Nonequilibrium excitations in ferromagnetic nanoparticles

In recent measurements of tunneling transport through individual ferromagnetic Co nanograins, Deshmukh, Guéron, Ralph et al. (DGR) [Phys. Rev. Lett. 83, 4148 (1999); M. M. Deshmukh et al., ibid 87, 226801 (2001)] observed a tunneling spectrum with discrete resonances, whose spacing was much smaller than what one would expect from naive independent-electron estimates. In a previous publication [S. Kleff, J. von Delft, M. Deshmukh, and D. C. Ralph, Phys. Rev. B 64, 220401 (2001)], we had suggested that this was a consequence of nonequilibrium excitations, and had proposed a “minimal model” for ferromagnetism in nanograins with a discrete excitation spectrum as a framework for analyzing the experimental data. In the present paper, we provide a detailed analysis of the properties of this model: We delineate which many-body electron states must be considered when constructing the tunneling spectrum, discuss various nonequilibrium scenarios, and compare their results with the experimental data of DGR. We show that a combination of nonequilibrium spin and single-particle excitations can account for most of the observed features, in particular the abundance of resonances, the resonance spacing, and the absence of Zeeman splitting.