Spin- and orbital-polarized multiple-scattering theory of magneto-x-ray effects in Fe, Co, and Ni G. Y. Guo Daresbury Laboratory, Warrington, Cheshire WA4 4AD, United Kingdom Received 27 August 1996 Systematic theoretical studies of various magneto-x-ray effects Faraday rotation, resonant magnetic x-ray scattering as well as magnetic circular dichroism at the K and L 2,3 edges in bcc Fe, fcc, and hcp Co, and fcc Ni have been carried out. Spin- and orbital-polarized multiple-scattering theory is used. It is found that the orbital polarization correction significantly increases the orbital moment and the magnitude of the K magnetic circular dichroism and Faraday rotation spectra which are then in reasonable agreement with available experi- ments. On the other hand, the orbital polarization only slightly affects the spin magnetic moment of all the systems studied and the L 2,3 magneto-x-ray spectra of Fe and Co. There is an overall agreement in the L 2,3 magneto-x-ray spectra between the theory and the experiments. However, some differences between the the- oretical and experimental magneto-x-ray spectra in between the L 3 and L 2 edges exist especially in Fe and Ni, indicating that one-electron theory is not fully adequate. The fundamental relations between the different magneto-x-ray spectra are emphasized. S0163-18299711917-8 I. INTRODUCTION The advent of intense, tunable, polarized synchrotron ra- diation sources has stimulated considerable interest in vari- ous magneto-x-ray effects and exploitation of these effects for probing the electronic structure and magnetism in solids see, e.g., Refs. 1–8. Magnetic circular dichroism MCD in x-ray absorption 1–3 is perhaps the best known magneto-x-ray effect mainly because it is becoming a powerful probe of element specific orbital as well as spin magnetic moments. 9–11 Other interesting magneto-x-ray effects such as Faraday rotation of linear polarization 4,8 and both linearly and circularly polarized resonant magnetic x-ray scattering 5–7 have also been explored. In this paper, theoretical magneto-x-ray spectra at the K and L 2,3 edges of bcc Fe, fcc and hcp Co, and fcc Ni obtained using the first-principles spin-polarized relativistic multiple scattering theory 12 are presented. The underlying electronic structures of bcc Fe, fcc Co, hcp Co, and fcc Ni, were cal- culated self-consistently within the framework of relativistic spin-density functional theory with the local spin-density ap- proximation LSDA. 13 The so-called orbital-polarization correction OPC has been included in both the electronic structure and x-ray spectrum calculations, and hence it is a spin- and orbital-polarized relativistic multiple-scattering theory SOPR-MST. It is well known that LSDA calcula- tions often give too small orbital moments by up to 50% in, e.g., Fe and Co systems see, e.g., Ref. 11. OPC was origi- nally proposed by Brooks 14 as an ad hoc but parameter-free remedy for this defect in LSDA. The aim of the present work is manifold. First, this is an attempt to describe the different magneto-x-ray effects in metallic systems within a single itinerant electron theory since the seemingly diverse magneto-x-ray effects are simply the different facets of the same physics. Including OPC in LSDA calculations is known to have pronounced effects on the calculated orbital moments see, e.g., Refs. 14 and 11. Furthermore, the magneto-x-ray phenomena and the orbital moment have the same origin, viz., the simultaneous presence of both spin- orbit coupling SOC and magnetization. Therefore, the sec- ond purpose of this work is to describe an implementation of OPC and to investigate the effects if any of OPC on the magneto-x-ray spectra. In recent years, x-ray MCD has been the subject of intensive band theoretical investigations. 15–25 In contrast, similar studies on resonant magnetic x-ray scat- tering have not been reported to date despite of intensive experimental interest. 5–7 The third purpose is therefore to extend the spin-polarized relativistic band theory to resonant magnetic x-ray scattering. Ebert et al. 15 have calculated MCD in x-ray absorption in a number of transition metal systems using spin-polarized relativistic multiple-scattering theory. It was found that the experimental K MCD spectrum of bcc Fe is rather well de- scribed by this first-principles theory. 16 Nevertheless, in fcc Ni, the sign of the theoretical K MCD near the threshold is different from that of measurements. 17 This qualitative dis- crepancy between the experiment and theory was attributed to the failure of LSDA. Theoretical studies of both MCD and Faraday rotation at the fcc Co Ref. 18 and bcc Fe Ref. 19 K edge have been reported by Strange and co-workers, who also used spin-polarized relativistic multiple-scattering theory. However, the sign of the theoretical MCD near the Co K edge 18 is again different from that of measurements, 17 and the theoretical and experimental Faraday rotation spectra have few similarities. More recently, Igarashi and Hirai 20 reported their K MCD calculations for Fe, Co, and Ni using a semiempirical tight-binding method and found that there is a good agreement between the theory and experiment for all three elements. The K x-ray absorption spectra are predomi- nantly determined by electric dipole transitions to the unoc- cupied p states. Since the unoccupied 4 p states in 3 d tran- sition metals are rather extended, the results of Igarashi and Hirai are not surprising. Indeed, the results of this work see Sec. IV below show that for all three elements, the theoret- ical K MCD and Faraday rotation spectra calculated using SOPR-MST are in satisfactory agreement with the experi- ments. Theoretical studies of MCD at the L 2,3 edges in various PHYSICAL REVIEW B 1 MAY 1997-I VOLUME 55, NUMBER 17 55 0163-1829/97/5517/1161910/$10.00 11 619 © 1997 The American Physical Society