Dzyaloshinskii-Moriya Gradients Unlock Topological Dimensional Reduction in Magnetic Hopfions

Abstract

Three-dimensional magnetic solitons retain topological protection only while their spin field remains continuous. Here we show that chemical inhomogeneity can break this protection in a controlled way, converting a hopfion-like toroidal texture into an effectively two-dimensional skyrmion string. Tilt-dependent Lorentz transmission electron microscopy, electron energy-loss spectroscopy, and micromagnetic simulations of pristine, uniformly Y-doped, and nonuniformly Y-doped disordered TiO2 nanoparticles embedded in a FeCrNiMn host reveal two regimes. Uniform Y doping enriches Ti3+/oxygen-vacancy localization centers and stabilizes closed rings with Hopf invariant QH approximately 1. Nonuniform Y doping forms a Ti4+-rich, vacancy-depleted boundary that creates a sharp q=D/(2A) gradient and a weak-moment leakage channel. This coupled mismatch torque and continuity leakage split the ring, leaving a skyrmion-string remnant and a field-sensitive helicity texture.