Magnetic excitations and orbital physics in the ferrimagnetic spinels Mn B2 O4 (B=Mn,V)

Using neutron scattering techniques, we have investigated spin wave excitations in noncollinear ferrimagnetic spinels Mn B2 O4 (B=Mn,V) with eg and t2g 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 Jc Jab ≈-0.06 (4) for Mn3 O4 (c>a=b) and ≈0.3 (1) for Mn V2 O4 (c<a=b). Resulting exchange couplings of Mn3 O4 can be qualitatively explained in terms of possible overlaps of t2g and eg electrons of Mn2+ and Mn3+ ions. On the other hand, those of Mn V2 O4, in particular, the strong Jc, seem to contradict with the antiferro-orbital state of V3+ (t 2g 2) ions that was proposed by a recent synchrotron x-ray study. Theoretical implications to the orbital physics are also discussed.