  We have investigated magnetic field dependences of a ferroelectric
incommensurate-helimagnetic order in a trigonal magneto-electric (ME)
multiferroic CuFe1-xAlxO2 with x=0.015, which exhibits the ferroelectric phase
as a ground state, by means of neutron diffraction, magnetization and
dielectric polarization measurements under magnetic fields applied along
various directions. From the present results, we have established the H-T
magnetic phase diagrams for the three principal directions of magnetic fields;
(i) parallel to the c axis, (ii) parallel to the helical axis, and (iii)
perpendicular to the c and the helical axes. While the previous dielectric
polarization (P) measurements on CuFe1-xGaxO2 with x=0.035 have demonstrated
that the magnetic field dependence of the `magnetic domain structure' results
in distinct magnetic field responses of P [S. Seki et al., Phys. Rev. Lett.,
103 237601 (2009)], the present study have revealed that the anisotropic
magnetic field dependence of the ferroelectric helimagnetic order `in each
magnetic domain' can be also a source of a variety of magnetic field responses
of P in CuFe1-xAxO2 systems (A=Al, Ga).
