  We study the renormalization of a single impurity potential in
one-dimensional interacting electron systems in the presence of magnetic field.
Using the bosonization technique and Bethe ansatz solutions, we determine the
renormalization group flow diagram for the amplitudes of scattering of up- and
down-spin electrons by the impurity in a quantum wire at low electron density
and in the Hubbard model at less than half filling. In the absence of magnetic
field the repulsive interactions are known to enhance backscattering and make
the impurity potential impenetrable in the low-energy limit. On the contrary,
we show that in a strong magnetic field the interaction may suppress the
backscattering of majority-spin electrons by the impurity potential in the
vicinity of the weak-potential fixed point. This implies that in a certain
temperature range the impurity becomes almost transparent for the majority-spin
electrons while it is impenetrable for the minority-spin ones. The impurity
potential can thus have a strong spin-filtering effect.
