Designing Nontrivial Real-Space Berry Curvature through Non-Monotonic Bulk Inversion Symmetry Breaking in Self-Intercalated Cr1+δTe2.

The real-space Berry curvature ( ${\Omega }_r$ ) in magnetic materials has gained significant attention for its potential applications in chiral spintronic devices. ${\Omega }_r$ manifests in chiral spin textures stabilized by the Dzyaloshinskii-Moriya interaction (DMI), which arises in inversion-asymmetric systems. Herein, the topological Hall effect (THE) in 2D ferromagnet Cr_1+δTe₂ as a function of the Cr intercalant (δ) is investigated. A nonlinear dependence of the THE amplitude induced by ${\Omega }_r$ on δ is identified, originating from non-monotonic bulk inversion symmetry breaking via Cr self-intercalation. Density-functional theory calculations further reveal a strong correlation between THE amplitude and bulk DMI strength (E _DMI), demonstrating both the mechanism of THE and the tunability of ${\Omega }_r$ in Cr_1+δTe₂. Remarkably, Cr_1.612Te₂ exhibits the largest THE amplitude observed to date (2.75 μΩ⋅cm) in the Cr_1+δTe₂ family, which is a strong candidate for the highest THE amplitude, given its magnetic anisotropy and E _DMI. Overall, by confirming the critical role of bulk DMI and magnetic anisotropy in engineering ${\Omega }_r$ , the most efficient strategy for designing ${\Omega }_r$ in 2D ferromagnetic materials through atomic-scale self-intercalation is proposed. These findings provide fundamental insights into the relationship between E _DMI and THE in Cr_1+δTe₂ and offer a promising approach for designing high-performance chiral spintronic devices.