  We have studied the crystal and magnetic structures of Fe-doped hexagonal
manganites LuMn1-xFexO3 (x = 0, 0.1, 0.2, and 0.3) by using bulk magnetization
and neutron powder diffraction methods. The samples crystalize consistently in
a hexagonal structure and maintain the space group P63cm from 2 to 300 K. The
N\'eel temperature TN increases continuously with increasing Fe-doping. In
contrast to a single {\Gamma}4 representation in LuMnO3, the magnetic ground
state of the Fe-doped samples can only be described with a spin configuration
described by a mixture of {\Gamma}3 (P63'cm') and {\Gamma}4 (P63'c'm)
representations, whose contributions have been quantitatively estimated. The
drastic effect of Fe-doping is highlighted by composition-dependent spin
reorientations. A phase diagram of the entire composition series is proposed
based on the present results and those reported in literature. Our result
demonstrates the importance of tailoring compositions in increasing magnetic
transition temperatures of multiferroic systems.
