We show the presence of a Casimir type force between domain walls in a two
dimensional Heisenberg antiferromagnet subject to geometrical fluctuations. The
type of fluctuations that we consider, called phason flips, are well known in
quasicrystals, but less so in periodic structures. As the classical ground
state energy of the antiferromagnet is unaffected by this type of fluctuation,
energy changes are purely of quantum origin. We calculate the effective
interaction between two parallel domain walls, defining a slab of thickness d,
in such an antiferromagnet within linear spin wave theory. The interaction is
anisotropic, and for a particular orientation of the slab we find that it
decays as 1/d, thus, more slowly than the electromagnetic Casimir effect in the
same geometry.Comment: 5 pages, 5 figures, minor modifications, accepted for publication in
EPJ
