Journal of Magnetism and Magnetic Materials 203 (1999) 280}282


       Fe/Cr interface magnetism in the external magnetic "eld
                                                  V.M. Uzdin *, N.S. Yartseva 
                     Institut fu(r Angewandte Physik, Heinrich-Heine-Universita(t Du(sseldorf, D-40225, Du(sseldorf, Germany
                                           Institute of Metal Physics, GSP-170, Ekaterinburg 620219, Russia


Abstract

   A method of self-consistent calculation of magnetic ordering in low-dimensional metallic structures in the presence of
an external magnetic "eld is developed on the basis of periodic Anderson model. Multitude of self-consistent solutions for
the magnetic moments distribution in interface region leads to a hysteresis-like dependence of the average magnetic
moment on value of the applied "eld. The shape of hysteresis loop calculated individually for Fe and for Cr atoms
changes signi"cantly depending on the structure of the interface region.   1999 Elsevier Science B.V. All rights reserved.

Keywords: Model Hamiltonian; Magnetic moments distribution; Hysteresis loop



   New phenomena which were discovered in Fe/Cr                               procedure. Outside the prism we used periodic boundary
multilayers have attracted a number of experimental                           conditions. The bottom layer (11) was uniform "lled by
methods for their investigations. However, the results                        the Fe atoms, and for modelling of a semi-in"nite sample
and interpretation of these experiments, even obtained by                     we accepted that the next layer (12) coincides with the
similar methods, often contradict one to another [1].                         previous. The algorithm parameters varying gives a pos-
One of the reasons of such contradictions is a sensitivity                    sibility to create the surfaces and interfaces with a di!er-
of the Fe/Cr multilayers properties to the interface mor-                     ent but controlled roughness. For determination of aver-
phology, which strongly depends on the details of prep-                       age values the sample construction was repeated 20
aration conditions. Theoretical calculations of the Fe/Cr                     times, so that every layer e!ectively contained
interface structure, taking into account a roughness and                      8;8;20"1280 independent sites. Table 1 displays
interdi!usion, also demonstrated a very complex behav-                        layer by layer the number of Fe atoms, Cr atoms, and
iour and existence of a number of self-consistent solu-                       empty sites for two Cr monolayers on the Fe substrate,
tions with close energies [2,3]. That is why the problem                      which are obtained by &epitaxy' algorithm with para-
of solution's stability relatively external perturbations,                    meters, corresponding to the relatively smooth (SI) and
such as an external magnetic "eld, have a principal im-                       rough (RI) interfaces. For each of these structures self-
portance for these systems.                                                   consistent calculations of the magnetic moments within
   In this paper we report the results of magnetic struc-                     PAM were performed. Due to s}d-interaction, which is
ture calculations of Cr overlayer on a rough Fe surface                       taken into account in PAM, d-levels of the Fe and Cr
within the collinear periodic Anderson model (PAM) in                         atoms have a "nite width  , which is a parameter of the
presence of the external magnetic "eld. The rough inter-                      model. E!ectively, for every element (either Fe or Cr) we
face was constructed using &epitaxy' algorithm [4,5],                         used three dimensionless parameters: x"(E! $)/  de-
which "lls sites of an ideal BCC lattice inside the prism                     termines the position of d-level relatively Fermi-level,
8;8;11 by the Fe and Cr atoms using a special random                          ;/  describes the Coulomb repulsion on the site in
                                                                              Hartree}Fock approximation, and </  is the hoping
                                                                              integral. The parameters were chosen to reproduce the
                                                                              magnetic moment and d-electron number for the bulk Fe
  * Corresponding author. Tel.: #49-211-8112284; fax: #49-                    and Cr.
211-8113658.                                                                    The self-consistent calculations of the magnetic mo-
  E-mail address: uzdin@uni-duesseldorf.de (V.M. Uzdin)                       ments were performed for 20 con"gurations of SI and RI.

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 9 ) 0 0 2 6 4 - 4



                      V.M. Uzdin, N.S. Yartseva / Journal of Magnetism and Magnetic Materials 203 (1999) 280}282                      281

