  Generally strong charge and magnetic inhomogeneities are observed in NQR/NMR
experiments on underdoped cuprates. It is not the case for the underdoped
HgBa$_2$CuO$_{4+\delta}$, the most symmetric and highest T$_c$ single layer
cuprate, whose magnetic inhomogeneity is strongly suppressed. Also neutron
scattering experiments reveal a unique pair of weakly dispersive magnetic modes
in this material. We propose that these special properties stem from the
symmetric positioning of the O-dopants between adjacent CuO$_2$ layers that
lead to a strong superexchange interaction between a pair of hole spins. In
this Letter we present a theoretical model, which gives a consistent
explanation to the anomalous magnetic properties of this material.
