## Effects of Non-Equilibrium Electron Excitations on Tunneling via Electron-in-a-Box States in Metal Nanoparticles

We have measured the tunneling current through well-resolved electrons-in-a-box quantum energy levels in nanometer-scale metal particles. Using a gate electrode, we tuned the degree to which the tunneling current produces non-equilibrium excitations within the particle, and studied the effects of such excitations. In magnetic particles, non-equilibrium effects drastically modify the tunneling spectrum, while in non-magnetic samples the widths and energies of the resonances are affected only slightly.

# People involved

Mandar Deshmukh, Edgar Bonet and Dan Ralph# Fabrication

Using electron-beam lithography, advanced etching techniques, and a sequence of metal depositions, we can contact a single nanometer-scale metal particle to external electrodes via oxide tunnel barriers. The I-V characteristics of such devices reveal the spectrum of quantum states in the metal nanoparticle. A capacitively-coupled gate electrode allows us to tune the device between the regime where only one state is available for tunneling and the non-equilibrium regime where many high-energy states can be excited.

Figure 1: Cross-sectional device schematic.

# Magnetic system

Fig. 2 shows the tunneling spectra of a magnetic cobalt nanoparticle as a function of the applied magnetic field [1]. The observed density of states is greater than expected from a simple "electron in a box" picture. We account for this fact by the assumption that some of the observed resonances are associated with tunneling transitions whose initial state is a non-equilibrium excited state of the system. We have verified this picture directly by adjusting the strength of non-equilibrium excitations using a gate voltage.The nonlinearities of the resonances as a function of magnetic field as well as their discontinuity at the magnetic switching field (-120 mT) reveal a strong coupling between the energy levels and the collective magnetization of the nanoparticle. Furthermore, the different behaviors from resonance to resonance show a variation in the magnetic anisotropy from state to state. A variation of 1 to 3% in the anisotropy constant has been shown to explain both the nonlinear behavior of a single resonance and the variations from resonance to resonance [1, 2].

Figure 2: Colorscale conductance plot of a cobalt nanoparticle as a
function of the applied magnetic field. Field is swept from positive to
negative values.

# Non-magnetic system

In the case of non-magnetic particles, the effects of non equilibrium excitations are less dramatic. Fig. 3 shows the tunneling spectrum of an aluminum nanoparticle as a function of gate voltage [3].The discontinuity in the spectrum is due to a gate-voltage-induced change in the background charge, and does not otherwise affect the energy states. The main features of this spectrum can be explained by tunneling transitions from the equilibrium ground state of a collection of non-interacting electrons. However, both a non-thermal broadening of some resonances as well as shifts in the resonance centers at resonance crossings are left unexplained by this simple model. A detailed study of these features shows that they are due to non-equilibrium effects together with a weakening of the superconducting correlations in the aluminum nanoparticle as the number of excitations grows.

Figure 3: Colorscale conductance plot of an aluminum nanoparticle as a
function of the gate voltage.

# References

- M. M. Deshmukh, S. Kelff, S. Guéron, E. Bonet, A. N. Pasupathy, J. von Delft, and D. C. Ralph, Magnetic Anisotropy Variations and Non-Equilibrium Tunneling in a Cobalt Nanoparticle, Phys. Rev. Lett 87, 226801 (2001). (cond-mat/0108166).
- Silvia Kleff, Jan von Delft, Mandar M. Deshmukh and D. C. Ralph, A Model for Ferromagnetic Nanograins with Discrete Electronic States, Phys. Rev. B 64, 220401(R) (2001). (cond-mat/0103626).
- Mandar M. Deshmukh, Edgar Bonet, A. N. Pasupathy and D. C. Ralph, Equilibrium and non-equilibrium electron tunneling via discrete quantum states, cond-mat/0106024 to appear in Phys. Rev. B.

Last updated: 2001-11-29