Strain-driven transition from $E$-type to $A$-type magnetic order in YMnO${}_3$ epitaxial films

Single-crystal (100)-oriented YMnO${}_3$ thin films grown on (110)-oriented SrTiO${}_3$ substrates have been studied by polarized extended x-ray absorption fine structure to determine the Mn-O bond lengths. Using a simple geometrical model and previously reported x-ray diffraction data on the same samples, the Mn-O-Mn bonding angles are calculated. We show that the epitaxy-induced in-plane anisotropic strain has a dramatic impact on the bonding angles, allowing the rationalization of the reported existence of cycloidal magnetic order and concomitant ferroelectricity in moderately strained films and the gradual suppression by larger strains. We shall argue that epitaxial strain allows shifting YMnO${}_3$ from an $E$-type to $A$-type antiferromagnetic ground state, crossing a cycloidal magnetic region.

Figure 1

(a) Sketch of a Mn oxide (001) plane in orthorhombic YMnO${}_3$ (Pbnm setting). Manganese and oxygen atoms are depicted in green (larger) and blue (smaller), respectively. Notice the alternating sequence of short (S) and long (L) Mn-O bonds occurring in the (001) plane. While the distance between Mn atoms (d) is obtained by XRD, the Mn-O bond lengths (L and S) are obtained by EXAFS. Finally, the bonding angle $\theta$ is calculated using the cosine law.

Figure 2

(a) Raw experimental EXAFS signals (symbols), the filtered signals (dashed lines), and the corresponding fit (solid line) for the two studied samples. Theoretically modeled curves for a single bond-length contribution are shown below for two indicated distances. (b) Fourier transform modulus (circles) and fitting (solid lines) from the EXAFS signals shown in panel (a). (c) and (d) $R$ factor as a function of long bond and short bond distances for the films with 106 nm and 49 nm thickness, respectively. $R$ factor shown in the legend measures the goodness of the fits (the lower $R$ factor the better fit).

Figure 3

Trend of the L and S distances in epitaxial YMnO${}_3$ thin films grown on (110)SrTiO${}_3$ substrates. The 106- and 49-nm-thick samples are depicted with circles. Circumference around the circles corresponds to the experimental uncertainty. Square symbol denotes the L and S values for bulk YMnO${}_3$ (from Ref. 11). The color scale indicates the bonding angle calculated from Eq. (1) and using a fixed $d$$=$3.88 Å, similar for both samples (Table ). The solid lines denote the bonding angle phase boundaries in bulk RMnO${}_3$ compounds of the $E$-type, cycloidal, and $A$-type magnetic orderings according to Ref. 7.