Mean-field theory for ferroelectricity in ${\text{Ca}}_3{\text{CoMnO}}_6$

An elastic Ising model for ${\text{CoMnO}}_6$ chain is proposed to explain the ferroelectricity induced by collinear magnetic order in ${\text{Ca}}_3{\text{CoMnO}}_6$, and then a mean-field theory with interchain spin interactions based on this model is developed. With inclusion of the dynamics of polarization domains at finite temperature, we address the rationality of our theory by the good agreement of the calculated electric polarization and dielectric susceptibility with the reported data on ${\text{Ca}}_3{\text{Co}}_{2-x}{\text{Mn}}_x{\text{O}}_6$ $\left(x\approx 0.96\right)$ [Y. J. Choi, H. T. Yi, S. Lee, Q. Huang, V. Kiryukhin, and S.-W. Cheong, Phys. Rev. Lett. 100, 047601 (2008)], a typical diatomic Ising spin chain system, while the predicted magnetic susceptibility shows some difference from experiment, the reason of which is discussed.

Figure 1

(Color online) (a) Two configurations of the up-up-down-down Ising chain with alternating Mn (small circle) and Co (big circle) ions. The dashed circle represents the original positions of the ions and the arrows indicate the spin directions. (b) Four consecutive layers of CCMO on the $ab$ plane. The real circle represents spin up and open circle represents spin down along the $c$ axis.

Figure 2

(Color online) Eight spin configurations for the three spins (${\text{S}}_1$, ${\text{S}}_2$, and ${\text{S}}_3$). They are classified into three groups with different polarizations: (a) $P=P_{\text{Mn}}+P_{\text{Co}}$, (b) $P=-\left(P_{\text{Mn}}+P_{\text{Co}}\right)$, (c) $P=0$.

Figure 3

(Color online) [(a)–(d)] Four exampled polarization domains viewed on the $ab$ plane. In (b) the bonds on the domain wall and bonds inside the domain are shown, by which parameter $\rho$ is calculated. (a) $\rho =0$, (b) $\rho =1/6$, (c) $\rho =2/9$, and (d) $\rho =1/3$. (e) shows the $ac$-plane projection of the domain shown in (b). (f) shows the three-dimensional pattern of the domain shown in (d).

Figure 4

(Color online) Electric polarization $P$ as a function of $T$, calculated from the MFT (open circle), $\text{MFT}+\text{DC}$ (open square), and taken from experiment (full circle, Ref. 14). (a) $h=0\text{T}$, (b) $h=4\text{T}$, and (c) $h=7\text{T}$.

Figure 5

(Color online) (a) Magnetic susceptibility $\chi$ and (b) dielectric susceptibility $\epsilon$ as a function of $T$, calculated by the MFT (open circle), $\text{MFT}+\text{DC}$ (open square), and taken from experiment (full circle, Ref. 14). The inset in (b) shows $\chi$ from $T=0\sim 90\text{K}$.

Figure 6

(Color online) (a) Four order parameters as a function of $T$ at $h=0$, and (b) probability $W_{\text{domain}}$ for polarization domain reversal as a function of $T$ under various magnetic field $h$ ($=0$, 4, and 7 T).