Magnetic phase transitions in single crystalline Mn$_{0.68}$Ni$_{0.32}$TiO$_3$

The magnetoelectric MnTiO$_3$ has the ilmenite structure and order antiferromagnetically with neighboring Mn$^{2+}$ spins antiparallel to each other both within the ab-plane and along the c-axis. We have observed a magnetic field induced electric polarization in the 32$\%$Ni-doped MnTiO$_3$. To understand the origin of this magnetoelectric effect, we have carried out neutron diffraction study on single crystalline Mn$_{0.68}$Ni$_{0.32}$TiO$_3$. The Mn$^{2+}$ spins order below 27 K and arrange in the same antiparallel manner as the parent compound, but with different spin direction. On cooling the magnetic phase goes through a second transition at 15 K, below which the spins lock into a new direction. We have also determined the spin structure under a magnetic field applied along the c-axis.