🔬 mesoscale physics

Role of $d$ -electron density of states in the quantum size effect \newline of Pt-Ni and Pt-Pd nanoparticles

This study demonstrates through $^{195}$ Pt NMR measurements that the $d$ -electron density of states is the critical factor governing the manifestation of the quantum size effect in Pt-Ni and Pt-Pd nanoparticles, with Ni content enhancing ferromagnetic correlations and revealing clear quantum energy discretization unlike in Pt-Cu systems.

Original authors: S. Kitagawa, T. Ihara, Y. Kinoshita, K. Ishida, K. Kusada, H. Kitagawa

Published 2026-08-25

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CC BY 4.0

Original authors: S. Kitagawa, T. Ihara, Y. Kinoshita, K. Ishida, K. Kusada, H. Kitagawa

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where the rules that govern a solid block of metal no longer apply because the metal has been shrunk down to the size of a speck of dust. In the realm of nanotechnology, particles this small behave differently than their larger counterparts, not just because they have more surface area, but because the electrons inside them are forced to occupy specific, discrete energy levels rather than a smooth, continuous flow. This phenomenon, known as the quantum size effect, is a fundamental prediction of physics that suggests the very nature of electricity and magnetism changes when matter is confined to a few billionths of a meter. For scientists, understanding exactly how and why this happens is crucial for designing the next generation of tiny electronic devices and efficient catalysts. However, proving that this effect is real and understanding what controls it has been difficult, largely because the surface of these tiny particles often reacts with air or other chemicals, masking the pure quantum behavior happening inside.

To cut through this confusion, a team of researchers at Kyoto University turned their attention to tiny spheres made of platinum mixed with either palladium or nickel. They wanted to see if the type of electron orbitals inside the metal atoms—the specific "rooms" where electrons live—determined whether these quantum effects would appear. While previous studies had shown that mixing platinum with copper, an element dominated by a different type of electron, seemed to suppress these quantum signatures, the behavior of platinum mixed with nickel and palladium remained unclear. The researchers synthesized these nanoparticles, coating them in a protective polymer to prevent them from rusting or clumping together, and then used a technique called nuclear magnetic resonance to listen to the magnetic whispers of the platinum atoms inside. This method allowed them to distinguish between the atoms on the surface and those deep in the center, providing a clear window into the electronic state of the metal without the noise of surface contamination.

The results revealed a striking difference depending on which metal was mixed with the platinum. When the researchers mixed platinum with palladium, the quantum behavior looked very similar to that of pure platinum. The temperature at which the quantum effects became noticeable shifted slightly, but this was entirely due to the size of the particles, not a change in the fundamental electronic structure. This confirmed that platinum and palladium are electronic twins in this context; their electrons behave in almost the same way, so mixing them does not alter the underlying quantum rules. The particles acted as a unified system where the size alone dictated the energy spacing between electron levels.

In contrast, when nickel was introduced into the mix, the story changed dramatically. As the amount of nickel increased, the temperature at which the quantum effects appeared dropped significantly. The researchers found that this shift was not random; it was directly linked to the fact that nickel atoms contribute more electrons to the energy levels where the action happens. By adding nickel, the researchers effectively crowded the available energy states, which squeezed the gap between them and made the quantum effects appear at lower temperatures. This systematic change provided strong evidence that the presence of these specific d-electrons is essential for the quantum size effect to manifest. Without them, or if they are replaced by electrons that behave differently, the effect fades away.

Furthermore, the study uncovered that the nickel-rich particles were teetering on the edge of a magnetic transformation. The analysis suggested that as the nickel concentration grew, the electrons began to align their magnetic spins more strongly, hinting at a state where the material is nearly ferromagnetic. This magnetic tendency, driven by the high density of electrons provided by the nickel, appeared to work hand-in-hand with the quantum size effects, influencing how the particles responded to temperature and magnetic fields. The researchers concluded that the quantum size effect is not merely a geometric trick of shrinking matter; it is deeply rooted in the electronic character of the atoms involved. For these tiny metallic particles to exhibit these unique quantum behaviors, they must be built from atoms that carry the right kind of electrons. This insight reshapes how scientists view the design of nanomaterials, suggesting that controlling the specific electronic makeup of a particle is just as important as controlling its size.

Technical Summary: Role of d-electron density of states in the quantum size effect of Pt-Ni and Pt-Pd nanoparticles

Problem Statement
The quantum size effect (QSE) in metallic nanoparticles arises from the discretization of electronic states, theoretically described by the Kubo gap ( $\delta_{\text{Kubo}}$ ), which is inversely proportional to the product of the number of atoms ( $N$ ) and the density of states at the Fermi energy ( $D(E_F)$ ). While QSE has been observed in platinum (Pt) nanoparticles via nuclear magnetic resonance (NMR), previous studies on Pt-Cu nanoparticles suggested that the effect is suppressed when the alloying element (Cu) primarily contributes s-electron states. This raises a critical question regarding the role of electronic structure: specifically, whether the presence of d-electrons is essential for the manifestation of QSE in metallic nanoparticles. This study investigates this hypothesis by examining bimetallic Pt $_{1-x}$ Pd $_x$ and Pt $_{1-x}$ Ni $_x$ nanoparticles, where Pd and Ni possess distinct d-electron characteristics compared to Pt and Cu.

