Full phase diagram of isolated skyrmions in a ferromagnet

Magnetic skyrmions are topological quasi particles of great interest for data storage applications because of their small size, high stability, and ease of manipulation via electric current. Theoretically, however, skyrmions are poorly understood since existing theories are not applicable to small skyrmion sizes and finite material thicknesses. Here, we present a complete theoretical framework to determine the energy of any skyrmion in any material, assuming only a circular symmetric 360$^\circ$ domain wall profile and a homogeneous magnetization profile in the out-of-plane direction. Our model precisely agrees with existing experimental data and micromagnetic simulations. Surprisingly, we can prove that there is no topological protection of skyrmions. We discover and confirm new phases, such as bi-stability, a phenomenon unknown in magnetism so far. The outstanding computational performance and precision of our model allow us to obtain the complete phase diagram of static skyrmions and to tackle the inverse problem of finding materials corresponding to given skyrmion properties, a milestone of skyrmion engineering

Quantum to classical crossover in the 2D easy-plane XXZ model

Ground-state and thermodynamical properties of the spin-1/2 two-dimensional easy-plane XXZ model are investigated by both a Green's-function approach and by Lanczos diagonalizations on lattices with up to 36 sites. We calculate the spatial and temperature dependences of various spin correlation functions, as well as the wave-vector dependence of the spin susceptibility for all anisotropy parameters $\Delta$. In the easy--plane ferromagnetic region $(-1< \Delta < 0)$, the longitudinal correlators of spins at distance $r$ change sign at a finite temperature $T_0(\Delta, {\bf r})$. This transition, observed in the 2D case for the first time, can be interpreted as a quantum to classical crossover.Comment: 4 pages, 6 figures, Contribution to the Ising Centennial Colloquium, ICM2000, Belo Horizonte, Brazil, August 200

A novel sampling theorem on the rotation group

We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O(L^6)$. For the common case of a low directional band-limit $N$, complexity is reduced to $O(N L^3)$. Our fast algorithms will be of direct use in speeding up the computation of directional wavelet transforms on the sphere. We make our SO3 code implementing these algorithms publicly available.Comment: 5 pages, 2 figures, minor changes to match version accepted for publication. Code available at http://www.sothree.or

Entanglement measurement with discrete multiple coin quantum walks

Within a special multi-coin quantum walk scheme we analyze the effect of the entanglement of the initial coin state. For states with a special entanglement structure it is shown that this entanglement can be meausured with the mean value of the walk, which depends on the i-concurrence of the initial coin state. Further on the entanglement evolution is investigated and it is shown that the symmetry of the probability distribution is reflected by the symmetry of the entanglement distribution.Comment: 9 pages, IOP styl

Immunohistological studies on neoplasms of female and male Onchocerca volvulus: filarial origin and absence of Wolbachia from tumor cells

Up to 5% of untreated female Onchocerca volvulus filariae develop potentially fatal pleomorphic neoplasms, whose incidence is increased following ivermectin treatment. We studied the occurrence of 8 filarial proteins and of Wolbachia endobacteria in the tumor cells. Onchocercomas from patients, untreated and treated with antibiotics and anthelminthics, were examined by immunohistology. Neoplasms were diagnosed in 112 of 3587 female and in 2 of 1570 male O. volvulus. The following proteins and other compounds of O. volvulus were expressed in the cells of the neoplasms: glutathione S-transferase 1, lysosomal aspartic protease, cAMP-dependent protein kinase, alpha-enolase, aspartate aminotransferase, ankyrin E1, tropomyosin, heat shock protein 60, transforming growth factor-beta, and prostaglandin E2. These findings prove the filarial origin of the neoplasms and confirm the pleomorphism of the tumor cells. Signs indicating malignancy of the neoplasms are described. Wolbachia were observed in the hypodermis, oocytes, and embryos of tumor-harbouring filariae using antibodies against Wolbachia surface protein, Wolbachia HtrA-type serine protease, and Wolbachia aspartate aminotransferase. In contrast, Wolbachia were not found in the cells of the neoplasms. Further, neoplasm-containing worms were not observed after more than 10 months after the start of sufficient treatment with doxycycline or doxycycline plus ivermectin