Kink walls and critical behavior of magnetization near the lock-in transition in layered superconductors

We consider the behavior of a layered superconductor in a magnetic field applied at very small angles with respect to the layers. The penetration of the field component perpendicular to the layers occurs as a result of the phase transition (lock-in transition). The boundary of the locked phase is calculated exactly. We argue that the penetration of the transversal field occurs by the formation of separated kink walls. The structure of field in the wall and the behavior of magnetization depend essentially upon the value of the field along layers Bx. At small Bx a kink wall is composed of separated magnetic flux tubes. Each tube contains flux that depends upon Bx and smaller than a flux quantum. At large Bx these tubes overlap and form a magnetic flux wall. The behavior of the magnetization near the transition is studied in detail. At large separations between kink walls they interact exponentially and their concentration sharply increases in the narrow region above the lock-in field. This leads to the appearance of a tiny peak in the field dependence of the magnetization, which can be used to indicate the lock-in transition