  The cross-tie domain wall structure in micrometre and sub-micrometre wide
patterned elements of NiFe, and a thickness range of 30 to 70nm, has been
studied by Lorentz microscopy. Whilst the basic geometry of the cross-tie
repeat units remains unchanged, their density increases when the cross-tie
length is constrained to be smaller than the value associated with a continuous
film. This occurs when element widths are sufficiently narrow or when the wall
is forced to move close to an edge under the action of an applied field. To a
very good approximation the cross-tie density scales with the inverse of the
distance between the main wall and the element edge. The experiments show that
in confined structures, the wall constantly modifies its form and that the need
to generate, and subsequently annihilate, extra vortex/anti-vortex pairs
constitutes an additional source of hysteresis.
