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Electrical and structural properties of pure and dysprosium doped $Na_{0.5}Bi_{0.5}TiO_{3}$ system: DFT and Monte Carlo simulation

The chemical ordering, electrical, optical, and magnetic properties of $Na_{0.5}Bi_{0.5}TiO_{3}$ (NBT) and 25$\%$ dysprosium doped NBT (DyNBT) were investigated in the framework of first-principles calculations using the full potential linearized augmented plane wave (FP-LAPW) method based on spin-polarized density functional theory implemented in the WIEN2k code. We demonstrated that NBT structure is stable in the 001 A-site configuration, while DyNBT presents an A-site disorder perceived by the minimal energy difference between the different A-site configurations. A significant magnetic moment of $5μB$ emerges in DyNBT system, while NBT is known to be non-magnetic. Dysprosium in NBT matrix seems to form an ionic bonding with oxygen atoms whereas Bi-O forms covalent bonding which is responsible for the decrease of the polarization value from 42.3 $μC/cm^{2}$ for NBT to 22.08 $μC/cm^{2}$ for the doped compound. In the second part, the transition temperature and the hysteresis loops of $Na_{0.5}(Bi_{1-x}Dy_{x})_{0.5}TiO_{3}$ system x = 0 - $25\%$ were investigated using the Monte Carlo simulation. We observed a decrease in the transition temperature as a function of dysprosium introduction. We pointed out from the hysteresis loops, an apparent decrease of the coercive field together with the remanent polarization as a function of doping and also as a function of temperature. Our proposed model was seen to approach the values of experimental studies.