Diamagnetic d-Orbitals Drive Magnetic Structure Selection in the Double Perovskite Ba₂MnTeO₆

B-site ordered A2B′B″O6 double perovskites have a variety of applications as magnetic materials. Here, we show that diamagnetic d10 and d0 B″ cations have a significant effect on the magnetic interactions in these materials. We present a neutron scattering and theoretical study of the Mn2+ double perovskite Ba2MnTeO6 with a 4d10 Te6+ cation on the B″-site. It is found to be a Type I antiferromagnet with a dominant nearest-neighbor J1 interaction. In contrast, the 5d0 W6+ analogue Ba2MnWO6 is a Type II antiferromagnet with a significant next-nearest-neighbor J2 interaction. This is due to a d10/d0 effect, where the different orbital hybridization with oxygen 2p results in different superexchange pathways. We show that d10 B″ cations promote nearest neighbor and d0 cations promote next-nearest-neighbor interactions. The d10/d0 effect could be used to tune magnetic interactions in double perovskites.