Using single crystal inelastic neutron scattering with and without the application of an external magnetic field and powder neutron diffraction, we have characterized magnetic interactions in Ba3Cr2O8. Even without a field, we found that there exist three singlet-to-triplet excitation modes in the (h, h, l) scattering plane. Our complete analysis shows that the three modes are due to spatially anisotropic interdimer interactions that are induced by lattice distortions of the tetrahedron of oxygens surrounding the Jahn-Teller active Cr5+(3d1). The strong intradimer coupling of J0=2.38(2) meV and weak interdimer interactions (|Jinter|< or =0.52(2) meV) makes Ba3Cr2O8 a good model system for weakly coupled s=1/2 quantum spin dimers.
Using elastic and inelastic neutron scattering we show that a cubic spinel, CdCr2O4, undergoes an elongation along the c axis (c > a = b) at its spin-Peierls-like phase transition at T(N) = 7.8 K. The Néel phase (T < T(N)) has an incommensurate spin structure with a characteristic wave vector Q(M) = (0, delta,1) with delta approximately 0.09 and with spins lying on the ac plane. This is in stark contrast to another well-known Cr-based spinel, ZnCr2O4, that undergoes a c-axis contraction and a commensurate spin order. The magnetic excitation of the incommensurate Néel state has a weak anisotropy gap of 0.6 meV and it consists of at least three bands extending up to 5 meV.
Using neutron scattering techniques, we have investigated spin wave excitations in noncollinear ferrimagnetic spinels MnB 2 O 4 ͑B =Mn,V͒ with e g and t 2g orbital degeneracies, respectively, that lead to tetragonal distortions along opposite directions. Linear spin wave analysis of the excitations yields spatially inhomogeneous nearest neighbor interactions in both tetragonal spinels. We find the ratio J c / J ab Ϸ −0.06͑4͒ for Mn 3 O 4 ͑c Ͼ a = b͒ and Ϸ0.3͑1͒ for MnV 2 O 4 ͑c Ͻ a = b͒. Resulting exchange couplings of Mn 3 O 4 can be qualitatively explained in terms of possible overlaps of t 2g and e g electrons of Mn 2+ and Mn 3+ ions. On the other hand, those of MnV 2 O 4 , in particular, the strong J c , seem to contradict with the antiferro-orbital state of V 3+ ͑t 2g 2 ͒ ions that was proposed by a recent synchrotron x-ray study ͓T. Suzuki et al., Phys. Rev. Lett. 98, 127203 ͑2007͔͒. Theoretical implications to the orbital physics are also discussed. DOI: 10.1103/PhysRevB.77.054412 PACS number͑s͒: 75.30.Et, 75.30.Ds, 75.50.Gg TABLE I. The optimal parameters used to calculate spin wave dispersions of Mn 3 O 4 ͓Fig. 2͑b͔͒ and MnV 3 O 4 ͑Fig. 3͒ ͑J and D are in meV͒.
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