Spin Dynamics and Phonons in Chromites CoCr_2O_4 and MnCr_2O_4

Spinel compounds are of great interest in both fundamental and application-oriented perspectives due to the geometric magnetic frustration inherent to their lattice and the resulting complex magnetic states. Here, we applied x-ray diffraction, magnetization, heat capacity and powder inelastic neutron scattering measurements, along with theoretical calculations, to study the exotic properties of chromite-spinel oxides CoCr_2O_4 and MnCr_2O_4. The temperature dependence of the phonon spectra provides an insight into the correlation between oxygen motion and the magnetic order, as well as the magnetoelectric effect in the ground state of MnCr_2O_4. Moreover, spin-wave excitations in CoCr_2O_4 and MnCr_2O_4 are compared with Heisenberg model calculations. This approach enables the precise determination of exchange energies and offers a comprehensive understanding of the spin dynamics and relevant exchange interactions in complicated spiral spin ordering.