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).
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