High-spin magnetic ground states of neutral dopant clusters in semiconductors

TL;DR

This work introduces a design paradigm for robust high-spin ground states in neutral dopant clusters embedded in semiconductors with multiple conduction-band valleys. By exploiting valley-degenerate interference in multi-valley hosts, the authors show how carefully arranged impurities can suppress targeted hopping and exchange pathways, stabilizing large-spin ground states that scale with system size through perimeter or fractal boundary effects. They develop a framework based on effective mass theory and tight-binding to construct explicit 2D and quasi-2D architectures in AlAs, Ge, and Si, including wheel-shaped building blocks, decorated lattices, and fractal tilings, achieving net spins up to ~70% of the fully polarized value in some geometries. The results provide a general design principle for valley-based high-spin engineering and outline feasible experimental routes via precision dopant implantation and quantum-simulation platforms to realize these states in practice.

Abstract

High-spin states hold significant promise for classical and quantum information storage and emerging magnetic memory technologies. Here, we present a systematic framework for engineering such high-spin magnetic states in dopant clusters formed from substitutional impurities in semiconductors. In single-valley materials such as gallium arsenide, impurity states are hydrogenic and exchange interactions generally favor low-spin configurations, except in special geometries. In contrast, multivalley semiconductors exhibit oscillatory form factors in their exchange couplings, enabling the controlled suppression of selected hopping processes and exchange couplings. Exploiting this feature, we demonstrate how carefully arranged impurities in aluminum arsenide, germanium, and silicon can stabilize ground states with a net spin that scale extensively with system size. Within effective mass theory and the tight-binding approximation for hopping, we construct explicit examples ranging from finite clusters to extended lattices and fractal-like tilings. In two dimensions, we identify several favorable dopant geometries supporting a net spin equal to around half of the fully polarized value in the thermodynamic limit, including one which achieves over $70\%$ polarization. Our results provide a general design principle for harnessing valley degeneracy in semiconductors to construct robust high-spin states and outline a pathway for their experimental realization via precision implantation of dopants.

Figures (9)

• Figure 1: Unit cells of (a) zincblende and (b) diamond cubic crystal structures. Both consist of two interpenetrating face-centered cubic lattices; however, zincblende has two distinct atomic species, shown here in light and dark blue.
• Figure 2: Wheel-shaped clusters with (a) three, (b) four, (c) five, (d) six, and (e) eight sites on the rim. When the hopping amplitude between the edge sites is sufficiently small, the central electron forms singlets with the ones along the perimeter. As a result, the edge spins align with each other, yielding a net high-spin magnetic state. For each cluster, we note here the maximum possible value of the ground-state spin, $S_{\mathrm{max}}$.
• Figure 3: Total spin of the ground state of the $J_1$--$J_2$ Heisenberg model on a 25-site cluster as a function of $J_2/J_1$, obtained via exact diagonalization. The inset depicts the lattice structure for nine plaquettes, with $J_1$ and $J_2$ bonds shown as solid and dashed lines, respectively. The red vertical dashed line indicates the value of $J_2/J_1$ realized in the square-lattice geometry when nearest-neighbor sites are placed $6\, a^{*}_B$ apart.
• Figure 4: Constant-energy surfaces in the Brillouin zone of (a) GaAs (b) AlAs, (c) Ge, and (d) Si, exhibiting one, three, four, and six valleys, respectively. The conduction band minima are located at the centers of the ellipsoids.
• Figure 5: (a) Decorated square lattice obtained by tiling the two-dimensional plane with five-site wheel-shaped clusters. By virtue of cancellation of the hopping integrals, the exchange interaction is nearly suppressed along the vertical and horizontal bonds (dashed lines). Representative nearest- and next-nearest-neighbor spin exchanges are labeled $J_1$ and $J_2$, respectively, and indicated by solid red lines. Unlike in Fig. \ref{['fig:GaAs']}, here, the next-nearest-neighbor bonds are twice the length of the nearest-neighbor ones (rather than $\times \sqrt{2}$ previously). (b) Generation $g=1$ cluster formed by arranging square plaquettes in a fractal-like pattern. Despite having fewer sites (21) than the uniform lattice in (a) (25), this cluster has a larger total spin of $S=11/2$ compared to $S=7/2$, owing to its greater perimeter contribution. Note that this cluster could also be tiled uniformly by translations to form an extended checkerboard lattice, rather than iterated fractally. (c) Generation $g=2$ fractal-like cluster, obtained by repeating the tiling process with the $g=1$ structure as the elemental unit. With $101$ sites, we attain a net ground-state spin of $S=51/2$. All of these high-spin configurations---whether realized as extended lattices or as fractal structures---can also be implemented with GaAs as the host semiconductor.