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 textit{et al.}, Phys. Rev. Lett. textbf{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 textit{ab-initio} methods [M. F. Islam textit{et al.}, Phys. Rev. B textbf{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.
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.
Frustrated triangular molecule magnets such as {Cu$_3$} are characterized by two degenerate S=1/2 ground-states with opposite chirality. Recently it has been proposed theoretically [PRL {bf 101}, 217201 (2008)] and verified by {it ab-initio} calculat
ions [PRB {bf 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 {Cu$_3$} chiral state energies ($Delta approx 0.02$ 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.
