Topological Aspects of Ferromagnets and Antiferromagnets

  • Fengjun Zhuo

Student thesis: Doctoral Thesis


This dissertation presents our theoretical study of fundamental topological properties of ferromagnetic and antiferromagnetic systems, including topological magnetic excitations and topological magnetic textures. In the first part, we explored the topological magnonic phases in various systems with Dzyaloshinskii-Moriya interaction using a linear spin-wave theory. We have calculated the magnonic Chern number, topological phase diagram, and magnon thermal Hall conductivity at low temperature with tunable interactions due to the lattice deformation. In particular, we have investigated the topological phase transitions between distinct topological magnonic phases characterized by magnonic Chern numbers. We have also studied the magnon band topology and magnonic edge states in each topological phase. We found a sign reversal of the thermal Hall conductivity during topological phase transitions. We explicitly demonstrated the correspondence of thermal Hall conductivity with the topological edge states and their propagation directions. In the second part, a magnonic metamaterial in the presence of spatially modulated Dzyaloshinskii-Moriya interaction was theoretically proposed and demonstrated by micromagnetic simulations. By analogy to the fields of photonics, we first established magnonic Snell’s law for spin waves passing through an interface between two media with different dispersion relations due to different Dzyaloshinskii-Moriya interactions. Based on magnonic Snell’s law, we found that spin waves can experience total internal reflection. The critical angle of total internal reflection was strongly dependent on the sign and strength of Dzyaloshinskii-Moriya interaction. Furthermore, spin-wave beam fiber and spin-wave lens were designed by utilizing the artificial magnonic metamaterials with inhomogeneous Dzyaloshinskii-Moriya interactions. In the last part, we studied the impact of spin Hall torque, spin transfer torque, and topological torque on the velocity-current relation of antiferromagnetic skyrmions with the aim of reducing the deformation. Using a combination of micromagnetic simulations and analytical derivations, we demonstrated that the lateral expansion of the antiferromagnetic skyrmion is reminiscent of the well-known Lorentz contraction identified in one-dimensional antiferromagnetic domain walls. We also showed that in the flow regime the lateral expansion is accompanied by a progressive saturation of the skyrmion velocity when driven by spin Hall and topological torques. This saturation occurs at much smaller velocities when driven by the topological torque, while the lateral expansion is reduced, preventing the skyrmion size from diverging at large current densities. Our findings suggested that a compromise must be made between skyrmion velocity and lateral expansion during the device design. In this respect, exploiting the topological torque could lead to better control of the skyrmion velocity in antiferromagnetic racetracks.
Date of AwardJun 2022
Original languageEnglish (US)
Awarding Institution
  • Physical Sciences and Engineering
SupervisorUdo Schwingenschloegl (Supervisor) & Aurelien Manchon (Supervisor)


  • Spintronics;Condensed Matter Physics;Topological materials;Magnons;Skyrmions;Spin waves.

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