Spin waves and exchange interactions in the antiferromagnetic garnets with Fe3+ in the octahedral sites

The results of an inelastic neutron scattering study of the spin wave spectrum for the garnet Fe₂Ca₃Si₃O₁₂(FeSiG) are presented. We compare the exchange parameters for this garnet and for the Ge-species (Fe₂Ca₃Ge₃O₁₂(feGeG)) having the same magnetic structure. We relate the differences found with structural information from powder neutron diffraction. In this way the super exchange paths viap orbitals of intermediate oxygen atoms can be identified. We discuss the effect of a small number (3.2(5)%) of Mn²⁺ impurities in the 24c sites. These lead to an effective ferromagnetic exchange between the Fe³⁺ ions and drastically renormalize the average exchange constants. An estimate for the Fe³⁺–Mn²⁺ indirect exchange between a and c sites of 6(1) K is obtained. The exchange parameters for the pure FeSiG are found to beJ ₁=1.16(4) K,J ₁=0.96(4K andJ ₂=–1.24(4) K for nearest and next nearest neighbours, respectively. These values apply for a moment of 4.02(4) _B per iron atom as obtained from a structure refinement of powder diffraction data. Finally we present results for FeSiG of a high resolution study of the excitations at the zone centre in an attempt to verify our earlier findings of a quantum spin wave gap for FeGeG. In contrast to the earlier measurements, we could follow the acoustical branch to much lower energies using a timeof-flight spectrometer. We found indications for a crossing of the two low lying spin wave branches, the acoustical one extrapolating to the anisotropy gap of 0.005 THz and the antiphase branch extrapolating to the quantum gap of 0.02 THz.