PHYSICAL REVIEW B VOLUME 59, NUMBER 2 1 JANUARY 1999-II Magnetic dichroism and spin-resolved photoemission from rough interfaces V. M. Uzdin,* D. Knabben, F. U. Hillebrecht, and E. Kisker Institute fu¨r Angewandte Physik, Heinrich-Heine-Universita¨t Du¨sseldorf, D-40225 Du¨sseldorf, Germany Received 22 June 1998 The magnetic structure of ultrathin Cr films on Fe is analyzed by taking into account the roughness of the surface and of the interface. An algorithm for the epitaxial growth of the film simulates the near-surface structure, and the magnetic moment distribution is calculated self-consistently in a periodic Anderson model. For rough interfaces we find that the layered antiferromagnetic structure of the Cr adlayer is quenched. Within this model we determine the spin polarization and the value of the magnetic linear dichroism to be expected in angle-resolved photoemission. Comparing with experimental data it is concluded that Cr grows on the Fe 001 in a Stranski-Kastranoff mode. We propose an explanation based on the confinement of the itinerant electrons within the Cr islands on the Fe substrate. S0163-1829 99 13801-3 INTRODUCTION interface region. In addition STM cannot provide data about the magnetic structure of the surface and interface region. Low-dimensional magnetic structures LDMS are of in- In magnetometer experiments4 the total magnetic moment terest both for technical applications in magnetic data storage of the sample is determined. If measurements are performed systems as well as in their own right. Exchange coupling in situ during the process of deposition, this can give direct between two ferromagnetic films via a nonmagnetic inter- information about interface magnetism. As this method gives layer is a key ingredient in such systems. For optimum per- data concerning the total magnetic moment of the sample, formance of these systems it is desirable to control the mag- the interpretation in terms of magnetization or magnetic mo- netic properties at the interface. In the case of a genuinely ments associated with a specific layers is a nontrivial prob- nonmagnetic interlayer, the influence of the interlayer on the lem. Furthermore, continued deposition of Cr leads to magnetic moments in the ferromagnetic FM layer near to changes of the magnetic moments of the atoms already the interface is of prime interest. In this case there may be present, and consequently it is not possible to find the Cr magnetic moments induced on the atoms in the interlayer by moments at an interface as a difference between moments of the interaction with the ferromagnetic layer. the sample before and after Cr deposition. A classical example of a system where the interface elec- It is furthermore important that in Cr-Fe systems the ad-/ tronic and magnetic structure was investigated thoroughly by interlayer atoms have sizeable magnetic moments on their various methods are Fe/Cr multilayers and Cr adlayers on own, not only because of the interaction with the Fe layer. Fe.1­7 The general problem with the interpretation of all ex- Therefore, it is very important for an understanding of inter- periments is connected to the detailed structural properties of face properties to know the magnetic moments associated the interface. Electronic structure calculations consistently with Fe and Cr atoms separately. Magnetometer data cannot yield a very large magnetic moment, of the order of 2.5 B , provide this knowledge. Mo¨ssbauer spectroscopy gives in- for a Cr monolayer on Fe. However, to date the experimental formation about the distribution of hyperfine fields hff and evidence for such a large moment is not conclusive. While consequently about magnetic moments localized on Fe atoms spectroscopic experiments have not shown a large Cr mag- in Fe-containing LDMS. If the sample is designed so that netic moment,1,2 a large Cr moment was apparently present only an interface layers contains the 57Fe isotope, whereas in the experiments by Turtur and Bayreuther.4 The short pe- the other layers are grown by 56Fe,9,10 then Mo¨ssbauer spec- riod oscillation of the interlayer coupling as observed for tra will provide valuable knowledge about interface magne- Fe/Cr/Fe trilayers grown on Fe whiskers is in qualitative tism. The interpretation, however, of Mo¨ssbauer spectra for agreement with theory for perfectly smooth interfaces. Un- LDMS is again a complicated problem, because one has to fortunately, to date no absolute determinations of the Cr take into account a nonrandom distribution of directions of magnetic moments for such high-quality interfaces have magnetic moments in LDMS,11,12 as well as a contribution of been carried out. The interdependence between geometric the 4s-electron polarization, which creates a direct contact and magnetic structures was investigated