The scientific enthusiasm for ultrathin Fe films on Cu(001) has now lasted for more than 20 years. Is there ferromagnetic iron with a face-centred cubic (fcc) structure? Does ferromagnetism in Fe hinge on the body-centred cubic (bcc) structure? In this contribution, we try to establish that the electron system gives evidence of ferromagnetic behaviour with fcc-like electronic bands. We examine a crystal-induced surface state, which is characteristic of fcc surface order. Furthermore, we compare electronic signatures of fcc and bcc: the d-band exchange splitting, image-potential-state energies and the work function. We conclude that, from the viewpoint of the electronic structure, Fe on Cu(001) is found to be ferromagnetic throughout the fcc-like phase. This result raises a new question: how much deviation from the relaxed fcc order is acceptable without losing the electronic signature of fcc?
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