The full zone-center optical phonon spectrum and the exchange coupling constant $J$ of the uniform collinear antiferromagnetic (AFM) ordered phase of $\mathrm{Zn}{\mathrm{Cr}}_2{\mathrm{O}}_4$ are calculated within density functional theory using the local spin density approximation (LSDA), the LSDA plus Hubbard $U$ $(\mathrm{LSDA}+U)$, and the spin-polarized generalized gradient approximation $\left(\sigma \text{−}\mathrm{GGA}\right)$. The AFM ordering is found to induce splittings in the infrared-active phonon modes, confirming the importance of spin-phonon coupling in $\mathrm{Zn}{\mathrm{Cr}}_2{\mathrm{O}}_4$. The $\sigma \text{−}\mathrm{GGA}$ and the $\mathrm{LSDA}+U$ give magnitudes of phonon frequencies close to experiment, while the LSDA frequencies are slightly softer. However, only the $\mathrm{LSDA}+U$ exchange constant and phonon splittings are consistent with experiment and previous calculations. A correspondence between the exchange constant and the splittings for the infrared-active phonon modes is found.

• Received 8 November 2006

DOI:https://doi.org/10.1103/PhysRevB.75.054304