Vacuum 54 (1999) 295-297 Hyperfine fields in Fe-Cr thin films W. Karas´ Department of Solid State Physics, Faculty of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, ul. Reymonta 19, 30-059 Krako&w, Poland Abstract We have calculated the electronic structure of the 2Cr/3Fe/2Cr slab in bcc(1 1 0) geometry using FLAPW method in the local spin density approximation (LDA). The main aim of this work was to compare the calculated values of the hyperfine fields (HD) with these obtained in the experiment carried out by Zukrowski et al. (J. Magn. Magn. Mater, 1995, 145, 97). Our calculation shows the influence of the ordering on the Fe hyperfine fields and for the measured Cr/3.3Fe/Cr film we suggest the existence of two different HD values in each Fe plane, differingby 0.4-0.8 T. The magnetic moments of chromium are near 0.7 on the surface and oppositely oriented in the plane, while subsurface moments are small and anti-parallel to iron spins. The moments of iron atoms on the interface are slightly reduced. 1999 Elsevier Science Ltd. All rights reserved. 1. Introduction 2. Details of calculations The Fe/Cr system attracts great interest because We have performed the self-consistent electronic struc- of its interesting properties: the giant magnetostric- ture calculation using the FLAPW method. The real tion [2], the exchange coupling [3-7] and the oscillatory system is modeled by the 7-layer film (2Cr/3Fe/2Cr) of exchange coupling [8] to name but a few (for reviews bcc (1 1 0) geometry. The lattice constant is taken as that see [9]). of the pure iron (a The Fe-conversion electron Mo¨ssbauer spectro- "5.417 a.u.), as in our previous calculations [13]. This is a plausible assumption due to scopy (CEMS) [10, 11] is an excellent technique, the very small mismatch between iron and chromium allowing especially for the investigation of the local lattice constants (0.7%). magnetic structure. Our work was stimulated by the For the exchange-correlation potential we have used experiment carried out by Zukrowski et al. [1] on the the parameterization scheme of Perdew-Zunger [14]. bcc (1 1 0) Cr/Fe/Cr sandwiches (see also [12]). In order The wave functions in muffin-tin spheres were obtained to explain their experimental results, we have performed in the scalar-relativistic approximation [13]. The Bril- the electronic structure calculation on bcc (1 1 0) louin zone integration was performed using 16-36 magi- 2Cr/3Fe/2Cr system using an all-electron FLAPW cal k# points. The hyperfine fields was obtained using method for thin films [13]. Our calculation shows a non-relativistic formula, to allow for comparison with that iron atoms should have two distinct values of the our older results [15]. The convergence was assumed hyperfine fields in each layer. The anti-ferromagnetic when the differences in hyperfine fields were smaller than chromium, even as a second neighbor, influences the 0.01 T. fields on Fe atoms. The difference between the fields We have not performed the energy minimization, thus in one layer, although small (0.38, 0.78 T) seems to fixing the geometry as described above, according to the be significant (see discussion below). The obtained experimental situation [1]. values for HD are smaller than the experimental ones, Our calculation was started with the superposed den- but it is probably due to the size effect (thin covering sity of free atoms. The Cr atom was allowed to have - only two layers of chromium - in our modeling initial antiferromagnetic configuration in both layers. calculation). The calculation was repeated , first starting from d Cr 0042-207X/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 9 8 ) 0 0 4 8 1 - 3 296 W. Karas´ / Vacuum 54 (1999) 295-298 configuration with total spin S"2, then with S". The Table 2 two calculations converged to the same final density. We Fermi contact term (in T) for Fe atoms in different layers; denotes think, that by allowing for system to stay in some meta- position of the iron atom in the 2-D elementary cell stable state with small antiferromagnetic admixture, we better simulated the real experimental samples, where the Cr covering was thick. 