Microscopic theory for the incommensurate transition in TiOCl

TL;DR

This paper presents a microscopic model explaining the incommensurate phase in TiOCl, linking lattice frustration to structural instability and matching experimental phonon data and incommensuration behavior.

Contribution

It introduces a microscopic mechanism based on lattice frustration and phonon interactions to explain the incommensurate transition in TiOCl, supported by experimental consistency.

Findings

Model reproduces measured phonon frequencies at 300K

Predicts incommensuration vector at transition temperature

Shows phonon softening and broadening near zone boundary

Abstract

We propose a microscopic mechanism for the incommensurate phase in TiOX compounds. The model includes the antiferromagnetic chains of Ti ions immersed in the phonon bath of the bilayer structure. Making use of the Cross-Fisher theory, we show that the geometrically frustrated character of the lattice is responsible for the structural instability which leads the chains to an incommensurate phase without an applied magnetic field. In the case of TiOCl, we show that our model is consistent with the measured phonon frequencies at $T=300K$ and the value of the incommensuration vector at the transition temperature. Moreover, we find that the dynamical structure factor shows a progressive softening of an incommensurate phonon near the zone boundary as the temperature decreases. This softening is accompanied by a broadening of the peak which gets asymmetrical as well when going towards the transition temperature. These features are in agreement with the experimental inelastic X-ray measurements.