Spin waves cause non-linear friction

Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate.Comment: 5 pages, 9 figure

Spin waves cause non-linear friction

Energy dissipation is studied for a hard magnetic tip that scans a soft magnetic substrate. The dynamics of the atomic moments are simulated by solving the Landau-Lifshitz-Gilbert (LLG) equation numerically. The local energy currents are analysed for the case of a Heisenberg spin chain taken as substrate. This leads to an explanation for the velocity dependence of the friction force: The non-linear contribution for high velocities can be attributed to a spin wave front pushed by the tip along the substrate.Comment: 5 pages, 9 figure

Lebensdauer lagenweisen Kristallwachstums - Lifetime of Layer-Wise Crystal Growth

The lifetime of layer-by-layer growth of crystal surfaces, mainly in the context of growth conditions found in molecular beam epitaxy (MBE), is the central issue of this thesis. These conditions imply a driven system far from equilibrium which relaxes due to surface diffusion. At first, the ceasing of layer-by-layer growth due to fluctuations in the particle supply is considered. A theory for the according lifetime is presented and confirmed for the one-dimensional surface. Special care is taken for the two-dimensional case where deviations from previous results are found, explained, and used to revise the assumptions on which the theory is based. In particular the applicability of the -- commonly accepted -- conserved KPZ continuum equation and the premise of a single morphologically relevant length scale are affected. The practically more relevant scenario of layer-by-layer growth's breakdown caused by barriers to interlayer transport (which give rise to the Villain instability) is studied. Data obtained fr om computer simulations is compared to the predictions of a linear stability analysis and is used to foretell the effect of counteracting variations of energy barriers. The latter enables to decide in which cases a strained surface is either hindering or advantageous for layer-by-layer growth. A mean field model describing surface growth, which lacked up to now a systematic treatment, is investigated. For the basic version, the asymptotic behavior is derived exactly and -- tuning the sole control parameter -- a transition from Poisson-like growth to persistent layer-by-layer growth is found together with a non-trivial powerlaw behavior right at the transition point. Finally the extensibility of the model to include a finite lifetime of layer-wise growth is examined. The damping of oscillations of certain surface-sensitive quantities is the manifestation of the surface's roughening which terminates the layer-by-layer growth. A scenario alternative to the roughening is suggested. It leads as well to damping of oscillations and consists of a step bunch which dissolves during growth and 'floods' an adjacent terrace. Growth simulations of this process are compared to a deterministic model and to experimental results. Finally several toy models for surface growth, subjected to noise reduction are considered. The latter technique makes possible layer-by-layer growth also in these models and the dependence of its lifetime on the degree of the noise reduction is studied. The main focus is on the behavior's relation to continuum equations and the corresponding universality classes, which are commonly used to classify the different models

Ritz‐type surface homogenization

Surfaces possess mechanical features on smaller scales that stand out against bulk phases, e.g., scaling of stiffness, curvature‐dependence, surfactant control and anchoring‐induced anisotropy. Continuum properties for the respective scales are often derived from ab initio simulations. This scale‐bridging however bears conceptual challenges and we highlight three aspects for the example of pure copper. First, free surface atoms relax and alter the boundary region in terms of interatomistic distances and resulting initital stresses. Second, eliminating the influence of finite thickness on the two‐dimensional continuum surface can be achieved by different averages or limit definitions, not all being physically consistent. Third, the continuum model of the surface is usually coupled to a continuum model of the bulk, which causes an approximation error itself. However, the bulk phase can not be eliminated direclty from the examination and simple averaging may even mask the aforementioned influences on the surface mechanics. A thermodynamically sound parameter identification across the scales is hence required. We present a Ritz‐type modeling approach for surfaces that ensures energy equivalence between atmostic and continuum simulations. The influences of relaxation, finite thickness and bulk approximation are identified by a mismatch in the energy contributions and accounted for by using appropriate homogenization limits

Spin excitations in a monolayer scanned by a magnetic tip

Energy dissipation via spin excitations is investigated for a hard ferromagnetic tip scanning a soft magnetic monolayer. We use the classical Heisenberg model with Landau-Lifshitz-Gilbert (LLG)-dynamics including a stochastic field representing finite temperatures. The friction force depends linearly on the velocity (provided it is small enough) for all temperatures. For low temperatures, the corresponding friction coefficient is proportional to the phenomenological damping constant of the LLG equation. This dependence is lost at high temperatures, where the friction coefficient decreases exponentially. These findings can be explained by properties of the spin polarization cloud dragged along with the tip.Comment: 6 pages, 5 figure

An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials

A fully parallel version of the contact dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. The iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics (2011