Studies of spin-orbit scattering in noble-metal nanoparticles using energy level tunneling spectroscopy

The effects of spin-orbit scattering on discrete electronic energy levels are studied in copper, silver, and gold nanoparticles. Level-to-level fluctuations of the effective g-factor for Zeeman splitting are characterized, and the statistics are found to be well described by random matrix theory predictions. The strength of spin-orbit scattering increases with atomic number and also varies between nanoparticles made of the same metal. We compare the spin-orbit scattering rates in the nanoparticles to weak-localization measurements on larger samples.

People Involved

Jason Petta and Dan Ralph

Motivation

For devices based on spin "Spintronics" the spin-relaxation time is a very important quantity. In such a device, the spin-relaxation time must be longer than the time to perform a specific function, oherwise the spin information will be lost and the device rendered useless. We can learn about spin-orbit scattering in metals by studying the magnetic field dependence of the "electrons-in-a-box" energy eignestates in metallic nanoparticles. In metals, coupling of the spin and orbital angular momentum causes spin-mixing, resulting in energy eignestates that are no longer pure spin-eigenstates, but admixtures of spin-up and spin-down eigenstates. By measuring the Zeeman splitting of the energy levels we can learn about the magnitude of spin-orbit scattering in a nanoparticle. Using perturbation theory arguments it can be shown that the magnitude of the Zeeman splitting is reduced from the free electron value of two by an amount proportional to the square of a spin-orbit scattering matrix element. This tells us that for particles with stong spin-orbit scattering (Au) we shoud find small g-factors, and for light elements (Cu) we should find g-factors that are close to two.

Figure 1. (a) I-V and (b) dI/dV-V curves for Cu #1. (c) Magnetic field dependence of peaks in dI/dV for energy levels that exhibit avoided level crossings. Inset: Device schematic.

Figure 2. Color scale plots of dI/dV-V in Cu (a-b), Ag (c), and Au (d) samples for fields ranging from 0-9 T. Arrows denote the avoided crossings of Fig. 1.

Figure 3. a) Integrated probability distribution -vs- g-factor for the numerically calculated g-factor distributions (solid lines) and from the samples in Fig. 2 (points). See table 1 for the fitting parameters. (b) Combined probability distribution for all Cu samples.

For more information see: PRL 87, 266801 (2001).

Last updated: 2001-11-30