The goal of this master thesis is to investigate the eect of electron-electron interaction on electronic properties of graphene that can be measured experimentally. A tight-binding model, which includes up to next-nearest-neighbor hopping, with parameters tted to density functional theory calculations, has been used to describe the electronic structure of graphene. The electron-electron interaction is described by the Hubbard model using a mean- eld approximation. Based on the analysis of dierent tight-binding models available in the literature, we conclude that a next-nearest-neighbor tight-binding model is in better agreement with density functional theory calculations, especially for the linear dispersion around the Dirac point. The Fermi velocity in this case is very close to the experimental value, which was measured by using a variety of techniques. Interaction-induced modi cations of the linear dispersion around the Dirac point have been obtained. Unlike the non-local Hartree-Fock calculations, which take into account the long-range electron-electron interaction and yield logarithmic corrections, in agreement with experiment, we found only linear modi cations of the Fermi velocity. The reasons why one cannot obtain logarithmic corrections using the mean- eld Hubbard model have been discussed in detail. The remaining part of the thesis is focused on calculations of the local density of states around a single substitutional impurity in graphene. This quantity can be directly compared to the results of the scanning tunneling microscopy in doped graphene. We compare explicitly non-interacting and interacting cases. In the latter case, we performed self-consistent calculations, and found that electron-electron interaction has a signi cant eect on the local density of states. Furthermore, the band gap at high-symmetry points of the Brillouin zone of a supercell, triggered by the impurity, is modi ed by interactions. We use a perturbative model to explain this eect and quantitative agreement with numerical results. In conclusion, it is expected that the long-range electron-electron nteraction is extremely strong and important in graphene. However, as this thesis has shown, interactions at the level of the Hubbard model and mean- eld approximation also introduce corrections to the electronic properties of graphene.
We study theoretically the effects of short-range electron-electron interactions on the electronic structure of graphene, in the presence of substitutional impurities. Our computational approach is based on the π orbital tight-binding model for graphene, with the electron-electron interactions treated self-consistently at the level of the mean-field Hubbard model. The finite impurity concentration is modeled using the supercell approach. We compare explicitly noninteracting and interacting cases with varying interaction strength and impurity potential strength. We focus in particular on the interaction-induced modifications in the local density of states around the impurity, which is a quantity that can be directly probed by scanning tunneling spectroscopy of doped graphene. We find that the resonant character of the impurity states near the Fermi level is enhanced by the interactions. Furthermore, the size of the energy gap, which opens up at high-symmetry points of the Brillouin zone of the supercell upon doping, is significantly affected by the interactions. The details of this effect depend subtly on the supercell geometry. We use a perturbative model to explain these features and find quantitative agreement with numerical results.
Quantum conductance is a phenomenon associated with nanowires / quantum point contacts where the current through a wire is quantized. Experiments have shown that this phenomenon can be manifested at room temperature using macroscopic wires. This project is aimed to recreate these experiments with emphasis on simplicity. By briefly contacting gold wires and measuring the current using an oscilloscope, current quantization can occasionally be seen as the contact breaks.
The impact of bismuth incorporation into the epitaxial layer of a (Ga,Mn)As dilute ferromagnetic semiconductor on its magnetic and electromagnetic properties is studied in very thin layers of quaternary (Ga,Mn)(Bi,As) compound grown on a GaAs substrate under a compressive misfit strain. An addition of a small atomic fraction of 1% Bi atoms, substituting As atoms in the layer, predominantly enhances the spin-orbit coupling strength in its valence band. The presence of bismuth results in a small decrease in the ferromagnetic Curie temperature and a distinct increase in the coercive fields. On the other hand, the Bi incorporation into the layer strongly enhances the magnitude of negative magnetoresistance without affecting the hole concentration in the layer. The negative magnetoresistance is interpreted in terms of the suppression of weak localization in a magnetic field. Application of the weak-localization theory for two-dimensional ferromagnets by Dugaev et al. to the experimental magnetoresistance results indicates that the decrease in spin-orbit scattering length accounts for the enhanced magnetoresistance in (Ga,Mn)(Bi,As).
Pulsed current-induced magnetization reversal is investigated in the layer of (Ga,Mn)(Bi,As) dilute ferromagnetic semiconductor (DFS) epitaxially grown under tensile misfit strain causing perpendicular magnetic anisotropy in the layer. The magnetization reversal, recorded through measurements of the anomalous Hall effect, appearing under assistance of a static magnetic field parallel to the current, is interpreted in terms of the spin-orbit torque mechanism. Our results demonstrate that an addition of a small fraction of heavy Bi atoms, substituting As atoms in the prototype DFS (Ga,Mn)As and increasing the strength of spin-orbit coupling in the DFS valence band, significantly enhances the efficiency of current-induced magnetization reversal thus reducing considerably the threshold current density necessary for the reversal. Our findings are of technological importance for applications to spin-orbit torque-driven nonvolatile memory and logic elements. Published under an exclusive license by AIP Publishing.
