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A self-consistent field theory is introduced and used to investigate the thermodynamics and spin dynamics of an $S = 1$ quantum spin system with a magnetic Skyrmion. The temperature dependence of the Skyrmion profile as well as the phase diagram are calculated. It is shown that the Skyrmion carries a phase transition to the ferromagnetic phase of first order with increasing temperature, while the magnetization of the surrounding ferromagnet undergoes a phase transition of second order when changing to the paramagnetic phase. Furthermore, the electric field driven annihilation process of the Skyrmion is described quantum mechanical by solving the time dependent Schr\"odinger equation. The results are compared with the trajectories of the semi-classical description of the spin expectation values using a differential equation similar to the classical Landau-Lifshitz-Gilbert equation.

The dynamics of a single magnetic Skyrmion in an atomic spin system under the influence of Scanning Tunneling Microscope is investigated by computer simulations solving the Landau-Lifshitz-Gilbert equation. Two possible scenarios are described: manipulation with aid of a spin-polarized tunneling current and by an electric field created by the scanning tunneling microscope. The dynamics during the creation and annihilation process is studied and the possibility to move single Skyrmions is showed.

The classical Landau-Lifshitz equation with damping term has been derived from the time evolution of a quantum mechanical wave function under the assumption of a non-hermitian Hamilton operator. Further, the trajectory of a classical spin $\mathrm{S}$ has been compared with the expectation value of the spin operator $\mathrm{\hat{S}}$. A good agreement between classical and quantum mechanical trajectories can be found for Hamiltonians linear in $\mathrm{\hat{S}}$ respectively $\mathrm{S}$. Quadratic or higher order terms in the Hamiltonian result in a disagreement.

Using exact diagonalization, Monte-Carlo, and mean-field techniques, characteristic temperature scales for ferromagnetic order are discussed for the Ising and the classical anisotropic Heisenberg model on finite lattices in one and two dimensions. The interplay between nearest-neighbor exchange, anisotropy and the presence of surfaces leads, as a function of temperature, to a complex behavior of the distance-dependent spin-spin correlation function, which is very different from what is commonly expected. A finite experimental observation time is considered in addition, which is simulated within the Monte-Carlo approach by an incomplete statistical average. We find strong surface effects for small nanoparticles, which cannot be explained within a simple Landau or mean-field concept and which give rise to characteristic trends of the spin-correlation function in different temperature regimes. Unambiguous definitions of crossover temperatures for finite systems and an effective method to estimate the critical temperature of corresponding infinite systems are given., Comment: 7 pages, 5 figures, EPJB (in press)

Domain walls in nano-constrictions are investigated with a focus on thermal properties. In general, the magnetization component perpendicular to the easy axis which in a domain wall usually occurs has a value different from the easy-axis bulk magnetization value with a separate phase transition at a critical temperature below the Curie temperature. Since this effect is the more pronounced the smaller the domain wall width is we investigate it especially in domain walls with a confined geometry, using analytical arguments, mean-field theory and Monte Carlo simulations. Our findings may contribute to the understanding of magneto-resistive effects in domain walls with sizes of only a few atomic layers, as e. g. in nano-contacts or nano-constrictions., Comment: 5 pages, 6 figures, to be published in Phys. Rev. Letters

The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. The transverse domain wall is observed for diameters smaller than the exchange length of the given material. Here, the system behaves effectively one-dimensional and the domain wall mobility agrees with a result derived for a one-dimensional wall by Slonczewski. For low damping the domain wall mobility decreases with decreasing damping constant. With increasing diameter, a crossover to a vortex wall sets in which enhances the domain wall mobility drastically. For a vortex wall the domain wall mobility is described by the Walker-formula, with a domain wall width depending on the diameter of the wire. The main difference is the dependence on damping: for a vortex wall the domain wall mobility can be drastically increased for small values of the damping constant up to a factor of $1/\alpha^2$., Comment: 5 pages, 6 figures

The KARMEN collaboration has reported the possible observation of a hitherto unknown neutral and weakly interacting particle x, which is produced in the decay pi -> mu + x with a mass m(x) = 33.9 MeV. We have searched for this hypothetical decay branch by studying muons from pion decay in flight with the LEPS spectrometer at the piE3 channel at PSI and find branching ratios BR(pi- to mu- anti-x) < 4e-7 and BR(pi+ to mu+ x) < 7e-8 (95\% C.L.). Together with the limit BR > 2e-8 derived in a recent theoretical paper our result would leave only a narrow region for the existence of x if it is a heavy neutrino., Comment: 10 pages, TeX (uses epsf), 3 Postscript figures uu-encoded