PHYSICAL REVIEW B VOLUME 57, NUMBER 15 15 APRIL 1998-I Overlayer-dependent magnetic moment and anisotropy of a Co monolayer on Cu 100... L. Szunyogh Center for Computational Materials Science, Gumpendorferstrasse 1a, A-1060, Vienna, Austria and Department of Theoretical Physics, Technical University Budapest, Budafoki uŽt 8, H-1521 Budapest, Hungary B. UŽjfalussy Center for Computational Materials Science, Gumpendorferstrasse 1a, A-1060, Vienna, Austria and Research Institute for Solid State Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary U. Pustogowa Center for Computational Materials Science, Gumpendorferstrasse 1a, A-1060, Vienna, Austria P. Weinberger Center for Computational Materials Science, Gumpendorferstrasse 1a, A-1060, Vienna, Austria and Institut fušr Technische Elektrochemie, Technische Universitašt Wien, Getreidemarkt 9/158, A-1060, Vienna, Austria Received 29 September 1997 An extensive study of the magnetic moment and of the magnetic anisotropy of a Co monolayer on a Cu 100 substrate capped by an additional 3d, 4d, or 5d monolayer is presented in terms of first-principles calcula- tions. While for the magnetic moment of the Co and the cap layer systematic trends can be traced that seem to be consistent with the Stoner model, the dependence of the magnetic anisotropy energy on the type of over- layer is found to be less straightforward. However, in some selected cases a correlation of the magnetic anisotropy with the specific features in the electronic structure of the Co and the cap layer can be pinpointed. S0163-1829 98 00915-1 Due to its theoretical challenge to solid state physics and Kohn-Rostoker SKKR method, which has been shown to technological importance in magneto-optical recording mag- be extremely suitable to calculate the electronic structure of netic anisotropies in thin films and multilayers of transition surfaces and interfaces.5­7 As in the calculations only spd metals have attracted considerable effort in research.1 In par- angular-momentum scattering channels were considered, La, ticular, the anomalous perpendicular magnetic anisotropy where 4 f states contribute to the valence band, was excluded PMA observed in ultrathin Co films on Au and Pt 111 from the present study. In order to obtain self-consistency, surfaces as coated by additional Ag, Cu, Au, or Pd layers energy integrations were performed along a semicircular seemed to indicate a close relationship between the material contour in the complex plane using 16 points according to an specific electronic structure and the surface magnetic asymmetric Gaussian sampling, and for the two-dimensional anisotropy.2 By using ab initio computational techniques, it Brillouin-zone integrations 45 k points in the corresponding then was shown that indeed the anomalous PMA is a conse- irreducible wedge IBZ were used. quence of the change in the interfacial hybridization between No attempt was made to account for surface reconstruc- the Co and the first cap layer as the thickness of the cap tion, relaxation, or strain, i.e., we assumed a perfect parent varies.3,4 fcc lattice8 corresponding to the experimental lattice constant So far experimental and theoretical studies have been of bulk copper (a 6.83 a.u. . Since, as is well known, such mainly confined to caps of noble transition metals Cu, Ag, lattice distortions do frequently occur at surfaces, the results Au or of Pd and Pt. In these studies the magnetic moment of presented in this paper only refer to a model study. This is the Co monolayer ultrathin film was found to be robust and most obvious for 4d and 5d overlayers where large lattice the actual value of the magnetic anisotropy energy MAE mismatch has to be expected when comparing the corre- resulted from a ``fine tuning'' of the electronic states of Co sponding bulk lattice constants to that of bulk Cu. However, near the Fermi level. In the case of Pd and Pt the spin polar- as far as trends are concerned, we believe that the present ization of the cap layers turned out to be also important. It is study represents a reliable theoretical description of the elec- the aim of the present paper to extend systematically the tronic structure of capped Co monolayers on Cu 100 . investigations of cap layers to all 3d, 4d, and 5d transition According to the force theorem see, e.g., Ref. 9 the ob- metal elements on top of a Co monolayer on a Cu 100 sub- tained self-consistent potentials were then used to calculate strate. the band-energy difference E b Eb Eb in terms of the For each system under consideration, self-consistent cal- fully relativistic spin-polarized SKKR method,10 where the culations have been performed within the local-spin-density superscripts and refer to a normal and a parallel to sur- approximation LSDA and the atomic-sphere approximation face orientation of the effective exchange field, respectively. ASA by solving the Pauli-Schrošdinger equation spin-orbit Here