Origin of the Large Polarization in Multiferroic ${\mathrm{YMnO}}_3$ Thin Films Revealed by Soft- and Hard-X-Ray Diffraction

We investigated the magnetic structure of an orthorhombic ${\mathrm{YMnO}}_3$ thin film by resonant soft x-ray and hard x-ray diffraction. We observed a temperature-dependent incommensurate magnetic reflection below 45 K and a commensurate lattice-distortion reflection below 35 K. These results demonstrate that the ground state is composed of coexisting $E$-type and cycloidal states. Their different ordering temperatures clarify the origin of the large polarization to be caused by the $E$-type antiferromagnetic states in the orthorhombic ${\mathrm{YMnO}}_3$ thin film.

Figure 1

Temperature dependence of the (0 $q_b$ 0) ($q_b\sim 0.5$) peak in $\pi$ (a) and $\sigma$ (b) incident x-ray polarizations. The intensity of the peaks increases monotonically with cooling. Panel (c) shows the experimental geometry with the definition of the azimuthal angle $\phi$. In panels (a) and (b), the data were taken with $\phi =0°$ at $h\nu =643.1\mathrm{eV}$ (Mn $2p_{3/2}\to 3d$ absorption edge).

Figure 2

Temperature dependence of the (0 $q_b$ 0) ($q_b\sim 0.5$) peak position (a) and intensity (b). The experimental geometry and the photon energy are the same as Fig. 1. In panel (a), the commensurate position of $q_b=1/2$ is shown as a dotted line.

Figure 3

Intensity of the (0 $q_b$ 0) ($q_b\sim 0.5$) peak as a function of photon energies at the Mn $2p\to$ $3d$ absorption edge at 44 K (a) and 11 K (b).

Figure 4

Azimuthal-angle dependence of the (0 $q_b$ 0) ($q_b\sim 0.5$) intensity. The solid lines are from the model with spins parallel to the $c$ axis.

Figure 5

Spin structures in the $E$-type (a) and the $ab$-cycloidal (b) states. Spin canting along the $c$ axis makes the magnetic (0 $q_b$ 0) peak have some intensity.

Figure 6

Temperature dependence of the (0 1 0) peak taken at $h\nu =12\mathrm{keV}$. In panel (b), peak intensities are plotted as a function of temperature together with the electric polarization (broken lines) taken from Ref. 12. The temperature of 35 K is also indicated as the onset of the (0 1 0) peak and the step onset of the spontaneous electric polarization.