Pergamon Progress in Surface Science,Vol. 50, NW 1-4, pp. 149-158, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in the USA. All rights reserved. 0079~6816(95)ooO50-X 0079-6816/95$29.00 THEORY OF IMAGE STATES AT MAGNETIC SURFACES M. Nekovee* and J. E. Inglesfieldt *Department of Physics, Imperial College, London SW7 2BZ, U.K. TResearch Institute for Materials, University of Nijmegen, NL 6525 ED Nijmegen, The Netherlands Abstract The interaction of the spin of an electron in an image state with surface mag- netism produces a spin-splitting which can be probed experimentally, most directly using spin-polarised inverse photoemission. There has been some debate about whether the spin-splitting is due to the spin-dependence of the surface potential barrier, or to the spin-dependence of the scattering of the surface state by the crystal potential. We have shown that in the case of image states at Fe(ll0) both effects contribute, but with opposite sign: the major effect is the effect of the crystal, and the potential barrier which has the opposite spin-polarization reduces the spin-splitting. -4 splitting of 55 meV is found for the n = 1 st,ate, which has been confirmed by experiment. The dispersion of the spin-split states is discussed, particularly their interac- tion with the spin-split continua which produces different surface resonance behaviour for the two spins. 1. Introduction Image-induced surface states, which have their origin in the long range image tail of the surface potential, have become in recent years a subject of extensive theoretical and experimental study [l-7]. This is because the energies of these states provide a detailed probe of the effective potential outside the surface, which is ultimately due to many-body interactions. ,4n exciting new topic concerns the spin-splitting of image states at a magnetic surface, which should provide information on surface magnetism [&lo]. Spin-polarised inverse photoemission enables this to be measured, and the first direct measurements were made on the Ni(ll1) surface where a splitting of 18 meV was found for the n = 1 state [ll]. Here we concentrate on Fe(ll0) -- Fe has a relatively high bulk magnetic moment (2.2 ps compared with 0.6 ps in Ni), so spin-splitt,ing effects should be larger. Following our prediction of a splitting of 55 meV for the 71 = 1 state [IL?], recent inverse photoemission measurements have found a splitting in precise agreement: 57 & 5 meV [13]. We shall discuss the origins of this splitting in this article, and also show how dispersion behaviour for the separate spin states differs as a consequence of their interactions with the spin-split bulk bands. 149