Magnetoelectric coupling tuned by competing anisotropies in Mn$_{1-x}$Ni$_{x}$TiO$_3$
A flop of electric polarization from $P$$\parallel$$c$ ($P_c$) to $P$$\parallel$$a$ ($P_a$) is observed in MnTiO$_3$ as a spin flop transition is triggered by a $c$-axis magnetic field, $H_{\|c}$=7 T. The critical magnetic field $H_{\|c}$ for $P_a$ is significantly reduced in Mn$_{1-x}$Ni$_x$TiO$_3$ (x=0.33). $P_a$ and $P_c$ have been observed with both $H_{\|c}$ and $H_{\|a}$. Neutron diffraction measurements revealed similar magnetic arrangements for the two compositions where the ordered spins couple antiferromagnetically with their nearest intra- and inter-planar neighbors. In the x=0.33 system, the uniaxial and planar anisotropies of Mn$^{2+}$ and Ni$^{2+}$ compete and give rise to a spin reorientation transition at $T_R$. A magnetic field, $H_{\|c}$, aligns the spins along $c$ for $T_R$$<$$T$$<$$T_N$. The rotation of the collinear spins away from the $c$-axis for $T$$<$$T_R$ alters the magnetic point symmetry and gives rise to a new ME susceptibility tensor form. Such linear ME response provides satisfactory explanation for the behavior of the field-induced electric polarization in both compositions. As the Ni content increases to x=0.5 and 0.68, the ME effect disappears as a new magnetic phase emerges.