Second Harmonic Generation in MnTiO$_{3}$

Optical Second Harmonic Generation (SHG) is a non-linear process observed in non-centrosymmetric materials. We have performed SHG in MnTiO$_{3}$ in the wavelength range of 900~nm -1500~nm. MnTiO$_{3}$ is anti-ferromagnetically ordered below 63 K ($T_{N}$ =63.5K). We study SHG as a function of temperature and magnetic field both above and below the N\'{e}el temperature to observe the effect of the spin order. When a magnetic field above the critical field ($B_{C }$= 6~T) is applied along the c-axis, MnTiO$_{3}$ exhibits spin flopping, and is thought to show ferrotoroidic symmetry.\footnote{H. Toyosaki et.al, \textit{APL} \textbf{93}, 072507 (2008)} We measured the magnetic field dependence of the second harmonic spectra of MnTiO$_{3}$ from 0~T to 10~T at temperatures ranging from 1.5~K to 150~K.