Figure 1

(a) Side and (b) top views of the two candidate InMnO${}_3$ structures. $P{6}_{3}cm$ is the ferroelectric phase of the h-$R$MnO${}_3$ compounds; $P\overline{3}c$ is the structure proposed for InMnO${}_3$ in this study. Arrows indicate the displacements from the high-symmetry $P{6}_3/mmc$ phase. The primitive unit cell is shaded grey. In contrast with the $P{6}_{3}cm$ phase, one In ion in the $P\overline{3}c$ unit cell remains at the high-symmetry $2b$ site, retaining the inversion symmetry. Note also the different tilt patterns of the MnO${}_5$ polyhedra toward or around corner $R$ ions. (c) Top views of ${\alpha }^{+}$ and ${\beta }^{-}$ domains in the $P{6}_{3}cm$ phase using the notation from Ref. 1 and one of six domains in the $P\overline{3}c$ phase. The phases $\varphi$, defined by the (counter) clockwise angle of tilting direction of upper (lower) oxygen layers relative to ${\alpha }^{+}$ domain, are also shown (Ref. 1). Note that the $P\overline{3}c$ phase has a tilt phase of 30${}^{\circ }$+$n·{60}^{\circ }$, and is obtained by averaging the tilt patterns and $R$-ion displacements of two $P{6}_{3}cm$ trimerization domains with different origins and orientations such as the ${\alpha }^{+}$ and ${\beta }^{-}$ domains.Reuse & Permissions

Figure 2

Synchrotron x-ray powder-diffraction patterns of InMnO${}_3$ at 293 K. Crosses represent data points and solid lines calculated intensities for $P\overline{3}c$. Differences for three structure models are also shown. Bragg reflections are indicated by tick marks (these are the same for $P{6}_{3}cm$, $P\overline{3}c$, and $P{6}_3/mcm$ models). The lower tick marks indicate reflections from In${}_2$O${}_3$ impurity. Arrows show reflections corresponding to unit-cell tripling.Reuse & Permissions

Figure 3

PFM images scaled relative to the response of periodically poled lithium niobate at room temperature, for (a) YMnO${}_3$ showing the known characteristic ferroelectric domain pattern, and for (b) InMnO${}_3$, where no ferroelectric domains are observed, and only topographical artifacts (c) are visible.Reuse & Permissions

Figure 4

SHG on (a) ErMnO${}_3$ and (b) InMnO${}_3$ at 5 K and 2.51 eV with light incident on the $z$-oriented surface of the single crystals along the [011] direction. The anisotropy measurement was obtained by rotating the linear polarization of the incident light at $\omega$ and of the detected intensity at 2$\omega$ simultaneously by 360${}^{\circ }$. Lines are fits of the SHG data according to Ref. 18. Scales in (a) and (b) differ by a factor 150. The twofold SHG signal of ErMnO${}_3$ indicates the presence of a spontaneous polarization whereas no indication for ferroelectricity in InMnO${}_3$ was found. Instead the sixfold pattern characteristic of the antiferromagnetic order in InMnO${}_3$ is observed.Reuse & Permissions

Figure 5

Calculated energy differences between the fully relaxed $P\overline{3}c$ phase and $P{6}_{3}cm$ phase, $\Delta E_{\mathrm{str}}$. Four exchange-correlation functionals, LDA, GGA, LDA+$U$, and GGA+$U$, and two spin configurations, FAFM and NCAFM (see text), were used. LDA/LDA+$U$ results for LuMnO${}_3$ are not shown because vasp does not provide an LDA Lu PAW potential. Positive $\Delta E_{\mathrm{str}}$ indicates that the ferroelectric $P{6}_{3}cm$ phase is stable over the $P\overline{3}c$ phase. The compounds are plotted in order of increasing $R$-site cation ionic radii, $R_R$ (Ref. 20).Reuse & Permissions

Figure 6

Calculated total and averaged local densities of states for InMnO${}_3$ and YMnO${}_3$ in the $P\overline{3}c$ phase. Zeroes of the horizontal axes are set to the top of the valence band. Valence bands are composed mainly of O-2$p$ and Mn-3$d$ orbitals. The difference of the electronic structures is mainly manifested at the formally unoccupied $R$ 5$s$ and 5$p$ local density of states.Reuse & Permissions

Figure 7

Charge density differences for valence-band electrons between (a) LuMnO${}_3$ and YMnO${}_3$ and (b) InMnO${}_3$ and YMnO${}_3$ in the $P\overline{3}c$ phase. For the comparison, the same atomic positions were chosen for the compounds that are compared. The structures are constructed by averaging the DFT-optimized structures for (a) LuMnO${}_3$ and YMnO${}_3$, and (b) InMnO${}_3$ and YMnO${}_3$. Red and blue regions correspond to excess and deficiency of charge in LuMnO${}_3$/InMnO${}_3$ compared with YMnO${}_3$. The yellow and light blue isosurfaces correspond to $0.03$ and $-0.03$ Å${}^{-3}$, respectively. Comparing with the charge density difference between LuMnO${}_3$ and YMnO${}_3$, InMnO${}_3$ shows noticeable differences from YMnO${}_3$ especially at the In site.Reuse & Permissions

Figure 8

Calculated (a) in-plane and (b) out-of-plane lattice constants in the $P{6}_{3}cm$ ($\circ$) and $P\overline{3}c$ ($\square$) phases. The experimental lattice constants are also shown ($\times$) (Refs. 6, 34 and 35). The dashed lines indicate the trend of $\mathrm{I}\mathrm{I}\mathrm{I}$b manganites for a guide to eyes.Reuse & Permissions

Figure 9

(a), (b) Calculated InMnO${}_3$ $P\overline{3}c$ and $P{6}_{3}cm$ structure energies relative to the equilibrium $P\overline{3}c$ phase as a function of in-plane lattice constant $a$ by the GGA and GGA+$U$. (c), (d) Energy differences $\Delta E_{\mathrm{str}}$ between the $P\overline{3}c$ and $P{6}_{3}cm$ phases. Positive values indicate that the ferroelectric $P{6}_{3}cm$ phase is stable over the $P\overline{3}c$ phase. The fitted lines were obtained with fourth-order polynomials. The vertical dashed lines indicate the calculated equilibrium lattice constants of InMnO${}_3$ $P\overline{3}c$ phase.Reuse & Permissions