Gehring and J.E.L. Bishop for their valuable discussions. References [1] M.R.J. Gibbs, R. Watts, W.J. Karl, A.L. Powell, R.B. Yates, Sensors Actuators A 59 (1997) 229.
[2] M. Weber, R. Koch, K.H. Rieder, Phys. Rev. Lett. 73 (8) (1994) 1166. [3] K. Narita, J. Yamasaki, H. Fukunaga, IEEE Trans. Magn. MAG-16 (2) (1980) 435. [4] R. Becker, M. Kersten, Z. Phys. 64 (1930) 64. [5] H.K. Lachowicz, A. Siemko, IEEE Trans. Magn. MAG-25 (5) (1989) 3605. [6] M.L. Spano, K.B. Hathaway, H.T. Savage, J. Appl. Phys. 53 (3) (1982) 2667. [7] T.H. O'Dell, Phys. Stat. Sol. (a) 68 (1981) 221. [8] M. Ali, R. Watts, W.J. Karl, M.R.J. Gibbs, J. Magn. Magn. Mater. 190 (1998) 199. [9] G. Joos, Theoretical Physics, Third ed., Blackie, London, 1958, pp. 176 (Chapter 8). [10] R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics, Vol. 2, Addison-Wesley, Reading, MA, 1964, pp. 38}10 (Chapter 8). [11] B.D. Cullity, Introduction to Magnetic Materials, Addison-Wesley, Reading, MA, 1972, p. 274 (Chapter 8). [12] Allied Signal Corporation data sheet, 1995. [13] A.P. Thomas. Ph.D. Thesis, University of Bath, 1991. [14] Telcon data sheet FeCo, 1998. [15] M.D. Cooke, L.C. Wang, R. Watts, G.A. Gehring, W.M. Rainforth, G.P. Heydon, R. Zuberek, H. Szymczak, to be published. [16] A.D. Mattingley, C. Shearwood, M.R.J. Gibbs, IEEE Trans. Magn. MAG-30 (6) (1994) 4806. [17] J. Wenda, H. Jankowski, A. Kulak, Thin Solid Films 148 (1987) 1.