We discuss the eigenvalue problem for a perfectly conducting bianisotropic cavity. We formulate the corresponding mathematical problem and we give a characterization of the eigenelements (non-zero eigenfrequencies and modes) via a perturbation argument involving the eigenelements of the hollow cavity.
Micromagnetic calculations are compared with faster model calculations of interacting nanoscopic magnetic islands representing an element of a shakti spin ice lattice. Several pathways for transitions between equivalent ground states are studied. The model calculations describe the interaction between the islands either with the point dipole approximation, or with a dumbbell approximation where the distance between the two poles is optimized to match the micromagnetic results. The closest agreement in the energy of both local minima as well as transition state configurations where one macrospin has rotated by 90° is obtained with a dumbbell model where the distance between the poles is ca. 20 % smaller than the island length.
The research of this Ph. D. thesis is in the field of Quantum Computation and Quantum Information. A key problem in this field is the fragile nature of quantum states. This be comes increasingly acute when the number of quantum bits (qubits) grows in order to perform large quantum computations. It has been proposed that geometric (Berry) phases may be a useful tool to overcome this problem, because of the inherent robustness of such phases to random noise. In the thesis we investigate geometric phases and quantum holonomies (matrix-valued geometric phases) in many-body quantum systems, and elucidate the relationship between these phases and the quantum correlations present in the systems. An overall goal of the project is to assess the feasibility of using geometric phases and quantum holonomies to build robust quantum gates, and investigate their behavior when the size of a quantum system grows, thereby gaining insights into large-scale quantum computation. In a first project we study the Uhlmann holonomy of quantum states for hydrogen-like atoms. We try to get into a physical interpretation of this geometric concept by analyzing its relation with quantum correlations in the system, as well as by comparing it with different types of geometric phases such as the standard pure state geometric phase, Wilczek-Zee holonomy, Lévay geometric phase and mixed-state geometric phases. In a second project we establish a unifying connection between the geometric phase and the geometric measure of entanglement in a generic many-body system, which provides a universal approach to the study of quantum critical phenomena. This approach can be tested experimentally in an interferometry setup, where the geometric measure of entanglement yields the visibility of the interference fringes, whereas the geometric phase describes the phase shifts. In a third project we propose a scheme to implement universal non-adiabatic holonomic quantum gates, which can be realized in novel nano-engineered systems such as quantum dots, molecular magnets, optical lattices and topological insulators. In a fourth project we propose an experimentally feasible approach based on “orange slice” shaped paths to realize non- Abelian geometric phases, which can be used particularly for geometric manipulation of qubits. Finally, we provide a physical setting for realizing non-Abelian off-diagonal geometric phases. The proposed setting can be implemented in a cyclic chain of four qubits with controllable nearest-neighbor interactions. Our proposal seems to be within reach in various nano-engineered systems and therefore opens up for first experimental test of the non-Abelian off-diagonal geometric phase.
Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are respectively the real and imaginary parts of a complex-valued geometric entanglement, which can be investigated in typical quantum interferometry experiments. We argue that the singular behavior of the complex-valued geometric entanglement at a quantum critical point is a characteristic of any quantum phase transition, by showing that the underlying mechanism is the occurrence of level crossings associated with the underlying Hamiltonian.
Geometric manipulation of a quantum system offers a method for fast, universal, and robust quantum information processing. Here, we propose a scheme for universal all-geometric quantum computation using non-adiabatic quantum holonomies. We propose three different realizations of the scheme based on an unconventional use of quantum dot and single-molecule magnet devices,which offer promising scalability and robust efficiency.
Theoretical calculations of optimal control paths minimizing the energy cost of the magnetization reversal in 1D magnetic nanowires are presented.The energy-efficient reversal mechanism is studied as a function of the nanowire length and Gilbert damping parameter. For short nanowires, theoptimal reversal mechanism corresponds to a uniform rotation of magnetization. If the length of the wire exceeds a certain critical length definedby the material parameters, switching time and damping, a standing spin wave emerges during magnetization switching. Comparison between thecalculated optimal control paths and minimum energy paths reveals that realization of high energy efficiency of switching does not necessarilytranslate to the minimization of the energy barrier between the target magnetic states.
Energy-efficient switching of nanoscale magnets requires application of a time-varying magnetic field characterized by microwave frequency. At finite temperatures, even weak thermal fluctuations induce perturbations in the magnetization that can accumulate in time, disrupt the phase locking between the magnetization and the applied field, and eventually compromise magnetization switching. It is demonstrated here that the magnetization reversal is mostly disturbed by unstable perturbations arising in a certain domain of the configuration space of a nanomagnet. The instabilities can be suppressed and the probability of magnetization switching enhanced by applying an additional stimulus such as a weak longitudinal magnetic field that ensures bounded dynamics of the perturbations. Application of the stabilizing longitudinal field to a uniaxial nanomagnet makes it possible to reach a desired probability of magnetization switching even at elevated temperatures. The principle of suppressing instabilities provides a general approach to enhancing thermal stability of magnetization dynamics.
