Lattice dynamics and magnetic exchange interactions in: A spinel with pyrochlore lattice

is a unique system in the family of cobalt spinels (= Sn, Ti, Ru, Mn, Al, Zn, Fe, etc.) in which magnetic Co ions stabilize on the pyrochlore lattice exhibiting a large degree of orbital frustration. Due to the complexity of the low-temperature antiferromagnetic (AFM) ordering and long-range magnetic exchange interactions, the lattice dynamics and magnetic structure of a spinel have remained puzzling. To address this issue, here we present theoretical and experimental investigations of the highly frustrated magnetic structure, and the infrared (IR) and Raman-active phonon modes in the spinel , which exhibits an AFM ordering below the Néel temperature  K and an associated cubic () to tetragonal () structural phase transition whose location at vs at a lower  K is controversial. Our density functional theory () calculations reveal that one needs to consider magnetic-exchange interactions up to the third-nearest neighbors to get an accurate description of the low-temperature AFM order in . At room temperature, three distinct IR-active modes () are observed at frequencies 680, 413, and 325 along with four Raman-active modes (1), (2), and at frequencies 760, 647, 550, and 308 , respectively, which match reasonably well with our calculated values. All the IR-active and Raman-active phonon modes exhibit signatures of moderate spin-phonon coupling. The temperature dependence of various parameters, such as the shift, width, and intensity, of the Raman-active modes is also discussed. Noticeable changes around  K and  K are observed in the Raman line parameters of the and (1) modes, which are associated with the modulation of the Co-O bonds in octahedra during the excitations of these modes.