Converging Periodic Boundary Conditions and Detection of Topological Gaps on Regular Hyperbolic Tessellations

Tessellations of the hyperbolic spaces by regular polygons are becoming popular because they support discrete quantum and classical models displaying unique spectral and topological characteristics. Resolving the true bulk spectra and the thermodynamic response functions of these models requires converging periodic boundary conditions and our work delivers a practical solution for this open problem on generic {p,q}-tessellations. This enables us to identify the true spectral gaps of bulk Hamiltonians and, as an application, we construct all but one topological models that deliver the topological gaps predicted by the K-theory of the lattices. We demonstrate the emergence of the expected topological spectral flows whenever two such bulk models are deformed into each other and, additionally, we prove the emergence of topological channels whenever a soft physical interface is created between different topological classes of Hamiltonians

Spectral and Combinatorial Aspects of Cayley-Crystals

Owing to their interesting spectral properties, the synthetic crystals over lattices other than regular Euclidean lattices, such as hyperbolic and fractal ones, have attracted renewed attention, especially from materials and meta-materials research communities. They can be studied under the umbrella of quantum dynamics over Cayley graphs of finitely generated groups. In this work, we investigate numerical aspects related to the quantum dynamics over such Cayley graphs. Using an algebraic formulation of the "periodic boundary condition" due to Lueck [Geom. Funct. Anal. 4, 455-481 (1994)], we devise a practical and converging numerical method that resolves the true bulk spectrum of the Hamiltonians. Exact results on the matrix elements of the resolvent, derived from the combinatorics of the Cayley graphs, give us the means to validate our algorithms and also to obtain new combinatorial statements. Our results open the systematic research of quantum dynamics over Cayley graphs of a very large family of finitely generated groups, which includes the free and Fuchsian groups.Comment: converging periodic bc for hyperbolic and fractal crystals, tested against exact result

The chiral Hall effect of magnetic skyrmions from a cyclic cohomology approach

We demonstrate the emergence of an anomalous Hall effect in chiral magnetic textures which is neither proportional to the net magnetization nor to the well-known emergent magnetic field that is responsible for the topological Hall effect. Instead, it appears already at linear order in the gradients of the magnetization texture and exists for one-dimensional magnetic textures such as domain walls and spin spirals. It receives a natural interpretation in the language of Alain Connes' noncommutative geometry. We show that this chiral Hall effect resembles the familiar topological Hall effect in essential properties while its phenomenology is distinctly different. Our findings make the re-interpretation of experimental data necessary, and offer an exciting twist in engineering the electrical transport through magnetic skyrmions.Comment: 14 pages, 5 figure

Unified topological characterization of electronic states in spin textures from noncommutative K-theory

The nontrivial topology of spin systems such as skyrmions in real space can promote complex electronic states. Here, we provide a general viewpoint at the emergence of topological electronic states in spin systems based on the methods of noncommutative K-theory. By realizing that the structure of the observable algebra of spin textures is determined by the algebraic properties of the noncommutative hypertorus, we arrive at a unified understanding of topological electronic states which we predict to arise in various noncollinear setups. The power of our approach lies in an ability to categorize emergent topological states algebraically without referring to smooth real- or reciprocal-space quantities. This opens a way towards an educated design of topological phases in aperiodic, disordered, or non-smooth textures of spins and charges containing topological defects.Comment: 5 pages, 2 figure

Imprinting and driving electronic orbital magnetism using magnons

Magnons, as the most elementary excitations of magnetic materials, have recently emerged as a prominent tool in electrical and thermal manipulation and transport of spin, and magnonics as a field is considered as one of the pillars of modern spintronics. On the other hand, orbitronics, which exploits the orbital degree of freedom of electrons rather than their spin, emerges as a powerful platform in efficient design of currents and redistribution of angular momentum in structurally complex materials. Here, we uncover a way to bridge the worlds of magnonics and electronic orbital magnetism, which originates in the fundamental coupling of scalar spin chirality, inherent to magnons, to the orbital degree of freedom in solids. We show that this can result in efficient generation and transport of electronic orbital angular momentum by magnons, thus opening the road to combining the functionalities of magnonics and orbitronics to their mutual benefit in the realm of spintronics applications.Comment: 9 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1910.0331

The interplay of Dzyaloshinskii-Moriya and Kitaev interactions for magnonic properties of Heisenberg-Kitaev honeycomb ferromagnets

The properties of Kitaev materials are attracting ever increasing attention owing to their exotic properties. In realistic two-dimensional materials, Kitaev interaction is often accompanied by the Dzyloshinskii-Moriya interaction, which poses a challenge of distinguishing their magnitude separately. In this work, we demonstrate that it can be done by accessing magnonic transport properties. By studying honeycomb ferromagnets exhibiting Dzyaloshinskii-Moriya and Kitaev interactions simultaneously, we reveal non-trivial magnonic topological properties accompanied by intricate magnonic transport characteristics as given by thermal Hall and magnon Nernst effects. We also investigate the effect of a magnetic field, showing that it does not only break the symmetry of the system but also brings drastic modifications to magnonic topological transport properties, which serve as hallmarks of the relative strength of anisotropic exchange interactions. Based on our findings, we suggest strategies to estimate the importance of Kitaev interactions in real materials.Comment: 6 pages, 4 figure

Revealing the higher-order spin nature of the Hall effect in non-collinear antiferromagnet Mn3Ni0.35Cu0.65N\mathrm{Mn_3Ni_{0.35}Cu_{0.65}N}

Ferromagnets generate an anomalous Hall effect even without the presence of a magnetic field, something that conventional antiferromagnets cannot replicate but noncollinear antiferromagnets can. The anomalous Hall effect governed by the resistivity tensor plays a crucial role in determining the presence of time reversal symmetry and the topology present in the system. In this work we reveal the complex origin of the anomalous Hall effect arising in noncollinear antiferromagnets by performing Hall measurements with fields applied in selected directions in space with respect to the crystalline axes. Our coplanar magnetic field geometry goes beyond the conventional perpendicular field geometry used for ferromagnets and allows us to suppress any magnetic dipole contribution. It allows us to map the in-plane anomalous Hall contribution and we demonstrate a 120$^\circ$ symmetry which we find to be governed by the octupole moment at high fields. At low fields we subsequently discover a surprising topological Hall-like signature and, from a combination of theoretical techniques, we show that the spins can be recast into dipole, emergent octupole and noncoplanar effective magnetic moments. These co-existing orders enable magnetization dynamics unachievable in either ferromagnetic or conventional collinear antiferromagnetic materials