  We predict that oblique breathers can be generated by a flow of two-component
Bose-Einstein condensate past a polarized obstacle which attracts one component
of the condensate and repels the other one. The breather exists if
intra-species interaction constants differ from the inter-species interaction
constant and it corresponds to the nonlinear excitation of the so-called
polarization mode with domination of the relative motion of the components.
Approximate analytical theory is developed for the case of small-amplitude
breathers that is in reasonable agreement with the exact numerical results.