we generally used 325 k points in the IBZ, ensuring a coupling neglected by means of the screened Korringa- relative accuracy of less than 10% for Eb as was checked in 0163-1829/98/57 15 /8838 4 /$15.00 57 8838 © 1998 The American Physical Society 57 BRIEF REPORTS 8839 FIG. 1. Calculated magnetic moments of the Co and the cap layer in M/Co/Cu 100 systems, where M denotes a 3d squares , 4d circles , or 5d triangles transition metal. Solid lines serve as a guide for the eye. some cases by increasing the number of k points up to 990. The MAE is then given by E Eb Edd , where Edd denotes to the magnetostatic dipole-dipole interaction. Figure 1 displays the calculated magnetic moments of the Co and cap layers. At the end of each d row the magnetic moment of Co is quite robust (1.6 B mCo 1.8 B), drop- ping, however, rapidly for Cr, Ru, and Ir in the 3d, 4d, and 5d series, respectively. Near the beginning of the 3d row mCo decreases monotonously, while for 4d and 5d caps it reaches a local maximum for Nb and Ta, respectively. In the case of an Os overlayer and at the very beginning of each of the d rows Sc, Y, and Hf the Co layer is found to be even nonmagnetic. As to be expected, 3d elements with a well-localized, open d shell Mn, Fe, Co, and Ni have large magnetic mo- ments as overlayers, reaching a maximum of 3.5 B for Mn. Concomitantly to the abrupt decrease of mCo for Cr, in the 3d row the magnetic moments of the corresponding caps are in turn strongly reduced below Mn. It should be noted that Cr shows a tendency for antiferromagnetic coupling with Co, a possible formation of an in-plane antiferromagnetism within the Cr layer, however, was not investigated. In the 4d and 5d rows much smaller maxima for the moment of the FIG. 2. Calculated paramagnetic local densities of states cap layer are present for Rh and Pt, respectively. Most of the LDOS's for the Co solid lines and the cap dashed lines layer in tendencies observed for the magnetic moments of the cap M/Co/Cu 100 systems. M: 3d upper panel and 5d lower panel layers can be related to those of 3d, 4d, and 5d monolayers transition metals. The zero of energy corresponds to the Fermi on Ag or Au substrates,11 which in turn fit fairly well the level. In each entry the label denotes the corresponding cap. simple Stoner criterion. For the cases of the 3d and 5d overlayer systems the local since E 2 2 dd 0.022 meV (mCo mcap) see, e.g., the Ap- densities of states LDOS of the Co and the corresponding pendix of Ref. 10 , Edd is only larger in magnitude than 0.1 cap layer as derived from self-consistent paramagnetic cal- meV for Mn, Fe, and Co overlayers. Therefore, in what fol- culations are shown in Fig. 2. In both cases, the d band of the lows we focus on the analysis of Eb . The calculated Eb's overlayer moves gradually up in the energy as its filling in- for the Co and cap layers as well as the total MAE including creases, and since concomitantly the atomic number de- also Edd) are shown in Fig. 3. It is important to mention creases, the overlayer's d band gets more and more delocal- that for an uncovered Co monolayer we obtained a value of ized. Since 5d bands are obviously more delocalized than the 0.38 meV for Eb , which is in excellent agreement with 3d bands, especially around the Fermi level EF , they give previous theoretical results.12 rise to a different kind of hybridization with the Co d states. Apparently, the variation of the MAE upon changing the The variation of the LDOS of Co at EF can well be corre- element forming the cap is much more complicated than that lated with the variation of mCo in Fig. 1. In particular, for 5d of the magnetic moments. As can be seen from Fig. 3, in caps, the minimum of mCo for Os and the subsequent maxi- most cases a cap enhances the MAE as compared to mum for W and Ta are clearly mapped in a corresponding Co/Cu 100 , although within a particular row of transition- minimum and maximum in the LDOS of Co at EF . metal elements the MAE changes sign several times. The Turning now to the results for the MAE, we first note that anomalous PMA mentioned in the Introduction shows up as 8840 BRIEF REPORTS 57 FIG. 4. Band energy anisotropies Eb as a function of the high- est occupied energy for Co/Cu 100 and M/Co/Cu 100 M Cu, FIG. 3. Calculated MAE for M/Co/Cu 100 systems. M: 3d Ag, Au, Rh, and Pt . Solid line, total; dashed line, contribution of squares , 4d circles , and 5d triangles transition metals. Upper Co; dotted line, contribution of cap. The energy zero refers to the and middle panel: Respective band energy contributions, Eb , of Fermi level. the Co and the cap layer. Lower panel: total MAE, E Eb Edd . Solid lines serve as guide for the eye. As seen in Fig. 4, the situation is remarkably different in a large positive value for a Cu and Ag cap. Surprisingly the presence of a Cu or Ag cap. While the previously men- enough, in the case of a Au cap the MAE is negative. In the