for Fe/Cr interface hff on the nuclei and in LDMS this may be not proportional by the number of experimental methods. Scanning tunneling to the local magnetic moment. microscopy STM has revealed direct information about the Recent investigations10,13 show that interface roughness is growth process on an atomic scale. Such experiments pro- extremely important for the magnetic structure, and this is vide knowledge only about the surface layer, not about the also reflected in the shape of the Mo¨ssbauer spectra. If for surface structure on the scale of few atomic layers below the the smooth interfaces the spectrum contains distinct satellites surface. Davies et al.8 found by STM for Cr overlayers on Fe corresponding to different local environments, a wide distri- that only one out of every four deposited Cr atoms remains bution of hff is observed for more rough interfaces such that in the surface layer whereas the others transfer trough the it is impossible to separate the contributions from different surface into the sample whereby an alloy is created in the configurations. Data about the distribution of magnetic mo- 0163-1829/99/59 2 /1214 9 /$15.00 PRB 59 1214 ©1999 The American Physical Society PRB 59 MAGNETIC DICHROISM AND SPIN-RESOLVED . . . 1215 ments on the Cr atoms can be obtained from mo¨ssbauer spectra only indirectly through the change of hff on Fe. As a result of these various complications a general picture of interface magnetic structure appears to be very ambiguous. Core-level photoemission has some advantages in com- parison with other methods mentioned above. First, it pro- vides information about the magnetism of Fe and Cr sepa- rately by investigating core levels with specific binding energies.2,14 Because of its high surface sensitivity, only the magnetic structure of a few surface atomic layers contributes to the signal. Furthermore, it gives information averaged over the acceptance area of the spectrometer which is large on the atomic scale. Accordingly, the overall characteristics FIG. 1. Random walk of the atom through the empty sites in the of the sample within the probing depth of 5 to 50 Å below bcc lattice. Solid circles correspond to filled sites. Site ``B'' con- the surface are determined. tains four vacant neighbor sites in the next layer, and transition to Magnetic circular dichroism in x-ray absorption was used any of these occurs with probability 0.25. Site ``D'' has only one to study the magnetic coupling between Cr and Fe and the nearest vacant site in the next layer. For variant a of the algorithm, coverage dependence of the Cr net magnetic moment15 in an the atom has to transfer from site D to E. For the b variant it may Fe film grown on GaAs. In these experiments, a monotonous stay with definite probability on site D so that site E remains vacant decay of the Cr magnetic signal was observed, which was as more atoms are added. interpreted to result from interface roughness. In x-ray ab- sorption, which averages over the film thickness of several to deviations from the ideal interface in the experiments. The monolayers, a signal oscillating between a decreasing maxi- purpose of the present paper is to make a first step towards a mum and zero should be observed if the growth mode was more realistic description of such interfaces and the size of layer by layer. The observed monotonous decrease15 was at- the net magnetic moment one may observe in a magnetically tributed to the large roughness of the Fe substrate as inferred sensitive photoemission experiment. The magnetic sensitiv- from scanning tunneling microscopy. This is in contrast to ity can either be realized by taking spin-resolved data, or by Cr films grown on surfaces of Fe whiskers.16 For such films making use of linear or circular magnetic dichroism. Our an oscillation of the surface magnetic moment around zero model analysis proceeds in three steps: first, a rough surface was detected by polarization analysis of secondary scattered or interface is generated by an epitaxy algorithm; second, the electrons, indicating a layer by layer growth on such sub- magnetic moments are calculated using an Anderson Hamil- strates. This oscillation only starts when the coverage ex- tonian model; and third, the magnetic signal is obtained as a ceeds about three layers. However, the size of the magnetic weighted average of the individual magnetic moments. The moment could not be determined from these experiments. weighting accounts for the attenuation of photoelectron in- In this paper we show that spectroscopic data together tensity due to transmission towards and through the surface. with a semiempirical model, which includes modeling of the We compare the results to experimental data on the coverage deposition process together with successive self-consistent