Modern nanofabrication techniques have opened the possibility to create novel functional materials, whose properties transcend those of their constituent elements. In particular, tuning the magnetostatic interactions in geometrically frustrated arrangements of nanoelements called artificial spin ice can lead to specific collective behaviour, including emergent magnetic monopoles, charge screening and transport, as well as magnonic response. Here, we demonstrate a spin-ice-based active material in which energy is converted into unidirectional dynamics. Using X-ray photoemission electron microscopy we show that the collective rotation of the average magnetization proceeds in a unique sense during thermal relaxation. Our simulations demonstrate that this emergent chiral behaviour is driven by the topology of the magnetostatic field at the edges of the nanomagnet array, resulting in an asymmetric energy landscape. In addition, a bias field can be used to modify the sense of rotation of the average magnetization. This opens the possibility of implementing a magnetic Brownian ratchet, which may find applications in novel nanoscale devices, such as magnetic nanomotors, actuators, sensors or memory cells.

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We study a three-dimensional (3d) classical chiral helimagnet at finite temperatures through analysis of a spin Hamiltonian, which is defined on a simple cubic lattice and consists of Heisenberg exchange, mono-axial Dzyaloshinskii-Moriya interactions and Zeeman energy due to magnetic field applied in the plane perpendicular to the helical axis. We take account of quasi-two-dimensionality of a known mono-axial chiral helimagnet CrNb3S6 and we adopt three methods: (i) a conventional mean-field (MF) analysis which we call 3dMF method, (ii) a hybrid method called 2dMC-1dMF, which is composed of a classical Monte Carlo (MC) simulation and MF approximation applied respectively to the intra-and inter-plane interactions, and (iii) a simple-MC simulation (3dMC) at zero field. Temperature dependence of magnetization calculated by the 3dMF method shows a cusp-like structure similar to that observed in experiments. In the absence of magnetic field, both 2dMC-1dMF and 3dMC yield close values of transition temperature. The 2dMC-1dMF provides a quantitative description of thermodynamic properties even under external field at an accessible numerical cost.

Competing magnetic anisotropies in chiral crystals with Dzyaloshinskii Moriya exchange interactions can give rise to non-trivial chiral topological magnetisation configurations with new and interesting properties. One such configuration is the magnetic soliton, where the moment continuously rotates about an axis. This magnetic system can be considered to be one dimensional and, because of this, it supports a macroscale coherent magnetisation, giving rise to a tunable chiral soliton lattice (CSL) that is of potential use in a number of applications in nanomagnetism and spintronics. In this work we characterise the transitions between the forced-ferromagnetic (F-FM) phase and the CSL one in CrNb 3 S 6 using differential phase contrast imaging in a scanning transmission electron microscope, conventional Fresnel imaging, ferro-magnetic resonance spectroscopy, and mean-field modelling. We find that the formation and movement of dislocations mediate the formation of CSL and F-FM regions and that these strongly influence the highly hysteretic static and dynamic properties of the system. Sample size and morphology can be used to tailor the properties of the system and, with the application of magnetic field, to locate and stabalise normally unstable dislocations and modify their dimensions and magnetic configurations in ways beyond that predicted to occur in uniform films. KeywordsChiral soliton lattice, CrNb 3 S 6 , dislocation, differential phase contrast, transmission electron microscopy, Lorentz microscopy, Fresnel microscopy, ferromagnetic resonance spectroscopy 1 arXiv:1903.09519v1 [cond-mat.mtrl-sci]

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We study the impurity effects on the Caroli-de Gennes-Matricon (CdGM) states, particularly on the level spacings in a vortex core in a topological s-wave superconductor (SC) by two methods, numerical and analytical. The topological s-wave SC belongs to the same class as a chiral p-wave SC, and thus there are two inequivalent vortices in terms of any symmetry operation. We take into account this inequivalence and numerically calculate the scattering rates based on an improved version of the Kopnin-Kravtsov (iKK) scheme, which enables us to treat the discrete levels in the presence of white-noise disorder. We also construct the Andreev equation for the topological s-wave SC and obtain the Andreev bound states analytically. We use a correspondence between the wave functions for the Bogoliubov-de Gennes equation and the Andreev equation in the iKK scheme and deduce the formula of scattering rates described by the wave function for the Andreev equation. With this formula, we discuss the origin of impurity scattering rates for CdGM states of the topological s-wave SC and the dependence on the types of vortex related to the inequivalence.

We numerically investigate the electronic structures around a vortex core in a bilayer superconducting system, with s-wave pairing, Rashba spin-orbit coupling and Zeeman magnetic field, with use of the quasiclassical Green's function method. The Bardeen-Cooper-Schrieffer (BCS) phase and the so-called pair-density wave (PDW) phase appear in the temperature-magnetic-field phase diagram in a bulk uniform system [Phys. Rev. B 86, 134514 (2012)]. In the low magnetic field perpendicular to the layers, the zero-energy vortex bound states in the BCS phase are split by the Zeeman magnetic field. On the other hand, the PDW state appears in the high magnetic field, and sign of the order parameter is opposite between the layers. We find that the vortex core suddenly shrinks and the zero-energy bound states appear by increasing the magnetic field through the BCS-PDW transition. We discuss the origin of the change in vortex core structure between the BCS and PDW states by clarifying the relation between the vortex bound states and the bulk energy spectra. In the high magnetic field region, the PDW state and vortex bound states are protected by the spin-orbit coupling. These characteristic behaviors in the PDW state can be observed by scanning tunneling microscopy/spectroscopy.