We present a detailed study of the influence of various interactions on the spin quantum tunneling in a Mn12 wheel molecule. The effects of single-ion and exchange (spin-orbit) anisotropy are first considered, followed by an analysis of the roles pla
yed by secondary influences, e.g. disorder, dipolar and hyperfine fields, and magnetoacoustic interactions. Special attention is paid to the role of the antisymmetric Dzyaloshinski-Moriya (DM) interaction. This is done within the framework of a 12-spin microscopic model, and also using simplified dimer and tetramer approximations in which the electronic spins are grouped in 2 or 4 blocks, respectively. If the molecule is inversion symmetric, the DM interaction between the dimer halves must be zero. In an inversion symmetric tetramer, two independent DM vectors are allowed, but no new tunneling transitions are generated by the DM interaction. Experiments on the Mn12 wheel can only be explained if the molecular inversion symmetry is broken, and we explore this in detail using both models, focussing on the asymmetric disposition and rounding of Berry phase minima associated with quantum interference between states of opposite parity. A remarkable behavior exists for the `Berry phase zeroes as a function of the directions of the internal DM vectors and the external transverse field. A rather drastic breaking of the molecular inversion-symmetry is required to explain the experiments; in the tetramer model this requires a reorientation of the DM vectors on one half of the molecule by nearly 180 degrees. This cannot be attributed to sample disorder. These results are of general interest for the quantum dynamics of tunneling spins, and lead to some interesting experimental predictions.
In a recent Letter [1], Wernsdorfer et al. report an experimental study of a Mn12 molecular wheel which shows essentially identical behavior to the Mn12 wheel studied by Ramsey et al. [2]. In their Letter, Wernsdorfer et al. use the same model of a d
imer of two exchange-coupled spins used in [2] as a basis to extend the study of the influence of the Dzyaloshinskii-Moriya (DM) interaction on the quantum tunneling of the magnetization of this system; in particular, they show that a tilt of the DM vector away from the uniaxial anisotropy axis can account for the asymmetric nature of the quantum interference minima associated with resonances between states of opposite parity, e.g., k = 1(A). We want to stress that the inclusion of DM interactions in a system with inversion symmetry cannot mix states of opposite parity; i.e., the parity operator commutes with the Hamiltonian. Consequently, the use by Wernsdorfer et al. of a single DM vector in a centrosymmetric dimer is strictly forbidden since it implicitly violates parity conservation. The authors correctly point out that the lack of an inversion center between each pair of manganese ions on the wheel justifies the possibility of local DM interactions, even though the complete molecule has an inversion center. However, these local DM interactions must also satisfy the molecular inversion symmetry; i.e., they cannot mix states of opposite parity.We agree that such DM interactions are not always completely innocuous; e.g., they can mix spin states having the same parity. Indeed, in kagome systems [3] (cited in [1]), this can lead to weak ferromagnetism. Nevertheless, the inversion symmetry of the lattice is preserved and parity is still conserved.
