Figure 1:
Profiles of vs. distance r from the vortex center,
for single static out-of-plane vortices at the center of a circular system
with 180 sites on a square lattice. The curves are labelled by the different
values of .
These results were obtained by the relaxation procedure described in the text
(Sec. ii), using a fixed boundary condition as described in
Sec. iv.
Now the approach is to make the spinwave perturbation calculation using the directions, , as the different local quantization axes for each site. This is similar in spirit to a spinwave calculation for an antiferromagnet, [25] in which the classical ground state can have sets of spins on the different sublattices aligned along different directions, and the perturbation analysis uses different coordinate systems for different sublattices.