Highly anisotropic orbitally dependent superexchange in cyano-bridged clusters containing Mn(III) and Mn(II) ions

We study the orbitally dependent magnetic exchange in cyanide-based clusters as a source of the barrier for reversal magnetization. We consider the Mn(III)-CN-Mn(II) dimer and linear Mn(II)-NC-Mn(III)-CN-Mn(II) trimer containing octahedrally coordinated Mn(III) and Mn(II) ions with special emphasis on the magnetic manifestations of the orbital degeneracy of the Mn(III) ion. The kinetic exchange mechanism involves the electron transfer from the single occupied t₂ orbitals of the Mn(II) ion [⁶A₁ (t₂³e²) ground state] to the singly occupied t₂ orbitals of the Mn(III) ion [³T₁(t ₂⁴) ground state] resulting in the charge-transfer ⁵T₂(t₂²e²] _Mn(III)-²T₂(t₂⁵) _Mn(II) state of the pair. The deduced effective exchange Hamiltonian that takes into account orbital degeneracy leads to an essentially non-Heisenberg energy pattern. The energy levels are shown to be dependent on both spin and orbital quantum numbers, thus providing direct information about the magnetic anisotropy of the system. Along with the magnetic exchange, the model includes an axial component of the crystal field and spin-orbit coupling operating within the ground ³T₁ (t₂ ⁴) cubic term of the Mn(III) ion. We have shown that under certain conditions both named interactions lead to the occurrence of the barrier for the reversal of magnetization, which significantly increases when passing from the dimer to the trimer. This provides a possible way for raising the magnetic barrier in the family of cyano-bridged manganese clusters.