Coexistence of polar displacements and conduction in doped ferroelectrics: an ab initio comparative study

Polar metals are rare because free carriers in metals screen electrostatic potential and eliminate internal dipoles. Degenerate doped ferroelectrics may create an approximate polar metallic phase. We use first-principles calculations to investigate $n$-doped LiNbO$_3$-type oxides (LiNbO$_3$ as the prototype) and compare to widely studied perovskite oxides (BaTiO$_3$ as the prototype). In the rigid-band approximation, substantial polar displacements in $n$-doped LiNbO$_3$ persist even at 0.3 $e$/f.u. ($\simeq$ 10$^{21}$ cm$^{-3}$), while polar displacements in $n$-doped BaTiO$_3$ quickly get suppressed and completely vanish at 0.1 $e$/f.u. Furthermore, in $n$-doped LiNbO$_3$, Li-O displacements decay more slowly than Nb-O displacements, while in $n$-doped BaTiO$_3$, Ba-O and Ti-O displacements decay approximately at the same rate. Supercell calculations that use oxygen vacancies as electron donors support the main results from the rigid-band approximation and provide more detailed charge distributions. Substantial cation displacements are observed throughout LiNbO$_{3-\delta}$($\delta = 4.2\%$), while cation displacements in BaTiO$_{3-\delta}$($\delta = 4.2\%$) are almost completely suppressed. We find that conduction electrons in LiNbO$_{3-\delta}$ are not as uniformly distributed as in BaTiO$_{3-\delta}$, implying that the rigid-band approximation should be used with caution in simulating electron doped LiNbO$_3$-type oxides. Our work shows that polar distortions and conduction can coexist in a wide range of electron concentration in $n$-doped LiNbO$_3$, which is a practical approach to generating an approximate polar metallic phase. Combining doped ferroelectrics and doped semiconductors may create new functions for devices.