Abstracts

Stephen Blundell

Abstract In non-relativistic quantum mechanics, the wave function of the electron can be described by a complex field. In a periodic lattice, the symmetry constraints imposed on this wave function can have interesting topological consequences. The Ahranov-Bohm effect, the Berry phase, the Hofstadter butterfly and topological insulators are all manifestations of these topological effects. Once we include spins decorating a lattice, we introduce the additional possibility of novel topological states described by those spins. In this talk, I will describe a number of these examples that illustrate the way in which the topological nature of the electron states leads to new emergent behaviour.

Elisa Davoli

Abstract In this talk, we investigate the influence of the bulk Dzyaloshinskii-Moriya interaction on the magnetic properties of composite ferromagnetic materials with highly oscillating heterogeneities, in the framework of Gamma-convergence and 2-scale convergence. In particular, we provide a quantitative counterpart to Dzyaloshinskii's predictions on helical structures. This is joint work with Giovanni Di Fratta.

Amalio Fernández-Pacheco

Abstract Magnetic topological textures such as domain walls, vortices, skyrmions… with excellent properties to store and process information, are the basis of new spintronic devices that have been proposed over the last years. The prospect for future computing applications and the fascinating fundamental physics that these magnetic objects present, makes the study of magnetic textures one of the key area of spintronics these days.
Normally, magnetic textures require either the usage of a restricted group of bulk materials, or synthetic thin-film systems that exploit interfacial effects. In this talk, I will present a different approach based on the exploitation of three-dimensional geometrical effects [1], which becomes possible thanks to advanced 3D nanofabrication.
To get full access to the rich phenomenology emerging when moving to 3D, we have recently developed a new framework for the 3D nano-printing of materials using focused electron beam induced deposition [2], which enables the fabrication of complex-shaped 3D magnetic structures with resolution of a few tens of nm.
Making use of this tool, in combination with advanced magneto-optical and X-ray magnetic microscopy methods, I will show how we can build 3D magnetic chiral nanostructures, where exchange and dipolar interactions are balanced to result in a very rich phenomenology. The freedom provided to control magnetic effects in this type of geometries has been exploited to form chiral interfaces between domain walls of opposite chirality, allowing us to imprint chiral domain walls and topological spin defects at localized regions [3]. Furthermore, helical structures may also form strongly coupled domain wall pairs, which result in complex stray magnetic field configurations with topological features [4].

References
[1] A. Fernández-Pacheco et al, Nature Communications 8, 1 (2017).
[2] L. Skoric, Nano Letters 20, 184 (2020).
[3] D. Sanz-Hernández et al, ACS Nano 14, 8084 (2020).
[4] C. Donnelly et al, Nature Nanotechnology (2021), in press.

Radu Ignat

Abstract We analyse a nonconvex variational model from micromagnetics with a nonlocal energy functional, depending on a small parameter \(\epsilon > 0\). The model gives rise to transition layers, called Néel walls, and we study their behaviour in the limit \(\epsilon \to 0\). The analysis has some similarity to the theory of Ginzburg-Landau vortices. In particular, it gives rise to a renormalised energy that determines the interaction (attraction or repulsion) between Néel walls to leading order. But while Ginzburg-Landau vortices show attraction for winding numbers of the same sign and repulsion for those of opposite signs, the pattern is reversed in this model. First, we show that the Néel walls stay separated from each other and second, we determine the interaction energy between them. The theory gives rise to an effective variational problem for the positions of the walls, encapsulated in a Gamma-convergence result. This is a joint work with R. Moser (Univ. of Bath).

Stavros Komineas

Abstract Skyrmions in antiferromagnets (AFM) with the Dzyaloshinskii-Moriya (DM) interaction exist for essentially the same reasons as in DM ferromagnets (FM). We show that they can travel as solitary waves with velocities up to a maximum value that depends on the DM parameter. The maximum velocity is set due to the phase transition to the spiral state. The skyrmion number, known to be linked to the dynamics of topological solitons in FM, is, here, unrelated to the skyrmion dynamical behavior. We will also present a similar study for propagating vortices in an easy-plane AFM.

Matthias Kurzke

Abstract We consider a thin film limit of the micromagnetic energy that exhibits formation of boundary vortices. Through rigorous estimates, the nonlocal, nonconvex micromagnetic energy can be reduced in a certain regime to a local problem. We discuss the energy expansion by Gamma-convergence and the interaction term, which can be computed by means of conformal mapping. For rectangular or circular samples, we have explicit asymptotic results on the minimal energy. This is joint work with Radu Ignat and partially with my PhD student Marco Baffetti.

Tom Lancaster

Abstract Topology has become a much-discussed part of current research in solid-state magnetism, providing an organising principle to classify field theories, and their ground states and excitations, that are now regularly realized in magnetic materials. Examples include topological excitations such as skyrmions which exist in the spin textures of an expanding range of magnetic systems, and one-dimensional spin-chain systems, where topological considerations are key in understanding their properties. Central to this story is the role of the sine-Gordon model, which was important in motivating Skyrme's work and also in understanding the properties of spin chains using field theories. From this starting point, I will review some of the states that we might expect to realize in magnetic materials, and provide two sets of examples of where and how these have been found. Firstly, I will present examples spin chains and ladders formed of molecular building blocks, where the versatility of carbon chemistry allows access to spin-Luttinger liquids, and sine-Gordon and Haldane chains. Secondly I shall discuss materials that host magnetic skyrmions and related excitations, along with the prospects for finding still more of these in the future.

Christof Melcher

Abstract We discuss skyrmionic field configurations on a spherical magnet. Exploiting the Hamiltonian structure and concepts of angular momentum, we present a new family of localized solutions to the (conservative) Landau-Lifshitz equation that are topologically distinct from the ground state and not equivariant. The approach illustrates emergent spin-orbit coupling arising from the loss of individual rotational invariance in spin and coordinate space.

Michele Ruggeri

Abstract The talk will be split into two parts. In the first one, we consider the numerical approximation of the Landau-Lifshitz-Gilbert equation (LLG) for the case in which the energy (and, hence, the effective field appearing in LLG) includes the Dzyaloshinki-Moriya interaction (DMI), the fundamental ingredient for the enucleation and stability of chiral magnetic skyrmions. We show that DMI leads to additional challenges in the analysis of numerical schemes and in computations, and provide answers to some of them. In the second part, we discuss a limiting model for micromagnetic thin films in the presence of bulk DMI, where we focus on the limiting behavior of the magnetization as the thickness of the film goes to zero. We show that the reduced model unveils some physics and discuss its practical implications for computations. The results presented in the talk have been obtained together with Elisa Davoli, Giovanni Di Fratta, Carl-Martin Pfeiler, and Dirk Praetorius (TU Wien).

Bernd Schroers

Abstract The theory of chiral magnetic skrymions in two-dimensional systems has a a number of remarkable geometrical features. Some of them are based on the interpretation of the DMI interaction in terms of a non-abelian gauge field, which allows one to write down and understand properties of static multi-skrymions. There are further geometrical surprises in the dynamics of skyrmions, in particular in their response to applied currents. In this talk I will review the geometrical features of chiral magnetic skyrmions, and report on some recent research on spin-orbit and spin-transfer torques.