Sustaining a detached plasma is important for the reduction of the heat load on a divertor. The externally controlled methods such as gas puffing in the divertor region, etc. have been studied for maintaining detached plasmas. In the recent LHD experiments, a resonant magnetic perturbation (RMP) is utilized to establish the detached plasma, which is one of the candidates to reduce the divertor heat load. The finite plasma response field has been detected when the RMP is imposed, and its behavior is investigated from the viewpoint of the magnetic island dynamics. A parameter of the phase difference, Δθ (defined as the phase difference between the plasma response field and the RMP), changes from antiphase to in-phase while the plasma transits from the attached to the detached states. Finally, when the Δθ reaches at certain critical value, Δθ crit , the plasma enters the detached state. Since this critical value does not have a dependency on plasma beta and collisionality, Δθ crit seems to be a threshold to establish the detached plasma. From the viewpoint of magnetic island dynamics, the behavior of Δθ approaching in-phase implies the "trend" of island growth. The detached plasma might be established in the case of the tendency for the plasma response field to reinforce the island width.