  Collapse calculations indicate that the hot newly born protoneutron stars
(PNS) rotate differentially so that strong toroidal magnetic field components
should exist in the outer crust where also the Hall effect appears to be
important when the Hall parameter \hat\beta=\omega_B \tau is of order unity.
The amplitudes of the induced toroidal magnetic fields are limited from above
by the Tayler instability. An important characteristic of the Hall effect is
its distinct dependence on the {\em sign} of the magnetic field. We find for
fast rotation that positive (negative) Hall parameters essentially reduce
(increase) the stability domain. It is thus concluded that the toroidal field
belts in PNS induced by their differential rotation should have different
amplitudes in both hemispheres which later are frozen in. Due to the effect of
magnetic suppression of the heat conductivity also the brightness of the two
hemispheres should be different. As a possible example for our scenario the
isolated neutron star RBS 1223 is considered which has been found to exhibit
different X-ray brightness at both hemispheres.
