Nanodomains in multiferroic hexagonal $R{\text{MnO}}_3$ films $\left(R=\text{Y},\text{Dy},\text{Ho},\text{Er}\right)$

A homogeneous distribution of ferroelectric nanoinclusions was observed by optical second harmonic generation in epitaxial films of hexagonal $R{\text{MnO}}_3$ $\left(R=\text{Y},\text{Dy},\text{Ho},\text{Er}\right)$ grown on ${\text{ZrO}}_2\left({\text{Y}}_2{\text{O}}_3\right)$ substrates. The inclusions correspond to secondary orientations in the $c$-axis-oriented films. Their volume density is in the range of ${10}^{-3}$ and their occurrence is independent of growth technique and film thickness in the range of 20–1000 nm. The inclusions behave as preferentially polarized ferroelectric nanodomains whereas the epitaxial film is in a ferroelectric single-domain state. In addition, the antiferromagnetic phase exhibits nanodomains of $<100\text{nm}$ which is three orders of magnitude below the extension of bulk antiferromagnetic domains in $R{\text{MnO}}_3$. Indications for a polarization-induced magnetic order different from that of the bulk are discussed.

Figure 1

Temperature-dependent and polarization-dependent SHG on ${\text{HoMnO}}_3$ bulk crystals and epitaxial films. (a) Temperature dependence of the SHG intensity from ${\chi }_{xxx}$ and ${\chi }_{yyy}$ from a flux-grown ${\text{HoMnO}}_3$ bulk sample for light incident along the $z$ axis. The signal couples to the antiferromagnetic ${\text{Mn}}^{3+}$ order. A spin reorientation at 40 K and the transition to the paramagnetic phase at 76 K are clearly visible. (b) Anisotropy of the SHG signal in (a) in the $P{\underset{̱}{6}}_3\underset{̱}{c}m$ phase at $41\text{K}<T<76\text{K}$. The $x$ axis is set as $0°$. (c) Temperature dependence of the SHG intensity from a ${\text{HoMnO}}_3$ film of 600 nm grown by PLD. The light is incident along the $z$ axis of the epitaxial film and both the incident fundamental and the detected SHG light are $x$ polarized. Even at 300 K, the SHG signal has not vanished. (d) Anisotropy of the SHG signal in (c). Solid lines in (b) and (d) are fits.

Figure 2

Ferroelectric origin of SHG in the $R{\text{MnO}}_3$ films. (a) HR-TEM image of a ${\text{YMnO}}_3$ film grown by MOCVD. Nanoscopic inclusions with secondary crystallographic orientation are observed in intrinsically hexagonal ${\text{YMnO}}_3$ films just as in epitaxially stabilized $R{\text{MnO}}_3$ films (Ref. 21). (b) SHG spectra for a ${\text{HoMnO}}_3$ film of 600 nm grown by PLD. The wave vector of the incident light includes an angle $\theta$ with the $z$ axis of the crystal which was achieved by rotating the crystal as sketched in the inset. Filled symbols: SHG spectrum at 300 K for $\theta =45°$. Open symbols: SHG spectrum at 10 K for $\theta =0°$. Inset: geometry of the SHG experiment.

Figure 3

Crystallographic inclusions and SHG intensity. (a) Sketch of the distribution of differently oriented ferroelectric ${\text{HoMnO}}_3$ nanoinclusions in the epitaxial $z$-oriented ${\text{HoMnO}}_3$ matrix. The local $z_n^{\prime }$ axes refer to the three possible orientations $\left(n=1,2,3\right)$ of the local $z$ axes of the inclusions in the $xy$ plane of the film. (b) Anisotropy of the SHG polarization $P_n^{\parallel }\left(2\omega \right)$ for $n=1,2,3$ in the range of $0°–360°$. The different amplitudes of the polarization reflect the anisotropic distribution of inclusions with $n=1,2,3$ (see text). (c) Anisotropy of the SHG signal for the SHG polarization in (b) fitting coherent (black line) or incoherent (gray line) interference of the SHG contributions from different crystallites. Symbols are SHG data obtained from a ${\text{HoMnO}}_3$ film of 50 nm grown by MOCVD. The fit confirms the model of coherent interference.

Figure 4

Distribution of ferroelectric nanodomains. A sketch of the distribution of differently oriented ferroelectric ${\text{HoMnO}}_3$ nanoinclusions in the epitaxial $z$-oriented ${\text{HoMnO}}_3$ matrix along with the resulting intensity and anisotropy of the SHG signal are shown. In contrast to Fig. 3, the direction of the local polarization of the nanoinclusions ($+p$, white; $-p$, black) was taken into account. (a) $z$ component of the polarization of the nanoinclusions in (b) and (d). (b) Sketch for equal distribution of nanoinclusions with $+p$ and $-p$. (c) The calculated SHG intensity for a distribution of nanoinclusions as in (b) cancels out, which is indicated by the dot at zero intensity. (d) Sketch for preferentially oriented polarization of the nanoinclusions, here along $+z_n^{\prime }$. (e) Fit (solid line) of the SHG intensity for a distribution of nanoinclusions as in (d). SHG data (filled circles) obtained from a ${\text{HoMnO}}_3$ film of 100 nm grown by MOCVD confirm the scenario in (d) while disagreeing with panels (b) and (c). Note that unlike in Fig. 3, a fit and SHG data corresponding to an isotropic distribution of inclusions with $n=1,2,3$ were chosen for simplicity.