Giant Improper Ferroelectricity in the Ferroaxial Magnet ${\mathrm{CaMn}}_7{\mathbf{O}}_{12}$

In rhombohedral ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$, an improper ferroelectric polarization of magnitude $2870\mu \mathrm{C}{\mathrm{m}}^{-2}$ is induced by an incommensurate helical magnetic structure that evolves below $T_{\mathrm{N}1}=90\mathrm{K}$. The electric polarization was found to be constrained to the high symmetry threefold rotation axis of the crystal structure, perpendicular to the in-plane rotation of the magnetic moments. The multiferroicity is explained by the ferroaxial coupling mechanism, which in ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ gives rise to the largest magnetically induced, electric polarization measured to date.

Figure 1

Left: The crystal structure of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ in both hexagonal and cubic lattices. Calcium and Mn1 ions are shown as yellow (light gray) and red (medium gray) large spheres, respectively. Mn2 and Mn3 ions are shown within their octahedral oxygen coordinations, and oxygen ions are shown as small black spheres. Right: A view of the ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ structure down the threefold axis showing the macroscopic structural rotation described by the axial vector, $\mathit{A}$. The primitive rhombohedral cell is shown with the calcium and Mn2 ions omitted for clarity.

Figure 2

(a) The electric polarization of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$, measured parallel to the hexagonal $c$ axis, and the three pseudocubic $⟨100⟩$ axes. Inset: A small increase in $\mathit{P}$ at $T_{\mathrm{N}2}$. (b) The magnetic susceptibility parallel and perpendicular to the hexagonal $c$ axis, measured with $H=500\mathrm{Oe}$, in both zero field cooled and field cooled (500 Oe) conditions. Inset: Reduction of the in-plane magnetic susceptibility at $T_{\mathrm{N}1}$. (c) The variation of the incommensurate magnetic propagation vectors ${\mathit{k}}_1$ (black circles), ${\mathit{k}}_2$ (blue triangles), and ${\mathit{k}}_3$ (red squares), refined against neutron powder diffraction data. The error bars are within the size of the data point. (d) The integrated intensity of the (1, $-1$, $1-k_z$) magnetic reflection at $d\sim 9\AA$. The black circles, blue triangles and red squares correspond to ${\mathit{k}}_1$, ${\mathit{k}}_2$, and ${\mathit{k}}_3$, respectively.

Figure 3

(a) Rietveld refinement against neutron powder diffraction data at 65 K. (b) Le Bail fit to data measured at 5 K. Top and bottom tick marks indicate the nuclear and magnetic peaks, respectively. The measured and calculated profiles are shown with dots and a continuous line, respectively. A difference curve (observed—calculated) is shown at the bottom.

Figure 4

(a),(b) The magnetic structure of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ in the $ab$ and $ac$ planes, respectively. Mn1, Mn2, and Mn3 ions are shown in red (medium gray), black, and yellow (light gray), respectively. The moments rotate in the $ab$ plane with a circular envelope as depicted in (b), perpendicular to the electric polarization $\parallel c$ axis. (c) The three triangular modes of symmetry equivalent Mn1 or Mn2 ions that correspond to ${\Gamma }_1$, ${\Gamma }_2$, and ${\Gamma }_3$. The magnetic structure of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ has ${\Gamma }_3$ symmetry, and the respective triangular mode of equivalent Mn1 sites is shown by the heavy line in (a).