dependence of magnetic dichroism or spin-resolved photo- calculations in a model Hamiltonian approach of the mag- emission. In doing so, we tacitly assume that these spectral netic moment distribution provide a key for the investigation properties can be used as a measure for the magnetic mo- of the subsurface layers on an atomic scale. An analogous ment. theoretical model was used for the explanation of the de- crease of the total magnetic moment of the Fe sample in the MAGNETIC MOMENTS AT ROUGH INTERFACES process of Cr covering.17 It was shown that total magnetic moment of the sample can oscillate or exponentially de- To describe magnetic moments at nonideal surfaces and crease, depending on the roughness of the interface. On the overlayers, we simulate this situation using the special algo- base of a similar modeling12 of a nonideal Fe/Cr interface it rithm epitaxy17,19 which allows us to create spatially inhomo- was demonstrated that interface roughness is essential for an geneous structures with different roughness. The algorithm adequate description of Mo¨ssbayer spectra. The surface sen- fills a prism consisting of 8 8 18 sites with Fe and/or Cr sitivity of photoemission makes it necessary to develop a atoms. Outside the prism the structure is repeated periodi- theory for the description of emission from the rough sur- cally. Initially, the bottom layer of the prism is covered uni- faces, which will be discussed in the next section. formly by Fe atoms, while all other sites are empty. The As an example of the application of the theory which will magnetic moments and d-electron numbers of the Fe atoms be developed below we will use the data obtained for Cr in the bottom layer are assumed to be equal to the bulk overlayer on Fe using spin-resolved core-level values for bcc Fe, and are kept constant during iterations photoemission2 and magnetic linear dichroism in core-level leading to self-consistency. photoemission.18 Spectroscopic experiments on Cr adlayers The epitaxy algorithm adds single Fe atoms to the top on Fe, e.g., spin-resolved photoemission and circular mag- level of the prism in a random procedure and lets them de- netic dichroism, suggest a relatively small surface Cr mag- scend through empty sites until further descending is blocked netic moment much less than the theoretical value 2.5 B . It by occupied sites. Figure 1 illustrates the random walk of an is plausible to attribute the discrepancy between theories for atom in the bcc lattice. Sites which are not yet filled by ideal interfaces and the small moments found experimentally atoms are depicted by empty circles. Transfer of atoms from 1216 UZDIN, KNABBEN, HILLEBRECHT, AND KISKER PRB 59 TABLE I. Layer by layer distribution of Fe atoms, Cr atoms, and empty sites for a set of structures generated by the a variant of algorithm ``epitaxy'' for different coverages. 0,5 0,8 1,0 Fe Cr Emp Fe Cr Emp Fe Cr Emp 1 2 35 1243 0 1 1279 0 6 1274 2 217 419 644 2 111 1167 4 219 1057 3 1062 185 33 231 680 369 231 822 227 4 1279 1 0 1047 228 228 1045 233 2 1,2 1,5 2,0 2,5 Fe Cr Emp Fe Cr Emp Fe Crr Emp Fe C Emp 1 0 5 1275 0 34 1246 0 2 1278 0 21 1259 2 3 358 919 2 646 632 0 200 1080 0 643 637 3 212 943 125 230 1008 42 4 1075 201 7 1249 24 4 1066 213 1 1049 231 0 214 1065 1 212 1051 0 5 1279 1 0 1279 1 0 1063 217 0 1045 235 0 6 1279 1 0 1279 1 0 one layer to the next layer occurs with equal probability to surface. The results in Table I were modeled by using the a any of the nearest-neighbor empty sites. Two variants of the variant for the Fe substrate, while the results in Table II were algorithm were applied. Within the first a variant the atoms obtained from the b algorithm for the Fe substrate to simu- are forced to move on to one of the available empty sites, late interface alloying. In both cases the a algorithm was in the second b an atom can stop its descent with definite used for modeling the Cr overlayer. As a result we obtain bcc probability even if not all the nearest places in the next layer lattices with sites occupied either by Fe or Cr atoms or va- are already filled. Obviously, the second variant will lead to cant. For each of these structures, we determine self- a rougher surface. consistently the local magnetic moment at every site. Mod- To simulate Cr overlayers on the Fe substrate we first eling of the sample and the self-consistent calculation of the distribute 320 atoms of Fe using both variants of the epitaxy magnetic moment distribution were repeated 20 times to ef- algorithm. For dense packing this corresponds to five layers. fectively average over a larger sample. Calculations of the This is sufficient for reproducing self-consistently the bulk magnetic moment distribution were performed within a peri- moments in the lower layers. After all the Fe atoms have