Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise

A new class of third order Runge-Kutta methods for stochastic differential equations with additive noise is introduced. In contrast to Platen's method, which to the knowledge of the author has been up to now the only known third order Runge-Kutta scheme for weak approximation, the new class of methods affords less random variable evaluations and is also applicable to SDEs with multidimensional noise. Order conditions up to order three are calculated and coefficients of a four stage third order method are given. This method has deterministic order four and minimized error constants, and needs in addition less function evaluations than the method of Platen. Applied to some examples, the new method is compared numerically with Platen's method and some well known second order methods and yields very promising results.Comment: Two further examples added, small correction

Target-skyrmions and skyrmion clusters in nanowires of chiral magnets

In bulk non-centrosymmetric magnets the chiral Dzyaloshinskii-Moriya exchange stabilizes tubular skyrmions with a reversed magnetization in their centers. While the double-twist is favorable in the center of a skyrmion, it gives rise to an excess of the energy density at the outskirt. Therefore, magnetic anisotropies are required to make skyrmions more favorable than the conical spiral state in bulk materials. Using Monte Carlo simulations, we show that in magnetic nanowires unusual skyrmions with a doubly twisted core and a number of concentric helicoidal undulations (target-skyrmions) are thermodynamically stable even in absence of single-ion anisotropies. Such skyrmions are free of magnetic charges and, since the angle describing the direction of magnetization at the surface depends on the radius of the nanowire and an applied magnetic field, they carry a non-integer skyrmion charge s > 1. This state competes with clusters of spatially separated s=1 skyrmions. For very small radii, the target-skyrmion transforms into a skyrmion with s < 1, that resembles the vortex-like state stabilized by surface-induced anisotropies

Pressure-induced ferromagnetism due to an anisotropic electronic topological transition in Fe1.08Te

A rapid and anisotropic modification of the Fermi-surface shape can be associated with abrupt changes in crystalline lattice geometry or in the magnetic state of a material. In this study we show that such an electronic topological transition is at the basis of the formation of an unusual pressure-induced tetragonal ferromagnetic phase in Fe$_{1.08}$Te. Around 2 GPa, the orthorhombic and incommensurate antiferromagnetic ground-state of Fe$_{1.08}$Te is transformed upon increasing pressure into a tetragonal ferromagnetic state via a conventional first-order transition. On the other hand, an isostructural transition takes place from the paramagnetic high-temperature state into the ferromagnetic phase as a rare case of a `type 0' transformation with anisotropic properties. Electronic-structure calculations in combination with electrical resistivity, magnetization, and x-ray diffraction experiments show that the electronic system of Fe$_{1.08}$Te is instable with respect to profound topological transitions that can drive fundamental changes of the lattice anisotropy and the associated magnetic order.Comment: 7 pages, 4 figur

Chiral skyrmions in thin magnetic films: new objects for magnetic storage technologies?

Axisymmetric magnetic lines of nanometer sizes (chiral vortices or skyrmions) have been predicted to exist in a large group of noncentrosymmetric crystals more than two decades ago. Recently these magnetic textures have been directly observed in nanolayers of cubic helimagnets and monolayers of magnetic metals. We develop a micromagnetic theory of chiral skyrmions in thin magnetic layers for magnetic materials with intrinsic and induced chirality. Such particle-like and stable micromagnetic objects can exist in broad ranges of applied magnetic fields including zero field. Chiral skyrmions can be used as a new type of highly mobile nanoscale data carriers

Low-temperature phase diagram of Fe1+yTe

We used low-temperature synchrotron x-ray diffraction to investigate the structural phase transitions of Fe1+yTe in the vicinity of a tricitical point in the phase diagram. Detailed analysis of the powder diffraction patterns and temperature dependence of the peak-widths in Fe1+yTe showed that two-step structural and magnetic phase transitions occur within the compositional range 0.11 $\leq y \leq$ 0.13. The phase transitions are sluggish indicating a strong competition between the orthorhombic and the monoclinic phases. We combine high-resolution diffraction experiments with specific heat, resistivity, and magnetization measurements and present a revised temperature-composition phase diagram for Fe1+yTe.Comment: 10 pages, 14 figure

