Coupling of Magnetic and Ferroelectric Hysteresis by a Multicomponent Magnetic Structure in ${\mathrm{Mn}}_2{\mathrm{GeO}}_4$

The olivine compound ${\mathrm{Mn}}_2{\mathrm{GeO}}_4$ is shown to feature both a ferroelectric polarization and a ferromagnetic magnetization that are directly coupled and point along the same direction. We show that a spin spiral generates ferroelectricity, and a canted commensurate order leads to weak ferromagnetism. Symmetry suggests that the direct coupling between the ferromagnetism and ferroelectricity is mediated by Dzyaloshinskii-Moriya interactions that exist only in the ferroelectric phase, controlling both the sense of the spiral rotation and the canting of the commensurate structure. Our study demonstrates how multicomponent magnetic structures found in magnetically frustrated materials like ${\mathrm{Mn}}_2{\mathrm{GeO}}_4$ provide a new route towards functional materials that exhibit coupled ferromagnetism and ferroelectricity.

Figure 1

(a) The orthorhombic ($Pnma$) magnetic unit cell of ${\mathrm{Mn}}_2{\mathrm{GeO}}_4$. ${\mathrm{Mn}}^{2+}$ ions occupy two sites: ${\mathrm{Mn}}_{\mathrm{ch}}$ ions (red) are at the $4(a)$ site, ${\mathrm{Mn}}_{\mathrm{pl}}$ ions (blue) are at the $4(c)$ site. Both the ${\mathrm{O}}^{2-}$ anions and ${\mathrm{Ge}}^{4+}$ cations are omitted for clarity. In the other panels we show the $T$ dependence of (b) the magnetization $M_i$ (at 0.01 T, field-cooled), (c) the relative dielectric constant ${ϵ}_i$ (at 0 T), and (d) the electric polarization $P_i$ (at 0 T), measured along all three principal axes.

Figure 2

The ${\mu }_{0}H$ and $T$ dependence of the neutron intensity at the C (a) (100) and (b) (120) positions for fields ${\mu }_{0}H\parallel \mathbf{c}$. For clarity, in each of (a) and (b) adjacent field data are displaced vertically by 10 000 counts per standard monitor. In (c) we show the $T$ dependence of the neutron intensity at the IC position $(q_h,1-q_k,0)$ for fields ${\mu }_{0}H\parallel \mathbf{c}$. The inset in (c) shows the ${\mu }_{0}H$ dependence at $T=1.7\mathrm{K}$ of the $q_h$ component of the incommensuration. In (d) we show the $({\mu }_{0}H,T)$ magnetic phase diagram for ${\mu }_{0}H\parallel \mathbf{c}$ determined by both magnetization (data not shown) and neutron diffraction. Paramagnetic (PM), C AFM, and $\mathrm{C}+\mathrm{IC}$ AFM structure phases are labeled. In panels (a)–(c), open (filled) symbols correspond to $T$-warming (cooling) data, and dashed lines correspond to guides for the eye. For all panels, error bars are of the order of the size of the data symbol.

Figure 3

The refined zero field magnetic structures of ${\mathrm{Mn}}_2{\mathrm{GeO}}_4$. In (a)–(c) we show the refined commensurate structures at $T=20\mathrm{K}$, (b) $T=7\mathrm{K}$ and (c) $T=1.4\mathrm{K}$. In (d) we show the refined incommensurate magnetic structure at $T=1.4\mathrm{K}$. In (d) the envelopes around the moments indicate the rotation plane of each ion.

Figure 4

(a) The magnetic field dependence of the magnetization for ${\mu }_{0}H\parallel \mathbf{c}$ and at selected temperatures. In (b) we show the magnetic field dependence of the electric polarization on poling the electric field.