Emergent Noncoplanar Spin Chirality through Magnetic and Nonmagnetic Substitution in the Kagome Antiferromagnet Mn$_3$Sn

Technical Summary: Emergent Noncoplanar Spin Chirality through Magnetic and Nonmagnetic Substitution in Mn3Sn

Problem Statement
Controlling noncoplanar spin textures in centrosymmetric magnets is a central challenge for realizing emergent Berry-phase phenomena, such as the topological Hall effect (THE). While momentum-space Berry curvature drives the intrinsic anomalous Hall effect (AHE), real-space Berry curvature arises from finite scalar spin chirality ($\chi_{ijk} = \mathbf{S}_i \cdot (\mathbf{S}_j \times \mathbf{S}_k)$) in noncoplanar spin textures. The kagome antiferromagnet Mn$_3$Sn is a prototypical system for studying these effects due to its inverse triangular spin structure, which breaks time-reversal symmetry and generates large Berry curvature. However, the mechanisms governing the stabilization of noncoplanar textures and the resulting topological transport via chemical substitution remain incompletely understood, particularly regarding the distinct roles of magnetic versus nonmagnetic dopants.

Methodology
The authors synthesized single crystals of Mn$_3$Sn and substituted variants (Mn$_{3.1}$Sn, Mn$_{2.9}$Cr$_{0.2}$Sn, and Mn$_{2.9}$Cu$_{0.2}$Sn) using the self-flux method. Structural and phase purity were confirmed via X-ray diffraction (XRD) and energy-dispersive X-ray spectroscopy (EDXS).

• Experimental Characterization: Magnetization ($M(T)$ and $M(H)$) and electrical transport (longitudinal resistivity $\rho_{zz}$ and Hall resistivity $\rho_{zx}$) were measured using a Physical Property Measurement System (PPMS) over a temperature range of 2–300 K. The Hall resistivity was extracted via antisymmetrization to eliminate longitudinal artifacts.
• Theoretical Analysis: Density Functional Theory (DFT) calculations were performed using the VASP package with the GGA-PBE functional, including spin-orbit coupling (SOC) and Hubbard $U$ corrections (Liechtenstein formalism). Magnetization density of states (MDOS) was calculated to probe anisotropic magnetic behavior and electronic structure reconstruction.
• Data Analysis: The total Hall resistivity was decomposed into ordinary ($R_0$), anomalous ($R_s$), and topological ($\rho_T$) components. The topological Hall resistivity was isolated by subtracting the fitted conventional contributions. Skyrmion (chiral spin) density ($n_{sk}$) and characteristic length scales ($\lambda_{sk}$) were estimated using the relation $\rho_T = P R_0 n_{sk} \phi_0$.

Key Results
The study reveals that magnetic (Cr) and nonmagnetic (Cu) substitutions at the Mn site drive fundamentally different magnetic ground states and topological transport responses:

1. Cr Substitution (Magnetic Dopant):

   • Magnetic Behavior: Cr substitution enhances low-temperature spin canting and preserves the in-plane easy-axis anisotropy characteristic of pristine Mn$_3$Sn. It suppresses the spin-glass freezing temperature and eliminates the spin-reorientation transition (TSR).
   • Transport: The system exhibits a pronounced, monotonic enhancement of the topological Hall effect at low temperatures. The maximum topological Hall resistivity ($\rho_T^{max} \approx 2.02$ $\mu\Omega$cm) occurs at 2 K.
   • Texture: The effective characteristic length scale of the noncoplanar texture is short ($\lambda_{sk} \sim 3.7$ nm), and the chiral spin density ($n_{sk}$) is high ($\sim 1.32 \times 10^{17}$ m$^{-2}$ at 2 K), decreasing monotonically with temperature.

2. Cu Substitution (Nonmagnetic Dopant):

   • Magnetic Behavior: Cu substitution induces a spin-reorientation transition at $T_{SR} \approx 193$ K, accompanied by a rotation of the magnetic easy axis from in-plane (above $T_{SR}$) to predominantly out-of-plane (below $T_{SR}$). This is driven by exchange dilution and band-filling effects.
   • Transport: A broad, non-monotonic topological Hall regime is observed between 150 K and 208 K, with a maximum $\rho_T^{max} \approx 2.24$ $\mu\Omega$cm near 208 K. A concurrent carrier-type crossover (from hole to electron dominance) signals a reconstruction of the electronic structure.
   • Texture: The effective characteristic length scale is substantially larger ($\lambda_{sk} \sim 39$ nm), comparable to B20 skyrmion hosts. The chiral spin density peaks at intermediate temperatures ($\sim 2.76 \times 10^{15}$ m$^{-2}$ at $\sim 200$ K).

3. DFT Insights:

   • Calculations confirm that Cr substitution enhances in-plane MDOS components, preserving easy-plane anisotropy.
   • Cu substitution causes a redistribution of MDOS where the out-of-plane component ($M_z$) exceeds in-plane contributions near the Fermi level, directly indicating the reversal of magnetic anisotropy observed experimentally.

Significance and Claims
The paper claims to establish chemical substitution as a powerful strategy for engineering real-space Berry curvature and tunable chiral spin textures in kagome antiferromagnets. The authors demonstrate that:

• Distinct Pathways: Exchange enhancement (via magnetic Cr) and exchange dilution (via nonmagnetic Cu) represent two fundamentally different pathways for tuning topological transport.
• Mechanism Decoupling: The magnitude and temperature range of the THE are not governed solely by net magnetization or magnetic anisotropy but by the complex interplay of electronic configuration, exchange interactions, and spin reorientation.
• Texture Engineering: The study provides a microscopic picture where dopant selection can dictate the characteristic length scale of noncoplanar textures, ranging from short-period textures ($\sim 3.7$ nm) to extended chiral spin configurations ($\sim 39$ nm).
• Intermediate Regime: The large, non-monotonic THE in the Cu-substituted compound within the spin-reorientation regime suggests enhanced chiral spin correlations and fluctuating noncoplanar textures, rather than a static skyrmion lattice.

The work concludes that by selectively modifying exchange interactions, magnetic anisotropy, and electronic structure, one can engineer specific topological Hall responses in kagome antiferromagnets, offering a general route to control emergent Berry-phase phenomena.