We present calculations of head to head domain wall structures in magn
etic strips of Ni80Fe20 with widths, w, ranging from 75 nm to 500 nm a
nd thicknesses, t, from 1 nm to 64 nm, Neglecting magnetocrystalline a
nd magnetostrictive anisotropy energies, minimization of exchange and
magnetostatic energy leads to one of two types of domain wall structur
es: 'transverse' walls with magnetization at the center of the wall di
rected transverse to the strip axis and 'vortex' walls where the magne
tization forms a vortex at the center of the wall, Calculation of the
domain wall energies leads to a proposed phase diagram for head to hea
d domain walls where transverse walls have lower energy when dimension
s are less than t(crit)w(crit) approximate to 130A/mu(0)M(s)(2).