Oscillatory Exchange Coupling in Magnetic Molecules

First-principles calculations based on the spin-dependent density functional theory (DFT) have revealed that the magnetic ground state of a finite linear carbon chain capped by two transition metal (TM) atoms alternates between ferromagnetic and antiferromagnetic configurations depending on the number of carbon atoms. The character of indirect exchange coupling in this nanoscale, quasi-zero dimensional systems is different from those analogous extended structures consisting of magnetic layers separated by a non-magnetic spacer (or magnetic impurities in a non-magnetic host material) and hence cannot be described as a Fermi surface property of the extended spacer (or the host material). We present a tight-binding model which provides a theoretical framework to the underlying mechanism of the exchange coupling in molecular structures. The model calculations are capable of reproducing the essential features of the DFT results for the indirect exchange coupling and the atomic magnetic moments in the TM-C$_n$-TM structures as functions of the number of carbon atoms. In nanostructures consisting of a few atoms the concepts of extended wavefunctions and the band-theory loose their validity, and hence the oscillatory exchange coupling turns out to be a consequence of quantum interference effects due to the spin-dependent onsite and hopping energies.