# Analysis Of Torque Measurements On Films With Oblique Anisotropy

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IEEE
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• Musicology

## Abstract

Analysis Of Torque Measurements On Films With Oblique Anisotropy - Magnetics Conference, 1993. INTERMAG '93., Digest of International ANALYSIS OF TORQUE MEASUREMENTS ON FILMS WITH OBLIQUE ANISOTROPY n=2 I Leon Abelmann, Cock Lodder MESA, University of Twente, Box 217, 7500 A E , Enschede, NL When an anistropy axis is oblique to the film plane the analysis of torque curves becomes complex because measurements in several planes are necessary [ 11. To analyse the anistropy in these films the common approach is to assume a physical model based on a priori assumptions like the type of crystal structure or the direction of columns. When one includes second order anistropy this is not a trivial task and a universal model is needed. Using spherical harmonics it is possible to give a general description of the anisotropy without assuming an a priori physical model. With torque measurements in five different planes we can describe the magnetic anisotropy in second and fourth order for any arbitrary sample. I 29.6 I 16.2 I -71.1 1 -12.5 I -62 I Assume that we only have anistropy axis and no anisotropy directions (like frozen-in fields) than we can desribe the energy E in the sample up to the fourth harmonic by: I JI n=l m=-2n Where 8 and cp indicate the direction of magnetization (fig 1) ; Y2,,,(B,cp) are the spherical harmonics [2] and the k2n,m the anisotropy coeficients. ,;p Y % . x/ Figure 1 Definition of coordinate system To determine the 14 anisotropy coeficients k,,? we need to measure in 5 different planes La, (table 1). We describe the torque measurements in rectangular (P,Q) or polar (L,a) coordinates. 2 2 Labc (r) = Pzn,abc cos(2ny) + QIn,obr sin (2nY) = &n,obc cos[2n(P+ a2tin,abc 11 ["I (2) "= 1 n=l With index abc as in table 1 and y the measurement angle (either 8 or 9). These five measurement result in 20 fourier coeficients of which a number are mutually dependent. The relation between the 20 fourier coefficients and the

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