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

## TL;DR

This study uses first-principles calculations to compare doped LiNbO₃ and BaTiO₃, revealing that polar displacements can coexist with conduction in doped LiNbO₃, suggesting potential for polar metallic phases and new device functionalities.

## Contribution

It demonstrates that polar distortions persist in doped LiNbO₃ at high electron concentrations, unlike in BaTiO₃, highlighting the potential for polar metals in LiNbO₃-type oxides.

## Key findings

- Polar displacements persist in doped LiNbO₃ at high doping levels.
- Polar displacements in doped BaTiO₃ vanish at lower doping levels.
- Conduction electrons are non-uniformly distributed in doped LiNbO₃.

## Abstract

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.