Insights into the orbital magnetism of noncollinear magnetic systems

The orbital magnetic moment is usually associated with the relativistic spin-orbit interaction, but recently it has been shown that noncollinear magnetic structures can also be its driving force. This is important not only for magnetic skyrmions, but also for other noncollinear structures, either bulk-like or at the nanoscale, with consequences regarding their experimental detection. In this work we present a minimal model that contains the effects of both the relativistic spin-orbit interaction and of magnetic noncollinearity on the orbital magnetism. A hierarchy of models is discussed in a step-by-step fashion, highlighting the role of time-reversal symmetry breaking for translational and spin and orbital angular motions. Couplings of spin-orbit and orbit-orbit type are identified as arising from the magnetic noncollinearity. We recover the atomic contribution to the orbital magnetic moment, and a nonlocal one due to the presence of circulating bound currents, exploring different balances between the kinetic energy, the spin exchange interaction, and the relativistic spin-orbit interaction. The connection to the scalar spin chirality is examined. The orbital magnetism driven by magnetic noncollinearity is mostly unexplored, and the presented model contributes to laying its groundwork

Chirality-driven orbital magnetic moments as a new probe for topological magnetic structures

When electrons are driven through unconventional magnetic structures, such as skyrmions, they experience emergent electromagnetic fields that originate several Hall effects. Independently, ground state emergent magnetic fields can also lead to orbital magnetism, even without the spin-orbit interaction. The close parallel between the geometric theories of the Hall effects and of the orbital magnetization raises the question: does a skyrmion display topological orbital magnetism? Here we first address the smallest systems with nonvanishing emergent magnetic field, trimers, characterizing the orbital magnetic properties from first-principles. Armed with this understanding, we study the orbital magnetism of skyrmions, and demonstrate that the contribution driven by the emergent magnetic field is topological. This means that the topological contribution to the orbital moment does not change under continous deformations of the magnetic structure. Furthermore, we use it to propose a new experimental protocol for the identification of topological magnetic structures, by soft x-ray spectroscopy.Comment: 17 pages, 5 figures, to be published in Nature Communication

Effective Altruism and Religion

A new movement is on the scene: effective altruism—the combination of love and efficiency, making the world a better place not just with a bleeding heart and empathy but with a radical focus on reason and evidence and never losing sight of the goal of maximal impact. Its adherents typically stem from strongly secular environments such as elite philosophy departments or Silicon Valley. So far, a religious perspective on this movement has been lacking. What can people of faith learn from effective altruism, how can they contribute, and what must they criticise? This volume offers a first examination of these questions, providing both a Buddhist and an Orthodox Jewish perspective on them, in addition to various Christian contributions. With contributions by Calvin Baker, Lara Buchak, Mara-Daria Cojocaru, Stefan Höschele, Markus Huppenbauer, Robert MacSwain, David Manheim, Kathryn Muyskens, Stefan Riedener, Dominic Roser and Jakub Synowiec.PublishedA new movement is on the scene: effective altruism—the combination of love and efficiency, making the world a better place not just with a bleeding heart and empathy but with a radical focus on reason and evidence and never losing sight of the goal of maximal impact. Its adherents typically stem from strongly secular environments such as elite philosophy departments or Silicon Valley. So far, a religious perspective on this movement has been lacking. What can people of faith learn from effective altruism, how can they contribute, and what must they criticise? This volume offers a first examination of these questions, providing both a Buddhist and an Orthodox Jewish perspective on them, in addition to various Christian contributions. With contributions by Calvin Baker, Lara Buchak, Mara-Daria Cojocaru, Stefan Höschele, Markus Huppenbauer, Robert MacSwain, David Manheim, Kathryn Muyskens, Stefan Riedener, Dominic Roser and Jakub Synowiec

Topological spin Hall effect in antiferromagnetic skyrmions

The topological Hall effect (THE), as one of the primary manifestations of non-trivial topology of chiral skyrmions, is traditionally used to detect the emergence of skyrmion lattices with locally ferromagnetic order. In this work we demonstrate that the appearance of non-trivial two-dimensional chiral textures with locally {\it anti}-ferromagnetic order can be detected through the spin version of the THE $-$ the topological spin Hall effect (TSHE). Utilizing the semiclassical formalism, here used to combine chiral antiferromagnetic textures with a density functional theory description of the collinear, degenerate electronic structure, we follow the real-space real-time evolution of electronic SU(2) wavepackets in an external electric field to demonstrate the emergence of sizeable transverse pure spin current in synthetic antiferromagnets of the Fe/Cu/Fe trilayer type. We further unravel the extreme sensitivity of the TSHE to the details of the electronic structure, suggesting that the magnitude and sign of the TSHE in transition-metal synthetic antiferromagnets can be engineered by tuning such parameters as the thickness or band filling. Besides being an important step in our understanding of the topological properties of ever more complex skyrmionic systems, our results bear great potential in stimulating the discovery of antiferromagnetic skyrmions