# Modulated, three-directional, and polar structural instability in layered $d^1$ NaTiO$_2$

## TL;DR

This study uses density functional calculations to investigate the structural phase transition in NaTiO$_2$, revealing phonon instabilities and modulated monoclinic structures linked to Ti $3d$ electronic states.

## Contribution

It demonstrates that the experimentally observed transition involves complex three-directional modulated structures driven by phonon instabilities and electronic bonding effects.

## Key findings

- Phonon dispersions show instabilities at specific wavevectors.
- The low-temperature structure is not energetically favored.
- Electronic structure indicates Ti $3d$ bonding instability.

## Abstract

I study the experimentally observed metal-to-metal structural phase transition in NaTiO$_2$ using density functional calculations. I do not find the previously proposed low-temperature structure energetically favorable with respect to the high-temperature rhombohedral structure. The calculated phonon dispersions of the rhombohedral phase show dynamical instabilities at several inequivalent parts of the Brillouin zone, including at the wavevector $(\frac{1}{2},\frac{1}{5},\frac{1}{5})$. These instabilities lead to monoclinic structures without inversion symmetry that are modulated along all three directions. The calculated electronic structures show that a local bonding instability of the Ti $3d$ states is associated with the structural transition.