Local disorder in Ln$_2$Ti$_2$O$_7$ (Ln = Gd, Tb, Dy) pyrochlores

The temperature dependences of extended X-ray absorption fine structure (EXAFS) and X-ray absorption near edge structure (XANES) spectra of Ln$_2$Ti$_2$O$_7$ (Ln = Gd, Tb, Dy) geometrically frustrated magnets with a pyrochlore structure are presented. The temperature dependences of the Ln-O and Ti-O interatomic bond lengths and Debye-Waller factors $\sigma^2$ characterizing the local static and dynamic disordering of bonds have been obtained in the temperature range of $10$–$300$ K. The stiffnesses of metal-oxygen bonds and the parameters of local disordering of the structure have been determined from the dependences $\sigma^2(T)$. The effect of the magnetic state of rare-earth ions on local features of the Ln$_2$Ti$_2$O$_7$ (Ln = Gd, Tb, Dy) structure has been described. The characteristics of local disorder in pyrochlores under study have been compared to dysprosium zirconate Dy$_2$Zr$_2$O$_7$ having a disordered fluorite structure.