Multiferroicity in TTF-CA Organic Molecular Crystals Predicted through Ab Initio Calculations

We show by means of ab initio calculations that the organic molecular crystal TTF-CA is multiferroic: it has an instability to develop spontaneously both ferroelectric and magnetic ordering. Ferroelectricity is driven by a Peierls transition of the TTF-CA in its ionic state. Subsequent antiferromagnetic ordering strongly enhances the opposing electronic contribution to the polarization. It is so large that it switches the direction of the total ferroelectric moment. Within an extended Hubbard model, we capture the essence of the electronic interactions in TTF-CA, confirm the presence of a multiferroic groundstate, and clarify how this state develops microscopically.

Figure 1

Schematic arrangement of TTF and CA molecules along the $a$ axis in (a) the neutral ($N$) (b) ionic ($I$) structural phases with finite spontaneous polarization, where arrows indicate the displacement of CA towards TTF due to the dimer formation, and (c) AF magnetic structure in the ionic phase.

Figure 2

Nonspin polarized band structure of $P1n1$ experimental structure of Ref. 8 along high symmetry directions [labeled as: $X=(\frac{1}{2},0,0)$, $S=(\frac{1}{2},0,\frac{1}{2})$, $Z=(0,0,\frac{1}{2})$, $\Gamma =(0,0,0)$, $Y=(0,\frac{1}{2},0)$, $U=(0,\frac{1}{2},\frac{1}{2})$, $T=(\frac{1}{2},\frac{1}{2},\frac{1}{2})$, $W=(\frac{1}{2},\frac{1}{2},0)$] and density of states (DOS) projected onto TTF and CA molecule and calculated using either PBE (left) or HSE (right) functional.

Figure 3

(a) HSE ferroelectric polarization along $a$ and $c$ axis ($P_a$ and $P_c$) for AF and NM states along the path connecting the $P{12}_1/n1$ ($\lambda =0$) and $P1n1$ ($\lambda =1$) crystal structure. (b) and (c) Decomposition of $P$ into electronic ($P_{\mathrm{ele}}$) and ionic ($P_{\mathrm{ionic}}$) contributions for the NM (panel b) and AF (panel c) states.

Figure 4

(a) Phase diagram showing undistorted to dimerized, and NM to AF transitions. The shaded region on left (right) indicates the ferroelectric (multiferroic) state. (b) Ionicity parameter $\rho =n_{\mathrm{TTF}}\mathrm{\text{−}}{n}_{\mathrm{CA}}$ as a function of $U$ for different values of $\alpha$. (c) The polarization computed within point charge model, and the magnetic moment as a function of $U$ for the same values of $\alpha$ as in (b).