Magnetic excitations and orbital physics in the ferrimagnetic spinels MnB₂O₄ (B=Mn,V)

Using neutron scattering techniques, we have investigated spin wave excitations in noncollinear ferrimagnetic spinels MnB₂O₄ (B=Mn,V) 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≈−0.06(4) for Mn₃O₄ (c>a=b) and ≈0.3(1) for MnV₂O₄ (c<a=b). Resulting exchange couplings of Mn₃O₄ can be qualitatively explained in terms of possible overlaps of t_2g and e_g electrons of Mn²⁺ and Mn³⁺ ions. On the other hand, those of MnV₂O₄, in particular, the strong J^c, seem to contradict with the antiferro-orbital state of V³⁺ (t_2g²) ions that was proposed by a recent synchrotron x-ray study [ T. Suzuki et al. Phys. Rev. Lett. 98 127203 (2007)]. Theoretical implications to the orbital physics are also discussed.