odic Anderson model by a recursive method in real been added, 64 is the coverage parameter Cr atoms space.20,21 The mass operator was calculated taking into ac- are added to the top of the prism using one of the two algo- count d-d interaction inside one coordination sphere of the rithms. The structure of the interface as obtained from vari- atom under consideration.22,23 ants a and b of ``epitaxy'' is given in Tables I and II. These Since the purpose of our discussion is to model the mag- tables show the number of Fe and Cr atoms as well as the netic structure of real interface, the magnetic moments are number of empty sites in each layer, beginning from the different not only between different layers, but also within TABLE II. Layer by layer distribution of Fe atoms, Cr atoms, and empty sites for the set of rough structures generated by combination of a and b variants of algorithm ``epitaxy'' for different coverages. 0,5 1,5 2,0 3,0 Fe Cr Emp Fe Cr Emp Fe Cr Emp Fe Cr Emp 1 2 0 1278 2 5 1273 1 20 1259 0 6 1274 2 25 3 1252 28 59 1193 21 153 1106 0 55 1225 3 163 300 1087 168 272 840 158 464 658 2 260 1018 4 467 98 715 480 496 304 467 646 167 17 608 655 5 771 143 366 795 377 108 761 500 19 141 885 264 6 976 105 199 958 253 69 957 291 32 464 783 33 7 1030 82 168 1022 177 81 1032 185 63 786 488 6 8 1033 72 175 1043 122 115 1045 129 106 971 286 23 9 1066 51 163 1061 80 139 1061 91 128 1031 172 77 10 1059 30 191 1043 50 187 1071 57 152 1035 126 119 11 1088 26 166 1080 29 171 1106 24 158 1047 92 141 12 1066 57 157 13 1120 22 138 PRB 59 MAGNETIC DICHROISM AND SPIN-RESOLVED . . . 1217 consistent with the layered antiferromagnetic AF structure of bulk Cr. The amount of intermixing is fairly limited, with some Fe incorporated in the first Cr layer, and a smaller amount of Cr in the top Fe layer. For these Cr atoms there is a ferromagnetic alignment with respect to Fe, probably as a result of the dominating interaction with the Cr in the ad- layer. The Cr moment in both layers is strongly enhanced compared to the bulk, but not as much as has been reported for a single Cr monolayer on Fe. A few Cr atoms occupy already sites in the top layer, and these have an even larger moment of about 2.5 B . This can be related to the low coordination number of these atoms associated with the small number of atoms in this layer. For all Cr layers, we find also some atoms with magnetic moment antiparallel to that of the ideal interface. These moments are smaller than those with orientation parallel to the ``ideal'' one, which we ascribe to increased frustration. For the rough interface lower two panels, Fig. 2 the situation is quite different. First we note that even down to the fifth substrate layer from the interface only about 80% of the sites are occupied by Fe with majority-spin orientation. Also, intermixing leads to Cr atoms being present down to this layer about 2%, see Table II . Furthermore, there is quite a significant number of empty sites. The Cr moments of about 1.3­ 1.5 B are largely antiparallel to those of Fe. Mag- netic moments parallel to Fe are also found, but again of much smaller magnitude. The ferromagnetic alignment is caused, e.g., by AF interaction between Cr-Cr nearest neigh- bors which are quite abundant even for Cr concentrations of a few %, in competition with the AF Cr-Fe interaction, with the concomitant frustration leading to a reduction of the magnetic moment. At the interface, the intermixing is much FIG. 2. Layer by layer distribution of magnetic moments on Fe stronger, to an extent that the interface is hardly recognize- and Cr atoms for the smooth S and rough R interface. Cr cover- able any more, at least in the Cr distribution. In the four age 2 ML. topmost Cr layers the ferro- and antiferromagnetically one layer there can be a significant variation of the magnetic aligned magnetic moments are of similar magnitude, with the moment because of the strongly varying surroundings of in- antiferromagnetic moments slightly winning out close to the dividual atoms. To illustrate the general trend of the mag- nominal interface. Taking into account also the relative netic moments in different layers, we performed an averag- abundance, the antiferromagnetic alignment dominates for ing for all subsets of Cr and Fe atoms within one layer and the layers close to the interface, while the topmost layers one spin orientation. The result is shown in Fig. 2 for 2 ML have a vanishing net moment. Cr on Fe, modeled either as a smooth upper two panels or We will now use this type of model to discuss experimen- as a rough interface lower . The lengths of the bars indicate tal core-level photoemission data which provide information the average magnetic moment in a particular layer, where the on the magnetic order of the overlayer either from spin po- layer