  We present a first principles LSDA+U study of the magnetic coupling constants
in the spinel magnets CoCr_2O_4 and MnCr_2O_4. 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.
