Element-selective local structural analysis around $B$-site cations in multiferroic $\mathrm{Pb}\left({\mathrm{Fe}}_{1/2}{\mathrm{Nb}}_{1/2}\right){\mathrm{O}}_3$ using x-ray fluorescence holography

X-ray fluorescence holography (XFH) measurements were carried out for multiferroic $\mathrm{Pb}\left({\mathrm{Fe}}_{1/2}{\mathrm{Nb}}_{1/2}\right){\mathrm{O}}_3$ (PFN) single crystal to investigate variations in the local structures around Nb ions with decreasing temperature from 300 to 100 K, in combination with single-crystal x-ray diffraction (XRD) experiments. We find that the Nb–Pb correlation is more significantly changed by cooling than the average structure derived from the single-crystal XRD experiments, indicating a mobile feature of Nb ions. Also, we analyze previously obtained XFH results around Fe ions in detail for comparison with those around Nb ions. In contrast to the case of Nb ions, the variation in the Fe–Pb correlation with decreasing temperature is well explained by the average structure from 300 K down to the Néel temperature of about 150 K. On the other hand, a remarkable positional fluctuation between Fe and Pb ions is observed at 100 K, which is evaluated to be 90% larger than that between Nb and Pb ions. This observation strongly indicates the presence of spin-lattice coupling in PFN. The present study clearly elucidates the differences of local environment around the Nb ions from that around the Fe ions located at the same $B$-site.

Figure 1

XRD pattern of the PFN powder. The wavelength of the x-ray is 0.46 Å. The calculated XRD pattern of monoclinic PFN is also shown.

Figure 2

Nb-$K\alpha$ hologram measured at the incident energy of 20.0 keV and the temperature of 300 K.

Figure 3

Reconstructed atomic images of Pb plane around Nb from 100 to 300 K in steps of 50 K. Circles indicate the ideal positions of Pb ions. The corresponding Pb plane is schematically illustrated in the lower part, which was drawn by using VESTA software [49].

Figure 4

Three-dimensional atomic images of the first NN Pb ion around Nb from 100 to 300 K in steps of 50 K. The 85% volume contours are displayed.

Figure 5

Temperature dependence of (a) $a/\sqrt{2}, b/\sqrt{2}, c$, (b) $\beta$ and a unit cell volume of PFN determined from single-crystal XRD measurements. The Rietveld structural refinement was done based on the monoclinic structure ($Cm$ space group).

Figure 6

Profiles of the first NN Pb ion around Nb in the direction of ${\langle 111\rangle }_{\text{cubic}}$ at 100, 150, 200, 250, and 300 K. Profiles obtained from (a) XFH results, (b) average structure (single-crystal XRD), and (c) Nb shift model are shown. The peak position of the profile at 300 K is taken as the origin of the horizontal axis. Dashed curves are Gaussians fitted to the profiles. An error bar displayed in (a) at 300 K was evaluated according to Ref. [50].

Figure 7

Temperature dependence of the distance between the Nb and the Pb ions obtained from the average structure and the Nb shift model. Distances of the six Pb ions (1)–(6) from the Nb position are displayed. The corresponding Pb ions are illustrated on the right, which was drawn by using VESTA software [49].

Figure 8

Calculated profile of the first NN Pb atomic image around Nb. The calculation was done by introducing Pb displacement of ${(-0.13,-0.09,-0.06)}_{\text{mono}}$ to the average structure at 100 K.

Figure 9

Temperature dependence of the first NN Pb atomic image intensity around Fe ions. The result of the XFH measurement is shown together with the calculated plots obtained from some structural models. The intensity is normalized by the XFH result at 300 K. The experimental data were taken from Ref. [36].

Figure 10

An example of the $B$-site atomic arrangement, in which a ${\mathrm{Fe}}^{3+}$ ion is surrounded by ${\mathrm{Nb}}^{5+}$ ions.

Figure 11

Schematic illustration of the deviations from the average structure of PFN above and below $T_{\text{N}}$ predicted from the present experimental results. The arrows indicate the shift of the constituent atoms, and the dashed lines in the left panel show the ${\mathrm{Fe}}^{3+}\text{−}{\mathrm{Pb}}^{2+}\text{−}{\mathrm{Fe}}^{3+}$ superexchange interactions.