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 MnB(2)O(4) (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)approximate to-0.06(4) for Mn(3)O(4) (c < a=b) and approximate to 0.3(1) for MnV(2)O(4) (c < a=b). 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 , Phys. Rev. Lett. 98, 127203 (2007)]. Theoretical implications to the orbital physics are also discussed.