  The free energy bounds for inhomogeneous current states in doped
antiferromagnetic insulators and spatial configurations of spin and charge
degrees of freedom in lightly and heavily underdoped phases of this strongly
correlated electron system are considered. It is shown that states are
characterized by a small parameter of geometric origin, which determines the
degree of packing in the knots of filament manyfolds of the order parameter
distributions. We found a hierarchy of the spatial scales for flat knots, which
gives rise to a free energy gain. A toroid moment in an underdoped state is
found for the first time. It is shown that in the percolation picture of charge
density distributions, that surround antiferromagnetic nanoclusters, the
optimal level of the hole density is in qualitative agreement with the
experimentally observed value.
