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Magnetic skyrmion crystal at a topological insulator surface

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 Added by Arun Paramekanti
 Publication date 2021
  fields Physics
and research's language is English
 Authors Stefan Divic




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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.



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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.
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The surface states of a topological insulator are described by an emergent relativistic massless Dirac equation in 2+1 dimensions. In contrast to graphene, there is an odd number of Dirac points, and the electron spin is directly coupled to the momentum. We show that a magnetic impurity opens up a local gap and suppresses the local density of states. Furthermore, the Dirac electronic states mediate an RKKY interaction among the magnetic impurities which is always ferromagnetic, whenever the chemical potential lies near the Dirac point. These effects can be directly measured in STM experiments. We also study the case of quenched disorder through a renormalization group analysis.
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.
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