Anisotropic ferromagnetism in carbon doped zinc oxide from first-principles studies

TL;DR

This study uses first-principles calculations to explore the magnetic properties of carbon-doped ZnO, revealing anisotropic ferromagnetism and optimal doping levels for $d^{0}$-ferromagnetism.

Contribution

It provides a detailed theoretical analysis of impurity stability and magnetic interactions in C-doped ZnO, highlighting anisotropic ferromagnetism and optimal doping concentrations.

Findings

C$_ ext{O}$ impurities are more stable than C$_ ext{Zn}$ under most conditions.

C$_ ext{O}$-C$_ ext{O}$ impurities interact ferromagnetically within the ab-plane.

Optimal C$_ ext{O}$ concentration for ferromagnetism is between 2% and 6%.

Abstract

A density functional theory study of substitutional carbon impurities in ZnO has been performed, using both the generalized gradient approximation (GGA) and a hybrid functional (HSE06) as exchange-correlation functional. It is found that the non-spinpolarized C$_\mathrm{Zn}$ impurity is under almost all conditions thermodynamically more stable than the C$_\mathrm{O}$ impurity which has a magnetic moment of $2\mu_{\mathrm{B}}$, with the exception of very O-poor and C-rich conditions. This explains the experimental difficulties in sample preparation in order to realize $d^{0}$-ferromagnetism in C-doped ZnO. From GGA calculations with large 96-atom supercells, we conclude that two C$_\mathrm{O}$-C$_\mathrm{O}$ impurities in ZnO interact ferromagnetically, but the interaction is found to be short-ranged and anisotropic, much stronger within the hexagonal $ab$-plane of wurtzite ZnO than along the c-axis. This layered ferromagnetism is attributed to the anisotropy of the dispersion of carbon impurity bands near the Fermi level for C$_{\mathrm{O}}$ impurities in ZnO. From the calculated results, we derive that a C$_{\mathrm{O}}$ concentration between 2% and 6% should be optimal to achieve $d^{0}$-ferromagnetism in C-doped ZnO.