numbering is as in Tables I and II. The widths of the larization or from magnetic dichroism. In the context of the bars indicate the numbers of atoms with spin orientation par- present discussion, we will suppose that the electron spin allel plotted to the right, positive moment or antiparallel to polarization in a core-level photoemission spectrum or the that of the Fe majority-spin orientation. Therefore the area of asymmetry in magnetic linear dichroism are proportional to the bars represents the total magnetic moment in a given the value of the local magnetic moment.24­26 In our discus- layer oriented either ferro- or antiferromagnetically with re- sion we will refer to the spin polarization, however, the same spect to that of Fe. The spacing of the bars is chosen equal to formulas can be used for analyzing dichroism spectra. For an the width for 100% of atoms in one subset. The variation of ideally smooth surface all the atoms in one atomic layer have the bar widths and appearance of the empty spaces between the same magnetic moment, such that the resulting spin po- bars come about from atoms with opposite spin orientation, larization can be written in the following way: sites being occupied by the other atomic species, or vacant S S S sites. f M1 M2 2M3 ¯ . 1 Figure 2 shows that the smooth interface has a behavior similar to that of an ideal interface: The magnetic moment in MSi is local magnetic moment of the atoms of type S (S the top Fe layer is reduced compared to the bulk, and the Cr Fe or Cr from the ith layer, and takes into account the moment in the interface layer is antiparallel that of Fe. The attenuation of the photoelectron signal arising from nonsur- two successive Cr layers are oriented antiferromagnetically, face layers due to the finite mean free path. As a simple 1218 UZDIN, KNABBEN, HILLEBRECHT, AND KISKER PRB 59 approach can be expressed through a universal escape depth , which depends on the kinetic energy of the photo- electrons, and a characteristic length L, which is the spacing of lattice planes parallel to the surface exp L cos / , 2 where is the emission angle referred to the surface normal. For real surfaces and interfaces with roughness, expressions 1 and 2 have to be modified for two reasons. Firstly, the local magnetic moment depends not only on the distance of the atom from the surface, but also on its local environment, i.e., the number of Fe and/or Cr neighboring atoms as well as their magnetic states. Secondly, the probability of electron scattering is determined not only by the number of the layers which the photoelectrons has to traverse i.e., distance from the surface , but also by the structure of the rough surface. For example, for a stepped 100 surface atoms that are in the different layers can still be surface atoms. If the surface has local defects such as atomic scale holes or islands, this will also affect the effective value of . To determine the polarization of photoelectron f i emitted from the ith layer, let us consider the top layer of the sample. All the atoms of this layer are surface atoms and conse- quently FIG. 3. Coverage dependence of polarization on Fe a and Cr f S 1 M 1 , b atoms for the samples with a ``smooth'' interface generated by where MS the a variant of algorithm ``epitaxy.'' Different symbols correspond 1 is the total magnetic moment of the S atoms in the to various values of the parameter . top layer. For the second layer, in which some atoms are covered by atoms of the first layer, whereas others are not S covered and are still surface atoms, we have M j Nj N N 1 j f 1 1 j . MS f j 1 f j j j 1 N f j N N N N N f S 1 1 S 1 2 M 2 N 1 N M2 1 1 N , As a result for total polarization F i 1fi we obtain where N i 1 1 is the number of atoms in the 1 layer not depen- Nj dent on the kind of atoms , N is the total number of the F MSi 1 1 N . places in this layer. i 1 j 1 Analogously, we have for the third layer In spectroscopy, usually the spin polarization is measured, which is given by the normalized difference between the N N N N f S 1 2 1 N2 2 N2 number of electrons with spin-up and spin-down projection 3 M 3 2 N N 1 N N 1 N N (I ) emitted from the surface as N N 1 1 2 I I N 1 N . I I . 3 I The first term in the figure bracket corresponds to transfer To obtain such a normalized polarization, we have to mul- of an electron through two filled layers above the emitting tiply F by the factor Z: layer, and the second term describes the situation of a pho- toelectron encountering an empty site in the top layer; the i 1 N third term corresponds to the case when the sites both in Z 1 NS j i 1 1 , layers 1 and 2 are empty, and effectively some atoms of the i 1 j 1 N third layer appear to be surface atoms. After simple reducing which takes into account the reduction of the number of for f 3 we have emitted electrons with decreasing concentration of that atomic species. Note, that I ZF for the Cr atoms does not N N f S 1 2 vanish when the coverage parameter approaches zero. 3 M 3 1 1 N 1 1 N . DISCUSSION In the general case one can obtain the following recurrent expressions for the contribution to the polarization from the Figures 3 and 4 show the spin polarization calculated as j 1 layer: described above for two sets of overlayers as a function of PRB 59 MAGNETIC DICHROISM AND SPIN-RESOLVED . . . 