Interplay between magnetism and octahedra distortion in the hybrid improper multiferroic Ca$_{\mathrm{3}}$Mn$_{\mathrm{1.9}}$Ti$_{\mathrm{0.1}}$O$_{\mathrm{7}}$

A novel microscopic mechanism has been proposed to search for ferroelectric material for realistic application. The instability of the polar phonon mode is driven by the simultaneous condensation of two nonpolar lattice modes associated with oxygen octahedron rotation and tilt modes, and is responsible for the polar symmetry observed in the Ruddlesden-Popper compounds. We have used single crystal neutron diffraction to investigate the temperature and pressure dependence of these oxygen octahedron distortions in Ca$_{\mathrm{3}}$Mn$_{\mathrm{1.9}}$Ti$_{\mathrm{0.1}}$O$_{\mathrm{7}}$ which has a structural transition at 365 K and antiferromagnetic order at 120 K. We observed a strong interplay between magnetism and the local oxygen distortion near the magnetic transition. The control of the magnetism through octahedron rotation is also discussed.