  We investigate the existence of spiral ordering in the planar spin
orientation of skyrmions localised on a face centered rectangular lattice
(FCRL). We use the non-linear sigma model (NLSM) to numerically calculate the
minimum energy configurations of this lattice around the $\nu=1$ quantum Hall
ground state. Our variational ansatz contains an angle $\theta$, characterising
the FCRL and an angle $q$, characterising the orientational order. As $\nu$ is
increased towards one, there is a smooth transition from the triangular lattice
(TL) characterised by $(\theta,q) = (120^o,120^o)$ to FCRLs with spiral
orientational order. The novel feature we find is that these phases are
characterised by $\theta, q)$ values such that $\theta+q = 240^o$ (same as the
TL phase). As $\nu$ incresaes further towards one, there is a sharp transition
from the FCRLs to the square lattice (SL), characterised by
$(\theta,q)=(90^o,180^o)$. Consequently, the parameter $\theta+q$ jumps sharply
at the FCRL-SL transition and can serve as an order parameter to characterise
it.

Mesoscale and Nanoscale Physics