First-principles study of structurally modulated multiferroic ${\text{CaMn}}_7{\text{O}}_{12}$

We study the electronic and magnetic structures of multiferroic ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ by first-principles calculations, based on the experimentally determined modulated crystal structure. We confirm the presence of a $3d$ orbital modulation of the Mn2 ${\text{(Mn}}^{3+}$) sites, previously inferred from the Jahn-Teller crystal distortions. Our results indicate that in the multiferroic phase the magnetic structure of the Mn3 ${\text{(Mn}}^{4+}$) sites is anharmonically modulated via orbitally mediated coupling with the structural modulation, and that the Dzyaloshinskii-Moriya and exchange striction mechanisms contribute equally to the polarization.

Figure 1

Experimental bond-length modulation in CMO:Mn2-O bond lengths along the local octahedral $x,y$, and $z$ (see inset) as a function of $R_z$, plotted across 15 unit cells along the $c$ axis.

Figure 2

Partial density of states for the Mn2 sites of structures A1, A2, and A3. The Fermi energy is at $E_F=0$.

Figure 3

(a) Side view of one unit cell of average crystal structure and magnetic configuration. Yellow (large) and blue (small) spheres represent Ca and Mn3 ions, respectively. Red (dark) and green (light) spheres with arrows represent Mn1 and Mn2 ions, respectively. Arrows denote magnetic moments of Mn ions. Nearest-neighbor exchange interactions are indicated by dotted lines. (b) Top view and (c) side view of one cluster centered at Mn32 atoms. Dotted lines indicate the splitting of $J_3$ and $J_4$ in the modulated structure.

Figure 4

(a),(b) Experimental data of modulated Mn32-Mn2 bond lengths and bond angles along the $c$ direction [9]. (c) ${\theta }_2$ from ab initio calculations. Red and black lines are fitted to Eq. (4). Dashed line is drawn at ${\theta }_2=0$. (d) The corresponding magnetic moments of the Mn3 ions.

Figure 5

Electric polarization of (a) the average structure and (b) the CM structure. Symbols denote results obtained from ab initio calculations. Lines represent fits to Eqs. (5) and (6).

Figure 6

Schematic illustrations of the splitting of the $J_4$ exchange interactions in the CM structure. The color scheme is the same as in Fig. 3.