Interplay of Electronic and Spin Degrees in Ferromagnetic SrRuO_{3}: Anomalous Softening of the Magnon Gap and Stiffness.

The magnon dispersion of ferromagnetic SrRuO_{3} was studied by inelastic neutron scattering experiments on single crystals as a function of temperature. Even at low temperature the magnon modes exhibit substantial broadening pointing to strong interaction with charge carriers. We find an anomalous temperature dependence of both the magnon gap and the magnon stiffness, which soften upon cooling in the ferromagnetic phase. Both effects trace the temperature dependence of the anomalous Hall effect and can be attributed to the impact of Weyl points, which results in the same relative renormalization in the spin stiffness and magnon gap.

Dynamical Defects in Rotating Magnetic Skyrmion Lattices.

The chiral magnet Cu_{2}OSeO_{3} hosts a Skyrmion lattice that may be equivalently described as a superposition of plane waves or a lattice of particlelike topological objects. A thermal gradient may break up the Skyrmion lattice and induce rotating domains, raising the question of which of these scenarios better describes the violent dynamics at the domain boundaries. Here, we show that in an inhomogeneous temperature gradient caused by illumination in a Lorentz transmission electron microscope different parts of the Skyrmion lattice can be set into motion with different angular velocities. Tracking the time dependence, we show that the constant rearrangement of domain walls is governed by dynamic 5-7 defects arranging into lines. An analysis of the associated defect density is described by Frank's equation and agrees well with classical 2D Monte Carlo simulations. Fluctuations of boundaries show a surgelike rearrangement of Skyrmion clusters driven by defect rearrangement consistent with simulations treating Skyrmions as point particles. Our findings underline the particle character of the Skyrmion.

SU(4) Skyrmions in the ν=±1 Quantum Hall State of Graphene.

We explore different Skyrmion types in the lowest Landau level of graphene at a filling factor ν=±1. In addition to the formation of spin and valley pseudospin Skyrmions, we show that another type of spin-valley entangled Skyrmions can be stabilized in graphene due to an approximate SU(4) spin-valley symmetry that is affected by sublattice symmetry-breaking terms. These Skyrmions have a clear signature in spin-resolved density measurements on the lattice scale, and we discuss the expected patterns for the different Skyrmion types.

Band Structure of Helimagnons in MnSi Resolved by Inelastic Neutron Scattering.

A magnetic helix realizes a one-dimensional magnetic crystal with a period given by the pitch length λh. Its spin-wave excitations-the helimagnons-experience Bragg scattering off this periodicity, leading to gaps in the spectrum that inhibit their propagation along the pitch direction. Using high-resolution inelastic neutron scattering, the resulting band structure of helimagnons was resolved by preparing a single crystal of MnSi in a single magnetic-helix domain. At least five helimagnon bands could be identified that cover the crossover from flat bands at low energies with helimagnons basically localized along the pitch direction to dispersing bands at higher energies. In the low-energy limit, we find the helimagnon spectrum to be determined by a universal, parameter-free theory. Taking into account corrections to this low-energy theory, quantitative agreement is obtained in the entire energy range studied with the help of a single fitting parameter.

Real-space and reciprocal-space Berry phases in the Hall effect of Mn(1-x)Fe(x)Si.

We report an experimental and computational study of the Hall effect in Mn(1-x)Fe(x)Si, as complemented by measurements in Mn(1-x)Co(x)Si, when helimagnetic order is suppressed under substitutional doping. For small x the anomalous Hall effect (AHE) and the topological Hall effect (THE) change sign. Under larger doping the AHE remains small and consistent with the magnetization, while the THE grows by over a factor of 10. Both the sign and the magnitude of the AHE and the THE are in excellent agreement with calculations based on density functional theory. Our study provides the long-sought material-specific microscopic justification that, while the AHE is due to the reciprocal-space Berry curvature, the THE originates in real-space Berry phases.

Topological insulators in magnetic fields: quantum Hall effect and edge channels with a nonquantized θ term.