A solution to energy-efficient magnetization switching in a nanoparticle with biaxial anisotropy is presented. Optimal control paths minimizing the energy cost of magnetization reversal are calculated numerically as functions of the switching time and materials properties, and used to derive energy-efficient switching pulses of external magnetic field. Hard-axis anisotropy reduces the minimum energy cost of magnetization switching due to the internal torque in the desired switching direction. Analytical estimates quantifying this effect are obtained based on the perturbation theory. The optimal switching time providing a tradeoff between fast switching and energy efficiency is obtained. The energy cost of switching and the energy barrier between the stable states can be controlled independently in a biaxial nanomagnet. This provides a solution to the dilemma between energy-efficient writability and good thermal stability of magnetic memory elements.
Recent experimental data demonstrate emerging magnetic order in platinum atomically thin nanowires. Furthermore, an unusual form of magnetic anisotropy-colossal magnetic anisotropy (CMA)-was earlier predicted to exist in atomically thin platinum nanowires. Using spin dynamics simulations based on first-principles calculations, we here explore the spin dynamics of atomically thin platinum wires to reveal the spin relaxation signature of colossal magnetic anisotropy, comparing it with other types of anisotropy such as uniaxial magnetic anisotropy (UMA). We find that the CMA alters the spin relaxation process distinctly and, most importantly, causes a large speed-up of the magnetic relaxation compared to uniaxial magnetic anisotropy. The magnetic behavior of the nanowire exhibiting CMA should be possible to identify experimentally at the nanosecond time scale for temperatures below 5 K. This time-scale is accessible in e.g., soft x-ray free electron laser experiments.
The skyrmion racetrack is a promising concept for future information technology. There, binary bits are carried by nanoscale spin swirls-skyrmions-driven along magnetic strips. Stability of the skyrmions is a critical issue for realising this technology. Here we demonstrate that the racetrack skyrmion lifetime can be calculated from first principles as a function of temperature, magnetic field and track width. Our method combines harmonic transition state theory extended to include Goldstone modes, with an atomistic spin Hamiltonian parametrized from density functional theory calculations. We demonstrate that two annihilation mechanisms contribute to the skyrmion stability: At low external magnetic field, escape through the track boundary prevails, but a crossover field exists, above which the collapse in the interior becomes dominant. Considering a Pd/Fe bilayer on an Ir(111) substrate as a well-established model system, the calculated skyrmion lifetime is found to be consistent with reported experimental measurements. Our simulations also show that the Arrhenius pre-exponential factor of escape depends only weakly on the external magnetic field, whereas the pre-exponential factor for collapse is strongly field dependent. Our results open the door for predictive simulations, free from empirical parameters, to aid the design of skyrmion-based information technology.
The formation of layer-heterogeneous periodic magnetic states in metallic systems is explained in terms of the dependence of the energy of itinerant electrons on the magnetic ordering of localized spins. The interaction of the local magnetic moments with conduction electrons with a certain spin projection is described by a set of spin-dependent delta-function potentials. A matrix method is developed permitting one to calculate the energy spectrum and the density of states of itinerant electrons in the presence of a layered magnetic heterogeneity. This method is used to explain oscillations of the interlayer exchange interaction in metallic magnetic superlattices and the stabilization of spin-density wave structures in transition metals and alloys.
A rate theory for thermally activated transitions in spin systems is presented. It is based on a transition-state approximation derived from Landau-Lifshitz equations of motion and quadratic expansion of the energy surface at minima and first order saddle points. While the flux out of the initial state vanishes at first order saddle points, the integrated flux over the hyperplanar transition state is nonzero and gives a rate estimate in good agreement with direct dynamical simulations of test systems over a range in damping constant. The preexponential factor obtained for transitions in model systems representing nanoclusters with 3 to 139 transition metal adatoms is on the order of 1011 to 1013s -1, similar to that of atomic rearrangements.
Calculations of stable and metastable magnetic states as well as minimum energy paths for transitions between states are carried out using a noncollinear extension of the multiple-impurity Alexander-Anderson model and a magnetic force theorem which is derived and used to evaluate the total energy gradient with respect to orientation of magnetic moments-an important tool for efficient navigation on the energy surface. By using this force theorem, the search for stable and metastable magnetic states as well as minimum energy paths revealing the mechanism and activation energy of transitions can be carried out efficiently. For Fe monolayer on W(110) surface, the model gives magnetic moment as well as exchange coupling between nearest and next-nearest neighbors that are in good agreement with previous density functional theory calculations. When applied to nanoscale Fe islands on this surface, the magnetic moment is predicted to be 10% larger for atoms at the island rim, explaining in part an experimentally observed trend in the energy barrier for magnetization reversal in small islands. Surprisingly, the magnetic moment of the atoms does not change much along the minimum energy path for the transitions, which for islands containing more than 15 atom rows along either [001] or [1 (1) over bar0] directions involves the formation of a thin, temporary domain wall. A noncollinear magnetic state is identified in a 7 x 7 atomic row Fe island where the magnetic moments are arranged in an antivortex configuration with the central ones pointing out of the (110) plane. This illustrates how the model can describe complicated exchange interactions even though it contains only a few parameters. The minimum energy path between this antivortex state and the collinear ground state is also calculated and the thermal stability of the antivortex state estimated.
