Ab Initio calculations of phonon splitting in antiferromagnetic Zn Cr2 O4

The full zone-center optical phonon spectrum and the exchange coupling constant J of the uniform collinear antiferromagnetic (AFM) ordered phase of Zn Cr2 O4 are calculated within density functional theory using the local spin density approximation (LSDA), the LSDA plus Hubbard U (LSDA+U), and the spin-polarized generalized gradient approximation (σ-GGA). The AFM ordering is found to induce splittings in the infrared-active phonon modes, confirming the importance of spin-phonon coupling in Zn Cr2 O4. The σ-GGA and the LSDA+U give magnitudes of phonon frequencies close to experiment, while the LSDA frequencies are slightly softer. However, only the 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.