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Register a new userTopological characterization of classical waves: the topological origin of magnetostatic surface spin waves
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We propose a topological characterization of Hamiltonians describing classical waves. Applying it to the magnetostatic surface spin waves that are important in spintronics applications, we settle the speculation over their topological origin. For a class of classical systems that includes spin waves driven by dipole-dipole interactions, we show that the topology is characterized by vortex lines in the Brillouin zone in such a way that the symplectic structure of Hamiltonian mechanics plays an essential role. We define winding numbers around these vortex lines and identify them to be the bulk topological invariants for a class of semimetals. Exploiting the bulk-edge correspondence appropriately reformulated for these classical waves, we predict that surface modes appear but not in a gap of the bulk frequency spectrum. This feature, consistent with the magnetostatic surface spin waves, indicates a broader realm of topological phases of matter beyond spectrally gapped ones.
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The existence of backscattering-immune spin-wave modes is demonstrated in magnetic thin films of nano-scale thickness. Our results reveal that chiral Magneto Static Surface Waves (cMSSWs), which propagate perpendicular to the magnetization direction in an in-plane magnetized thin film, are robust against backscattering from surface defects. cMSSWs are protected against various types of surface inhomogeneities and defects as long as their frequency lies inside the gap of the volume modes. Our explanation is independent of the topology of the modes and predicts that this robustness is a consequence of symmetry breaking of the dynamic magnetic fields of cMSSWs due to the off-diagonal part of the dipolar interaction tensor, which is present both for long- (dipole dominated) and short-wavelength (exchange dominated) spin waves. Micromagnetic simulations confirm the robust character of the cMSSWs. Our results open a new direction in designing highly efficient magnonic logic elements and devices employing cMSSWs in nano-scale thin films.
The surface of a topological insulator hosts Dirac electronic states with the spin-momentum locking, which constrains spin orientation perpendicular to electron momentum. As a result, collective plasma excitations in the interacting Dirac liquid manifest themselves as coupled charge- and spin-waves. Here we demonstrate that the presence of the spin component enables effective coupling between plasma waves and spin waves at interfaces between the surface of a topological insulator and insulating magnet. Moreover, the helical nature of spin-momentum locking textures provides the phase winding in the coupling between the spin and plasma waves that makes the spectrum of hybridized spin-plasma modes to be topologically nontrivial. We also show that such topological modes lead to a large thermal Hall response.
The dipolar (magnetostatic) interaction dominates the behavior of spin waves in magnetic films in the long-wavelength regime. In an in-plane magnetized film, volume modes exist with a negative group velocity (backward volume magnetostatic spin waves), in addition to the forward surface-localized mode (Damon-Eshbach). Inside the film of finite thickness $L$, the volume modes have a nontrivial spatial dependence, and their two-dimensional dispersion relations $omega(mathbf{k})$ can be calculated only numerically. We present explicit perturbative expressions for the profiles and frequencies of the volume modes, taking into account an in-plane applied field and uniaxial anisotropy, for the regimes $lVert mathbf{k}L rVert gg 1$ and $lVert mathbf{k}L rVert ll 1$, which together provide a good indication of the behavior of the modes for arbitrary wavevector $mathbf{k}$. Moreover, we derive a very accurate semianalytical expression for the dispersion relation $omega(mathbf{k})$ of the lowest-frequency mode that is straightforward to evaluate using standard numerical routines. Our results are useful to quickly interpret and control the excitation and propagation of spin waves in (opto-)magnetic experiments.
Propagation of backward magnetostatic surface spin waves (SWs) in exchange coupled Co/FeNi bilayers are studied by using Brillouin light scattering (BLS) technique. Two types of SWs modes were identified in our BLS measurements. They are magnetostatic surface waves (MSSWs) mode and perpendicular standing spin waves (PSSWs) mode. The dispersion relations of MSSWs obtained from the Stokes and Anti-Stokes measurements display respectively positive and negative group velocities. The Anti-Stokes branch with positive phase velocities and negative group velocities, known as backward magnetostatic surface mode originates from the magnetostatic interaction of the bilayer. The experimental data are in good agreement with the theoretical calculations. Our results are useful for understanding the SWs propagation and miniaturizing SWs storage devices.
We study the spin waves of the triangular skyrmion crystal that emerges in a two dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii-Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic backscattering. Our results illustrate how topological phases can occur in self-generated emergent superlattices at the mesoscale.
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