The effect of hydrogen adsorption on the magnetic properties of an Fe 3 cluster immersed in a Cu(111) surface has been calculated using density functional theory and the results used to parametrize an Alexander-Anderson model which takes into account the interaction of d electrons with itinerant electrons. A number of adatom configurations containing one to seven H atoms were analyzed. The sequential addition of hydrogen atoms is found to monotonically reduce the total magnetic moment of the cluster with the effect being strongest when the H atoms sit at low-coordinated sites. Decomposition of the charge density indicates a transfer of 0.3 electrons to each of the H atoms from both the Fe atoms and from the copper substrate, irrespective of adsorption site and coverage. The magnetic moment of only the nearest neighbor Fe atoms is reduced, mainly due to increased population of minority spin d states. This can be modeled by increased indirect coupling of d states via the conduction s band in the Alexander-Anderson model.
A method for finding minimum energy paths of transitions in magnetic systems is presented. The path is optimized with respect to orientation of the magnetic vectors while their magnitudes are fixed or obtained from separate calculations. The curvature of the configuration space is taken into account by: (1) using geodesics to evaluate distances and displacements of the system during the optimization, and (2) projecting the path tangent and the magnetic force on the tangent space of the manifold defined by all possible orientations of the magnetic vectors. The method, named geodesic nudged elastic band (GNEB), and its implementation are illustrated with calculations of complex transitions involving annihilation and creation of skyrmion and antivortex states. The lifetime of the latter was determined within harmonic transition state theory using a noncollinear extension of the Alexander-Anderson model.
The stability of magnetic states and the mechanism for magnetic transitions can be analyzed in terms of the shape of the energy surface, which gives the energy as a function of the angles determining the orientation of the magnetic moments. Minima on the energy surface correspond to stable or metastable magnetic states and can represent parallel, antiparallel or, more generally, non-collinear arrangements. A rate theory has been developed for systems with arbitrary number, N, of magnetic moments, to estimate the thermal stability of magnetic states and the mechanism for magnetic transitions based on a transition state theory approach. The minimum energy path on the 2N-dimensional energy surface is determined to identify the transition mechanism and estimate the activation energy barrier. A pre-exponential factor in the rate expression is obtained from the Landau-Lifshitz-Gilbert equation for spin dynamics. The velocity is zero at saddle points so it is particularly important in this context to realize that the transition state is a dividing surface with 2N -1 degrees of freedom, not just a saddle point. An application of this rate theory to nanoscale Fe islands on W(110) has revealed how the transition mechanism and rate depend on island shape and size. Qualitative agreement is obtained with experimental measurements both for the activation energy and the pre-exponential factor. In particular, a distinct maximum is observed in the pre-exponential factor for islands where two possible transition mechanisms are competing: Uniform rotation and the formation of a temporary domain wall. The entropy of the transition state is enhanced for those islands making the pre-exponential factor more than an order of magnitude larger than for islands were only the uniform rotation is viable.
Theoretical calculations of thermal spin transitions in nanoscale clusters on a surface are presented. The mechanisms for magnetization reversal are identified and the activation energy and pre-exponential factor for the rate are evaluated using a recently developed harmonic transition state theory and a Heisenberg-type Hamiltonian. A maximum is found in the pre-exponential factor as a function of cluster size corresponding to a crossover from a uniform rotation mechanism to temporary domain wall formation. As the islands grow, the energy barrier increases up to a limit where the domain wall is fully established. For larger islands, the minimum energy path becomes flat resulting in a significant recrossing correction to the transition state theory estimate of the rate. The parameters of the Hamiltonian are chosen to mimic Fe clusters on a W(110) surface, a system that has previously been studied extensively in the laboratory and the calculated results are found to be in close agreement with the reported measurements.
The two-dimensional Heisenberg exchange model with out-of-plane anisotropy and a Dzyaloshinskii-Moriya interaction is employed to investigate the lifetime and stability of antiferromagnetic (AFM) skyrmions as a function of temperature and external magnetic field. An isolated AFM skyrmion is metastable at zero temperature in a certain parameter range set by two boundaries separating the skyrmion state from the uniform AFM phase and a stripe domain phase. The distribution of the energy barriers for the AFM skyrmion decay into the uniform AFM state complements the zero-temperature stability diagram and demonstrates that the skyrmion stability region is significantly narrowed at finite temperatures. We show that the AFM skyrmion stability can be enhanced by an application of magnetic field, whose strength is comparable to the spin-flop field. This stabilization of AFM skyrmions in external magnetic fields is in sharp contrast to the behavior of their ferromagnetic counterparts. Furthermore, we demonstrate that the AFM skyrmions are stable on timescales of milliseconds below 50 K for realistic material parameters, making it feasible to observe them in modern experiments.