tioned maximum at 0.9 eV moves up in energy and is 3d and 4d rows, when going from the end Cu and Ag to considerably smaller than in the uncapped case, the subse- roughly the middle Fe and Ru the contribution of Co to quent maximum located at 0.2 eV above E E F for the b is gradually decreasing and then starts to oscillate. The Co/Cu 100 system is enhanced and shifted below E biggest negative value of E F , caus- b for Co is found for a Pt over- layer, while the only noticeable contribution from a cap layer ing thus a strong positive MAE in these two cases. Recalling refers to Rh. again the arguments of perturbation theory, this enhancement In the following, E of the MAE is due to the hybridization of Co d states with b is analyzed by considering the fol- lowing quantity: sp states of the cap layer, which results in a lowering of the Co d z2 states around EF , and also the minimum in the dxz,yz E states below E b d n * , 1 F disappears. b The case of a Au cap, however, is much more similar to where that of the uncovered system, since a minimum of the d b and n( ) denote the bottom of the valence band xz,yz and the LDOS, respectively, and which has frequently been states is located just below EF and therefore Eb( ) drops used to show the band filling properties of the MAE.3,12 In rapidly for 0.5 eV 0.3 eV. Although eventually Fig. 4, for some selected cases Eb( ) is plotted together vanishing at EF , the contribution of the Au layer to Eb( ) with its Co and cap contributions roughly in the regime of is generally larger than that of Cu or Ag, which in turn can the Co minority band. be related to the larger spin-orbit coupling. In Fig. 4 we also In the uncovered case, Eb( ) reaches a maximum of show the cases of a Rh and a Pt cap. Apparently, in these more than 1.5 meV at about 0.9 eV and then drops rapidly cases the cap layers contribute as much to Eb( ) as the Co to negative values, being negative also at EF . Above EF , a layer. This might be a consequence of the enhanced spin maximum and a minimum in Eb( ) are found at about 0.2 polarization in the cap layers which, especially for Pt, is eV and 0.4 eV, respectively. In terms of perturbation accompanied by a large spin-orbit coupling, causing thus the theory,13 this characteristic curve of Eb( ) can mainly be giant values of Eb( ) seen in the corresponding entry of attributed to the distribution of minority dxz,yz and dz2 states: Fig. 4. dxz,yz states have a pronounced minimum just below EF , Finally, it is interesting to note that the variation of mCo while dz2 states are located well around EF .14 with respect to the cap layer as seen in Fig. 2 can hardly be 57 BRIEF REPORTS 8841 correlated with the corresponding variation of E only studies based on ab initio techniques are able to predict b of Co in Fig. 4. This is, in particular, obvious for the series of Cu, Ni, correctly the MAE of technologically important materials. Co, and Fe as well as for that of Ag, Pd, and Rh, where m This is even more compulsory if, as in fact is necessary, one Co first slightly increases and then decreases, remaining, how- aims to include also structural and/or compositional anoma- ever, roughly of the same size, while E lies related to surfaces and interfaces, which may affect con- b of Co remarkably drops. Although the main qualitative reasoning for these siderably the value of the MAE in these systems.3 Progress variations can be deduced from the overlap of the Co and the in research to include these effects is currently under way. cap states, a detailed investigation of such an argumentation This paper resulted from a collaboration within the TMR in terms of perturbation theory and of spin-orbit induced Network on ``Ab initio calculations of magnetic properties coupling for each of the different cases shown, lies beyond of surfaces, interfaces and multilayers'' Contract No. the purpose of the present paper. ERB4061PL951423 . In addition, financial support by the The trends found in the size of the magnetic moments Austrian Ministry of Science GZ 308.941/2-IV/3/95 and follow closely the Stoner model of ferromagnetism. Accord- the Hungarian National Scientific Research Foundation ing to our results the MAE depends in a rather complicated OTKA Nos. T022609 and T021228 is kindly acknowl- manner on the material of the cap, indicating that ultimately edged. 1 U. Gradmann and J. Mušller, Phys. Status Solidi 27, 313 1968 ; Weinberger, Phys. Rev. B 52, 8807 1995 . P. F. Carcia, A. D. Meinhaldt, and A. Suna, Appl. Phys. Lett. 47, 7 K. Wildberger, R. Zeller, and P. H. Dederichs, Phys. Rev. B 55, 178 1985 ; P. F. Carcia, J. Appl. Phys. 63, 5066 1988 ; F. J. A. 10 074 1997 . den Broeder, D. Kuiper, A. P. van de Mosselaer, and W. Hov- 8 P. Weinberger, Philos. Mag. B 77, 509 1997 . ing, Phys. Rev. Lett. 60, 2769 1988 ; M. Sakurai, T. Takahata, 9 G. H. O. Daalderop, P. J. Kelly, and M. F. H. 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