Peak effect phenomena, surface superconductivity and paramagnetic   Meissner effect in a spherical single crystal of niobium
  We have explored the vortex phase diagram in a spherical single crystal of niobium (T ~ 9.3 K) via isothermal and temperature dependent dc magnetization and ac-susceptibility measurements. The crystal has extremely weak pinning that can be inferred from the reversibility of loops below T_c. However, one can visualize the peak effect (PE) feature in the isothermal M-H loops up to T = 8 K. The PE is also prominent in isothermal ac-susceptibility data for H > 750 Oe. An interesting observation in the present study is the prominent fingerprints of surface superconductivity, starting just above the collapse of pinning at the peak position of the PE and ending at the surface critical field (H_c3). We have also observed the paramagnetic Meissner effect in field-cooled magnetization data recorded at relatively large fields in this crystal. A vortex phase diagram is constructed by marking the peak positions of the PE (H_p), the upper critical field (H_c2) and the surface critical field (H_c3). Unlike a previous report which shows the existence of a multi-critical point in the phase dia-gram of a Nb crystal, where H_p, H_c2 and H_c3 lines meet, we do not observe a multi-critical point in our weak pinning crystal. 
Pradip Das, C. V. Tomy, H. Takeya, S. Ramakrishnan and A. K. Grover