Element-selective local structural analysis around B -site cations in multiferroic Pb(Fe1/2Nb1/2)O3 using x-ray fluorescence holography

X-ray fluorescence holography (XFH) measurements were carried out for multiferroic $\mathrm{Pb}({\mathrm{Fe}}_1/2{\mathrm{Nb}}_1/2){\mathrm{O}}₃$ (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 N\'eel 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.