Using first-principles calculations, we report structural and electronic properties of CO, NO2 and NO molecular adsorption on beta-In2Se3 in comparison to a previous study on a-phase. Analysis and comparison of adsorption energies and extent of charge transfer indicates beta-In2Se3 to be selective in detecting gas molecules. We found NO molecules acting as charge donor whereas CO and NO2 molecules as charge acceptors, respectively, experiencing physisorption in all cases. Owing to enhanced adsorption, faster desorption and improved selectivity of the gas molecules discussed in detail, we conclude beta-In2Se3 to be a superior gas sensing material ideal for chemoresistive-type gas sensing applications.
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.
We discuss the eigenvalue problem for a perfectly conducting hollow cavity under a strict functional analytic point of view. We make use of a variant of the classical spectral theorem for compact selfadjoint operators and we pay extra attention on the null space of the Maxwell operator. We also discuss the corresponding inhomogeneous problem, where currents are present, even when they may depend on the fields.
This paper is concerned with the estimation of the volume fraction and the anisotropy of a two-component composite from measured bulk properties. An algorithm that takes into account that measurements have errors is developed. This algorithm is used to study data from experimental measurements for a nanocomposite with an unknown nanostructure. The dependence on the nanostructure is quantified in terms of a measure in the representation formula introduced by D Bergman. We use composites with known nanostructures to illustrate the dependence on the underlying measure and show how errors in the measurements affect the estimates of the structural parameters.
Using non-equilibrium Green's function, we study the spin-dependent electron transport properties in a zigzag silicene nanoribbon. To produce and control spin polarization, it is assumed that two ferromagnetic strips are deposited on the both edges of the silicene nanoribbon and an electric field is perpendicularly applied to the nanoribbon plane. The spin polarization is studied for both parallel and anti-parallel configurations of exchange magnetic fields induced by the ferromagnetic strips. We find that complete spin polarization can take place in the presence of perpendicular electric field for anti-parallel configuration and the nanoribbon can work as a perfect spin filter. The spin direction of transmitted electrons can be easily changed from up to down and vice versa by reversing the electric field direction. For parallel configuration, perfect spin filtering can occur even in the absence of electric field. In this case, the spin direction can be changed by changing the electron energy. Finally, we investigate the effects of nonmagnetic Anderson disorder on spin dependent conductance and find that the perfect spin filtering properties of nanoribbon are destroyed by strong disorder, but the nanoribbon retains these properties in the presence of weak disorder.
We study time-dependent electronic and spin transport through an electronic level connected to two leads and coupled with a single-molecule magnet via exchange interaction. The molecular spin is treated as a classical variable and precesses around an external magnetic field. We derive expressions for charge and spin currents by means of the Keldysh nonequilibrium Green's functions technique in linear order with respect to the time-dependent magnetic field created by this precession. The coupling between the electronic spins and the magnetization dynamics of the molecule creates inelastic tunneling processes which contribute to the spin currents. The inelastic spin currents, in turn, generate a spin-transfer torque acting on the molecular spin. This back-action includes a contribution to the Gilbert damping and a modification of the precession frequency. The Gilbert damping coefficient can be controlled by the bias and gate voltages or via the external magnetic field and has a nonmonotonic dependence on the tunneling rates.
A coupled atomistic spin and lattice dynamics approach is developed which merges the dynamics of these two degrees of freedom into a single set of coupled equations of motion. The underlying microscopic model comprises local exchange interactions between the electron spin and magnetic moment and the local couplings between the electronic charge and lattice displacements. An effective action for the spin and lattice variables is constructed in which the interactions among the spin and lattice components are determined by the underlying electronic structure. In this way, expressions are obtained for the electronically mediated couplings between the spin and lattice degrees of freedom, besides the well known interatomic force constants and spin-spin interactions. These former susceptibilities provide an atomistic ab initio description for the coupled spin and lattice dynamics. It is important to notice that this theory is strictly bilinear in the spin and lattice variables and provides a minimal model for the coupled dynamics of these subsystems and that the two subsystems are treated on the same footing. Questions concerning time-reversal and inversion symmetry are rigorously addressed and it is shown how these aspects are absorbed in the tensor structure of the interaction fields. By means of these results regarding the spin-lattice coupling, simple explanations of ionic dimerization in double-antiferromagnetic materials, as well as charge density waves induced by a nonuniform spin structure, are given. In the final parts, coupled equations of motion for the combined spin and lattice dynamics are constructed, which subsequently can be reduced to a form which is analogous to the Landau-Lifshitz-Gilbert equations for spin dynamics and a damped driven mechanical oscillator for the ionic motion. It is important to notice, however, that these equations comprise contributions that couple these descriptions into one unified formulation. Finally, Kubo-like expressions for the discussed exchanges in terms of integrals over the electronic structure and, moreover, analogous expressions for the damping within and between the subsystems are provided. The proposed formalism and types of couplings enable a step forward in the microscopic first principles modeling of coupled spin and lattice quantities in a consistent format.
