Non-collinear first-principles studies of the spin-electric coupling in frustrated triangular molecular magnets

Abstract: Frustrated triangular molecular magnets (MMs) with anti-ferromagnetic ground states (GS) are an important class of magnetic systems with potential applications in quantum information processing. The two-fold degenerate GS of these molecules, characterized by spin chirality, can be utilized to encode qubits for quantum computing. Furthermore, because of the lack of inversion symmetry in these molecules, an electric field couples directly states of opposite chirality, allowing a very efficient and fast control of the qubits. In this work we present a theoretical method to calculate the spin-electric coupling for triangular MMs with effective {\it local} spins $s$ larger than 1/2, which is amenable to a first-principles implementation based on density functional theory (DFT). In contrast to MMs where the net magnetization at the magnetic atoms is $\mu_{\rm B}/2$ ($\mu_{\rm B} $ is the Bohr magneton), the DFT treatment of frustrated triangular MMs with larger local magnetizations requires a fully non-collinear approach, which we have implemented in the NRLMOL DFT code. As an example, we have used these methods to evaluate the spin-electric coupling for a spin $s = 5/2$ ${\mathrm{Fe_3}}$ triangular MM, where this effect has been observed experimentally for the first time quite recently. Our theoretical and computational methods will help elucidate and further guide ongoing experimental work in the field of quantum molecular spintronics.