Skyrmionium meta-matter: a topologically heterogeneous magnetic crystal with emergent hybrid dynamics

Abstract: We introduce and systematically investigate a new class of topological magnetic textures, skyrmionium meta-matter, composed of skyrmioniums (Skm, $Q=0$) and skyrmions (Sk, $Q=-1$) arranged in periodic lattices mimicking the richness of atomic materials. Pure skyrmionium lattices are unstable against elongation distortions and relax into the spiral phase, but even a small fraction of skyrmions acts as topological "pins" that stabilize diverse mixed Skm--Sk crystals. We classify these states by topological stoichiometry (Skm$_n$Sk$_m$) and show that each composition hosts multiple metastable polymorphs with distinct plane-group symmetries. Structural transformations between polymorphs are achieved by varying the lattice spacing, suggesting experimental control via pressure or strain. The collective spin dynamics is explored for both in-plane and out-of-plane AC magnetic fields. The resulting absorption spectra show resonant modes beyond the two rotational and one breathing mode of conventional skyrmion lattices. We identify hybrid excitations unique to Skm--Sk crystals, including (i) deformation-assisted rotations, where skyrmions acquire polygonal shapes and rotate, and (ii) orbital modes, where breathing skyrmioniums induce circular motion of confined skyrmions without changing their size. Mode frequencies span sub-GHz to above 10 GHz, consistent with exchange and DMI energy scales. Our results establish skyrmionium-based meta-matter as a versatile platform for tunable, topologically heterogeneous magnetic lattices with rich structural and dynamical properties, paving the way for reconfigurable magnonic and spintronic applications.