Here we report on detailed studies of the magnetic properties of the wurtzite (Ga,Mn)As cylindrical shells. Ga0.94Mn0.06As shells have been grown by molecular beam epitaxy at low temperature as a part of multishell cylinders overgrown on wurtzite (Ga,In)As nanowires cores, synthesized on GaAs (111)B substrates. Our studies clearly indicate the presence of a low temperature ferromagnetic coupling, which despite a reasonably high Mn contents of 6% is limited only to below 30 K. A set of dedicated measurements shows that despite a high structural quality of the material the magnetic order has a granular form, which gives rise to the dynamical slowdown characteristic to blocked superparamagnets. The lack of the long range order has been assigned to a very low hole density, caused primarily by numerous compensation donors, arsenic antisites, formed in the material due to a specific geometry of the growth of the shells on the nanowire template. The associated electrostatic disorder has formed a patchwork of spontaneously magnetized (macrospin) and nonmagnetic (paramagnetic) volumes in the material. Using high field results it has been evaluated that the total volume taken by the macrospins constitute about 2/3 of the volume of the (Ga,Mn)As whereas in the remaining 1/3 only paramagnetic Mn ions reside. By establishing the number of the uncoupled ions the two contributions were separated. The Arrott plot method applied to the superparamagnetic part yielded the first experimental assessment of the magnitude of the spin-spin coupling temperature within the macrospins in (Ga,Mn)As, TC = 28 K. In a broader view our results constitute an important contribution to the still ongoing dispute on the true and the dominant form(s) of the magnetism in this model dilute ferromagnetic semiconductor.
We study thermally induced spin resolved current in a zigzag silicene nanoribbon when the left and right leads are respectively affected by ferromagnetic (FM) and anti-ferromagnetic (AFM) exchange fields (FM/normal/AFM junction). We show that pure spin current is generated due to the leads temperature difference and the junction can work as a spin Seebeck diode. The pure spin current can be easily controlled by a perpendicular electric field and the junction, in this case, can work as a spin current switch. In addition, we study the effect of a single vacancy and show that the vacancy can slightly destroy the pure spin current property which leads to induce a weak spin polarized current. In the presence of both vacancy and electric field, current with high and tunable spin polarization can be achieved.
We provide a theoretical background for electric-field-assisted thermally activated writing and deleting of magnetic skyrmions in ultrathin transition-metal films. We apply an atomistic spin model, which includes the exchange interaction, the Dzyaloshinskii-Moriya interaction, and the magnetocrystalline anisotropy energy. The strengths of the magnetic interactions are taken from density functional theory (DFT) calculations for a Pd/Fe bilayer on the Ir(111) surface. We systematically vary all magnetic interactions up to ±10% treating the magnetoelectric effect in linear response. The critical magnetic fields marking the onset of the skyrmion phase and the field-polarized phase shift considerably upon varying the interaction constants due to the electric field. Based on harmonic transition state theory, we calculate the transition rates for skyrmion nucleation and annihilation, which are in good agreement with experimental values for Pd/Fe/Ir(111). The field-dependent variation of energy barriers and preexponential factors leads to large changes of the transition rates, which are accompanied by changes in skyrmion radii. Finally, we simulate the electric-field-dependent writing and deleting of magnetic skyrmions in Pd/Fe/Ir(111) based on the master equation and transition rates obtained using the magnetic interactions calculated via DFT for electric fields of E=±0.5 V/Å. The magnetic-field-dependent skyrmion probability follows a Fermi-Dirac distribution function of the free energy difference of the skyrmion state and the ferromagnetic (FM) state. The probability function for the opposite electric field directions is in striking agreement with experimental results [Romming, Science 341, 636 (2013)0036-807510.1126/science.1240573].
Locally induced, magnetic order on the surface of a topological insulator nanowire could enable room-temperature topological quantum devices. Here we report on the realization of selective magnetic control over topological surface states on a single facet of a rectangular Bi2Te3 nanowire via a magnetic insulating Fe3O4 substrate. Low-temperature magnetotransport studies provide evidence for local time-reversal symmetry breaking and for enhanced gapping of the interfacial 1D energy spectrum by perpendicular magnetic-field components, leaving the remaining nanowire facets unaffected. Our results open up great opportunities for development of dissipation-less electronics and spintronics.
The impact of hydrostatic pressure on magnetic anisotropy energies in (Ga, Mn) As thin films with in-plane and out-of-plane magnetic easy axes predefined by epitaxial strain was investigated. In both types of sample we observed a clear increase in both in-plane and out-of-plane anisotropy parameters with pressure. The out-of-plane anisotropy constant is well reproduced by the mean-field p-d Zener model; however, the changes in uniaxial anisotropy are much larger than expected in the Mn-Mn dimer scenario.