We investigate how a magnetic field induces one-dimensional edge channels when the two-dimensional surface states of three-dimensional topological insulators become gapped. The Hall effect, measured by contacting those channels, remains quantized even in situations where the θ term in the bulk and the associated surface Hall conductivities, σ(xy)(S), are not quantized due to the breaking of time-reversal symmetry. The quantization arises as the θ term changes by ±2πn along a loop around n edge channels. Model calculations show how an interplay of orbital and Zeeman effects leads to quantum Hall transitions, where channels get redistributed along the edges of the crystal. The network of edges opens new possibilities to investigate the coupling of edge channels.

Nonlinear conductance of long quantum wires at a conductance plateau transition: where does the voltage drop?

We calculate the linear and nonlinear conductance of spinless fermions in clean, long quantum wires, where short-ranged interactions lead locally to equilibration. Close to the quantum phase transition, where the conductance jumps from zero to one conductance quantum, the conductance obtains a universal form governed by the ratios of temperature, bias voltage, and gate voltage. Asymptotic analytic results are compared to solutions of a Boltzmann equation which includes the effects of three-particle scattering. Surprisingly, we find that for long wires the voltage predominantly drops close to one end of the quantum wire due to a thermoelectric effect.

Long-range crystalline nature of the Skyrmion lattice in MnSi.

We report small angle neutron scattering of the Skyrmion lattice in MnSi using an experimental setup that minimizes the effects of demagnetizing fields and double scattering. Under these conditions, the Skyrmion lattice displays resolution-limited Gaussian rocking peaks that correspond to a magnetic correlation length in excess of several hundred micrometers. This is consistent with exceptionally well-defined long-range order. We further establish the existence of higher-order scattering, discriminating parasitic double scattering with Renninger scans. The field and temperature dependence of the higher-order scattering arises from an interference effect. It is characteristic for the long-range crystalline nature of the Skyrmion lattice as shown by simple mean-field calculations.

Partial order in the non-Fermi-liquid phase of MnSi.

Only a few metallic phases have been identified in pure crystalline materials. These include normal, ferromagnetic and antiferromagnetic metals, systems with spin and charge density wave order, and superconductors. Fermi-liquid theory provides a basis for the description of all of these phases. It has been suggested that non-Fermi-liquid phases of metals may exist in some heavy-fermion compounds and oxide materials, but the discovery of a characteristic microscopic signature of such phases presents a major challenge. The transition-metal compound MnSi above a certain pressure (p(c) = 14.6 kbar) provides what may be the cleanest example of an extended non-Fermi-liquid phase in a three-dimensional metal. The bulk properties of MnSi suggest that long-range magnetic order is suppressed at p(c) (refs 7-12). Here we report neutron diffraction measurements of MnSi, revealing that sizeable quasi-static magnetic moments survive far into the non-Fermi-liquid phase. These moments are organized in an unusual pattern with partial long-range order. Our observation supports the existence of novel metallic phases with partial ordering of the conduction electrons (reminiscent of liquid crystals), as proposed for the high-temperature superconductors and heavy-fermion compounds.

Quantum order in the chiral magnet MnSi.

Systems lacking inversion symmetry, such as selected three-dimensional compounds, multilayers and surfaces support Dzyaloshinsky-Moriya (DM) spin-orbit interactions. In recent years DM interactions have attracted great interest, because they may stabilize magnetic structures with a unique chirality and non-trivial topology. The inherent coupling between the various properties provided by DM interactions is potentially relevant for a variety of applications including, for instance, multiferroic and spintronic devices. The, perhaps, most extensively studied material in which DM interactions are important is the cubic B20 compound MnSi. We review the magnetic field and pressure dependence of the magnetic properties of MnSi. At ambient pressure this material displays helical order. Under hydrostatic pressure a non-Fermi liquid state emerges, where a partial magnetic order, reminiscent of liquid crystals, is observed in a small pocket. Recent experiments strongly suggest that the non-Fermi liquid state is not due to quantum criticality. Instead it may be the signature of spin textures and spin excitations with a non-trivial topology.