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Na$_{0.5}$(Bi$_3$/4RE$_{1/4}$)$_{0.5}$TiO$_3$ (RENBT, RE = Nd, Gd, Dy, andHo) compounds were investigated in the framework of first-principlescalculations using the full potential linearized augmented plane wave (FP-LAPW)method based on the spin-polarized density functional theory implemented in theWIEN2k code. Combined charge density distribution and Ti K-edge x-rayabsorption spectra revealed that the RENBT compositions with high polarizationvalues were accompanied by a higher TiO$_6$ distortion, DyNBT, and NdNBTcompounds. The effect of the rare-earth elements on the polarization wereconfirmed experimentally with the collection of the hysteresis loops. Theinvestigation of the electronic properties of the compounds highlighted theemergence of a magnetization owing to the 4f orbital effect of the rare-earthelements. Besides, the investigation of the chemical ordering showed ashort-range chemical ordering for the pure composition and an increased A-sitedisorder for dysprosium doped NBT system. The increased disorder may speak forincreased relaxor properties in the RE doped compositions.

Rare-earth effect on the physical properties of Na$_{0.5}$Bi$_{0.5}$TiO$_3$ system: A Density Functional Theory investigation