The conduction-electron-spin-resonance (CESR) spectra of small metallic particles are expected to exhibit very different behavior from those of bulk metals and are expected to depend on particle size. In particular, Kawabata has made a comprehensive theoretical study of the size dependence of the CESR line shape and predicts that, for very small diameters, the small-particle g shift contains a contribution which adds to the bulk g shift and which is proportional to the square of the particle diameter. In this paper we develop a formalism which enables us to reexamine the behavior of the g shift as a function of particle size, and we compare the predictions of this formalism with existing experimental data. The formalism we use is based upon a calculation of the g shift in bulk sodium by De Graaf and Overhauser, in which the conduction-electron wave functions are approximated by single orthogonalized plane waves. For a model cubic particle of sodium, we construct orthogonalized standing waves (OSW) by orthogonalizing stationary free-electron waves to the s and p core states. For clusters containing 8, 27, and 64 atoms, using both single and multiple OSW approximations, we first study the effect on the electronic-energy-level spectrum and charge density of altering the (arbitrary in our model) relation between the size of the cubic box in which the conduction electrons are confined and the number of atoms in the cluster. We then calculate in both approximations different contributions to the g shift and show that, in contrast with Kawabata's prediction, the major size-dependent contribution to this quantity can be written g(L)=[1-±(aL)] g(), where a is the lattice constant, ± is a parameter of the order of unity, L is the length of an edge of the cubic box, and g() is the bulk g shift. Finally, we show that the term in the g shift that Kawabata calculated for small clusters is an approximation to the term in the bulk g-shift formalism which is usually denoted as g. We calculate it in the case of a cubic sodium particle and find that it is smaller than Kawabata predicts. Our results, which are qualitatively correct for metals other than sodium, are in good agreement with recent data obtained for small magnesium particles. On the basis of this formalism, we conclude that the major size dependence of the CESR g shift comes from a surface effect.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics