We have investigated the suppression of flux jumps and the enhancement of trapped field on a thin, high-J MgB₂ bulk (30 mm in diameter and 7 mm in thickness) for the pulsed field magnetization (PFM) using a split-type coil with a soft iron yoke, and compared the results to those magnetized using the split-type coil without a yoke and a solenoid-type coil with a yoke. A maximum-trapped field, B, of 0.71 T at 14 K was achieved on the bulk surface without flux jumps by using the split coil with yoke. On the other hand, low B values with flux jumps were observed for the cases using the split-type coil without a soft iron yoke, and the solenoid-type coil with a yoke. These results reproduce previous ones for a thick, high-J MgB₂ bulk (22 mm in diameter and 15 mm in thickness), for which the trapped field was enhanced to a record high value of B=1.10 T at 13 K by PFM using the split-type coil with a yoke.