Emergence of Nontrivial Topological Magnon States in Skyrmionium Lattices with Zero Topological Charge

We predict the emergence of nontrivial topological magnon states in the skyrmionium lattice with zero topological charge. We propose the concept of weighted magnetic flux, which provides a clear physical picture for this anomalous phenomenon. We also map the skyrmionium lattice onto the Haldane model, offering an alternative framework for interpreting this. Our findings challenge the conventional wisdom that such states are linked to nonzero topological charge in skyrmion lattices, offering a new perspective in topological magnonics. To facilitate experimental validation, we propose two methods for preparing the skyrmionium lattice and calculate the induced magnon thermal Hall conductivity, which is a key indicator in transport measurements.