Spin-Electric Coupling in Molecular Magnets

Abstract

We study the triangular antiferromagnet Cu3 in external electric fields, using symmetry group arguments and a Hubbard model approach. We identify a spin-electric coupling caused by an interplay between spin exchange, spin-orbit interaction, and the chirality of the underlying spin texture of the molecular magnet. This coupling allows for the electric control of the spin (qubit) states, e.g. by using an STM tip or a microwave cavity. We propose an experimental test for identifying molecular magnets exhibiting spin-electric effects. [5,6,7], or the decoherence and the transition from quantum to classical behavior [8]. SMMs with antiferromagnetic coupling between neighboring spins are especially promising for the encoding and manipulation of quantum information [9,10,11,12], for they act as effective two-level systems, while providing additional auxiliary states that can be exploited for performing quantum gates, even in the presence of untunable couplings between the qubits [13]. Intra-and inter-molecular couplings of SMMs can be engineered by molecular and supra-molecular chemistry [14], enabling a bottom-up design of molecule-based devices [15].While the properties of SMMs can be modfied during the synthesis, control on the time scales required for quantum information processing remains a challenge. The standard spin-control technique is electron spin resonance (ESR) driven by ac magnetic fields B ac (t) [8,16,17,18]. For manipulation on the time scale of 1 ns (Rabi frequency Ω R ∼ 10 9 s −1 ) B ac should be of the order of 10 −2 T, which, however, is difficult to achieve. The spatial resolution of 1 nm, required for addressing a single molecule, is also prohibitively small. At these spatial and temporal scales, the electric control is preferable, because strong electric fields can be applied to small regions by using, for example, STM tips [19,20,21]. Also, the quantized electric field inside a microwave cavity can be used [22,23,24,25] to control single qubits and to induce coupling between them even if they are far apart.Here we identify and study an efficient spin-electric coupling mechanism in SMMs which is based on an interplay of spin exchange, spin-orbit interaction (SOI), and lack of inversion symmetry. Spin-electric effects induced solely by SOI [26] have been proposed [27] and experimentally demonstrated [28] in quantum dots. However, these SOI effects scale with the system size L as L 3 [27], making them irrelevant for the much smaller SMMs. Thus, additional ingredients-such as broken symmetriesmust be present in SMMs for an efficient coupling between spin and applied electric field.In the following, we demonstrate the possibility of such spin-electric effects in SMMs by focusing on a specific example, namely an equilateral spin triangle, Cu 3 [29]. In this SMM, the low energy states exhibit a chiral spin texture and, due to the absence of inversion symmetry, electric fields couple states of opposite chirality. Moreover, SOI couples the chirality to the total spin, and thus an effective spin-electri...

Low-Temperature Properties of the Quantum Heisenberg Antiferromagnet on Some One-Dimensional Lattices Containing Equilateral Triangles

“…Third, one may add to spin Hamiltonian (1) small extra terms which remove the degeneracy due to the chirality. Manipulation with chirality attracts much interest nowadays [10][11][12]. Fourth, the elaborated scheme may be applied to the Hubbard model on the lattices shown in Fig.…”

Finite-temperature decoherence of spin states in a {Cu3} single molecular magnet

“…In the following discussion, a typical case of triangular spin-1 2 molecular magnet Cu 3 [27] is considered. At the low energies, the states of the system are represented by the quantum numbers of three spin-1 2 s i labelling three Cu 2+ ions and the orbital states are quenched.…”

“…where ω so is the effective spin-orbit interaction and can be calculated by the general symmetry group method [27]. Applying a local and planar electric field ǫ(t) with the frequency ω, the perturbed spin-electric interaction Hamiltonian H ǫ in the ground state subspace is described as,…”

“…It is possible to apply time-dependent strong electric field close to single molecular magnet via a scanning tunnel microscopic tip [27,28]. It has been found out that an electric field can be coupled to low-energy spin states of different chirality due to the absence of spin inversion symmetry in some single molecular magnets, such as Cu 3 [27] , V 15 [29], Co 3 [30], Dy 3 [31] and Mn 12 [9,10], etc.…”

“…It has been found out that an electric field can be coupled to low-energy spin states of different chirality due to the absence of spin inversion symmetry in some single molecular magnets, such as Cu 3 [27] , V 15 [29], Co 3 [30], Dy 3 [31] and Mn 12 [9,10], etc. The effective spin electric coupling relies on the detailed structure of single molecular magnets at low energies [32].…”