Designing Nontrivial Real‐Space Berry Curvature through Non‐Monotonic Bulk Inversion Symmetry Breaking in Self‐Intercalated Cr_1+δTe₂

The real-space Berry curvature ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow><mml:msub><mml:mi>Ω</mml:mi> <mml:mi>r</mml:mi></mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) in magnetic materials has gained significant attention for its potential applications in chiral spintronic devices. <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow><mml:msub><mml:mi>Ω</mml:mi> <mml:mi>r</mml:mi></mml:msub> </mml:mrow> </mml:mrow> </mml:math> 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 (<i>δ</i>) is investigated. A nonlinear dependence of the THE amplitude induced by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow><mml:msub><mml:mi>Ω</mml:mi> <mml:mi>r</mml:mi></mml:msub> </mml:mrow> </mml:mrow> </mml:math> on <i>δ</i> 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 (<i>E</i> _DMI), demonstrating both the mechanism of THE and the tunability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow><mml:msub><mml:mi>Ω</mml:mi> <mml:mi>r</mml:mi></mml:msub> </mml:mrow> </mml:mrow> </mml:math> 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 <i>E</i> _DMI. Overall, by confirming the critical role of bulk DMI and magnetic anisotropy in engineering <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow><mml:msub><mml:mi>Ω</mml:mi> <mml:mi>r</mml:mi></mml:msub> </mml:mrow> </mml:mrow> </mml:math> , the most efficient strategy for designing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow><mml:msub><mml:mi>Ω</mml:mi> <mml:mi>r</mml:mi></mml:msub> </mml:mrow> </mml:mrow> </mml:math> in 2D ferromagnetic materials through atomic-scale self-intercalation is proposed. These findings provide fundamental insights into the relationship between <i>E</i> _DMI and THE in Cr_1+δTe₂ and offer a promising approach for designing high-performance chiral spintronic devices.