Nature of the Magnetic Order and Origin of Induced Ferroelectricity in ${\mathrm{TbMnO}}_3$

The magnetic structures which endow ${\mathrm{TbMnO}}_3$ with its multiferroic properties have been reassessed on the basis of a comprehensive soft x-ray resonant scattering (XRS) study. The selectivity of XRS facilitated separation of the various contributions (Mn $L_2$ edge, Mn $3d$ moments; Tb $M_4$ edge, Tb $4f$ moments), while its variation with azimuth provided information on the moment direction of distinct Fourier components. When the data are combined with a detailed group theory analysis, a new picture emerges of the ferroelectric transition at 28 K. Instead of being driven by the transition from a collinear to a noncollinear magnetic structure, as has previously been supposed, it is shown to occur between two noncollinear structures.

Figure 1

Scan along the $[010]$ direction in reciprocal space at an incident photon energy corresponding to the $L_2$ edge of Mn. r.l.u. denotes reciprocal-lattice units.

Figure 2

(a) Temperature dependence of the integrated intensity of the (0, $\tau$, 0), (0, $2\tau$, 0), and (0, $1-2\tau$, 0) measured at the Mn $L_2$ edge and the (0, $\tau$, 1) measured at the Tb $M_4$ edge. (b) Temperature dependence of the incommensurability $\tau$ measured from the peak position of the (0, $\tau$, 0) measured at the Mn $L_2$ edge.

Figure 3

Azimuthal dependence of the (a) (0, $\tau$, 0), (b) (0, $2\tau$, 0), and (c) (0, $1-2\tau$, 0) superlattice reflections at the Mn $L_2$ edge in the noncollinear phase at 26 K (red circles). The azimuthal dependence of the (0, $\tau$, 0) at 32 K in the collinear phase is shown for comparison in the top panel (blue squares). The red solid (blue dashed) lines show simulations to the azimuthal dependencies at 26 K (32 K). The origin of the azimuth corresponds to the condition where the $[001]$ direction lies in the scattering plane.

Figure 4

(a) Proposed magnetic structure in the region $28\mathrm{K}<T<41\mathrm{K}$ projected onto both the crystallographic $b\mathrm{\text{−}}c$ (left) and $a\mathrm{\text{−}}c$ (right) planes. (b) Proposed magnetic structure below 28 K.