Structural coherence and ferroelectric order in nanosized multiferroic YMnO${}_3$

Atomic-scale structure studies involving synchrotron x-ray diffraction (SXRD) and pair distribution function (PDF) analysis on a series of YMnO${}_3$ particles with sizes ranging from 467 $\pm$ 42 (bulk) to 10 $\pm$ 1 nm are presented. Studies reveal that while the nanoparticles retain most of the characteristics of the layered hexagonal-type structure of the bulk, substantial local atomic displacements arise with diminishing particle size. The displacements lead to a very substantial loss of structural coherence in the particles of size smaller than 100 nm. The displacements mostly affect the yttrium (Y) atoms and to a lesser extent the Mn-O sublattice in YMnO${}_3$. We argue that the increased displacement of Y atoms along the polar $c$ axis of the hexagonal unit cell may result in enhanced local ferroelectric distortions with decreasing particle size. The planar, that is, $a$- and $b$-axis direction displacements of Y atoms, however, may interfere with the cooperative ferroelectricity of nanosized YMnO${}_3$, so future efforts to employ YMnO${}_3$ in nanoscale applications should take them into account.

Figure 1

Fragment from the room temperature hexagonal structure of YMnO${}_3$ featuring layers of MnO${}_5$ polyhedra (brown) and two types of Y atoms (black and magenta) in between. Note the displacement of two types of Y atoms, ΔY ≠ 0, with respect to each other in this ferroelectric YMnO${}_3$ phase. In the high-temperature paraelectric phase Y atoms occupy centrosymmetric positions and ΔY $=$ 0.

Figure 2

SXRD patterns of YMnO${}_3$ for particles with size ranging from 467 $\pm$ 42 nm to 10 $\pm$ 1 nm. For clarity only a relatively low-angle portion of the XRD patterns is shown. Sharp Bragg peaks are seen in the XRD patterns for the larger size particles. The peaks broaden and merge into an intensive diffuse component with diminishing particle size. The dotted line marks the so-called superlattice peaks as explained in the text.

Figure 3

Observed (dots) and Rietveld fit (continuous line) SXRD patterns of YMnO${}_3$ particles of selected sizes. The fits were done employing a hexagonal structure model (S.G. $P$6${}_{3}cm$). The quality of the fits worsens (follow the broken arrow lines) with diminishing particle size. Selected peaks are marked with the respective Miller (hkl) indices.

Figure 4

Evolution of the hexagonal unit cell volume with particles' size of YMnO${}_3$ as obtained from (a) Rietveld fits to the SXRD patterns and (b) PDF fits of Fig. 7b. An exponential increase (red line) in the unit cell volume with diminishing particle size is observed. Note YMnO${}_3$ particles of a larger (>38 nm) size are crystalline in nature and so are very well approximated by a model featuring a periodic lattice of hexagonal ($P$6${}_{3}cm$) symmetry. The unit cell of this lattice is a very well defined quantity. The particles of smaller (<38 nm) size are less crystalline in nature yet fairly well approximated by a model based on the same hexagonal lattice where only Y atoms have been released from the symmetry constraints of S.G. $P$6${}_{3}cm$. The unit cell of the modified lattice remains a well defined quantity that may be directly compared to the unit cell of the unmodified lattice.

Figure 5

Evolution of the ferroelectricity “local order parameter” OP $=$ $2^{*}{d}_z$(Y1)+$4^{*}{d}_z$(Y2) with particle size derived from Rietveld (line in orange) and PDF analyzes (line in wine red). An exponential fit approximates the evolution quite well. The parameter is seen to increase in absolute value with diminishing particle size.

Figure 6

Low-$r$ part of the experimental atomic PDFs $G$($r$) for YMnO${}_3$ particles. The PDF peaks are well defined with the larger size particles reflecting the high degree of crystallinity in those samples. The PDF peaks progressively broaden with diminishing particle size, indicating an increased degree of structural disorder at the nanoscale. Peaks corresponding to first metal-oxygen and metal-metal (M${}_E$ $=$ Y, Mn) correlations are labeled with the respective atomic pairs.

Figure 7

(a) Experimental (symbol), model 1 (line in orange), and model 2 (line in wine red) PDFs for YMnO${}_3$ particles of sizes from 45 to 467 nm. Data in the range of 1–12 Å are only shown for the sake of clarity. The model 1 data are computed strictly observing the constraints of a hexagonal lattice of $P$6${}_{3}cm$ symmetry. The model 2 data are also computed on the basis of a hexagonal structure (S.G. $P$6${}_{3}cm$), where Y atoms have been allowed to move within a plane between Mn-O${}_5$ polyhedra. Note in (a) this breaking of the local Y atoms symmetry hardly affects the quality of the PDF fits indicating very limited, if any, planar disorder of Y atoms. With the smaller size particles (b) the breaking of the local Y atoms symmetry substantially improves the fits to the atomic PDFs especially in the range of $r$ values from 2 to about 10 Å. No attempts to improve the fits further were made since in this work we concentrate on the Y atoms' relative positioning that is at the structural origin of the ferroelectricity in YMnO${}_3$.

Figure 8

Variation of Y atoms displacements along $x$, $y$, and $z$ directions as determined by atomic PDF analysis. The displacements along the $x$ and $y$ directions feature planar disorder, whereas along the $z$ direction contribute to the local ferroelectric order. The dashed line fits show an exponentially increase (in absolute values) in both planar ($x$,$y$) disorder and contribution ($z$ displacement) to the ferroelectricity in YMnO${}_3$ with diminishing particle size.