We report on a study of the electronic and magnetic properties of the triangular antiferromagnetic ͕Cu 3 ͖ single-molecule magnet, based on spin-density-functional theory. Our calculations show that the low-energy magnetic properties are correctly described by an effective three-site spin s =1/ 2 Heisenberg model, with an antiferromagnetic exchange coupling J Ϸ 5 meV. The ground-state manifold of the model is composed of two degenerate spin S =1/ 2 doublets of opposite chirality. Due to lack of inversion symmetry in the molecule these two states are coupled by an external electric field, even when spin-orbit interaction is absent. The spin-electric coupling can be viewed as originating from a modified exchange constant ␦J induced by the electric field. We find that the calculated transition rate between the chiral states yields an effective electric dipole moment d = 3.38ϫ 10 −33 C mϷ e10 −4 a, where a is the Cu separation. For external electric fields Ϸ 10 8 V / m this value corresponds to a Rabi time Ϸ 1 ns and to a ␦J on the order of a few eV.

The quantum anomalous Hall effect (QAHE) has recently been reported to emerge in magnetically doped topological insulators. Although its general phenomenology is well established, the microscopic origin is far from being properly understood and controlled. Here, we report on a detailed and systematic investigation of transition metal (TM) doped Sb 2 Te 3. By combining density functional theory calculations with complementary experimental techniques, i.e., scanning tunneling microscopy, resonant photoemission, and x-ray magnetic circular dichroism, we provide a complete spectroscopic characterization of both electronic and magnetic properties. Our results reveal that the TM dopants not only affect the magnetic state of the host material, but also significantly alter the electronic structure by generating impurity-derived energy bands. Our findings demonstrate the existence of a delicate interplay between electronic and magnetic properties in TM doped topological insulators. In particular, we find that the fate of the topological surface states critically depends on the specific character of the TM impurity: while V-and Fe-doped Sb 2 Te 3 display resonant impurity states in the vicinity of the Dirac point, Cr and Mn impurities leave the energy gap unaffected. The single-ion magnetic anisotropy energy and easy axis, which control the magnetic gap opening and its stability, are also found to be strongly TM impurity dependent and can vary from in plane to out of plane depending on the impurity and its distance from the surface. Overall, our results provide general guidelines for the realization of a robust QAHE in TM doped Sb 2 Te 3 in the ferromagnetic state.

We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by calculating the transmission coefficient as a function of energy ͑−2 Ͻ E Ͻ 2 in units of the hopping integral in the tight-binding Hamiltonian͒ and disorder, q ͑probability that a given site of the lattice is not available to the particle͒. Our study based on finite-size scaling suggests the existence of delocalized states that depends on energy and the amount of disorder present in the system. For energies away from the band center ͑E =0͒, delocalized states appear only at low disorder ͑q Ͻ 15%͒. The transmission near the band center is generally very small for any amount of disorder and therefore makes it difficult to locate the transition to delocalized states if any, but our study does indicate a behavior that is weaker than power-law localization. Apart from this localization-delocalization transition, we also find the existence of two different kinds of localization regimes depending on energy and the amount of disorder. For a given energy, states are exponentially localized for sufficiently high disorder. As the disorder decreases, states first show power-law localization before showing a delocalized behavior.

Combining density-functional theory calculations and microscopic tight-binding models, we investigate theoretically the electronic and magnetic properties of individual substitutional transitionmetal impurities (Mn and Fe) positioned in the vicinity of the (110)

Frustrated triangular molecule magnets such as {Cu3} are characterized by two degenerate S=1/2 ground-states with opposite chirality. Recently it has been proposed theoretically [PRL 101, 217201 (2008)] and verified by ab-initio calculations [PRB 82, 155446 (2010)] that an external electric field can efficiently couple these two chiral spin states, even in the absence of spin-orbit interaction (SOI). The SOI is nevertheless important, since it introduces a splitting in the ground-state manifold via the Dzyaloshinskii-Moriya interaction. In this paper we present a theoretical study of the effect of the SOI on the chiral states within spin density functional theory. We employ a recently-introduced Hubbard model approach to elucidate the connection between the SOI and the Dzyaloshinskii-Moriya interaction. This allows us to express the Dzyaloshinskii-Moriya interaction constant D in terms of the microscopic Hubbard model parameters, which we calculate from first-principles. The small splitting that we find for the {Cu3} chiral state energies (∆ ≈ 0.02 meV) is consistent with experimental results. The Hubbard model approach adopted here also yields a better estimate of the isotropic exchange constant than the ones obtained by comparing total energies of different spin configurations. The method used here for calculating the DM interaction unmasks its simple fundamental origin which is the off-diagonal spin-orbit interaction between the generally multireference vacuum state and single-electron excitations out of those states