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Register a new userBulk and surface topological indices for a skyrmion string
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The magnetic skyrmion is a topological magnetic vortex, and its topological nature is characterized by an index called skyrmion number which is a mapping of the magnetic moments defined on a two-dimensional space to a unit sphere. In three-dimensions, a skyrmion, i.e., a vortex penetrating though the magnet naturally forms a string, which terminates at the surfaces of the magnet or in the bulk. For such a string, the topological indices, which control its topological stability are less trivial. Here, we show theoretically, in terms of numerical simulation for the current-driven motion of a skyrmion string in a film sample with the step edges on the surface, that the topological indices relevant to the stability are the followings; (i) skyrmion number along the developed surface, and (ii) the monopole charge in the bulk defined as the integral over the surface enclosing a singular magnetic configuration. As long as the magnetic configuration is slowly varying, the former is conserved while its changes is associated with nonzero monopole charge. The skyrmion number and the monoplole charge offer a coherent understanding of the stability of the topological magnetic texture and the nontrivial dynamics of skyrmion strings.
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Here we report the investigation of the anomalous Hall effect in the magnetically doped topological insulator (V,Bi,Sb)2Te3. We find it contains two contributions of opposite sign. Both components are found to depend differently on carrier density, leading to a sign inversion of the total anomalous Hall effect as a function of applied gate voltage. The two contributions are found to have different magnetization reversal fields, which in combination with a temperature dependent study points towards the coexistence of two ferromagnetic orders in the system. Moreover, we find that the sign of total anomalous Hall response of the system depends on the thickness and magnetic doping density of the magnetic layer. The thickness dependence suggests that the two ferromagnetic components originate from the surface and bulk of the magnetic topological insulator film. We believe that our observations provide insight on the magnetic behavior, and thus will contribute to an eventual understanding of the origin of magnetism in this material class. In addition, our data bears a striking resemblance to anomalous Hall signals often associated with skyrmion contributions. Our analysis provides a straightforward explanation for both the magnetic field dependence of the Hall signal and the observed change in sign without needing to invoke skyrmions, and thus suggest that caution is needed when making claims of effects from skyrmion phases.
We show that skyrmions on the surface of a magnetic topological insulator may experience an attractive interaction that leads to the formation of a skyrmion-skyrmion bound state. This is in contrast to the case of skyrmions in a conventional chiral ferromagnet, for which the intrinsic interaction is repulsive. The origin of skyrmion binding in our model is the molecular hybridization of topologically protected electronic orbitals associated with each skyrmion. Attraction between the skyrmions can therefore be controlled by tuning a chemical potential that populates/depopulates the lowest-energy molecular orbital. We find that the skyrmion-skyrmion bound state can be made stable, unstable, or metastable depending on the chemical potential, magnetic field, and easy-axis anisotropy of the underlying ferromagnet, resulting in a rich phase diagram. Finally, we discuss the possibility to realize this effect in a recently synthesized Cr doped ${left(mathrm{Bi}_{2-y}mathrm{Sb}_{y}right)}_{2}mathrm{Te}_3$ heterostructure.
We consider a magnetic skyrmion crystal formed at the surface of a topological insulator. Incorporating the exchange interaction between the helical Dirac surface states and the periodic Neel or Bloch skyrmion texture, we obtain the resulting electronic band structures. We discuss the properties of the reconstructed skyrmion bands, namely the impact of symmetries on the energies and Berry curvature. We find substantive qualitative differences between the Neel and Bloch cases, with the latter generically permitting a low-energy tight-binding representation whose parameters are tightly constrained by symmetries. We explicitly construct the associated Wannier orbitals, which resemble the ring-like chiral bound states of helical Dirac fermions coupled to a single skyrmion in a ferromagnetic background. We construct a two-band tight-binding model with complex nearest-neighbor hoppings which captures the salient topological features of the low-energy bands. Our results are relevant to magnetic topological insulators (TIs), as well as to TI-magnetic thin film heterostructures, in which skyrmion crystals may be stabilized.
Frustrated topological spin textures have unique properties that may enable novel spintronic applications, such as the helicity-based information storage. Here we report the statics and current-induced dynamics of two-dimensional (2D) pancake skyrmions in a stack of weakly coupled frustrated magnetic monolayers, which form a three-dimensional (3D) skyrmion string. The Bloch-type skyrmion string is energetically more stable than its Neel-type counterpart. It can be driven into translational motion by the dampinglike spin-orbit torque and shows the damping-dependent skyrmion Hall effect. Most notably, the skyrmion string can be transformed to a dynamically stable bimeron string by the dampinglike spin-orbit torque. The current-induced bimeron string rotates stably with respect to its center, which can spontaneously transform back to a skyrmion string when the current is switched off. Our results reveal unusual physical properties of 3D frustrated spin textures, and may open up new possibilities for spintronic applications based on skyrmion and bimeron strings.
We introduce a new resistance measurement method that is useful in characterizing materials with both surface and bulk conduction, such as three-dimensional topological insulators. The transport geometry for this new resistance measurement configuration consists of one current lead as a closed loop that fully encloses the other current lead on the surface, and two voltage leads that are both placed outside the loop. We show that in the limit where the transport is dominated by the surface conductivity of the material, the four-terminal resistance measured from such a transport geometry is proportional to $sigma_b/sigma_s^2$, where $sigma_b$ and $sigma_s$ are the bulk and surface conductivities of the material, respectively. We call this new type of measurement textit{inverted resistance measurement}, as the resistance scales inversely with the bulk resistivity. We discuss possible implementations of this new method by performing numerical calculations on different geometries and introduce strategies to extract the bulk and surface conductivities. We also demonstrate inverted resistance measurements on SmB$_6$, a topological Kondo insulator, using both single-sided and coaxially-aligned double-sided Corbino disk transport geometries. Using this new method, we are able to measure the bulk conductivity, even at low temperatures, where the bulk conduction is much smaller than the surface conduction in this material.
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