1219 For low Cr coverages, e.g., for 0.5, the polarization is smaller for larger . However, for this value of it decreases with more slowly. As a result there is a distinct coverage 0 for which the spin polarization does not depend on . For a smooth interface as in Fig. 3 a this takes place for 0 of the order 0.5­1 ML, whereas for rough interfaces as in Fig. 4 a 0 is of the order of 1.5­2 ML. If is changed by changing the takeoff angle between the sample surface and the di- rection of the electron beam, there will be no dependence of the magnetic signal on this angle at this coverage. As is seen from Figs. 3 and 4, this specific coverage depends on the surface roughness. Actually we propose that value of this specific coverage can be used to characterize the amount of interface roughness. Note that the Cr signal for the same coverage has another dependence on . The polarization of the Cr signal may oscillate or decrease monotonically with depending on the surface roughness and on the interdiffusion in the interface region. For Cr, there is a general decrease of the polarization which is much faster than for the Fe substrate. This is related to antiferromagnetic coupling between Cr atoms. The dependence of the Cr po- larization on the escape depth is analogous to that found for the Fe substrate: a small leads to a more rapid decrease of the polarization with coverage. This is in part caused by a transfer of Cr atoms through the Fe surface to vacant Fe sites. For such Cr atoms embedded in the Fe matrix we find a moment opposite to Fe, and consequently there is a nega- tive contribution to the spin polarization. The role of such inner atoms is reduced with a decrease of the escape depth parameter. Subsurface Cr atoms for rough surfaces have magnetic moments, ordered in both directions and their con- FIG. 4. Coverage dependence of polarization on Fe a and Cr tributions cancel much faster with increasing Cr coverage. b atoms for the samples with a ``rough'' interface generated by If oscillatory behavior does occur, the oscillations are combination of a and b variants of algorithm ``epitaxy.'' Different more pronounced for small . The maximum of the polar- symbols correspond to various values of the parameter . ization is obtained for 2 ML coverage when the polarization the Cr coverage. The results correspond to relatively smooth has the same sign as that of the Fe substrate. For ideally and rough surfaces, respectively, as generated by variants a smooth surfaces this behavior is quite natural. The first Cr and b of our epitaxy algorithm. All magnetic moments for monolayer on Fe has a surface-enhanced moment opposite to these spatially inhomogeneous systems were calculated self- the Fe moments. When the next ideally smooth Cr layer is consistently, and the Fermi level was chosen so that the total deposited, it will have a surface-enhanced moment opposite number of d electrons in the system remained constant. Dif- to the previous one. Furthermore it will reduce the value of ferent symbols in Figs. 3 and 4 correspond to various values the magnetic moment of the previous layer, because those of the escape length parameter . We point out, however, atoms are not at the surface any more. This leads to a change that the general tendency of the expected spin polarization or of the sign of the polarization with every additional mono- magnetic dichroism within this model does not depend on layer. Roughness will erode such an oscillation but as can be the specific value of this parameter. seen from Fig. 3 b it does not destroy oscillations for rela- We note first that the magnetic signal of the Fe decreases tively smooth surfaces. For rough interfaces this signature of monotonically with coverage . This is connected with the the antiferromagnetic structure is fully destroyed Fig. 4 b . decrease of the Fe magnetic moments under the action of Cr Turning now to experimental data, Fig. 5 shows the spin neighbors. The higher the Cr coverage, the more Fe atoms polarization and the magnetic linear dichroism obtained in have a reduced magnetic moment. We assume further that photoemission experiments for Cr films grown epitaxially on additional scattering of photoelectrons by the Cr overlayer Fe substrates. The common observation in all the experi- atoms