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Supplementary information for our manuscript, entitled Spontaneous Skyrmion Ground States of Magnetic Metals, cond-mat/0603103, is presented. The physical nature of the gradient terms of our generalized micromagnetic model for ferromagnets with softened longitudinal fluctuations is explained. The relationship of our micromagnetic model with the spin fluctuation theory of itinerant-electron magnets is discussed. Experimental estimates of the parameter eta, which accounts for an effective reduced longitudinal stiffness, are presented for real materials from published polarized neutron scattering experiments on EuS, Ni and MnSi. The available experimental data clearly show that eta is significantly reduced for the latter two systems. It is suggested that particle-hole excitations are at the root of this longitudinal softness in itinerant-electron ferromagnets. The current status of the experimental evidence supporting spontaneous, amorphous skyrmion textures in MnSi and other materials is reviewed. Finally, we also address the general potential of skyrmion textures in chiral magnets for other fields of physics.
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Since the 1950s Heisenberg and others have attempted to explain the appearance of countable particles in quantum field theory in terms of stable localized field configurations. As an exception Skyrmes model succeeded to describe nuclear particles as localized states, so-called skyrmions, within a non-linear field theory. Skyrmions are a characteristic of non-linear continuum models ranging from microscopic to cosmological scales. Skyrmionic states have been found under non-equilibrium conditions, or when stabilised by external fields or the proliferation of topological defects. Examples are Turing patterns in classical liquids, spin textures in quantum Hall magnets, or the blue phases in liquid crystals, respectively. However, it is believed that skyrmions cannot form spontaneous ground states like ferromagnetic or antiferromagnetic order in magnetic materials. Here, we show theoretically that this assumption is wrong and that skyrmion textures may form spontaneously in condensed matter systems with chiral interactions without the assistance of external fields or the proliferation of defects. We show this within a phenomenological continuum model, that is based on a few material-specific parameters that may be determined from experiment. As a new condition not considered before, we allow for softened amplitude variations of the magnetisation - a key property of, for instance, metallic magnets. Our model implies that spontaneous skyrmion lattice ground states may exist quite generally in a large number of materials, notably at surfaces and in thin films as well as in bulk compounds, where a lack of space inversion symmetry leads to chiral interactions.
Low-temperature scanning tunneling spectroscopy is used to study electronic structure and dynamics of d-like surface states of trivalent lanthanide metals from La to Lu. The magnetic exchange splitting of these states is found to scale with the 4f spin multiplied by an effective exchange-coupling constant that increases with 4f occupancy in an approximately linear way. The dynamics of the surfaces states, as revealed by the lifetime width, is dominated by electron-phonon scattering in the occupied region and by electron-magnon scattering in the unoccupied region, respectively.
Filamentary textures can take the form of braided, rope-like superstructures in nonlinear media such as plasmas and superfluids. The formation of similar superstructures in solids has been predicted, for example from flux lines in superconductors. Ho
wever, their observation has proved challenging. Here, we use electron microscopy and numerical methods to reveal braided superstructures of magnetic skyrmions in thin crystals of B20-type FeGe. Their discovery opens the door to applications of rich topological landscapes of geometric braids in magnetic solids.
Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung. The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations. It is demonstrated that both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and three-quarters of the saturation magnetization.
We study a two-lane two-species exclusion process inspired by Lin et al. (C. Lin et al. J. Stat. Mech., 2011), that exhibits a non-equilibrium pulsing phase. Particles move on two parallel one-dimensional tracks, with one open and one reflecting boundary. The particle type defines the hopping direction. When only particles hopping towards the open end are allowed to change lane, the system exhibits a phase transition from a low density phase to a pulsing phase depending on the ratio between particle injection and type-changing rate. This phase transition can be observed in the stochastic model as well as in a mean-field description. In the low density phase, the density profile can be predicted analytically. The pulsing phase is characterised by a fast filling of the system and - once filled - by a slowly backwards moving front separating a decreasing dense region and an expanding low density region. The hopping of the front on the discrete lattice is found to create density oscillations, both, in time and space. By means of a stability analysis we can predict the structure of the dense region during the emptying process, characterised by exponentially damped perturbations, both at the open end and near the moving front.
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