Helical scattering signatures of strain and electronic textures in YbFe${}_{2}$O${}_{4}$ from three-dimensional reciprocal-space imaging

Helical scattering signatures of strain and electronic textures in YbFe $_{2}$ O $_{4}$ from three-dimensional reciprocal-space imaging

Alexander J. Hearmon, Dharmalingam Prabhakaran, Harriott Nowell, Federica Fabrizi, Matthias J. Gutmann, and Paolo G. Radaelli

Phys. Rev. B 85, 014115 – Published 27 January 2012

Abstract

The insulating ternary oxide YbFe $_{2}$ O $_{4}$ displays an unusual frustration-driven incommensurate charge-ordering (CO) transition, linked to possible ferroelectricity. Based on high-resolution synchrotron data, we report a detailed structural model showing that the CO phase is an incommensurate charge-density wave and cannot be ferroelectric, since the electrical dipole moments are also incommensurately modulated. The change between continuous and “spotty” helices of scattering at the CO transition is attributed to three-dimensional fluctuations of the direction of the ordering wave vector.

Received 21 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.014115

Authors & Affiliations

Alexander J. Hearmon^1,2,*, Dharmalingam Prabhakaran¹, Harriott Nowell², Federica Fabrizi¹, Matthias J. Gutmann³, and Paolo G. Radaelli¹

¹Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
²Diamond Light Source Ltd., Harwell Science and Innovation Campus, Didcot, OX11 0DE, United Kingdom
³ISIS Facility, STFC-Rutherford Appleton Laboratory, Didcot, OX11 OQX, United Kingdom

^*a.hearmon@physics.ox.ac.uk

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Vol. 85, Iss. 1 — 1 January 2012

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Images

Figure 1
(a) The simplest ordering model of Fe $^{2 +}$ and Fe $^{3 +}$ on adjacent FeO layers in $R$ Fe $_{2}$ O $_{4}$ (Ref. 1). Lower panel: Oxygen displacement pattern in a single FeO plane. The arrows can also be used to illustrate the conventional $120^{\circ}$ magnetic structure of a triangular Heisenberg magnet. The CO and crystallographic unit cells are indicated. (b) and (c) Reciprocal-space sections from laboratory data collected on YbFe $_{2}$ O $_{4}$ at 150 K, respectively the $(h, k, 12)$ and $(h, - 2.33, l)$ layers. Bragg peaks in (b) are subject to the selection rule $- h + k + l = 3 n$ and are surrounded by hexagons of satellites. (d) Synchrotron data showing the $(h, - 2.33, l)$ layer at 360 K: The streaks observed at low $T$ (c) become more diffuse for $T > T^{*}$ . The satellites shown in (c) and (d) are marked with a box in (b). (e) Three-dimensional isointensity plot of the $(0.33, - 2.66, l)$ satellite at 150 K (synchrotron data).Reuse & Permissions
Figure 2
Three-dimensional reciprocal-space isointensity plots of the satellite helices. (a) and (b): Helices below and above $T^{*}$ . At low $T$ intensity is concentrated onto peaks separated by $\sim c^{*} / 3$ . (c) Three adjacent helices ( $T = 360$ K). The pitch of each helix is 3 $c^{*}$ , but the phase varies according to the position in the $(a^{*}, b^{*})$ plane. (d) Two helices at $T = 360$ K, for $24 < l < 10$ r.l.u., illustrating the selection rule for the handedness (denoted RH/LH for right/left). (e) Schematic reciprocal space reconstruction of several satellites at 150 K. The reciprocal lattice is shown below (white circles) with the locations of the satellites (red/dark circles) projected downward.Reuse & Permissions
Figure 3
Schematic picture of the oxygen displacements within the YbFe $_{2}$ O $_{4}$ structure. Apical oxygens (within the YbO $_{2}$ layers) are displaced vertically according to a sinusoidal modulation (dashed line), while the oxygens in the Fe $_{2}$ O $_{2}$ layers are displaced in plane (part of the displacement pattern is shown by the arrows). As shown, the modulations follow the commensurate $\sqrt{3} \times \sqrt{3}$ structure. The same modes are propagated with incommensurate $q$ to generate the final structure.Reuse & Permissions
Figure 4
Real-space diagrams of YbFe $_{2}$ O $_{4}$ . (a) The oxygen distortions involved in the six possible pyramids in the $\sqrt{3} \times \sqrt{3}$ structure. (b) Example of an incommensurate oxygen displacement pattern in the FeO planes, made up from a continuous variation of the configurations in (a). The irons are shaded according to their effective valence determined by Eq. (1), and the direction of $q = (1 / 3 + δ, 1 / 3 + δ)$ is indicated by a bold arrow.Reuse & Permissions
Figure 5
(a) Reciprocal-space sketch indicating contributions from the two propagation vectors, $q_{1}$ and $q_{2}$ , to the helical scattering pattern. The black circles represent Bragg peaks and the gray shows the location of the satellite helix. (b) and (c) Calculated intensities along the $(1 / 3, - 2 / 3, l)$ rod from the $q_{1}$ and $q_{2}$ structures, respectively. (d) Overall pattern expected given equal contributions from both structures, which is compared against the data in Fig. 6.Reuse & Permissions
Figure 6
Reciprocal space sections and simulations at $T = 150$ K. Data (left-hand panels) and calculations (right-hand panels) are shown for six reciprocal-space cuts. The calculated intensities are derived from the oxygen displacement model described in the text. The intensities [all of which are scaled to those in (a) and (b)] are indicated by the color bars.Reuse & Permissions

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