is spin independent and only leads to a decrease of the ments is an antiferromagnetic alignment of the Fe and Cr number of photoelectrons, but not to a change of the normal- magnetic moments. Spin-polarized photoemission data are ized polarization 3 . The decrease of the polarization with shown for the Fe 3p and Cr 3p core-level spectra as a func- is more rapid for smaller escape depth small . The tion of Cr coverage for several Cr films on an Fe 100 thin- strongest decrease of Fe magnetic moments under the action film substrate. From low-energy electron diffraction investi- of Cr neighbors takes place for the surface atoms, whose gations of the Fe films it had been concluded that the films moments are enhanced for the free surface. Small leads a grown on Cu3Au(100) were more disordered than those on smaller contribution of inner Fe atoms whose magnetic mo- the Ag 100 substrate.2 The magnetic linear dichroism for ments change only a little with Cr coverage. the Cr 2p level shows a weak indication of an oscillatory 1220 UZDIN, KNABBEN, HILLEBRECHT, AND KISKER PRB 59 well established both experimentally28 and theoretically.29 For Fe/Cr multilayers, spin-polarized QW-like states were analyzed within the framework of ab initio calculations29 and it was shown that a QW-model yields a better description of the oscillatory exchange coupling in iron-chromium systems than Ruderman-Kittel-Kasuya-Yosida-like models. Recently quantum-size effects were considered as the origin of the formation of needlelike metallic islands on the surfaces.30 Let us consider a Cr island with thickness L on an ideal Fe surface, and further suppose that at least electrons with one spin projection are fully confined within the island. If L is much less than the area of the island, we can use an infinite FIG. 5. Experimental spin-polarization in Cr 3p photoemission QW model for describing the transverse movement of the spectra as function of Cr coverage for Cr/Fe/Cu3Au 100 filled confined electrons, and a free-electron approach for the elec- circles and Cr/Fe/Ag 100 empty circles ; Cr 2p magnetic linear tron movement in plane. In this case the density of states will dichroism for Cr/Fe/Ag 100 filled squares and Cr/Fe/W 110 have the form empty square . mS dependence-albeit without a change of sign-of the dichro- n , ism on the Cr coverage. 2 2 n Comparison of the experimental and theoretical curves where suggests some conclusions about the microscopic structure n 2 2n2/2m2L2 is the energies of electrons in QW, S is the area of island. of the Cr overlayer. For smooth surfaces, the theoretical We assume that the Fermi energy of the system is fixed model predicts a monotonous change of the spin polarization by the large number of electrons in the Fe substrate. In this up to two monolayers Cr coverage, and even a change of case the total number of confined electrons is not fixed. To spin polarization near this point. The dichroism experiment, compare the states with different distribution of island thick- in contrast, shows an oscillation and a maximum instead of a nesses we have to consider the thermodynamic potential minimum for two monolayers coverage. This can be ex- E plained if one supposes a nonuniform growth of the second FN of the electrons in all QW's. For the single well we have layer, which leads to an overlayer consisting of patches with 1 and 3 monolayer coverage, while the occurrence of 2 ML Sm 2FnL 1 2 2 coverage is suppressed. This will increase the absolute value L 4 2 1 3 2m nL 1 2nL 1 of the dichroism for the Cr signal. Further deposition of Cr FL2 leads to the filling of the space around islands, which de- 2 3nL 1 creases the dichroism. 1 2 2 3nL 2m 10 . 4 The behavior suggested here is consistent with a large FL2 part of the presently available experimental data. Pierce Here nL is the number of quantum levels below the Fermi et al.16 found that there is a ``defect'' in the antiferromag- energy. The analysis of this problem can be significantly netic ordering between 1 and 4 layers coverage giving a simplified if instead of L we consider the quantity L phase change in electron-spin polarization P(Cr), although cl , where cl is the quasiclassical contribution, for the thicker coverage they were able to observe oscilla- L L L which can be obtained from Eq. 4 by substitution of the tions of P(Cr) as a function of Cr thickness with a period of integer number n two atomic layers. Idzerda et al.15 found a monotonous de- L by its quasiclassical value : crease of the x-ray magnetic circular dichroism XMCD sig- 2m F nal with Cr thickness for Cr overlayers on Fe. Bo¨ske et al.27 nL L. found for the XMCD signal of 2 ML Cr on Fe 100 the same sign as for 1 ML, contrary to the simple model of layer-by- A straightforward calculation shows that clL contains layer growth. They connected such behavior to a special only contributions proportional to the L1, L0, L 3: three-dimensional island growth. Turtur and Bayreuther3 found a rapid decrease of the total magnetic moment of an Fe Sm 2 8 1 1 cl F film sample on deposition of a Cr overlayer. This led them to L 4 2 15 2 30 3 . 