Role of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>d</mml:mi> </mml:math> -electron density of states in the quantum size effect of Pt-Ni and Pt-Pd nanoparticles

Abstract

We investigated the quantum size effect (QSE) in bimetallic Pt$_{1-x}$Pd$_x$ and Pt$_{1-x}$Ni$_x$ nanoparticles, using $^{195}$Pt nuclear magnetic resonance measurements. The temperature and size dependencies of the anomaly in the nuclear spin-lattice relaxation rate divided by temperature $1/T_1T$ in the Pt$_{1-x}$Pd$_x$ nanoparticles suggest similar electron states between Pt and Pd atoms and are well understood by the QSE. The temperature and composition variations of $1/T_1T$ and Knight shift reveal a systematic increase in the density of states and reduction of the characteristic energy scale $T^*$ with increasing Ni content, consistent with the Kubo gap $\delta_{\mathrm{Kubo}}$. In contrast to Pt$_{1-x}$Cu$_x$ nanoparticles where the QSE is suppressed, the Pt$_{1-x}$Ni$_x$ nanoparticles exhibit clear signatures of quantum energy discretization. This discrepancy highlights the essential role of $d$-electrons in the manifestation of the QSE. Furthermore, analysis of the modified Korringa parameter $K(\alpha)$ suggests enhanced ferromagnetic correlations with increasing Ni concentration, approaching a ferromagnetic quantum critical regime. These results provide experimental evidence that $d$-electron density of states plays a crucial role in the manifestation of the QSE in the nanoparticles formed by the metallic $d$-electron atoms.