Narrow dip around zero magnetic field in magnetization hysteresis loops of thin YBCO superconducting films

A narrow dip is observed around zero magnetic field in magnetization curves M(B) of superconducting YBCO films with about 10 nm thickness. This anomaly occurs in the same field range with an anomaly of ac surface impedance Z(B) found recently in thin YBCO films. Because the thickness of our films is considerably less than the London penetration depth, two-dimensional limit of the critical state model is applied. In the framework of this model the magnetic field dependence of the critical current density jc(B) is found. The obtained jc(B) function agrees well with that found in the ac surface impedance investigation.