newfield = ogr.FieldDefn("aa", ogr.OFTReal)
erasedlayer.ResetReading()
erasedlayer.CreateField(newfield)
for i in range(erasedlayer.GetLayerDefn().GetFieldCount()):  # iterate on parcelle features to get the names
    print(erasedlayer.GetLayerDefn().GetFieldDefn(i).GetName())
erasedlayer.ResetReading()
for feature in erasedlayer:
    feature.SetField("aa", feature.GetGeometryRef().GetArea())

Traceback (most recent call last):
  File "/home/bench/PycharmProjects/histcult/Rpg.py", line 190, in <module>
    feature.SetField("aa", feature.GetGeometryRef().GetArea())
  File "/usr/lib/python3/dist-packages/osgeo/ogr.py", line 4808, in SetField
    return _ogr.Feature_SetField(self, *args)
RuntimeError: Invalid field name: 'aa'