  We study states with spontaneous spin current, emerging in frustrated
antiferromagnetic spin-$S$ chains subject to a strong external magnetic field.
As a numerical tool, we use a non-Abelian symmetry realization of the density
matrix renormalization group. The field dependence of the order parameter and
the critical exponents are presented for zigzag chains with S=1/2, 1, 3/2, and
2.
