Spin-wave dispersion in half-doped LaSrNiO

Recent neutron scattering measurements reveal spin and charge ordering in the half-doped nickelate, La${}_{3\mathrm{/}2}$ Sr${}_{1\mathrm{/}2}$ NiO${}_4$. Many of the features of the magnetic excitations have been explained in terms of the spin waves of diagonal stripes with weak single-ion anisotropy. However, an optical mode dispersing away from the (\pi,\pi) point was not captured by this theory. We show here that this apparent optical mode is a natural consequence of stripe twinning in a diagonal stripe pattern with a magnetic coupling structure which is two-fold symmetric, i.e. one possessing the same spatial rotational symmetry as the ground state.