Electron transport in mesoscopic systems, such as quantum point contacts and Aharonov-Bohm rings are investigated numerically in a tight-binding language with a recursive Green's function algorithm. The simulation reveals among other things the quantized nature of the conductance in point contacts, the Hall conductance, the decreasing sensitivity to scattering impurities in a magnetic field, and the periodic magnetoconductance in an Aharonov-Bohm ring. Furthermore, the probability density distributions for some different setups are mapped, making the transmission coefficients, the quantum Hall effect, and the cyclotron radius visible, where the latter indicates the correspondance between quantum mechanics and classical physics on the mesoscopic scale.
The work in this thesis is basically divided into two related but separate investigations.
The first part treats simple chemical reactions of adsorbate molecules on metallic surfaces, induced by means of a scanning tunneling probe (STM). The investigation serves as a parameter free extension to existing theories. The theoretical framework is based on a combination of density functional theory (DFT) and non-equilibrium Green's functions (NEGF). Tunneling electrons that pass the adsorbate molecule are assumed to heat up the molecule, and excite vibrations that directly correspond to the reaction coordinate. The theory is demonstrated for an OD molecule adsorbed on a bridge site on a Cu(110) surface, and critically compared to the corresponding experimental results. Both reaction rates and pathways are deduced, opening up the understanding of energy transfer between different configurational geometries, and suggests a deeper insight, and ultimately a higher control of the behaviour of adsorbate molecules on surfaces.
The second part describes a method to calculate STM images in the low bias regime in order to overcome the limitations of localized orbital DFT in the weak coupling limit, i.e., for large vacuum gaps between a tip and the adsorbate molecule. The theory is based on Bardeen's approach to tunneling, where the orbitals computed by DFT are used together with the single-particle Green's function formalism, to accurately describe the orbitals far away from the surface/tip. In particular, the theory successfully reproduces the experimentally well-observed characteristic dip in the tunneling current for a carbon monoxide (CO) molecule adsorbed on a Cu(111) surface. Constant height/current STM images provide direct comparisons to experiments, and from the developed method further insights into elastic tunneling are gained.
The main body of this thesis describes how to calculate scanning tunneling microscopy (STM) images from first-principles methods. The theory is based on localized orbital density functional theory (DFT), whose limitations for large-vacuum STM models are resolved by propagating localized-basis wave functions close to the surface into the vacuum region in real space. A finite difference approximation is used to define the vacuum Hamiltonian, from which accurate vacuum wave functions are calculated using equations based on standard single-particle Green’s function techniques, and ultimately used to compute the conductance. By averaging over the lateral reciprocal space, the theory is compared to a series of high-quality experiments in the low- bias limit, concerning copper surfaces with adsorbed carbon monoxide (CO) species and adsorbate atoms, scanned by pure and CO-functionalized copper tips. The theory compares well to the experiments, and allows for further insights into the elastic tunneling regime.
A second significant project in this thesis concerns first-principles calculations of a simple chemical reaction of a hydroxyl (oxygen-deuterium) monomer adsorbed on a copper surface. The reaction mechanism is provided by tunneling electrons that, via a finite electron-vibration coupling, trigger the deuterium atom to flip between two nearly identical configurational states along a frustrated rotational motion. The theory suggests that the reaction primarily occurs via nuclear tunneling for the deuterium atom through the estimated reaction barrier, and that over-barrier ladder climbing processes are unlikely.
We present a method used to intuitively interpret the scanning tunneling microscopy (STM) contrast by investigating individual wave functions originating from the substrate and tip side. We use localized basis orbital density functional theory, and propagate the wave functions into the vacuum region at a real-space grid, including averaging over the lateral reciprocal space. Optimization by means of the method of Lagrange multipliers is implemented to perform a unitary transformation of the wave functions in the middle of the vacuum region. The method enables (i) reduction of the number of contributing tip-substrate wave function combinations used in the corresponding transmission matrix, and (ii) to bundle up wave functions with similar symmetry in the lateral plane, so that (iii) an intuitive understanding of the STM contrast can be achieved. The theory is applied to a CO dimer adsorbed on a Cu(1 1 1) surface scanned by a single-atom Cu tip, whose STM image is discussed in detail by the outlined method.
