Optical phonons, spin correlations, and spin-phonon coupling in the frustrated pyrochlore magnets CdCr 2 O 4 and ZnCr 2 O 4

We report on infrared, Raman, magnetic susceptibility, and specific-heat measurements on ${\text{CdCr}}_{2}{\text{O}}_{4}$ and ${\text{ZnCr}}_{2}{\text{O}}_{4}$ single crystals. We estimate the nearest-neighbor and next-nearest-neighbor exchange constants from the magnetic susceptibility and extract the spin-spin correlation functions obtained from the magnetic susceptibility and the magnetic contribution to the specific heat. By comparing with the frequency shift of the infrared optical phonons above ${T}_{N}$, we derive estimates for the spin-phonon coupling constants in these systems. The observation of phonon modes which are both Raman and infrared active suggest the loss of inversion symmetry below the N\'eel temperature in ${\text{CdCr}}_{2}{\text{O}}_{4}$ in agreement with theoretical predictions by Chern et al. [Phys. Rev. B 74, 060405(R) (2006)]. In ${\text{ZnCr}}_{2}{\text{O}}_{4}$ several new modes appear below ${T}_{N}$ but no phonon modes could be detected which are both Raman and infrared active.