  We investigate the classical ground state configurations of a collection of
skyrmions in the limit of vanishing L\'ande $g$ factor. We show that in this
limit, the skyrmions which are large and overlapping, behave qualitatively
differently from small skyrmions. We investigate the system in various regimes
of spin stiffness. We find that in all regimes, at $g=0$, the ground state
configuration is a rectangular skyrmion lattice with N\'eel orientational
ordering. The charge distribution has a higher symmetry of a face-centered
rectangular lattice and the $z$-component of the spin polarization is zero. We
also present general argument for the vanishing of spin polarization at $g=0$
at finite temperature and in the presence of disorder and discuss some
experimental consequences of our results.
