Unveiling the three-dimensional magnetic texture of skyrmion tubes

Magnetic skyrmions are stable topological solitons with complex non-coplanar spin structures. Their nanoscopic size and the low electric currents required to control their motion has opened a new field of research, skyrmionics, that aims for the usage of skyrmions as information carriers. Further advances in skyrmionics call for a thorough understanding of their three-dimensional (3D) spin texture, skyrmion–skyrmion interactions and the coupling to surfaces and interfaces, which crucially affect skyrmion stability and mobility. Here, we quantitatively reconstruct the 3D magnetic texture of Bloch skyrmions with sub-10-nanometre resolution using holographic vector-field electron tomography. The reconstructed textures reveal local deviations from a homogeneous Bloch character within the skyrmion tubes, details of the collapse of the skyrmion texture at surfaces and a correlated modulation of the skyrmion tubes in FeGe along their tube axes. Additionally, we confirm the fundamental principles of skyrmion formation through an evaluation of the 3D magnetic energy density across these magnetic solitons.

Two-loop superstring five-point amplitudes. Part III. Construction via the RNS formulation: even spin structures

The contribution from even spin structures to the genus-two amplitude for five massless external NS states in Type II and Heterotic superstrings is evaluated from first principles in the RNS formulation. Using chiral splitting with the help of loop momenta this problem reduces to the evaluation of the corresponding chiral amplitude, which is carried out using the same techniques that were used for the genus-two amplitude with four external NS states. The results agree with the parity-even NS components of a construction using chiral splitting and pure spinors given in earlier companion papers [29] and [33].

Magnetic particles and strings in iron langasite

Magnetic topological defects can store and carry information. Replacement of extended defects, such as domain walls and Skyrmion tubes, by compact magnetic particles that can propagate in all three spatial directions may open an extra dimension in the design of magnetic memory and data processing devices. We show that such objects can be found in iron langasite, which exhibits a hierarchy of non-collinear antiferromagnetic spin structures at very different length scales. We derive an effective model describing long-distance magnetic modulations in this chiral magnet and find unusual two- and three-dimensional topological defects. The order parameter space of our model is similar to that of superfluid 3He-A, and the particle-like magnetic defect is closely related to the Shankar monopole and hedgehog soliton in the Skyrme model of baryons. Mobile magnetic particles stabilized in non-collinear antiferromagnets can play an important role in antiferromagnetic spintronics.

Spin photonics: from transverse spin to photonic skyrmions

Spin angular momentum associated with circular polarization is a fundamental and important aspect of photons both in classical and quantum optics. The interaction of this optical spin with matter and structures results in many intriguing optical effects and state-of-the-art applications covered under the emerging subject of spin optics. Distinct from longitudinal optical spin along the mean wavevector, transverse spin, the corresponding vector of which is perpendicular to the mean wavevector, prevails and plays a significant role in confined electromagnetic waves such as focused beams, guided waves, and evanescent waves. In the optical near-field, these transverse spins are generated owing to the spatial variation of the kinetic momentum of confined electromagnetic waves, where the spin and orbital angular momenta are strongly coupled, leading to many interesting topological spin structures and properties. Several reviews on optical transverse spins have been published in recent years in which their concepts and the various configurations producing them were introduced systematically. Here, we introduce in this review the underlying physics and dynamics of transverse spin and the resultant topological structures and properties such as the photonic skyrmions and merons. We term this sub-area ‘spin photonics’, its scope being to cover the design and research of spin structures in strongly confined electromagnetic fields with unique properties and applications. The concepts and framework reviewed have importance in optics, topological photonics, metrology, and quantum technologies and may be used to extend spin-dynamics concepts to fluidic, acoustic, and gravitational waves.

Magneto-optical spectroscopy on Weyl nodes for anomalous and topological Hall effects in chiral MnGe

Physics of Weyl electrons has been attracting considerable interests and further accelerated by recent discoveries of giant anomalous Hall effect (AHE) and topological Hall effect (THE) in several magnetic systems including non-coplanar magnets with spin chirality or small-size skyrmions. These AHEs/THEs are often attributed to the intense Berry curvature generated around the Weyl nodes accompanied by band anti-crossings, yet the direct experimental evidence still remains elusive. Here, we demonstrate an essential role of the band anti-crossing for the giant AHE and THE in MnGe thin film by using the terahertz magneto-optical spectroscopy. The low-energy resonance structures around ~ 1.2 meV in the optical Hall conductivity show the enhanced AHE and THE, indicating the emergence of at least two distinct anti-crossings near the Fermi level. The theoretical analysis demonstrates that the competition of these resonances with opposite signs is a cause of the strong temperature and magnetic-field dependences of observed DC Hall conductivity. These results lead to the comprehensive understanding of the interplay among the transport phenomena, optical responses and electronic/spin structures.

Spin structures of the ground states of four body bound systems with spin 3 cold atoms

We consider the case that four spin-3 atoms are confined in an optical trap. The temperature is so low that the spatial degrees of freedom have been frozen. Exact numerical and analytical solutions for the spin-states have been both obtained. Two kinds of phase-diagrams for the ground states (g.s.) have been plotted. In general, the eigen-states with the total-spin S (a good quantum number) can be expanded in terms of a few basis-states $$f_{S,i}$$ f S , i . Let $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ be the probability of a pair of spins coupled to $$\lambda =0, 2, 4$$ λ = 0 , 2 , 4 , and 6 in the $$f_{S,i}$$ f S , i state. Obviously, when the strength $$g_{\lambda }$$ g λ of the $$\lambda $$ λ -channel is more negative, the basis-state with the largest $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ would be more preferred by the g.s.. When two strengths are more negative, the two basis-states with the two largest probabilities would be more important components. Thus, based on the probabilities, the spin-structures (described via the basis-states) can be understood. Furthermore, all the details in the phase-diagrams, say, the critical points of transition, can also be explained. Note that, for $$f_{S,i}$$ f S , i , $$P_{f_{S,i}}^{\lambda }$$ P f S , i λ is completely determined by symmetry. Thus, symmetry plays a very important role in determining the spin-structure of the g.s..