Field dependence of magnetic correlations through the polarization flop transition in multiferroic ${\text{TbMnO}}_3$: Evidence for a magnetic memory effect

The field-induced multiferroic transition in ${\text{TbMnO}}_3$ has been studied by neutron scattering. Apart from strong hysteresis, the magnetic transition associated with the flop of electronic polarization exhibits a memory effect: after a field sweep, ${\text{TbMnO}}_3$ does not exhibit the same phase as that obtained by zero-field cooling. The strong changes in the magnetic excitations across the transition perfectly agree with a rotation of the cycloidal spiral plane, indicating that the inverse Dzyaloshinski–Moriya coupling causes the giant magnetoelectric effect at the field-induced transition. The analysis of the zone-center magnetic excitations identifies the electromagnon of the multiferroic high-field phase.

Figure 1

(Color online) Top: Sketch of the magnetic spiral structure in zero field inducing an electric polarization ${\mathit{P}}_c$. Bottom: The rotation from ${\mathit{P}}_c$ to ${\mathit{P}}_a$ in the high-field phase is supposed to originate in a concomitant flop of the spiral rotation axis from $\mathit{a}$ to $\mathit{c}$.

Figure 2

(Color online) (a) Cut through reciprocal space along $\mathit{Q}=\left(0k1\right)$ for a complete field cycle $H_a=0\text{T}\to 12\text{T}\to 0\text{T}$ and ${\mathit{H}}_a\parallel \mathit{a}$. The open points mark the positions of the magnetic superstructure reflections; the dashed lines denote the phase transitions between the LF-IC and the HF-C phase as determined in Ref. 24. (b) Field dependence of the incommensurability ${\epsilon }_b$ for the complete field cycle. The gray shaded regions mark regimes with coexistence of both magnetic phases; the solid lines are included as guides to the eye. (c) Hysteresis of the magnetization measured with ${\mathit{H}}_a\parallel \mathit{a}$ essentially sensing the alignment of Tb moments. Note that there is a minor hysteresis at the LF-IC to HF-C transition.

Figure 3

(Color online) (a) Energy scans at the magnetic zone center $\mathit{Q}=\left[0{\epsilon }_b\left(H\right)1\right]$ in the LF-IC phase at $H=0\text{T}$ and in the HF-C phase at $H=12\text{T}$, both recorded with $E_f=4.66\text{meV}$. The zero-field data are the same as those shown in Ref. 23. (b) High-resolution data of the 12 T spectrum for $E_f=2.98\text{meV}$. (c) Raw-data scans for various magnetic fields and (d) difference spectra derived from the data presented in (c). The solid lines correspond to fits to the data in (a)–(c). The vertical bars mark the position of the magnetic excitations at zero field. The small diamonds label a region with a spurious contribution in the 12 T spectra.

Figure 4

(Color online) Dispersion of the magnetic excitations in ${\text{TbMnO}}_3$ along the $\mathit{c}$ and the $\mathit{b}$ directions at zero field and at a high magnetic field. The lines are guides to the eye in the $\mathbf{b}$ direction and fits with the ${\text{LaMnO}}_3$-type magnon dispersion along $\mathit{c}$. The zero-field data were taken from Refs. 23, 27.

Figure 5

(Color online) Comparisons of raw-data energy scans in the HF-C phase for three equivalent $\mathit{Q}$ positions on (a) a logarithmic scale and (b) on a linear scale. The solid lines denote fits to the data and the gray vertical bars mark the HF magnon-frequencies. The small black diamonds denote regions with spurious contributions for $\mathit{Q}=\left(00.251\right)$.