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Register a new userUnified topological characterization of electronic states in spin textures from noncommutative K-theory
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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.
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Quantum oxide materials possess a vast range of properties stemming from the interplay between the lattice, charge, spin and orbital degrees of freedom, in which electron correlations often play an important role. Historically, the spin-orbit coupling was rarely a dominant energy scale in oxides. It however recently came to the forefront, unleashing various exotic phenomena connected with real and reciprocal-space topology that may be harnessed in spintronics. In this article, we review the recent advances in the new field of oxide spin-orbitronics with a special focus on spin-charge interconversion from the direct and inverse spin Hall and Edelstein effects, and on the generation and observation of topological spin textures such as skyrmions. We highlight the control of spin-orbit-driven effects by ferroelectricity and give perspectives for the field.
Topologically non-trivial spin textures, such as skyrmions and dislocations, display emergent electrodynamics and can be moved by spin currents over macroscopic distances. These unique properties and their nanoscale size make them excellent candidates for the development of next-generation logic gates, race-track memory, and artificial synapses for neuromorphic computing. A major challenge for these applications - and the investigation of nanoscale magnetic structures in general - is the realization of detection schemes that provide high resolution and sensitivity. We study the local magnetic properties of disclinations, dislocations, and domain walls in FeGe, and reveal a pronounced response that distinguishes the individual spin textures from the helimagnetic background. Combination of magnetic force microscopy and micromagnetic simulations links the non-linear response to the local magnetic susceptibility. Based on the findings, we propose a read-out scheme using superconducting micro-coils, representing an innovative approach for detecting topologically non-trivial spin textures and domain walls in device-relevant geometries.
Two-dimensional (2D) van der Waals (vdW) materials show a range of profound physical properties that can be tailored through their incorporation in heterostructures and manipulated with external forces. The recent discovery of long-range ferromagnetic order down to atomic layers provides an additional degree of freedom in engineering 2D materials and their heterostructure devices for spintronics, valleytronics and magnetic tunnel junction switches. Here, using direct imaging by cryo-Lorentz transmission electron microscopy we show that topologically nontrivial magnetic-spin states, skyrmionic bubbles, can be realized in exfoliated insulating 2D vdW Cr2Ge2Te6. Due to the competition between dipolar interactions and uniaxial magnetic anisotropy, hexagonally-packed nanoscale bubble lattices emerge by field cooling with magnetic field applied along the out-of-plane direction. Despite a range of topological spin textures in stripe domains arising due to pair formation and annihilation of Bloch lines, bubble lattices with single chirality are prevalent. Our observation of topologically-nontrivial homochiral skyrmionic bubbles in exfoliated vdW materials provides a new avenue for novel quantum states in atomically-thin insulators for magneto-electronic and quantum devices.
The recent discovery of higher-order topological insulators (HOTIs) has significantly extended our understanding of topological phases of matter. Here, we predict that second-order corner states can emerge in the dipolar-coupled dynamics of topological spin textures in two-dimensional artificial crystals. Taking a breathing honeycomb lattice of magnetic vortices as an example, we derive the full phase diagram of collective vortex gyrations and identify three types of corner states that have not been discovered before. We show that the topological zero-energy corner modes are protected by a generalized chiral symmetry in the sexpartite lattice, leading to particular robustness against disorder and defects, although the conventional chiral symmetry of bipartite lattices is absent. We propose the use of the quantized $mathbb{Z}_{6}$ Berry phase to characterize the nontrivial topology. Interestingly, we observe corner states at either obtuse-angled or acute-angled corners, depending on whether the lattice boundary has an armchair or zigzag shape. Full micromagnetic simulations confirm the theoretical predictions with good agreement. Experimentally, we suggest using the recently developed ultrafast Lorentz microscopy technique [M{o}ller emph{et al}.,{arXiv:1907.04608}] to detect the topological corner states by tracking the nanometer-scale vortex orbits in a time-resolved manner. Our findings open up a promising route for realizing higher-order topologically protected corner states in magnetic systems and finally achieving topological spintronic memory and computing.
Spin polarized two-dimensional electronic states have been previously observed on metallic surface alloys with giant Rashba splitting and on the surface of topological insulators. We study the surface band structure of these systems, in a unified manner, by exploiting recent results of k.p theory. The model suggests a different way to address the effect of anisotropy in Rashba systems. Changes in the surface band structure of various Rashba compounds can be captured by a single effective parameter which quantifies the competition between the Rashba effect and the hexagonal warping of the constant energy contours. The same model provides a unified phenomenological description of the surface states belonging to materials with topologically trivial and non-trivial band structures.
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