Orbital Magnetism and Spin-Selective Nodal-Surface Topology in Halogen-Deficient Pd/Pt Square Quantum Dots

Abstract

Magnetic amplification and anisotropy control in atomically thin systems are largely governed by the interplay of structural symmetry breaking and electronic reorganization under reduced dimensionality. In this work, we study a novel coordination-modified square nanodot architecture, TM$_{9}$X$_{12}$, derived from its TM$_{9}$X$_{16}$ counterpart using density functional theory. It is observed that, when Pd- and Pt-based halides are considered as single-atom-thick, zero-dimensional configuration, halogen-deficient systems consistently exhibit z-axis dominated g-shifts, that increase by $\sim$ 3.1--5.1 times in bromide-coordinated environments, and up to $\sim$ 286 times for iodine-based frameworks, at the ECP (LANL2DZ) level. We show that halogen truncation enhances g-factors by increasing the connectivity of nodal loops, which creates multiple orbital circulation paths and amplifies the spin-orbit effect under a magnetic field. Moreover, the orbital susceptibility of iodine-coordinated Pt- and Pd-based nanoflakes undergoes a magnetic character inversion upon atom truncation, with an approximately 12-times increase in orbital anisotropy. We introduce a rotation-invariant spherical-harmonic orbital fingerprint to capture radial and angular correlations in the probability density. This fingerprint remains nearly unchanged across spin-dependent orbitals even at estimated magnetic stability temperatures above 2000 K. In addition, we identify spin-dependent rearrangement and modifications of orbital nodal surfaces under reduced halogen coordination. It is also found that spin-channel asymmetry further restructures these surfaces across different coordination environments, and channel-specific entanglement of nodal loops exhibits substantial reconfiguration in halogen-deficient dots, as quantified by linking-number analysis. Overall, such findings suggest that controlling orbital magnetic response with reshaped nodal surfaces in structurally transformed nanoflakes could guide the design of future nano-spintronics and quantum information materials.