To describe vibrationally mediated configuration changes of adsorbates on surfaces we have developed a theory to calculate both reaction rates and pathways. The method uses the T-matrix to describe excitations of vibrational states by the electrons of the substrate, adsorbate, and tunneling electrons from a scanning tunneling probe. In addition to reaction rates, the theory also provides the reaction pathways by going beyond the harmonic approximation and using the full potential energy surface of the adsorbate which contains local minima corresponding to the adsorbates different configurations. To describe the theory, we reproduce the experimental results in [T. Kumagai et al., Phys. Rev. B 79, 035423 (2009)], where the hydrogen/deuterium atom of an adsorbed hydroxyl (OH/OD) exhibits back and forth flipping between two equivalent configurations on a Cu(110) surface at T = 6 K. We estimate the potential energy surface and the reaction barrier, similar to 160 meV, from DFT calculations. The calculated flipping processes arise from (i) at low bias, tunneling of the hydrogen through the barrier, (ii) intermediate bias, tunneling electrons excite the vibrations increasing the reaction rate although over the barrier processes are rare, and (iii) higher bias, overtone excitations increase the reaction rate further.
We consider a system of few electrons trapped in a two-dimensional circularquantum dot with harmonic confinement and in the presence of ahomogeneous magnetic field, with focus on the role of e-e interaction. Byperforming the exact diagonalization of the Hamiltonian in second quantization,the low-lying energy levels for spin polarized system are obtained. The singlet-triplet oscillation in the ground state of the two-electron system showing up inthe result is explained due to the role of Coulomb interaction. The splitting ofthe lowest Landau level is another effect of the e-e interaction, which is alsoobserved in the results.
We show that stable skyrmions with diameters of a few nanometers can emerge in atomic Pd/Fe bilayers on the Rh(111) surface. Based on density functional theory we calculate the exchange and the Dzyaloshinskii-Moriya interaction as well as the magnetocrystalline anisotropy energy. The latter two terms are driven by spin-orbit coupling and significantly reduced compared to Pd/Fe bilayers on Ir(111) as expected since Rh and Ir are isoelectronic 4d and 5d transition metals. However, there is still a spin spiral ground state at zero magnetic field. Atomistic spin dynamics simulations show that a skyrmion phase occurs at small magnetic fields of ∼1 T. Skyrmion diameters amount to 2-8 nm and skyrmion lifetimes are up to 1 h at temperatures of 25-45 K.
van der Waals (vdW) crystals with unparalleled electromechanical properties have been explored for transformative devices. Currently, the availability of 2D vdW crystals is rather limited in nature as they are only obtained from certain mother crystals with intrinsically possessed layered crystallinity and anisotropic molecular bonding. Recent efforts to transform conventionally non-vdW three-dimensional (3D) crystals into ultrathin 2D-like structures have seen rapid developments to explore device building blocks of unique form factors. Herein, we explore a "peel-and-stick" approach, where a nonlayered 3D platinum sulfide (PtS) crystal, traditionally known as a cooperate mineral material, is transformed into a freestanding 2D-like membrane for electromechanical applications. The ultrathin (???10 nm) 3D PtS films grown on large-area (>cm2) silicon dioxide/silicon (SiO_{2}/Si) wafers are precisely "peeled" inside water retaining desired geometries via a capillary-force-driven surface wettability control. Subsequently, they are "sticked" on strain-engineered patterned substrates presenting prominent semiconducting properties, i.e., p-type transport with an optical band gap of ∼1.24 eV. A variety of mechanically deformable strain-invariant electronic devices have been demonstrated by this peel-and-stick method, including biaxially stretchable photodetectors and respiratory sensing face masks. This study offers new opportunities of 2D-like nonlayered semiconducting crystals for emerging mechanically reconfigurable and stretchable device technologies.
This study reports on the controlled vapor-phase anion exchange conversion of three-dimensional (3D) platinum(II) sulfide (PtS) thin films to two-dimensional platinum ditelluride (2D PtTe2) van der Waals (vdW) layers. The low temperature (i.e., 400 ?) thermal tellurization of chemical vapor deposition (CVD)-grown PtS thin films leads to the formation of 2D PtTe2 vdW layers with a modulated crystallographic orientation, i.e., a mixture of horizontally and vertically oriented 2D layers. This chemical conversion enables the tunable electrical transport accompanying semiconducting-to-metallic transition as well as negative photoresponsiveness in the 2D PtTe2 layers. Density functional theory (DFT) calculations verify the thermodynamic principle for the conversion in the frame of free energy landscapes. The present work suggests a new chemical route for controlling the atomic and chemical structures of 2D transition metal dichalcogenides (TMDs) toward their wafer-scale modulation of electrical and opto-electrical properties.
The supercurrent through a quantum point contact coupled to a nanomagnet strongly depends on the dynamics of the nanomagnet's spin. We employ a fully microscopic model to calculate the transport properties of a junction coupled to a spin whose dynamics is modeled as Larmor precession brought about by an external magnetic field and find that the dynamics affects the charge and spin currents by inducing transitions between the continuum states outside the superconducting gap region and the Andreev levels. This redistribution of the quasiparticles leads to a nonequilibrium population of the Andreev levels and an enhancement of the supercurrent which is visible as a modified current-phase relation as well as a nonmonotonous critical current as function of temperature. The nonmonotonous behavior is accompanied by a corresponding change in spin-transfer torques acting on the precessing spin and leads to the possibility of using temperature as a means to tune the back-action on the spin.