Magnetoelectric phase diagrams of orthorhombicRMnO3(R=Gd, Tb, and Dy)
Magnetoelectric phase diagrams have been investigated for rare-earth manganites with orthorhombically distorted perovskite structure, $R{\mathrm{MnO}}_{3}$ ($R=\mathrm{Gd}$, Tb, and Dy). A variety of magnetic and electric phases emerge with varying $R$-site ion, temperature, and magnetic field in these systems. The magnetoelectric phase diagram varies sensitively with the direction of a magnetic field relative to the crystallographic axes. Although the ground state of ${\mathrm{GdMnO}}_{3}$ with the largest ionic radius of $R({r}_{R})$ is not ferroelectric in zero magnetic fields $(H=0)$, a ferroelectric phase with electric polarization $(P)$ along the $a$ axis appears by applying $H(>\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{T})$ along the $b$ axis. Both ${\mathrm{TbMnO}}_{3}$ and ${\mathrm{DyMnO}}_{3}$ show a ferroelectric order with $P$ along the $c$ axis even at $H=0$ below a lock-in transition temperature where nonzero wave vectors for magnetic and lattice modulations become nearly constant. These systems also exhibit a flop of the ferroelectric polarization ($P\ensuremath{\Vert}c$ to $P\ensuremath{\Vert}a$) when $H$ is applied along the $a$ or $b$ axis. By contrast, the application of $H$ above $\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ along the $c$ axis completely suppresses the ferroelectricity in ${\mathrm{TbMnO}}_{3}$. Possible origins of the observed evolution of magnetoelectric phases are discussed in consideration of magnetism and lattice distortion in the perovskite rare-earth manganites.