  A growth diagram of Lu-Fe-O compounds on MgO (111) substrates using pulsed
laser deposition is constructed based on extensive growth experiments.
  The LuFe$_2$O$_4$ phase can only be grown in a small range of temperature and
O$_2$ pressure conditions.
  An understanding of the growth mechanism of Lu-Fe-O compound films is offered
in terms of the thermochemistry at the surface.
  Superparamagnetism is observed in LuFe$_2$O$_4$ film and is explained in
terms of the effect of the impurity h-LuFeO$_3$ phase and structural defects .
