DOMAIN STRUCTURES DUE TO INDUCED ANISOTROPY AND STRESSES IN FILM HEADS

R. E. Jones, Jr., and R. D. Holmes International Business Machines Corporation

General Products Division San Jose, CA 95193

P. Kasiraj International Business Machines Corporation

Almaden Research Center San Jose, CA 95193

The domain wall structure of film heads can lead to time-lags and fluctuations in the heads playback output.1 anisotropy as well as by induced anisotropy.1 We will consider the superposition of these two anisotropies which results in a locally varying uniaxial anisotropy near the head backgap using the coordinates of Figure 1. The total local anisotropy energy will be given by the s u m of induced and stress anisotropy terms:

In turn the domain wall structure can be influenced by magnetostriction

% = eK + e,, = K,sin20 + 3/2rl,Aaain2(B-q3), (1)

assuming a stress anisotropy in the radial direction and an induced anisotropy along I$ = 0. Since the superposition of two uniaxial anisotropies is another uniaxial anisotropy, Equation (1) can be expressed

% = Asin2(e-a)+ E, (2)

where A, B and a depend on position. If it is assumed that 180 degree walls always follow the direction of local anisotropy (neglecting exchange and magnetostatic energies) and that the induced anisotropy constant is known, then domain patterns can be used to deduce 3/2 1, ACT. Minimizing energy with respect to 0, Equation (1) gives:

3/2A,Ao = - Kusin2cl/sin2(a-q3),

which allows the product 3/2 A, A o to be determined i f a and K, are known.

As a specific example, we consider the case where 3/2 1, Aa varies inversely with r’:

(3)

312 A, AU = Ku(3ro/Zy . (4)

CH2731 - 8/89/0000 - AA-7 $01 .OO @ 1989 IEEE

The direction of local anisotropy, a, and the anisotropy magnitude, A, derived using Equations (l), (2) and (4), is shown in Figure 2. Along 4 = 4 2 , the anisotropy near the edge of the backgap is in the radial direction (the direction of the stress anisotropy). The anisotropy magni- tude drops to zero at r = 3J2 , where the induced and stress anisotropies are perpendicular and equal. Beyond this point the induced anisotropy dominates, and the total anisotropy is in the I$ = 0 direction. Near the “isotropy point” the anisotropy also can be in the I$ = n/4 or I$ = 3n/4 directions. Along I$ = 0 the stress and induced anisotropy contributions add, so the total anisotropy is large and the hard axis permeability is small.

If the direction of magnetization is due only to a minimization of anisotropy energy, then domain walls will follow anisotropy “streamlines” (lines generated by following the angle a). Examples are shown in Figure 3 of domain walls corresponding to the anisotropy shown in Figure 2.

. ~ c m l .I*I. bmr..n the magr*1k.Uon end In. L28.3 0-0 *xi,

FI~UI. 1. Coordin*l.l

- 4 -

Figurn 3. Domain Wall$

If the product 3/2 A, B o is negative, a different pattern of anisotropy occurs. The minimum in stress anisotropy energy occurs when the magnetization is circumferential. For the inverse rz dependence considered before, the “isotropy point” exists on the I$ = 0 axis at r = 3rd2. The anisotropy magnitude along the I$ = n/2 axis is increased, again because the two anisotropies add, and the permeability along this a x i s will decrease. Examples of domain wall patterns taken from the literature show at least qualitative agreement with those predicted.

References

1. R. E. Jones, Jr., IEEE Trans. Magn. MAG-15, 1619 (1979). 2. R. D. Hempstead and J. B. Money, US. Patent 4,242.710.

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