Exchange shift of stripe domains in antiferromagnetically coupled multilayers

Antiferromagnetically coupled multilayers with perpendicular anisotropy, as [CoPt]/Ru, Co/Ir, Fe/Au, display ferromagnetic stripe phases as the ground states. It is theoretically shown that the antiferromagnetic interlayer exchange causes a relative shift of domains in adjacent layers. This ``exchange shift'' is responsible for several recently observed effects: an anomalous broadening of domain walls, the formation of so-called ``tiger-tail'' patterns, and a ``mixed state'' of antiferromagnetic and ferromagnetic domains in [CoPt]/Ru multilayers. The derived analitical relations between the values of the shift and the strength of antiferromagnetic coupling provide an effective method for a quantitative determination of the interlayer exchange interactions.Comment: 4 pages, 3 figure

Pressure-induced phase transitions and high-pressure tetragonal phase of Fe1.08Te

We report the effects of hydrostatic pressure on the temperature-induced phase transitions in Fe1.08Te in the pressure range 0-3 GPa using synchrotron powder x-ray diffraction (XRD). The results reveal a plethora of phase transitions. At ambient pressure, Fe1.08Te undergoes simultaneous first-order structural symmetry-breaking and magnetic phase transitions, namely from the paramagnetic tetragonal (P4/nmm) to the antiferromagnetic monoclinic (P2_1/m) phase. We show that, at a pressure of 1.33 GPa, the low temperature structure adopts an orthorhombic symmetry. More importantly, for pressures of 2.29 GPa and higher, a symmetry-conserving tetragonal-tetragonal phase transition has been identified from a change in the c/a ratio of the lattice parameters. The succession of different pressure and temperature-induced structural and magnetic phases indicates the presence of strong magneto-elastic coupling effects in this material.Comment: 11 page

Precursor phenomena at the magnetic ordering of the cubic helimagnet FeGe

We report on detailed magnetic measurements on the cubic helimagnet FeGe in external magnetic fields and temperatures near the onset of long-range magnetic order at $T_C= 278.2(3)$ K. Precursor phenomena display a complex succession of temperature-driven crossovers and phase transitions in the vicinity of $T_C$. The A-phase region, present below $T_C$ and fields $H<0.5$ kOe, is split in several pockets. Relying on a modified phenomenological theory for chiral magnets, the main part of the A-phase could indicate the existence of a $+\pi$ Skyrmion lattice, the adjacent A$_2$ pocket, however, appears to be related to helicoids propagating in directions perpendicular to the applied field.Comment: 5 pages, 4 figure

Skyrmionic textures in chiral magnets

In non-centrosymmetric magnets the chiral Dzyaloshinskii-Moriya exchange stabilizes Skyrmion-strings as excitations which may condense into multiply modulated phases. Such extended Skyrmionic textures are determined by the stability of the localized "solitonic" Skyrmion cores and their geometrical incompatibility which frustrates regular space-filling. We present numerically exact solutions for Skyrmion lattices and formulate basic properties of the Skyrmionic states.Comment: Conference information: The International Conference on Magnetism (ICM), Karlsruhe, July 26 - 31, 200

Chiral Skyrmionic matter in non-centrosymmetric magnets

Axisymmetric magnetic strings with a fixed sense of rotation and nanometer sizes (chiral magnetic vortices or Skyrmions) have been predicted to exist in a large group of non-centrosymmetric crystals more than two decades ago. Recently these extraordinary magnetic states have been directly observed in thin layers of cubic helimagnet (Fe,Co)Si. In this report we apply our earlier theoretical findings to review main properties of chiral Skyrmions, to elucidate their physical nature, and to analyse these recent experimental results on magnetic-field-driven evolution of Skyrmions and helicoids in chiral helimagnets.Comment: 13 pages, 7 figures, invited talk - JEMS-2010 ( 23-28 August, Krakow, Poland