Electronic structure and spin exchange interactions in Na(2)V(3)O(7): a vanadium(IV) oxide nanotubular phase.

The electronic structure of the inorganic nanotubular phase Na(2)V(3)O(7) has been studied by means of first-principles DFT calculations. The magnetic behavior in this system is relatively complex to study because there are as many as 30 different exchange interactions in the unit cell. The coupling constants are computed directly from the energy differences of several spin configurations. It is found that because of the special geometry of the nanotube, the nearest-neighbor coupling constants are not the only important ones and other next-nearest-neighbor constants cannot be neglected. In contrast with previous studies, it is found that at least 12 different coupling constants must be considered to correctly describe the spin arrangement in this system. However, to get more meaningful values for the smaller constants, a larger set of at least 17 constants must be explicitly taken into account. The lowest-energy collinear spin configuration is found to exhibit ferromagnetic coupling between the rings of the nanotube, whereas the coupling can be ferro- or antiferromagnetic within those rings. This leads to two important spin-frustrated interactions. Use of the so-called dimer approximation (i.e., substituting 16 paramagnetic V(IV) ions of the nanotube by 16 diamagnetic Ti(IV) ions, thus keeping the total charge of the system constant and leaving only two magnetic centers) is found to give invaluable hints concerning the nature of the magnetic interactions. This procedure may be helpful to analyze the magnetic properties of similar non-trivial systems with many paramagnetic centers.