Interlayer Coupling in Magnetic/Pd Multilayers
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Abstract The Anderson model of local-state conduction electron mixing is applied to the problem of interlayer magnetic coupling in metallic multilayered structures with palladium (Pd) spacer layers. An oscillation period of 5 spacer monolayers and the tendency towards ferromagnetic bias of the interlayer magnetic coupling that we obtain are consistent with the experimental data.
The discovery of oscillatating interlayer magnetic couplings between ferromagnetic layers separated by a nonmagnetic metallic spacer [1] and of the related giant magnetoresistance effect [2], has stimulated a lot of experimental and theoretical activity. It has been shown that the periods of the coupling are related to the topology of the Fermi surface of the spacer layers. This interpretation has been confirmed by model and first-principles calculations, and is also supported by experiments [3, 4]. There are, however, other aspects of the coupling, e. g., the bias (ferro- or antiferro-magnetic) of the interlayer magnetic coupling, which have not been fully explained. For Fe(001) layers separated by Pd(001) spacers of thickness between 4 and 12 ML the interlayer magnetic coupling is observed to have a strong ferromagnetic bias as seen in the experiments [5]. Above a 13 ML thickness of the Pd spacer the coupling begins to be antiferromagnetic. Metallic Pd is believed to be near the threshold of becoming ferromagnetic. The non-relativistic calculations of Moruzzi and Marcus [6] and of Chen et al. [7] predicted the onset of ferromagnetism in fcc palladium with a 5% expanded lattice. In a recent publication the ferromagnetic bias of the coupling in magnetic multilayer structures with a Pd spacer is explained in terms of the Pd as an almost ferromagnetic media [3]. Alternatively, in this paper, we interpret this ferromagnetic bias to be a consequence of a competition between RKKY-like and superexchange couplings, with RKKY coupling being dominant. The RKKY-like coupling comes from intermediate states which correspond to spin excitations of the Fermi sea. States corresponding to electron-hole pair production in the Fermi sea, with an attendant spin-flip, contribute to the RKKY coupling as [8];
jRKKY(q)
=
n1,n2,k
[ I1Vniiv I'I Vn,•kiI O(@F --. ,k)O(e,,k, --F) (np' -E+)2
-
+ C.C.]
,n~k
(1)
where 0 is a step function, 6 F is the Fermi energy, k' = k + q + G, G is a vector of the reciprocal lattice, e+ is the energy of the local impurity state, and Vnk represents the strength of the s - d mixing interaction [9]. 177 Mat. Res. Soc. Symp. Proc. Vol. 384 0 1995 Materials Research Society
The superexchange coupling arises from charge excitations in which electrons from local states are promoted above the Fermi sea (one from each layer) providing a second contribution to the coupling in addition to the RKKY coupling [8]:
js(q) = - E
[ IV.
I'
I Vý2 k' 12 O(e6,k
-
eF)O(e,2 k, - eF) + C.c.] ek A;
E- )
(6, 2 k'
n1 ,n 2 ,k
(2)
E+
The real space coupling between two sheets of spins can be obtained by Fourier transforming Eqs. (1) and (2)
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