We have observed a surprising negative exchange splitting of the n = 1
image-potential surface state at Fe(001) using spin resolved inverse
photoemission, indicating that the minority-spin level has a lower ene
rgy than the majority-spin level. Calculations show the negative sign
results from two superimposing effects. A true reverse polarization of
the image state, which hybridizes with bulk bands, which is then enha
nced by matrix element effects in inverse photoemission.