Topological magnon bands for magnonics

Abstract

Topological excitations in magnetically ordered systems have attracted much attention lately. We report on topological magnon bands in ferromagnetic Shastry-Sutherland lattices whose edge modes can be put to use in magnonic devices. The synergy of Dzyaloshinskii-Moriya interactions and geometrical frustration are responsible for the topologically nontrivial character. Using exact spin-wave theory, we determine the finite Chern numbers of the magnon bands which give rise to chiral edge states. The quadratic band crossing point vanishes due the present anisotropies, and the system enters a topological phase. We calculate the thermal Hall conductivity as an experimental signature of the topological phase. Different promising compounds are discussed as possible physical realizations of ferromagnetic Shastry-Sutherland lattices hosting the required antisymmetric Dzyaloshinskii-Moriya interactions. Routes to applications in magnonics are pointed out. PACS numbers:Topological phases 1,2 exist in both fermionic and bosonic systems and constitute a fast developing research area. Although the theoretical understanding of fermionic topological systems has made impressive progress, topological bosonic excitations have gained considerable attention only in the past few years. Despite the increasing conceptual knowledge of topological matter, only very few materials have been identified with topological properties compared to the large number of potential topological materials 3 . Even less is known about potential applications. This is, in particular, true for topological bosonic signatures 4 . Thus, it is a major challenge to theoretically predict and experimentally verify topological bosonic fingerprints in order to move towards useful applications.In the research of topological properties in condensed matter, the magnetic degrees of freedom have increased in importance. Magnetic data storage is already a ubiquitous everyday technology 5 . Recently, magnetic spin waves, so-called magnons, themselves are used to carry and to process information which is called " magnonics " 6-8 . Adding topological aspects the field of magnonics 9 considerably enhances the possibilities to build efficient devices for which we will make a proposal in this paper.The challenge in finding topological signatures in magnetically ordered spin systems are the small Dzyaloshinskii-Moriya (DM) interactions 10,11 which induce only small Berry curvatures. The size of the DM terms relative to the isotropic coupling is roughly as large as |g − 2|/2, i.e., the deviation of the g factor from 2, because both result from spin-orbit coupling. Thus, the DM terms are generically too small to induce detectable topological effects. In strongly frustrated systems, however, the relative size of the DM terms can indeed be comparable to the isotropic couplings 12 .Another issue is the localization of edge modes. Employing the wording of semiconductor physics, one must distinguish direct (at fixed wave vector) and indirect gaps (allowing for changes in the wave vector)...

Chiral magnonic edge states in ferromagnetic skyrmion crystals controlled by magnetic fields

“…Realizing such control could be attained in topological magnon insulators [16][17][18], systems with a spatially periodic magnetic texture that support topologically protected magnonic edge states. A promising platform for the nascent field of topological magnonics [19][20][21] are ferromagnetic skyrmion crystals (FM-SkXs) [22,23], whose magnetic texure is shown in Fig. 1.…”

Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions

“…Quantum magnets are particularly promising since they have for long been a versatile platform to realise complex quantum states of matter including bosonic analogs of novel fermionic phases. The wide range of available quantum magnets with different lattice geometries and the ability to tune their properties readily by external magnetic field make them ideal testbed for realising bosonic analogs of topological states of matter [63,227,54,193,228,89,68,70,229,230,231,232,233,234 [1,87,88]. In this work, we have used experimentally determined Hamiltonian parameters [235] for the microscopic model that have been demonstrated to reproduce faithfully the experimentally observed behavior of the material [87].…”

“…The nature of DM-interaction chosen for the study(Fig To study low energy excitations (magnons) above the magnetic ground state, we have used the linearized HP transformation [63,67]. The HP transformation is a versatile and extensively used approach to study low energy magnons [192,193,63,54,180,67,173,71,68]. In this work, we have extended the HP approach to study magnon excitations above complex magnetic orders with longer periodicity.…”

“…Furthermore Lu et al [52] demonstrate that even in absence of scalar spin chirality in the antiferromagnetic systems, the topological Berry-phase of magnons can be generated via quantum fluctuations of scalar spin-chirality. Other studied frustrated lattice systems for topological magnon system are frustrated star-lattice [53] and Shastry Sutherland (SS)-lattice [54] with ferromagnetic ground state.…”

“…This results in an even richer variety of magnetic orderings including collinear, coplanar and non-coplanar spin configurations, several of which host topological magnons [58,189]. Previous studies of topological magnons for the SS lattice were restricted to the dimer [1] and the ferro-magnetic phases [54]. In recent past there has been a growing interest in studying topological magnons in non-collinear spin configurations in frustrated lattices.…”