3. Discussion The results of the calculation are summarized in Tables 1 and 2. From Table 1 one sees that in the surface layer of chromium the moments (&0.7-0.8 , only small enhancement in comparison to bulk ) are aligned tween chromium - seems to be most suited. The experi- anti-parallel to each other, whereas in the interface they mentally obtained fields (25.8 and 34.8 T) are in quite are small, parallel to each other but anti-parallel to the a good qualitative agreement with ours (see Table 2). iron moments in agreement with the conclusion of Xu However, our calculation suggests that it should be two and Freeman [16, 17]. The iron moments are only affec- different fields in each iron layer for this system. The ted at the interface. It is worthwhile to notice, that there is differences are &0.38 T at the interface and &0.76 T in practically no charge transfer between atoms in the same the central layer. Theoretically, such differences could be layer. resolved by the Mo¨ssbauer experiment, as the spectral Table 2 summarizes our results for the hyperfine field resolution is about 0.3 T. The new analysis of the experi- (only Fermi contact term included). Due to anti-parallel ment [18] on the above mentioned system has shown alignment of the chromium moments there are small but only, that on the basis of the statistical analysis our detectable differences in the fields on iron the atoms in model cannot be rejected. The poor resolution is prob- the same layer. This is due to the delicate balance in the ably due to imperfections, which are present at the iron- magnetic interactions of the constituent atoms (Fe-Fe, chromium interface in the real probe. Fe-Cr, Cr-Cr) as discussed in [16]. The central layer In conclusion, we calculated hyperfine fields for H 2Cr/3Fe/2Cr slab, predicting two different fields in each D is smaller than the bulk one in contrast to other investigated systems [15]. iron layer. The present experiment does not allow to We compared our calculation with the CEMS verify unambiguously our results. measurements carried out by Zukrowski et al. [1]. Among the measured sandwiches, Cr/3.3Fe/Cr system - consisting of 3.3 monolayers of iron sandwiched be- Acknowledgements The author would like to thank Dr. J. Zukrowski for refitting the experimental data and helpful discussion. Table 1 Charges and moments ( This work was supported by the Polish Science Research ) in layers for 2Cr/3Fe/2Cr film: S - surface layer, C - central layer; * - Cr, - Fe denote positions of the given Council, grant No. P03B 080 10. element in the 2-D elementary cell References [1] Zukrowski J, Liu G, Fritzsche H, Gradmann U. J Magn Magn Mater 1995;145:57. [2] Baibich MN, Broto JM, Fert A, Nguyen Van Dau F, Petroff F, Etienne P, Creuzet G, Friederich A, Chazelas J. Phys Rev Lett 1988;61:2472. [3] Gru¨berg P, Schreiber R, Pang Y, Brodsky MB, Sowers H. Phys Rev Lett 1986;57:2442 [4] Saurenbach F, Walz U, Hinchey L, Gru¨nberg, P, Zinn, W, J Appl Phys, 1988;63:3473. [5] Binasch G, Gru¨nberg P, Saurenbach F, Zinn, W, Phys Rev B 1989;39:4828. [6] Tomaz MA, Antel WJ, O'Brien WL, Harp GR, Phys Rev B 1997;55:3716. [7] Freyss M, Stoeffler D, Dreysse´ H, Phys Rev B 1997;56:6047. [8] Stiles MD, Phys Rev B 1996;54:14 679. W. Karas´ / Vacuum 54 (1999) 295-297 297 [9] Fert A, Gru¨nberg P, Barthelemy A, Petroff F, Zinn W. J Magn [13] Karas´ W, Noffke J, Fritsche L. J Chim Phys 1989;86:861. Magn Mater 1995;140-144: 1; In Heinrich B, Bland JAC, editors. [14] Perdew JP, Zunger A. Phys Rev B 1980;23:5048. Ultrathin magnetic Structures II, Ch. 2. Berlin: Springer, 1994;45. [15] Karas´ W, Korecki J, Przybylski M, J Magn Magn Mater [10] Korecki J, Gradmann U. Phys Rev Lett 1985;55:2491. 1995;140-144:665. [11] Przybylski M, Gradmann U, Korecki J, J Magn Magn Mater [16] Xu J-H, Freeman AJ, J Magn Magn Mater 1990;86: 26. 1987;69:199. [17] Xu J-H, Freeman AJ. Phys Rev B 1993;47:165. [12] Landes J, Sauer C, Brand RA, Zinn W, Mantl S, Kajcsos ZS. [18] Zukrowski J. Private communication. J Magn Magn Mater 1990;86:71.