We present a first principles LSDA+U study of the magnetic coupling constants in the spinel magnets CoCr2O4 and MnCr2O4. Our calculated coupling constants highlight the possible importance of AA interactions in spinel systems with magnetic ions on both A and B sites. Furthermore, we show that a careful analysis of the dependence of the magnetic coupling constants on the LSDA+U parameters provides valuable insights in the underlying coupling mechanisms and allows to obtain a quantitative estimate of the magnetic coupling constants. We discuss in detail the capabilities and possible pitfalls of the LSDA+U method in determining magnetic coupling constants in complex transition metal oxides.

C. E. thanks Craig Fennie, Ram Seshadri, Nicola Spaldin, and Andrew Millis for useful discussions. This work was supported by the NSF?s Chemical Bonding Centers program, Grant No. CHE-0434567 and by the MRSEC Program of the NSF under the Award No. DMR-0213574. We also made use of central facilities provided by NSF-MRSEC Award No. DMR-0520415

PUBLISHED