Methodology
The researchers synthesized Pt $_{1-x}$ Pd $_x$ and Pt $_{1-x}$ Ni $_x$ nanoparticles using a polyol reduction method with polyvinylpyrrolidone (PVP) as a stabilizer to prevent oxidation and particle aggregation. Particle sizes were controlled to ranges of approximately 3.8–5.4 nm for Pd-alloys and 3.8–9.9 nm for Ni-alloys. The formation of solid-solution alloys was confirmed via X-ray diffraction (XRD) and transmission electron microscopy (TEM).

The primary experimental technique employed was $^{195}$ Pt nuclear magnetic resonance (NMR). Measurements included:

Spin-lattice relaxation rate ( $1/T_1$ ): Measured as a function of temperature to identify the characteristic temperature $T^*$ , below which $1/T_1T$ increases anomalously, signaling the Kubo gap.
Knight shift ( $K$ ): Analyzed to determine local electronic density of states and magnetic correlations.
Modified Korringa parameter ( $K(\alpha)$ ): Calculated to assess the strength of ferromagnetic or antiferromagnetic correlations.

The study utilized a spin-echo technique with field-swept spectra to distinguish between signals originating from the inner (bulk-like) and outer (surface) regions of the nanoparticles.

Key Results

Pt $_{1-x}$ Pd $_x$ Nanoparticles: The temperature dependence of $1/T_1T$ showed a characteristic increase below $T^*$ followed by a maximum, consistent with QSE. However, the value of $T^*$ did not vary significantly with Pd concentration ( $x$ ). This indicates that the electronic states of Pd atoms are sufficiently similar to those of Pt atoms, and the observed variations in $T^*$ were primarily driven by particle size differences rather than changes in $D(E_F)$ .
Pt $_{1-x}$ Ni $_x$ Nanoparticles: In contrast to the Pd system, increasing Ni content led to a systematic decrease in $T^*$ for both inner and outer regions. This reduction correlates with an increase in the bulk density of states ( $D(E_F)$ ) due to Ni substitution, consistent with the Kubo relation $\delta_{\text{Kubo}} \propto [ND(E_F)]^{-1}$ .
Magnetic Correlations: Analysis of the Knight shift and the modified Korringa parameter $K(\alpha)$ revealed that $K(\alpha)$ decreases with increasing Ni concentration, reaching values as low as 0.03. This suggests the emergence of strong ferromagnetic correlations, approaching a ferromagnetic quantum critical regime at $x \approx 0.3$ .
Comparison with Pt-Cu: Unlike Pt $_{1-x}$ Cu $_x$ nanoparticles, where QSE signatures were diminished at high Cu concentrations, the Pt $_{1-x}$ Ni $_x$ system retained clear signatures of quantum energy discretization despite the presence of strong magnetic fluctuations.

Key Contributions

Electronic Structure Dependence of QSE: The study provides experimental evidence that the manifestation of QSE in metallic nanoparticles is not solely a geometric phenomenon but is critically dependent on the electronic structure of the constituent atoms. Specifically, the presence of d-electrons near the Fermi level is identified as a necessary condition for the discrete level structure to significantly influence low-temperature spin dynamics.
Differentiation of s- and d-electron Roles: By comparing Pt-Pd, Pt-Ni, and previously studied Pt-Cu systems, the authors demonstrate that s-electron dominant alloys (Pt-Cu) suppress QSE, whereas d-electron rich alloys (Pt-Ni) enhance or maintain QSE signatures, even in the presence of enhanced magnetic correlations.
Correlation with Kubo Gap: The systematic reduction of $T^*$ with increasing Ni content provides direct experimental validation of the Kubo gap's dependence on $D(E_F)$ in bimetallic nanoparticles.

Significance and Claims
The authors claim that these results offer experimental proof that d-electron density of states plays a crucial role in the manifestation of the QSE in nanoparticles formed by metallic d-electron atoms. The findings suggest that the QSE in metallic nanoparticles should be reconsidered from the perspective of electron correlation and electronic structure, rather than viewing it purely through a nearly-free-electron model. The study highlights that while the average energy scale ( $T^*$ ) remains related to the inverse of the total density of states, the detailed low-temperature response is sensitive to the specific electronic nature (d-electron vs. s-electron) of the alloying elements. This insight is presented as fundamental for understanding the interplay between QSE and many-body effects in nanoscale systems.

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