The external magnetic "eld H shifts the energy of spin up               ing from the zero "eld. An initial con"guration was
states relatively spin down states on the value of 2   H.               chosen so that all Fe atoms have the same direction of the
The calculations were performed for 39 values of H start-               magnetic moments, whereas the Cr moments are ordered
                                                                        either along or opposite to the Fe moments with prob-
Table 1                                                                 ability 0.5. The value   H/ , being a normalised mag-
Layer by layer distribution of the Cr atoms, Fe atoms, and              netic "eld, changes in the following way: 0P
empty sites for two monolayers of Cr coverage on the Fe                 !0.7P0P0.6P0P0.7 with a step equal to 0.1. For
substrate in the case of &smooth' and &rough' interface                 each successive value of the magnetic "eld we used the
                                                                        self-consistent solution obtained for the previous "eld
Layer      Smooth interface              Rough interface                value as the initial con"guration.
                                                                           Fig. 1 shows the average projection on the parallel to
           Cr         Fe         Emp     Cr      Fe         Emp         applied magnetic "eld axis of the magnetic moments for
 1               3          0    1277      24          1    1255        the Fe and Cr atoms in one layer as a function of the
 2          225             0    1055    178       19       1083        applied "eld value. Fig. 1a and Fig. 1b corresponds,
 3         1051             2    227     496      156       628         respectively, to the 4th and 5th layers of the SI (see Table
 4         1056        223         1     630      459       191         1). The number of the Fe and Cr atoms are given in the
 5          222       1058         0     487      768        25         frame of the "gures also. Hysteresis-like form of the
 6               3    1277         0     287      961        32         curves re#ects the plurality of the self-consistent solu-
 7               0    1280         0     166     1053        61         tions and their dependence on the initial con"guration
 8               0    1280         0     112     1049       119         used for the self-consistent procedure. The shape of the
 9               0    1280         0       85    1037       158         loops essentially depends on the number of layers. It
10               0    1280         0       54    1076       150         demonstrates that the moments in the di!erent interface
11               0    1280         0       38    1101       131
12               0    1280         0        0    1280         0         layers have a di!erent response on the external perturba-
                                                                        tion, and consequently that the approach of an uniform




























Fig. 1. Dependence of the average projection of the Cr and Fe magnetic moment in one layer on the parallel to the external magnetic
"elds axis versus the parameter   H/ . a } for the 4th layer SI, b } for the 5th layer SI, c } for the 3rd layer RI, d } for 6th layer RI.



282                  V.M. Uzdin, N.S. Yartseva / Journal of Magnetism and Magnetic Materials 203 (1999) 280}282

magnetisation of Fe layers failed for these systems. The             presence of external "eld it can be enhanced up to 2   .
4th layer (Fig. 1a) is "lled mostly by the Cr atoms. Their           These facts are in good agreement with out previous
magnetic moments are surface enhanced and antifer-                   calculations of Cr overlayers on the Fe substrate [3],
romagnetically (AF) coupled with the Fe substrate. When              which show a large local moment but zero average.
the magnetic "eld gives a spin-#op transition in the                   Note, that all the calculations were performed within
semi-in"nite Fe (about   H/ "$0.4) the magnetic mo-                  the collinear model. For the rough interfaces with a
ments of the Cr atoms change their direction on the                  number of frustrations the canted spin structures are
opposite one. The Fe atoms in the 4th layer are much                 expected. Taking into account the possibility of the non-
more #exible: the value and direction of the average Fe              collinear states have to decrease essentially the value of
moment can be changed essentially by the relatively                  spin-#op magnetic "eld.
small external "eld. Next 5th layer (Fig. 1b) shows very
stable moment of the Cr and Fe atoms, which stays                      This work is partially supported by INTAS Project
almost unchanged till the spin-#op "eld. The magnetic                No. 96-0531 and RFBR No. 98-02-17517. VMU would
moments directions of the Cr and Fe atoms coincide in                like to express his gratitude to the Alexander von Hum-
this layer in spite of the AF coupling of Cr with respect to         boldt foundation for support.
the Fe substrate.
  Dependencies obtained for the RI (layers 3 and 6) are
shown in Fig. 1c and Fig. 1d. The hysteresis loops for all           References
Fe layers look similar to each other and the magnetic
moments of the Fe atoms appear to be very stable. The                [1] H. Dreysse, C. Demangeat, J.A.C. Bland, G. Bayreuther
moments of Cr, on contrary, show a di!erent behaviour                    (Eds.), Workshop on Fe/Cr Interface Magnetism, Stras-
for the di!erent layers. The Cr atoms transferred inside                 bourg, 2}3 June 1996.
the Fe substrate (Fig. 1d) have the moments opposite to              [2] A. Vega, C. Demangeat, H. Dreysse, A. Chouairi, Phys. Rev.
the Fe moments, and only slightly change up to the large                 B 51 (1995) 11546.
                                                                     [3] N.S. Yartseva, V.M. Uzdin, C. Demangeat, Comput. Mater.
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are also Cr ones, the magnetic moment can be easily                  [4] A.K. Kazansky, V.M. Uzdin, Phys. Rev. B 52 (1995) 9477.
reoriented (Fig. 1c): the average projection of the mag-             [5] C. Demangeat, V.M. Uzdin, J. Magn. Magn. Mater. 165
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