QUANTUM OSCILLATIONS IN A CONFINED ELECTRON-GAS

When metals are structured on nanometre length scales, their electrons are subject to confinement effects: the response of a confined electr on gas is governed by Friedel oscillations(1) of the electron density and Rudermann-Kittel-Kasuya-Yosida oscillations(2) of the spin density , Spatial oscillations of electron density have been observed directly at surfaces (in the vicinity of defects and steps) by scanning tunnel ling spectroscopy(3,4). But it has proved more difficult to probe such oscillations in bulk materials and over large distances(5). Here we r eport the detection of quantum oscillations in a three-dimensional ele ctron gas confined to a half space by a surface, To facilitate this de tection, we have inserted an atomically thin ferromagnetic cobalt film at a variable distance tau from the surface of a copper single crysta l. The cobalt film induces(5) a total spin polarization P in the condu ction electrons of the copper and, by virtue of the confining effects of the copper-vacuum interface, P varies as a function of tau. Our mea surements of P reveal both quantum oscillations (the wavelengths of wh ich are governed by the extremal diameters of the copper Fermi surface ) and a decay with tau that are consistent with theoretical expectatio ns(2). These observations show that a consequence of improving the qua lity of nanostructured materials is that long-range quantum interactio ns can emerge more effectively, so that even distant boundaries and de fects can become pivotal in determining physical properties.