Local control of improper ferroelectric domains in ${\mathrm{YMnO}}_3$

Improper ferroelectrics are described by two order parameters: a primary one, driving a transition to long-range distortive, magnetic, or otherwise nonelectric order, and the electric polarization, which is induced by the primary order parameter as a secondary, complementary effect. Using low-temperature scanning probe microscopy, we show that improper ferroelectric domains in ${\mathrm{YMnO}}_3$ can be locally switched by electric field poling. However, subsequent temperature changes restore the as-grown domain structure as determined by the primary lattice distortion. The backswitching is explained by uncompensated bound charges occurring at the newly written domain walls due to the lack of mobile screening charges at low temperature. Thus, the polarization of improper ferroelectrics is in many ways subject to the same electrostatics as in their proper counterparts, yet complemented by additional functionalities arising from the primary order parameter. Tailoring the complex interplay between primary order parameter, polarization, and electrostatics is therefore likely to result in novel functionalities specific to improper ferroelectrics.

Figure 1

Creation of improper ferroelectric domains in ${\mathrm{YMnO}}_3$ by local cryogenic-temperature electric-field poling. (a) Pristine domain structure measured by PFM at 120 K. (b) A square-shaped area (white arrow) of reversed polarization is created by scanning while applying $+45$ V to the AFM tip in contact with the surface. The bright line protruding from the lower end of the square was caused by moving the AFM tip into position for the poling with the poling voltage applied. When the same voltage is applied to an area polarized in the direction of the applied voltage, surface charging results in a diffuse change of contrast (black arrow). (c) The same area of the sample surface imaged after remaining at 120 K for 6 days after the poling. The artificially created domain is still present, whereas the surface-charged area has disappeared. (d) At 250 K the domain structure abruptly reverts to the original configuration in (a). A minor variation in contrast between panels (a)–(d) is due to differences in scan speed and tip wear over the duration of six days.

Figure 2

Elimination of improper ferroelectric domains in ${\mathrm{YMnO}}_3$ by local low-temperature electric-field poling. (a) A down-polarized as-grown bubble domain in an up-polarized environment measured by PFM at 120 K. (b) The polarization of the bubble domain is reversed by scanning a window of $2\mu \mathrm{m}\times 2\mu \mathrm{m}$ covering the bubble with $+45$ V applied to the AFM tip. Note that the outline of the original domain is still visible in the PFM image. (c) When increasing the temperature to 250 K, the original bubble domain in (a) is reestablished.

Figure 3

Spatially integrated bulk ferroelectric properties of ${\mathrm{YMnO}}_3$. (a) Temperature-dependent dielectric constant for selected frequencies measured by dielectric spectroscopy. The dashed lines denote the temperatures below which the intrinsic ferroelectric properties of the sample can be measured. (b) Time-dependent decay of the saturated polarization $[p_{\mathrm{r}}\left(t\right)=P_{\mathrm{meas}}\left(t\right)/P_{\mathrm{sat}}$, see text]. At 120 K, the polarization is retained for several days, whereas at 140 K $p_{\mathrm{r}}\left(t\right)$ relaxes towards equilibrium, i.e., $p_{\mathrm{r}}=50\%$, within a few hours. Inset: ferroelectric hysteresis loop measured at 120 K and 1 Hz.

Figure 4

Electrostatic contrast at as-grown and electric-field-induced domain walls at 120 K. (a) PFM scan of the sample surface. An electric-field-induced surface domain is highlighted by the white arrow. (b) EFM scan measuring the surface charge $Q$ of the same area as in (a). Even though the PFM contrast is the same for both as-grown and electric-field-induced domains, the EFM contrast of the respective domain walls differs strongly between the two differently generated domains. Some domains which appear disconnected in the PFM image are in fact connected by channel-like domains below the resolution limit. This can be seen in the EFM image where the topological domain structure becomes evident.

Figure 5

Schematic cross section of tip-electric-field-induced domain configurations and distribution of uncompensated charges ($-$). Arrows denote the polarization direction of the respective domains. (a) Creation of a new domain at the surface, as described in Fig. 1. (b) Deleting an as-grown bubble domain from the surface, as described in Fig. 2. Vertical dimensions not to scale.