Can the double exchange cause antiferromagnetic spin alignment?

The effect of the double exchange in a square-planar mixed-valence dⁿ⁺¹ − dⁿ⁺¹ − dⁿ − dⁿ–type tetramers comprising two excess electrons delocalized over four spin cores is discussed. The detailed analysis of a relatively simple d² − d² − d¹ − d¹–type tetramer shows that in system with the delocalized electronic pair the double exchange is able to produce antiferromagnetic spin alignment. This is drastically different from the customary ferromagnetic effect of the double exchange which is well established for mixed-valence dimers and tetramers with one excess electron or hole. That is why the question “Can double exchange cause antiferromagnetic spin alignment?” became the title of this article. As an answer to this question the qualitative and quantitative study revealed that due to antiparallel directions of spins of the two mobile electrons which give competitive contributions to the overall polarization of spin cores, the system entirely becomes antiferromagnetic. It has been also shown that depending on the relative strength of the second-order double exchange and Heisenberg–Dirac–Van Vleck exchange the system has either the ground localized spin-triplet or the ground delocalized spin-singlet.