InMnO3 : a fully frustrated multiferroic

InMnO$_3$ is a peculiar member of the hexagonal manganites h-RMnO$_3$ (where R is a rare earth metal element), showing crystalline, electronic and magnetic properties at variance with the other compounds of the family. We have studied high quality samples synthesized at high pressure and temperature by powder neutron diffraction. The position of the Mn ions is found to be close to the threshold $\it{x}=1/3$ where superexchange Mn-Mn interactions along the $\it{c}$ axis compensate. Magnetic long range order occurs below $T_{\rm N}$= 120(2) K with a magnetic unit cell doubled along $\it{c}$, whereas short range two dimensional dynamical spin correlations are observed above $T_{\rm N}$. We propose that pseudo-dipolar interactions are responsible for the long period magnetic structure.