Order Parameters and Phase Diagram of Multiferroic $R{\mathrm{Mn}}_2{\mathrm{O}}_5$

The generic magnetic phase diagram of multiferroic $R{\mathrm{Mn}}_2{\mathrm{O}}_5$ (with $R=\mathrm{Y}$, Ho, Tb, Er, Tm), which allows different sequences of ordered magnetic structures for different $R$’s and different control parameters, is described using order parameters which explicitly incorporate the magnetic symmetry. A phenomenological magnetoelectric coupling is used to explain why some of these magnetic phases are also ferroelectric. Several new experiments, which can test this theory, are proposed.

Figure 1

Left-hand side (LHS): Schematic 3D phase diagram for $q_x$ ($q_z$) near $\frac{1}{2}$ ($\frac{1}{4}$). $J_x$ and $J_z$ are parameters which control $q_x$ and $q_z$. The red surface separates PM and ${\mathrm{II}}_1$. Below the blue surface one has $q_z=\frac{1}{4}$, in phases ${\mathrm{IC}}_1$ and ${\mathrm{IC}}_2$. The green surfaces represent ${\mathrm{II}}_1\to {\mathrm{II}}_2$ and ${\mathrm{IC}}_1\to {\mathrm{IC}}_2$. Below the orange surfaces $q_x=\frac{1}{2}$, in phases CI or CC. RHS: a cut at constant $q_x\ne 1/2$. The dashed and dotted lines represent proposed trajectories for specific RMO’s, as $T$ is varied.

Figure 2

Schematic diagram of the $\mathbf{a}$ and $\mathbf{b}$ components of the ${\mathrm{Mn}}^{3+}$ spins in a single $a\mathrm{\text{−}}b$ plane of YMO for the CC phase. The glide $m_x$ consists of a mirror plane $M$ at $x=a/4$ followed by a translation $b/2$ along $y$. LHS: the structure given in Table III of Ref. 5 (with the $\mathbf{c}$ components not shown). RHS: the structure given in Fig. 2 [38] of Ref. 17 (who reported zero $\mathbf{c}$ components of spin).