Charge Order in ${\mathrm{LuFe}}_2{\mathbf{O}}_4$: Antiferroelectric Ground State and Coupling to Magnetism

X-ray scattering by multiferroic ${\mathrm{LuFe}}_2{\mathrm{O}}_4$ is reported. Below 320 K, superstructure reflections indicate an incommensurate charge order with propagation close to $(\frac{1}{3}\frac{1}{3}\frac{3}{2})$. The corresponding charge configuration, also found by electronic structure calculations as most stable, contains polar $\mathrm{Fe}/\mathrm{O}$ double layers with antiferroelectric stacking. Diffuse scattering at 360 K, with $(\frac{1}{3}\frac{1}{3}0)$ propagation, indicates ferroelectric short-range correlations between neighboring double layers. The temperature dependence of the incommensuration indicates that charge order and magnetism are coupled.

Figure 1

Scattered intensity at $(hh\ell )$ at 130, 200, 295, and 360 K. Lowest panel: $(\frac{1}{3}\frac{1}{3}\ell )$ cut at 360 K with fit by Gaussians. Strong structural reflections reach intensities $>{10}^4\mathrm{\text{counts}}/\mathrm{\text{monitor}}$, strong superstructure reflections $\sim 40$. The higher overall intensity at 295 K is due to wider detector slits being used. Horizontal lines mark $hh=\frac{1}{3}$. Insets: Specific heat near 320 K; sketch of $hk\ell$ positions of maxima in diffuse scattering at 360 K, with symbols indicating domains as in Fig. 3a.

Figure 2

Incommensurate satellites. (a) Intensity at $(hk13.5)$ at 130 K (the two strongest peaks reach $\sim 19\mathrm{\text{counts}}/\mathrm{mon}$). (b) Detail around (0,0,13.5). (c) Intensity around $(\frac{1}{3}\frac{1}{3}14.5)$ (marked by ○).

Figure 3

Commensurate approximation of the charge configuration. (a) Integrated intensities of $(\frac{1}{3}\frac{1}{3}\frac{o}{2})$ type reflections. Reflections associated with different domains are indicated by different symbols (see text). (b) Scattered intensity at $(hk19.5)$. (c,d) Charge configuration for domain A for $T<T_{\mathrm{CO}}$ [c] and $T>T_{\mathrm{CO}}$ [(d), short range]. Shown are the Fe ions (see legend) of the 6 (3) $\mathrm{Fe}/\mathrm{O}$ double layers of the $\sqrt{3}\times \sqrt{3}\times 2$ ($\times 1$) supercell. The direction of the local polarization for each double layer is indicated by an arrow. The two sites of the primitive cell are numbered (see text).

Figure 4

$T$ dependence of CO on warming. (a) $(hh13.5)$ scans. (b) Scans $\parallel (1\overline{2}0)$ through $(\frac{1}{3}\frac{1}{3}14)$. (c) $(\frac{1}{3}\frac{1}{3}13.5)$ rocking curves. (d) Peak intensities of three reflections vs $T$. (e) Incommensuration $\tau (T)$.