Static wall structure in bubble films under large in-plane fields

Abstract

The domain wall structure in a magnetic bubble domain film is considered for the case in which an in‐plane field is applied which is either perpendicular or parallel to the wall plane. It is shown that a fairly simple analytical solution to the problem of the static wall structure may be obtained when the in‐plane field exceeds μ0Ms because it is then possible to assume that the problem is one‐dimensional.

The peak velocity of a domain wall in a magnetic bubble film under a large in-plane field

“…The static structure of the domain wall under such conditions has been the subject of a previous paper [14] where it was shown that the magnetostatic field from the two doniaiiis lying upon either side of the wall could be neglected when the in-plane field was such that pOMs < B, < p0M,Q. A solution to the problem of the static wall structure was then obtained in which 171 was a function of y only, rotating in (y, z ) across the wall region, M always having a component parallel to y.…”

“…It is implicit in the Landau-Lifshitz model that 1 < M , and A/M9 is identical to the now well established Gilbert damping parameter [16]. The vector P in (3) is the total effective magnetic field made up from the exchange, anisotropy, magnetostatic and applied fields [14]. The magnetonieclianical ratio is written as -lyI because this ratio is negative in nearly all materials.…”

“…When a large in-plane field, B,, is applied perpendicular t o the wall plane and poM, < B, < p,,M,Q, the static structure of the wall may be found quite simply [14] and involves a rotation of M in (y, z ) as we pass from the domain y < 0, M , = M,, t o the doniain y > 0, M , = -MS. The static structure cannot be given explicitly in this case, as could be done for the Landau-Lifshitz wall in equations (4) and ( 5 ) , but the functions involved have a very similar form to tanh (y/d) and sech (y/d), and (6), (7), and (8) are similarly modified with y = 4 2 now being the initial condition.…”

“…Following this argument, the next step is to substitute (4) into (12) and obtain in place of (21). This neglects the tilt of &I within the domains on either side of the wall, brought about by the applied in-plane field [14], but this may be neglected because it involves a term (1 -(By/poMsQ)2)1/2 which will be very close to unity in practice. Using (26) the z component of ( , equation (25).…”

“…The factor of TC in (31) comes from equation (4.7) of [ll], the result of integrating our equation (5) from --co t o + co. The general theory of wall motion does not cover the case considered here, however, in which a very large in-plane field is applied so that the initial wall structure [14] is completely different to the dynamic wall structure and, in addition, the angle y is not independent of y. Such a case can only be dealt with approximately.…”