Finite-size effects and the stabilized spin-polarized jellium model for metal clusters

TL;DR

This study investigates finite-size effects on spin polarization in metal clusters using a stabilized jellium model, revealing how geometry influences spin configurations and the applicability of Hund's rule versus maximum spin compensation.

Contribution

It introduces a detailed analysis of equilibrium $r_s$ values in spin-polarized clusters, showing the importance of geometry in determining spin rules within the stabilized jellium model.

Findings

Closed-shell clusters have increasing $ar{r}_s(N,)$ with $$

Open-shell clusters exhibit a decreasing $ar{r}_s(N,)$ for some $$ range

Spherical geometry breaking is necessary for the maximum spin compensation rule

Abstract

In the framework of spherical geometry for jellium and local spin density approximation, we have obtained the equilibrium $r_s$ values, $\bar{r}_s(N,\zeta)$, of neutral and singly ionized "generic" $N$-electron clusters for their various spin polarizations, $\zeta$. Our results reveal that $\bar{r}_s(N,\zeta)$ as a function of $\zeta$ behaves differently depending on whether $N$ corresponds to a closed-shell or an open-shell cluster. That is, for a closed-shell one, $\bar{r}_s(N,\zeta)$ is an increasing function of $\zeta$ over the whole range $0\le\zeta\le 1$, and for an open-shell one, it has a decreasing part corresponding to the range $0<\zeta\le\zeta_0$, where $\zeta_0$ is a polarization that the cluster assumes in a configuration consistent with Hund's first rule. In the context of the stabilized spin-polarized jellium model, our calculations based on these equilibrium $r_s$ values, $\bar{r}_s(N,\zeta)$, show that instead of the maximum spin compensation (MSC) rule, Hund's first rule governs the minimum-energy configuration. We therefore conclude that the increasing behavior of the equilibrium $r_s$ values over the whole range of $\zeta$ is a necessary condition for obtaining the MSC rule for the minimum-energy configuration; and the only way to end up with an increasing behavior over the whole range of $\zeta$ is to break the spherical geometry of the jellium background. This is the reason why the results based on simple jellium with spheroidal or ellipsoidal geometries show up MSC rule.