Ilvnaniic Distortion i n a Magnetic Ihnia.iii Wall Contailling J,oosc:Iy Sl ) ; rcc~ l 2 r \!l$l,.<

A. Bagnkrks, Ail. Redjdal and F. 13. Ilumplircy Dept. of E.C.S. Engineering, Boston Unive7-sily,

44 Cummington Street, Boston, M A 02.?1,5.

The dynamics of a magnetic domain wall containing 27r vertical Bloch lines (27rVBL) lias been investigated using numerical methods. The wall is the kind found in thin film insulat.ors with a large anisotropy perpendicular to the plane of the film. T h e initial structure consistk of equally spaced winding 27r VBLs. The wall is driven by an applied field along the easy axis of anisotropy perpendicular to the film plane. The 27rVBLs are gyrotropically driven by the wall moti,on. Both the wall and the 27rVBLs are observed in the simulation for a \vide range of applied fields. Since the analytical expressions for the dynamics of walls and V13l,s require a rigid wall assumption, the simulation presented here complements tha t approacli by focusing on the dynamic distortion of the wall and wall structure as they are di-ivcil by an applied field.

Distortion of the initial equilibrium structure is apparent for all fields. Even thougll t,iic, wall is not planer a t equilibrium the maximum excursion from planer can be used as ii 111ei~- sure of wall distortion. After dynamic equilibrium has established, we find tha t the distortion initially decreases then increases nearly monotonically as the drive field increases. Tllc dis- tortion of the 2nVBLs as they are pushed gyroscopically by the wall is more interesting. ?‘lit: equilibrium structure of a 27rVBL has a 27r twist of the in-plane angle with the twist on two surfaces slightly offset alon the wall. The offset makes a very convenient measure of the 27rVBL ”width”. Figure 1 sf~ows the 27rVBL width as a function of t ime with the drive field on the wall as a parameter. It can be seen that there are two regions of similar behavior and a third higher region not shown. For reiativeiy iow fields (to 60 Oe), the 27r VBL is squeezed to become smaller. The width decreases as the field increases in the same range as t h e wall micro-deformation decreases. The dynamic structure is very stable with time. The waIl mobility slowly increases with held and the VBL mobility decreases markedly w i t h field, through this region, as can be seen in figure 2. The ratio of the VBI, to wall velocity, therefore. decreases from about 6 at 10 Oe to about 3.5 at 60 Oe.

1

0.6

0 2

-0 2

0 6

- 1 0 2 0 4 0 60 8 0 100

Time (nsec)

Figure 1: VBL width as a fiinction of time, external field as a parameter

0 20 4 0 6 0 8 0 100 110 External Field (00)

Figure 2: Wall and VBL riiobility a t dynamic equilibrium as a function of ficld.

A t iiitcriiicdi;ttcr licrlds rcpresented by 70 Oe to 100 Oc i r i figiir-c 1 , t l ic 2?rVl3l,s cx tv i l d aiitl part. aud a dynamic equilibrium with equally spaced nVI3L’s is rcaclicd. Consit1cral)Ici time is requircd at the beginning (70 Oe) to reach dynamic equilibrium. ‘I‘lic dyrianiics of this region has becn previously reported since it is tlie same as for the higlier drive fields when the initial structure contains equally spaced 7rVBL’s (1). It can be seen i n figure 2 that there is an abrupt change in mobility goin from the lower region to this intermediate region probably associated with the breakup of &e 27r VBLs into 7r VBLs. After the breakup, the VBL mobility slowly decreases and the wall mobility increases with increasing field. The VBL to wall velocity ratio changes from about 6 to 5.

In the high drive region with fields above about 110 Oe, dynamic equilibrium is slow to establish and the distortion is extreme. At some drive fields, Bloch point pairs arc formed alternatively on the bottom and top surfaces with the process repeated in time. Distortion in this region is nearly impossible to quantify and is most conveniently presentcd using a short video. Either a video or contours will be presented. It should be understood that the appearance of Blocli points in a digitized simulation presents a question as to tlie reliability of the results since the Bloch point necessarily occurs between the nodes of the simulation. However the interpretation, t he dynamics in this region can highlight where the stress areas are in the magnetic material.

The simulations were made by solving the Landau Lifshitz Gilbert (LLG) equation nu- merically on a 125 times 128 times 16 node lattice. The simulation program is running on the massively parallel Connection Machine 2 (2). We start with a stripe domain of two walls and a 2rVBL in each wall at equilibrium, and apply a periodic field perpendicular to tlie plane of the film. This field reverses direction in the center of the domain. Both walls move in the same direction and the field reversal moves with the walls to stay in the center of the domains. In this way, t he demagnetizing field of the stripe array remains at it’s equilibrium value for zero applied field allowing us to simulate steady state structures.

References:

(1) A . Bagnkrks and F.B. Humphrey, ”Dynamics of Magnetic Domain Walls with Loosely Spaced Vertical Bloch Lines”, IEEE Trans. Magn. 28, 2344 (1992). (2) R. Silcs, P.R. Kotiuga, and F.B. Humphrey, ”Three-Dimensional Micromagnetic Siniu- 1a.tioiis on the Connection Machine”, J. Appl. Phys., 67, 5S21 (1990).

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