  We study current carrying helical edge states in a two-dimensional
topological insulator coupled to an environment of localized spins, i.e. a spin
bath. The localized spins mediate elastic spin-flip scattering between the
helical edge states, and we show how this induces a spin-bath magnetization for
a finite current through the edge states. The magnetization appears near the
boundaries of the topological insulator, while the bulk remains unmagnetized,
and it reaches its maximal value in the high bias regime. Furthermore, the
helical edge states remain ballistic in steady state, if no additional
spin-flip mechanisms for the localized spins are present. However, we
demonstrate that if such mechanisms are allowed, then these will induce a
finite current decrease from the ballistic value.
