Unusual giant magnetostriction in the ferrimagnet Gd${}_{2\mathrm{/}3}$Ca${}_{1\mathrm{/}3}$MnO${}_3$

We report an unusual giant linear magnetostrictive effect in the ferrimagnet Gd${}_{2\mathrm{/}3}$Ca${}_{1\mathrm{/}3}$MnO${}_3$ ($T_c\approx$80 K). Remarkably, the magnetostriction, negative at high temperature ($T\approx T_c$), becomes positive below 15 K when the magnetization of the Gd sublattice overcomes the magnetization of the Mn sublattice. A rather simple model where the magnetic energy competes against the elastic energy gives a good account of the observed results and confirms that Gd plays a crucial role in this unusual observation. Unlike previous works in manganites where only striction associated with 3$d$ Mn orbitals is considered, our results show that the lanthanide 4$f$ orbitals related striction can be very important too and it cannot be disregarded.