5 the suggestion that the first two Cr layers on Fe have in fact parallel magnetic moments opposite to the magnetic moment After summation of the contribution to cl over all the of Fe substrate. The common feature of the results is that in QW's on the sample surface, we will obtain the term propor- the low coverage regime the distribution of thicknesses is not tional to the total volume of all islands which is constant for Poisson-like.15 the given coverage parameter , and a term proportional to For explaining these experiments, where a non-Poisson the total area of the islands also constant for a coverage three-dimensional growth of the Cr islands on Fe was clearly exceeding one monolayer . The third contribution in Eq. 5 revealed, we will put forward a simple theory based on the appears to be small even for monolayer islands and can be idea of confinement of itinerant electrons within the Cr is- omitted. As a result, when the coverage is fixed, for the lands on Fe surface. The existence of confined quantum-well determination of the distribution of islands on thickness it is QW states for electrons in highly perfect layer structures is enough to compare L instead of . i Li Li Li PRB 59 MAGNETIC DICHROISM AND SPIN-RESOLVED . . . 1221 interface region leads to erosion of the islands, so that our picture can be applied only for part of the sample surface. Despite these restrictions, confinement of the electrons in QW's definitely favors a non-Poisson distribution of island thicknesses. Clearly, the proposed model is only one of a number of conceivable mechanisms which may lead to the experimentally observed behavior. The growth of three- dimensional islands for higher thicknesses reduces the de- pendence of polarization on coverage and leads to the same effect as alloying in the interface region. The suppression of 2 ML islands can be one reason for the oscillation of the MCD signal which was obtained in our experiment as well as an apparent FM ordering of the first and the second Cr monolayer.4,27 For a better understanding of the magnetic properties of FIG. 6. L a.u. and number of quantum levels in the well the Fe-Cr interface a better characterization of the interface versus L. is desirable. Soft x-ray reflectivity studies can be very help- ful for assessing the surface or interface roughness. Clearly, In Fig. 6, the dependence of L for the single QW and such studies are highly desirable for a system like Cr on Fe, the number of quantum levels in the well versus their width and we are sure will be carried out very soon. In combination L is shown. L oscillates with L and decreases as L 2. with the soft x-ray Kerr effect, either by employing circularly This means that the main contribution to the L arises i Li polarized light or with linearly polarized light, in transverse from electrons localized in the narrowest QW, much as the geometry would even allow us to distinguish between chemi- electrons in narrowest QW determine the oscillations of ex- cal and magnetic roughness, which would be extremely use- change coupling in metallic magnetic superlattices and sand- ful in the present context.32 wich systems.31 Note that for Cr islands on an Fe 100 sur- face, the thickness of the QW can be changed only discretely ACKNOWLEDGMENTS in steps of one half of the lattice constant. The period of oscillation in Fig. 6 is about 2 A, i.e., of the same order as This work was supported by Deutscher Akademischer the lattice constant. Hence, if for the islands with thickness 2 Austauschdienst Grant No. ARC 313 and INTAS Grant ML, will be larger than for 1 and 3 ML, the formation of No. 96-0531 . Funding by the Bundesministerium fu¨r Fors- 2 ML islands will be suppressed. chung und Technologie BMFT under Grant No. 05 621 Our model of infinite QW's is too simple to explain the PFA 7 as well as by the Deutsche Forschungsgemeinschaft behavior of real systems in every detail. The finite depth and DFG within Project No. SFB 166/G7 is gratefully acknowl- the shape of the QW have a strong influence on the phase edged. V.M.U. would like to express his gratitude to the and even period of the oscillation L . Alloying in the Alexander von Humboldt-Stiftung for financial support. *Permanent address: St. Petersburg University, V.O. 14 Linia 29, Leng, and W. Zinn, J. Magn. Magn. Mater. 161, 49 1996 . 199178 St. Petersburg, Russia. 11 V. M. Uzdin and N. S. Yartseva, Comput. Mater. Sci. 10, 211 1 C. Carbone and S. F. 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