Transverse field-induced nucleation pad switching modes during domain wall injection Page: 3 of 14
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nucleation pads required this to allow reasonable memory requirements and calculation times.
Where domain walls propagation in wires was of interest, the maximum mesh size in wires was 5 nm
laterally and 20 nm through the wire thickness. This asymmetric mesh results in much faster
calculations for these thicknesses than a uniform 5 nm mesh size throughout and tests showed little
variation between the two methods for the wires. The material properties of bulk permalloy were
used in the model, with exchange stiffness A = 1.3x10" J/m, saturation magnetization MS = 800
kA/m, magneto-crystaline anisortopy K = 0 Jm3 and damping constant a = 0.01. For simulations of
switching fields, a linearly increasing magnetic field (1 Oe/ns) was applied parallel to the wire long
axis. The structures were discretized using a tetrahedral mesh with a maximum cell width of 20 nm.
The dimensions of the simulated structures mimicked the essential features of the experimental
structures, although edge roughness was neglected from the model.
Results and Discussion
Figures 2 - 5 show M-TXM images of nucleation pads and 200 nm, 300 nm and 500 nm wide
wires in sample set A under various H~ and H,. Note that H, > 0 Oe and Hy < 0 Oe in figs. 2 and 3,
but HX 0 Oe and H, > 0 Oe in figs. 4 and 5; and figs. 3 and 4 show two nominally identical
structures, not the same structure. In all the structures, the remanent magnetization state of the
pad with no transverse field [part (a) of Figs. 2 - 5] consists of a uniform magnetization aligned with
the wire axis, with closure domains at the edges facing and joining the wire. When H, = 0 Oe and Hx
= 20 Oe, the magnetization state of the pad buckles, forming either eight [Figs. 2(b) and 5(b)] or six
[Figs. 3(b) and 4(b)] domains, half of which have magnetizations rotated away from the x-axis. As H~
is increased, the rotation of the domains become larger and the non-rotated domains shrink [Figs.
2(a)-(d), 3(a)-(d), 4(a)-(d) and 5(a)-(d)]. By H~L = 100 Oe (125 Oe for the 500 nm wide wire), the
magnetization in each pad is aligned with the field, and a domain wall is either left at the junction
with the wire [Figs. 2(e) and 3(e)], or injected into the wire [Figs. 4(e) and 5(e)].
When a transverse field is applied in addition to the axial field, more complex modes of
magnetization reversal are seen in the pad. In the pad with the 200 nm wide wire under H, = -12 Oe
[Figs. 2(f)-(j)], the magnetization enters a six-domain state when HX 20 Oe [Fig. 2(f) and (g)], but
changes into a four-domain state at H, = 40 Oe [Fig. 2(h) and (i)], before the pad completes
magnetization reversal at Hx - 100 Oe [Fig. 2(j). The magnetization states of the pads with 300 nm
wide wires under a transverse field [Figs. 3(f)-(j) and 4(f)-(j)] appear to be distorted forms of the
magnetization state with no transverse field when H < 40 Oe. However, these low field
distortions are complements of each other: in one pad wire closure domains are expanded and the
central domain is reduced [Figs. 3(f)-(h)], whereas in the other wire the closure domains are reduced
and the central domain is expanded [Figs. 4(f)-(h)]. These distortions precede differences in the
ongoing evolution of magnetization, with the former pad undergoing almost complete reversal
between H = 80 - 100 Oe [Figs. 3(i) and (j)] while the latter forms a Landau pattern, or vortex, at
H =-80 Oe [Fig. 4(i)] that is expelled at higher fields to complete the magnetization reversal [Fig.
4(j)]. The pad with a 500 nm wide wire under H, = 9 Oe forms a six-domain state when (H, < 20 Oe
[Figs. 5(f) and (g)], but this changes to a vortex state at higher fields [Figs. 5(h) and (i)]. The vortex is
gradually driven out of the pad as H, is increased, until a uniform magnetization state is reached at
Hz = 125 Oe [Fig. 5(j)].
While we have not studied the effect of wire width on the magnetization state of the pad
comprehensively, similar magnetization states were observed in pads with different width wires
attached. For example, figures 2(b) and 5(b) show similar magnetization configurations in pads with
200 nm and 500 nm wide wires attached, respectively, while figures 2(f)-(j) and 3(f)-(j), and figures
4(f)-(j) and 5(f)-(j) each show very similar magnetization reversal pathways under transverse fields.
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Bryan, M. T.; Fry, P. W.; Schrefl, T.; Gibbs, M. R. J.; Allwood, D. A.; Im, M.-Y. et al. Transverse field-induced nucleation pad switching modes during domain wall injection, article, March 12, 2010; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc1014610/m1/3/: accessed April 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.