# Native defects in the Co$_2$Ti$Z$ ($Z=$ Si, Ge, Sn) full Heusler alloys: formation and influence on the thermoelectric properties

## TL;DR

This study uses first-principles calculations to analyze native defects in Co$_2$Ti$Z$ full Heusler alloys and their impact on thermoelectric properties, explaining the experimentally observed negative Seebeck coefficient.

## Contribution

It provides a detailed theoretical analysis of native defect formation energies and their effects on transport properties in Co$_2$Ti$Z$ alloys, linking defects to thermoelectric behavior.

## Key findings

- Co vacancies and Ti$_ ext{Sn}$ anti-site have negative formation energies.
- Defects significantly alter the Seebeck coefficient, sometimes making it negative.
- Native defects can explain the experimentally observed negative Seebeck coefficient.

## Abstract

We have performed first-principles investigations on the native defects in the full Heusler alloys Co$_2$Ti$Z$ ($Z$ one of the group IV elements Si, Ge, Sn), determining their formation energies and how they influence the transport properties. We find that Co vacancies (Vc) in all compounds and the Ti$_\text{Sn}$ anti-site exhibit negative formation energies. The smallest positive values occur for Co in excess on anti-sites (Co$_Z$ or Co$_\text{Ti}$) and for Ti$_Z$. The most abundant native defects were modeled as dilute alloys, treated with the coherent potential approximation in combination with the multiple-scattering theory Green function approach. The self-consistent potentials determined this way were used to calculate the residual resistivity via the Kubo-Greenwood formula and, based on its energy dependence, the Seebeck coefficient of the systems. The latter is shown to depend significantly on the type of defect, leading to variations that are related to subtle, spin-orbit coupling induced, changes in the electronic structure above the half-metallic gap. Two of the systems, Vc$_\text{Co}$ and Co$_Z$, are found to exhibit a negative Seebeck coefficient. This observation, together with their low formation energy, offers an explanation for the experimentally observed negative Seebeck coefficient of the Co$_2$Ti$Z$ compounds as being due to unintentionally created native defects.