We study J-kink domain walls in D = 4 massive CP 1 sigma model. The domain walls are not static but stationary, since they rotate in an internal S1 space with a frequency ω and a momentum k along the domain wall. They are characterized by a conserved current Jμ = (Q,J), and are classified into magnetic (J 2 < 0), null (J2 = 0), and electric (J2 > 0) types. Under a natural assumption that a low ...