Anisotropic magnetic field responses of ferroelectric polarization in the trigonal multiferroic CuFe_1-x Al_x O₂ (x=0.015 )

We have investigated magnetic field dependences of a ferroelectric incommensurate-helimagnetic order in a trigonal magnetoelectric multiferroic CuFe_1-x Al_x O₂ 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 CuFe_1-x Al_x O₂ with x=0.035 have demonstrated that the magnetic field dependence of the "magnetic domain structure" results in distinct magnetic field responses of P, 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 CuFe_1-x Al_x O₂ systems (A=Al,Ga).