Heavy ions frequently appear as minor components in space plasmas, for example as charged helium in the solar wind and heavy ions in the vicinity of comets. Both the different components of ions and the associated plasma waves are observed by extraterrestrial in situ measurements. These plasma waves appear as large-amplitude magnetic field fluctuations in space plasmas. They must be described appropriately by means of multifluid equations. Because of the nonlinear nature of these waves, we here investigate nonlinear waves in multi-ion plasmas. Solitary waves that can only exist in a magnetized bi-ion plasma are presented. We employ a perturbation theory at the linear solution of a left-hand circularly polarized, low-frequency (below the proton gyrofrequency) plasma wave and take only the first nonlinear terms into account. Thus the multifluid equations are reduced to a single equation of the type of a nonlinear Schrödinger equation. The derived soliton solution is valid for magnetic field amplitudes lower than 10% of the ambient unperturbed magnetic field. The solutions are discussed for plasma parameters that are typical of the solar wind. A density enhancement can be observed within the soliton, where the helium ion density is more enhanced than the proton density.