Journal of Magnetism and Magnetic Materials 198}199 (1999) 680}682 Structure of Cr overlayers on Fe surfaces: a new approach for the interpretation of spin-resolved photoemission and magnetic dichroism spectra V.M. Uzdin*, D. Knabben, F.U. Hillebrecht, E. Kisker Institut fu(r Angewandte Physik, Du(sseldorf, D-40225, Du(sseldorf, Germany Abstract Results of investigations of Cr overlayers on Fe surfaces by magnetic linear dichroism in the angular distribution and spin-resolved core level photoemission are analysed within the framework of a new model approach. It includes a special algorithm for modelling epitaxial growth of overlayers with di!erent roughness together with self-consistent calculations of the magnetic moment distribution within a Periodic Anderson Model. On this basis the value of the magnetic dichroism and the spin polarisation in photoemission as functions of the Cr coverage can be modelled also for rough surfaces. The comparison of experimental spectra and theoretical coverage dependencies obtained for the di!erent surface roughnesses leads to conclusions about the microscopic structure of Cr overlayers. 1999 Elsevier Science B.V. All rights reserved. Keywords: Magnetic dichroism; Core-level photoemission; Surface and interface roughness The number of contradictory conclusions about the ness and interdi!usion and a description of photoemis- magnetic structure of Cr overlayers on Fe substrates sion from rough surfaces. The analysis proceeds in three re#ects the complexity of this system and its sensitivity to steps: "rst, a rough surface or interface is generated surface roughness, which depends on the details of by an epitaxy algorithm; second, the magnetic moments sample preparation. Spin-polarised electron spectro- are calculated using an Anderson periodic model; and scopy and magnetic dichroism in angle-resolved core third, the magnetic signature of the photoemission signal level photoemission prove to be very e$cient tools for is expressed in terms of a weighted averages investigation of such a system because they represent of the individual magnetic moments. The weighting of a combination of a chemical and a magnetic probe [1}5]. the moments is important because of the "nite escape The surface sensitivity of photoemission makes it neces- depths of the photoelectrons. In addition we suggest that sary to develop a theory for the description of emission for rough surfaces the concept of surface atoms itself from rough surfaces for the interpretation of experi- needs revision. mental spectra. This paper proposes such a theory, We suppose that electron polarisation in a core-level which includes a self-consistent calculation of the mag- photoemission experiment and the magnetic linear dich- netic moments, that takes into account interface rough- roism is proportional to the value of the localised mag- netic moments. For an ideally smooth surface, all the atoms in one atomic layer have the same magnetic mo- ment, such that the resulting spin polarisation can be * Corresponding author. Tel.: #49-211-81-12284; fax: #49- written as 211-81-13658. E-mail address: uzdin@uni-duesseldorf.de (V.M. Uzdin) I"M1 # M1 # M1 #2, 0304-8853/99/$ } see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 9 8 ) 0 1 1 9 5 - 0 V.M. Uzdin et al. / Journal of Magnetism and Magnetic Materials 198}199 (1999) 680}682 681 where M1G is the local magnetic moment of S type atoms (S"Fe or Cr) from ith layer, and takes into account the attenuation of the photoelectron signal arising from non-surface layers due to the "nite mean free path. In a simple approach, can be expressed through a univer- sal escape depth , which depends on the kinetic energy of the photoelectrons, and a characteristic length ¸, which is proportional to the lattice constant and deter- mined by geometry of experiment: "exp(!¸/ ). For rough interfaces, where a given atomic layer may contain Fe and Cr atoms with di!erent magnetic mo- Fig. 1. Coverage dependence of polarisation on Cr atoms for ments as well as empty sites, we obtain for the normalised a Cr overlayer on Fe with &smooth' interface generated by di!erence between the number of electrons with spin up algorithm &epitaxy' (interface region is 2}3 layers). Di!erent and spin down projection emitted from the surface symbols correspond to various values of the parameter . (I"(I>!I\)/(I>#I\)) the following expression: N M1 H G G \ 1#( !1) N I" N N1 H G G \ 1#( !1) N , where M1G and N1G are the total magnetic moment and d-electron number on S type atoms in the i-layer; NH/N is the fraction of the "lled sites in layer j. To model rough surfaces and interfaces, we use an &epitaxy' algorithm [6], which "lls the sites of the ideal bcc lattice inside a prism of 8;8;20 atoms (Fe or Cr) using a special random procedure. Outside