Impact of Stealthy Hyperuniform Magnetic Impurity Configurations on Bulk Magnetism in a Two-dimensional Heisenberg Model

Abstract

We investigate an antiferromagnetic quantum Heisenberg model on a square lattice with high-spin magnetic impurities to clarify how random and stealthy hyperuniform impurity configurations influence the bulk magnetic properties. Stealthy hyperuniform configurations are generated using generalized cost functions that interpolate between square-lattice-like and triangular-lattice-like arrangements. Using linear spin-wave theory for the mixed-spin model, we demonstrate that triangular-lattice-like arrangements yield a larger average staggered magnetization than both random and square-lattice-like cases. This enhancement originates from sublattice effects: while the square-lattice-like configuration enforces nearest-neighbor impurities to occupy opposite sublattices due to its bipartite structure, the triangular-lattice-like arrangement allows same-sublattice nearest-neighbor pairs, thereby strengthening cooperative magnetic enhancement.

Figures (6)

• Figure 1: Antiferromagnetic quantum Heisenberg model with higher-spin impurities.
• Figure 2: (a) SHU impurity configurations (I). Large red and blue circles represent impurities in the sublattices $A$ and $B$, respectively. The gray circles represent $S=1/2$ host spins. (b) Structure factor $S(\bm{k})$ of the configuration (I). Dashed line indicates the boundary of the window function. (c) SHU impurity configurations (II) and its structure factors (d) $S({\bm k})$, (e) $S_A({\bm k})$, and (f) $S_B({\bm k})$.
• Figure 3: (a) Local magnetization profile around an isolated magnetic impurity. A red circle denotes the $S = 2$ spin. The magnitude of the magnetic moment is represented by the density plot, with red (blue) corresponding to the same (opposite) sublattice as the impurity site. (b) Squares (circles) represent the magnitudes of the local magnetization in the same (opposite) sublattice as an isolated impurity as a function of the distance $\xi$ from the impurity site.
• Figure 4: Magnetization profiles of the spin system on a $16 \times 16$ square lattice with 10 impurities arranged in (a) a random configuration, (b) configuration (I), and (c) configuration (II). Panels (d) and (e) show the results for systems with clustered impurity configurations. Red (blue) circles denote $S = 2$ spins on sublattice $A$ ($B$). The magnitude of the local magnetic moment is represented by the density plot, with red (blue) corresponding to sublattice $A$ ($B$).
• Figure 5: Normalized histgrams of the average sublattice magnetization $M_{\mathrm{AF}}$ for random and SHU impurity configurations. Comparison between random point patterns (blue, 100 samples) and SHU configuration (I) (green, 40 samples). Dashed lines indicate the corresponding mean values. Comparison between random point patterns (blue, 100 samples) and SHU configuration (II) (red, 40 samples).