We investigate the effect of an external magnetic field on the physical properties of the acceptor hole statesassociated with single Mn acceptors placed near the (110) surface of GaAs. Cross-sectional scanning tunnelingmicroscopy images of the acceptor local density of states (LDOS) show that the strongly anisotropic hole wavefunction is not significantly affected by a magnetic field up to 6 T. These experimental results are supported bytheoretical calculations based on a tight-binding model of Mn acceptors in GaAs. For Mn acceptors on the (110)surface and the subsurfaces immediately underneath, we find that an applied magnetic field modifies significantlythe magnetic anisotropy landscape. However, the acceptor hole wave function is strongly localized around theMn and the LDOS is quite independent of the direction of the Mn magnetic moment. On the other hand, for Mnacceptors placed on deeper layers below the surface, the acceptor hole wave function is more delocalized andthe corresponding LDOS is much more sensitive on the direction of the Mn magnetic moment. However, themagnetic anisotropy energy for these magnetic impurities is large (up to 15 meV), and a magnetic field of 10 Tcan hardly change the landscape and rotate the direction of the Mn magnetic moment away from its easy axis.We predict that substantially larger magnetic fields are required to observe a significant field dependence of thetunneling current for impurities located several layers below the GaAs surface.

Combining density functional theory calculations and microscopic tight-binding models, we investigate theoretically theelectronic and magnetic properties of individual substitutional transition-metal impurities (Mn and Fe) positioned in the vicinity of the (110) surface of GaAs. For the case of the [Mn2+](0) plus acceptor-hole (h) complex, the results of a tight-binding model including explicitly the impurity d electrons are in good agreement with approaches that treat the spin ofthe impurity as an effective classical vector. For the case of Fe, where both the neutral isoelectronic [Fe3+](0) and the ionized [Fe2+](-)states are relevant to address scanning tunneling microscopy (STM) experiments, the inclusion of d orbitals is essential. We find that the in-gap electronic structure of Fe impurities is significantly modified by surface effects. For the neutral acceptor state [Fe2+, h](0), the magnetic-anisotropy dependence on the impurity sublayer resembles the case of [Mn2+, h](0). In contrast, for [Fe3+](0) electronic configuration the magnetic anisotropy behaves differently and it is considerably smaller. For this state we predict that it is possible to manipulate the Fe moment, e. g., by an external magnetic field, with detectable consequences in the local density of states probed by STM.

Using a microscopic finite-cluster tight-binding model, we investigate the trend of the magnetic anisotropy energy as a function of the cluster size for an individual Mn impurity positioned in the vicinity of the (1 1 0) GaAs surface. We present results of calculations for large cluster sizes containing approximately 10⁴ atoms, which have not been investigated so far. Our calculations demonstrate that the anisotropy energy of a Mn dopant in bulk GaAs, found to be non-zero in previous tight-binding calculations, is purely a finite size effect that vanishes with inverse cluster size. In contrast to this, we find that the splitting of the three in-gap Mn acceptor energy levels converges to a finite value in the limit of the infinite cluster size. For a Mn in bulk GaAs this feature is related to the nature of the mean-field treatment of the coupling between the impurity and its nearest neighbor atoms. We also calculate the trend of the anisotropy energy in the sublayers as the Mn dopant is moved away from the surface towards the center of the cluster. Here the use of large cluster sizes allows us to position the impurity in deeper sublayers below the surface, compared to previous calculations. In particular, we show that the anisotropy energy increases up to the fifth sublayer and then decreases as the impurity is moved further away from the surface, approaching its bulk value. The present study provides important insights for experimental control and manipulation of the electronic and magnetic properties of individual Mn dopants at the semiconductor surface by means of advanced scanning tunneling microscopy techniques.

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 VAs--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 substitutionalMn impurities in GaAs. Our approach is based on the mixed quantum-classical schemefor spin dynamics, with coupled equations of motions for the quantum subsystem, representing thehost, and the localized spins of magnetic dopants, which are treated classically. In the case ofa single Mn impurity, we calculate explicitly the time evolution of the Mn spin and the spins ofnearest-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 scalesof the system, namely the spin-orbit interaction strength and the value of the p-d exchange couplingbetween the impurity spin and the host carriers. For a pair of Mn impurities, we find signaturesof 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 theexchange coupling and spin-orbit interaction strength, as well as on the initial spin-configuration andseparation between the impurities. Our results provide insight into the dynamic interaction betweenlocalized magnetic impurities in a nano-scaled magnetic-semiconductor sample, in the extremelydilute(solotronics) regime.

We present results of theoretical studies of transition metal dopants in GaAs, based on microscopic tight-binding model and ab-initio calculations. We focus in particular on how the vicinity of surface affects the properties of the hole-acceptor state, its magnetic anisotropy and its magnetic coupling to the magnetic dopant.  In agreement with STM experiments, Mn substitutional dopants on the (110) GaAs surface give rise to a deep acceptor state, whose wavefunction is localized around the Mn center. We discuss a refinement of the theory that introduces explicitly the d-levels for the TM dopant. The explicit inclusion of d-levels is particularly important for addressing recent STM experiments on substitutional Fe in GaAs. In the second part of the paper we discuss an analogous investigation of single dopants in Bi₂Se₃ three-dimensional topological insulators, focusing in particular on how substitutional impurities positioned on the surface affect the electronic structure in the gap.  We present explicit results for Bi_Se antisite defects and compare with STM experiments.

We investigate the properties of a single substitutional Mn impurity and its associated acceptor state on the (111) surface of Bi$_2$Se$_3$ topological insulator. Combining \textit{ab initio} calculations with microscopic tight-binding modeling, we identify the effects of inversion-symmetry and time-reversal-symmetry breaking on the electronic states in the vicinity of the Dirac point. In agreement with experiments, we find evidence that the Mn ion is in ${+2}$ valence state and introduces an acceptor in the bulk band gap. The Mn-acceptor has predominantly $p$--character, and is localized mainly around the Mn impurity and its nearest-neighbor Se atoms. Its electronic structure and spin-polarization are determined by the hybridization between the Mn $d$--levels and the $p$--levels of surrounding Se atoms, which is strongly affected by electronic correlations at the Mn site. The opening of the gap at the Dirac point depends crucially on the quasi-resonant coupling and the strong real-space overlap between the spin-chiral surface states and the mid-gap spin-polarized Mn-acceptor states.