We report on a study of the electronic and magnetic properties of the triangular antiferromagnetic {Cu3} 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 approximate to 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 delta J induced by the electric field. We find that the calculated transition rate between the chiral states yields an effective electric dipole moment d = 3.38 x 10(-33) C m approximate to e10(-4)a, where a is the Cu separation. For external electric fields epsilon approximate to 10(8) V/m this value corresponds to a Rabi time tau approximate to 1 ns and to a delta J on the order of a few mu eV.

The ground state of frustrated (antiferromagnetic) triangular molecular magnets is characterized by two total-spin S = 1/2 doublets with opposite chirality. According to a group theory analysis [M. Trif et al., Phys. Rev. Lett. 101, 217201 (2008)] an external electric field can efficiently couple these two chiral spin states, even when the spin-orbit interaction (SOI) is absent. The strength of this coupling, d, is determined by an off-diagonal matrix element of the dipole operator, which can be calculated by ab-initio methods [M. F. Islam et al., Phys. Rev. B 82, 155446 (2010)]. In this work we propose that Coulomb-blockade transport experiments in the cotunneling regime can provide a direct way to determine the spin-electric coupling strength. Indeed, an electric field generates a d-dependent splitting of the ground state manifold, which can be detected in the inelastic cotunneling conductance. Our theoretical analysis is supported by master-equation calculations of quantum transport in the cotunneling regime. We employ a Hubbard-model approach to elucidate the relationship between the Hubbard parameters t and U, and the spin-electric coupling constant d. This allows us to predict the regime in which the coupling constant d can be extracted from experiment.

We consider a model of an artificial atom with interacting electrons having both spin degrees of freedom and orbital degeneracies. The interaction includes both spin and orbital exchange couplings, which favour a spin polarized ground state with nonzero orbital moment. For the two-electron problem with l=1 orbital degeneracy we enumerate all the eigenstates of the system with and without spin-orbit interaction. We then study quantum transport for the case in which the atom is weakly connected to metallic leads, focusing in particular on the effect of the spin-orbit interaction on the tunnelling conductance. We also discuss how spin-orbit interaction and an external magnetic field influence the conductance when the leads are spin-polarized and tunnelling magneto-resistance is expected.

5.

Nossa, Javier

et al.

Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering. Lunds universitet.

Islam, Fhokrul

Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.

Canali, Carlo M.

Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.

Pederson, M. R.

US DOE, Off Basic Energy Sci, Washington, DC 20585 USA.

Using first-principles methods, we study theoretically the properties of an individual {Fe-4} single-molecule magnet (SMM) attached to metallic leads in a single-electron transistor geometry. We show that the conductive leads do not affect the spin ordering and magnetic anisotropy of the neutral SMM. On the other hand, the leads have a strong effect on the anisotropy of the charged states of the molecule, which are probed in Coulomb blockade transport. Furthermore, we demonstrate that an external electric potential, modeling a gate electrode, can be used to manipulate the magnetic properties of the system. For a charged molecule, by localizing the extra charge with the gate voltage closer to the magnetic core, the anisotropy magnitude and spin ordering converges to the values found for the isolated {Fe-4} SMM. We compare these findings with the results of recent quantum transport experiments in three-terminal devices.

For device applications of single molecule magnets (SMMs) in high-density information storage and quantum-state control it is essential that the magnetic properties of the molecules remain stable under the influence of metallic contacts or surface environment. Recent tunneling experiments [1, 2] on N@C60 and {\{}Fe4{\}} SMM have shown that these molecules preserve their magnetic characteristics when they are used as the central island of single-electron transistors. Although quantum spin models have been used extensively to study theoretically tunneling spectroscopy of SMMs, it has been shown recently that the orbital degrees of freedom, which is absent in spin models, can significantly affect the tunneling conductance [3]. In this work we present first-principles calculations of the neutral and charged states of N@C60 and {\{}Fe4{\}} SMMs, and discuss a strategy to include their properties into a theory of quantum transport. We also present results of the magnetic anisotropy for the different charge states of Fe4 and discuss their relevance for experiments [2] in the sequential tunneling and cotunnelling regimes.

7.

Nossa, Javier

et al.

Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.

Islam, Fhokrul

Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.

Canali, Carlo M.

Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.

Pederson, Mark

US Department of Energy SC22.1, Washington DC 20585-1290.

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 [M. Trif et al., Phys. Rev. Lett. 101, 217201 (2008)] and verified by ab initio calculations [M. F. Islam et al., Phys. Rev. B 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 (DM) 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 one-band Hubbard-model approach adopted and analyzed 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.