We investigate theoretically the effect of nearby As (arsenic) vacancies on the magnetic properties of substitutional Mn (manganese) impurities on the GaAs (110) surface, using a microscopic tight-binding model which captures the salient features of
the electronic structure of both types of defects in GaAs. The calculations show that the binding energy of the Mn-acceptor is essentially unaffected by the presence of a neutral As vacancy, even at the shortest possible ${rm V}_{rm As}$--Mn separation. On the other hand, in contrast to a simple tip-induced-band-bending theory and in agreement with experiment, for a positively charged As vacancy the Mn-acceptor binding energy is significantly reduced as the As vacancy is brought closer to the Mn impurity. For two Mn impurities aligned ferromagnetically, we find that nearby charged As vacancies enhance the energy level splitting of the associated coupled acceptor levels, leading to an increase of the effective exchange interaction. Neutral vacancies leave the exchange splitting unchanged. Since it is experimentally possible to switch reversibly between the two charge states of the vacancy, such a local electric manipulation of the magnetic dopants could result in an efficient real-time control of their exchange interaction.
We present results of tight-binding spin-dynamics simulations of individual and pairs of substitutional Mn impurities in GaAs. Our approach is based on the mixed quantum-classical scheme for spin dynamics, with coupled equations of motions for the qu
antum subsystem, representing the host, and the localized spins of magnetic dopants, which are treated classically. In the case of a single Mn impurity, we calculate explicitly the time evolution of the Mn spin and the spins of nearest-neighbors As atoms, where the acceptor (hole) state introduced by the Mn dopant resides. We relate the characteristic frequencies in the dynamical spectra to the two dominant energy scales of the system, namely the spin-orbit interaction strength and the value of the p-d exchange coupling between the impurity spin and the host carriers. For a pair of Mn impurities, we find signatures of the indirect (carrier-mediated) exchange interaction in the time evolution of the impurity spins. Finally, we examine temporal correlations between the two Mn spins and their dependence on the exchange coupling and spin-orbit interaction strength, as well as on the initial spin-configuration and separation between the impurities. Our results provide insight into the dynamic interaction between localized magnetic impurities in a nano-scaled magnetic-semiconductor sample, in the extremely dilute (solotronics) regime.
We report on microscopic tight-binding modeling of surface states in Bi$_2$Se$_3$ three-dimensional topological insulator, based on a sp$^3$ Slater-Koster Hamiltonian, with parameters calculated from density functional theory. The effect of spin-orbi
t interaction on the electronic structure of the bulk and of a slab with finite thickness is investigated. In particular, a phenomenological criterion of band inversion is formulated for both bulk and slab, based on the calculated atomic- and orbital-projections of the wavefunctions, associated with valence and conduction band extrema at the center of the Brillouin zone. We carry out a thorough analysis of the calculated bandstructures of slabs with varying thickness, where surface states are identified using a quantitative criterion according to their spatial distribution. The thickness-dependent energy gap, attributed to inter-surface interaction, and the emergence of gapless surface states for slabs above a critical thickness are investigated. We map out the transition to the infinite-thickness limit by calculating explicitly the modifications in the spatial distribution and spin-character of the surface states wavefunction with increasing the slab thickness. Our numerical analysis shows that the system must be approximately forty quintuple-layers thick to exhibit completely decoupled surface states, localized on the opposite surfaces. These results have implications on the effect of external perturbations on the surface states near the Dirac point.
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.
Combining field-theoretical methods and ab-initio calculations, we construct an effective Hamiltonian with a single giant-spin degree of freedom, capable of the describing the low-energy spin dynamics of ferromagnetic metal nanoclusters consisting of
up to a few tens of atoms. In our procedure, the magnetic moment direction of the Kohn-Sham SDFT wave-function is constrained by means of a penalty functional, allowing us to explore the entire parameter space of directions, and to extract the magnetic anisotropy energy and Berry curvature functionals. The average of the Berry curvature over all magnetization directions is a Chern number - a topological invariant that can only take on values equal to multiples of one half, representing the dimension of the Hilbert space of the effective spin system. The spin Hamiltonian is obtained by quantizing the classical anisotropy energy functional, after performing a change of variables to a constant Berry curvature space. The purpose of this article is to examine the impact of the topological effect from the Berry curvature on the low-energy total-spin-system dynamics. To this end, we study small transition metal clusters: Co$_{n}$ ($n=2,...,5$), Rh$_{2}$, Ni$_{2}$, Pd$_{2}$, Mn$_{x}$N$_{y}$, Co$_{3}$Fe$_{2}$.
