By directly measuring electrical hysteresis loops using the Positive-Up Negative-Down (PUND) method, we determined accurately the remanent ferroelectric polarization $P_r$ of orthorhombic $R$MnO${}_3$ ($R$ $=$ Ho, Tm, Yb, and Lu) compounds below their $E$-type spin ordering temperatures. We found that LuMnO${}_3$ has the largest $P_r$ of 0.17 $\mu$C/cm${}^2$ at 6 K in the series, the value of which allows us to predict that its single-crystal form can produce a $P_r$ of at least 0.6 $\mu$C/cm${}^2$ at 0 K. Furthermore, at a fixed temperature, $P_r$ decreases systematically with increasing rare earth ion radius from $R$ $=$ Lu to Ho, exhibiting a strong correlation with the variation of the in-plane Mn–O–Mn bond angle and Mn–O distances. Our experimental results suggest that the contribution of the Mn $t_{2g}$ orbitals may dominate the ferroelectric polarization.

• Received 14 August 2011

DOI:https://doi.org/10.1103/PhysRevB.85.184406