Executive Summary : | Magnonics, a field dedicated to the study of the generation, transport, and manipulation of magnons, and their detection in magnetic insulators, has experienced significant advancements in recent years. Its promising attributes, including low power consumption, negligible heat dissipation, tuneability, and better information processing with long-distance propagation, position magnonic devices as a compelling option for future technology [1-3]. However, the transportation and manipulation of magnons are greatly hindered by inevitable scattering from impurities, phonons, and other magnons. In this context, the topological properties of magnons have garnered significant attention recently. In a topological magnonic insulating state (TMI), magnons can potentially be transported in a non-dissipative manner along surfaces or edges due to the non-trivial topology of magnon band structures, protected by chiral symmetry. It is predicted that topological magnonic states can originate from inversion and time-reversal symmetry breaking via Dzyaloshinskii-Moriya interactions, magnetic textures, and magnetic dipolar interactions in magnetically ordered systems with special crystal symmetries such as Kagome and Honeycomb lattice, as well as in nanostructures [4-7]. However, the experimental detection of topological states of magnons is quite challenging, and the thermal magnon Hall effect (TMHE) has provided a promising avenue in this direction. The observed TMHE in insulating pyrochlore ferromagnets have been explained by considering the topological edge states [8-9]. subsequently, TMHE has also been observed in other systems i.e. garnets, kagome lattices, and frustrated quantum magnets with a signature of TMI [10-13]. since the special crystal symmetry and magnetic texture are potential ingredients for TMI, the quantum magnets with kagome and non-collinear magnetic lattices become natural choices for exploring TMI. Notably, magnonic Weyl states have been recently observed in the ferrimagnetic multiferroic Cu2OseO3 through inelastic neutron scattering [14]. In this context, we propose to carry out investigations of magnon transport in selected magnetic insulators with kagome lattice and magnetic textures with the target of discovering new TMIs. Here, we plan to study swedenborgite CaBaT₄O₇ (T = Co, Fe) systems first, which are known to be magnetic multiferroics and are known to comprise of kagome and triangular lattices formed by magnetic ions with a non-collinear magnetic ground state [15]. Another intriguing class of systems is the frustrated rare-earth perovskites (RETO3, where RE = rare-earth elements and T = Cr, Fe, and Mn). These magnetic multiferroics exhibit non-collinear magnetic orders, which arise from magnetic frustration and play a crucial role in promoting ferroelectricity [16]. Given that magnon transport is profoundly influenced by device dimensions and geometry, the investigation of nanofabricated structures becomes particularly intriguing. |