the prism we Fig. 2. Coverage dependence of polarisation on Cr atoms for Cr chose periodic boundary conditions. Variation of the overlayer on Fe with &smooth' interface generated by &epitaxy' parameters in the algorithm allows one to create samples (interface region is 10}11 layers). Di!erent symbols correspond with di!erent interface roughness. For determination of to various values of the parameter . the average, the sample construction was repeated 20 times, and for each of these con"gurations the d-electron number and the magnetic moment on every site were the polarisation coincides with that of the Fe atoms, calculated within Periodic Anderson Model [6]. A distri- occurs at Cr coverage 2 ML. For ideally smooth surfaces bution of the magnetic moments is determined self-con- such behaviour is quite natural. The "rst Cr monolayer sistently in the mean-"eld approximation by taking into on Fe has a surface-enhanced moment opposite to the Fe account the d}d interaction in the "rst coordinate sphere moments. When another &ideally smooth' Cr layer is of the atoms. Parameters of the model were chosen so as deposited, it will have a surface-enhanced moment oppo- to reproduce the bulk Fe and Cr moments and the site to that of the previous layer. Furthermore, it will d-electron numbers. reduce the value of the magnetic moment of the previous The coverage dependencies of the polarisation on Cr layer, because the atoms in that layer cease to be at the atoms as calculated for a smooth interface (2}3 layers surface. That is why with every monolayer one can expect containing both Fe and Cr atoms) and for a rough a change of the sign of polarisation. Roughness will erode interface (Fe and Cr intermixed in 10}11 layers) are such an oscillation, but as is seen in Fig. 1, it does not depicted in Figs. 1 and 2. In both cases, the Cr polarisa- destroy the oscillation for relatively smooth surfaces. For tion is negative for low Cr coverage [1}5]. This is related rough interfaces, this signature of the antiferromagnetic to the antiferromagnetic coupling between the Cr sub- structure is fully destroyed, as is seen in Fig. 2. monolayer and the Fe substrate. The polarisation may Comparison of the experimental [4] and theoretical oscillate [3,4] or decrease monotonically with coverage curves suggests some conclusions about the microscopic [2,5], depending on the surface roughness and interdi!u- structure of the Cr overlayer. Theory predicts a mono- sion in the interface region. In the case of an oscillatory tonic change of the spin polarisation up to 2 ML Cr behavior, the oscillations are more pronounced for small coverage, and even a change of sign of polarisation . The maximal positive polarisation, when the sign of near this point for smooth surfaces. The dichroism 682 V.M. Uzdin et al. / Journal of Magnetism and Magnetic Materials 198}199 (1999) 680}682 experiment, in contrast, shows an oscillation and a max- References imum instead of a minimum for 2 ML coverage [4]. This contradiction can be explained if one supposes a non- [1] F.U. Hillebrecht, Ch. Roth, R. Jungblut, E. Kisker, A. uniform growth of the second layer. If the growth of the Bringer, Europhys. Lett. 19 (1992) 711. overlayer passes through that stage when the formation [2] Y.U. Idzerda, L.H. Tjeng, H.-J. Lin, J. Gutierrez, G. Meigs, of the second Cr ML is suppressed, then instead of C.T. Chen, Phys. Rev. B 48 (1993) 4144. uniform coverage we obtain a superposition of 1 and [3] T.G. Walker, A.W. Pang, H. Hopster, S.F. Alvarado, Phys. Rev. Lett. 69 (1992) 1121. 3 ML coverages and an increase of the absolute value of [4] D. Knabben, Th. Koop, H.A. DuKrr, F.U. Hillebrecht, G. van dichroism on Cr atoms results. Further deposition of Cr der Laan, J. Electron Spectrosc. Relat. Phenom. 86 (1997) leads to the "lling of the space around islands, which 201. decreases the absolute value of dichroism. The physical [5] T. BoKske, W. Clemens, D. Schmitz, J. Kojnok, M. SchaKfer, reason for the three-dimensional growth can be connec- V. Cros, G.Y. Guo, W. Eberhardt, Appl. Phys. A 61 (1995) ted with electron con"nement in the Cr islands on Fe and 119. with an oscillation of the energy of these electrons with [6] A.K. Kasansky, V.M. Uzdin, Phys. Rev. B 52 (1995) 9477. thickness of islands [7], in a similar manner to the quan- [7] V.M. Uzdin, D. Knabben, F.U. Hillebrecht, E. Kisker, Phys. tum well model for exchange coupling oscillation [8]. Rev. B 59 (1999) 1214. The same mechanism may be responsible for the non- [8] V.M. Uzdin, N.S. Yartseva, J. Magn. Magn. Mater. 156 (1996) 193. Poisson island growth reported in Refs. [2,5]. Acknowledgements This work is partially supported by INTAS Project No. 96-0531. VMU would like to express his gratitude to the Alexander von Humboldt foundation for support.