Peak effect in single crystal MgB$_2$ superconductor for ${\bf   H}\parallel c$-axis
  We have studied the phase diagram of MgB$_2$ superconductor using a single crystal for ${\bf H}\parallel c$-axis. For the first time we report the existence of peak effect in the screening current in MgB$_{2}$ single crystal for ${\bf H}\parallel c$-axis. In the magnetic field regime $10<H<13.5$ kOe the local fundamental diamagnetic moment displays a very narrow diamagnetic step, with a temperature width of the same size as the zero dc-magnetic field transition. For higher field this step is transformed to a peak which is related with the peak effect in the screening current. Finally, for $H<10$ kOe the diamagnetic step is transformed to a gradual transition. Our findings for the vortex matter phase diagram for the MgB$_2$ are closely related with theoretical predictions concerning the vortex matter phase diagram of a type II superconductor in the presence of weak point disorder. 
M. Pissas, S. Lee, A. Yamamoto, and S. Tajima