
within the media. It provides a relatively uncompli-
cated way to perform optical calculations but for
the magneto-optical case is limited to the polar Kerr
effect at normal incidence. The second, a matrix
method, is a more general approach and is conven-
iently used for multilayer systems.
See also: Magneto-optic Effects, Enhancement of;
Magneto-optic Multilayers; Magneto-optic Record-
ing: Total Film Stack, Layer Configuration
Bibliography
Atkinson R, Lissberger P H 1993 Correct formulation of first-
order magneto-optical effects in multilayer thin films on
terms of characteristic matrices and derivation of a related
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Gamble R, Lissberger P H, Parker M R 1985 A simple analysis
for the optimization of normal Polar magneto-optical Kerr
effect in multilayer coatings containing a magnetic film. IEEE
Trans. Magn. 21, 1651–3
Heavens O S 1991 Optical Properties of Thin Solid Films. Dover
Publications Inc, New York
Hunt R P 1966 Magneto-optic scattering from thin solid films.
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Lissberger P H 1970 Optical applications of dielectric thin films.
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Acta 12, 13–45
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Magneto-optical Materials. IOP Publishing Ltd, Bristol, UK
W. R. Hendren
Queen’s University of Belfast, UK
Multilayers: Interlayer Coupling
The exchange coupling of magnetic films across me-
tallic interlayers was first observed in 1986 for dys-
prosium and gadolinium films separated by yttrium
interlayers, and for iron films separated by chromium
interlayers (Salamon et al. 1986, Majkrzak et al. 1986,
Gru
¨
nberg et al. 1986. For ferromagnetic films like
those of gadolinium and iron, the coupling leads to
parallel or antiparallel alignment of the magneti-
zations on opposite sides of the interlayer, depending
on the interlayer thickness D, as seen in Figs. 1(a) and
1(b) respectively. For obvious reasons, the coupling
leading to (a) is called ‘‘ferromagnetic’’(F), and to
(b) ‘‘antiferromagnetic’’ (AF). For films with helical
magnetic structure like dysprosium, the coupling leads
to an angle, c, between the magnetic moments on
both sides of the yttrium interlayer, which depends on
the yttrium thickness, as seen in Fig. 1(c). The actual
alignment is also affected by other interactions, like
anisotropy or an external field, H
ext
. Large enough
fields, H
ext,
overcome the coupling and align the mag-
netizations parallel.
In 1990, it was established (Parkin et al. 1990) that
the oscillation of the magnetic coupling between F
and AF alignment, as a function of interlayer thick-
ness, is a general phenomenon of transition metal
ferromagnets separated by nonmagnetic interlayers.
Previously oscillations had only been seen for gado-
linium separated by yttrium. The discovery in 1988 of
the giant magnetoresistance (GMR) effect in the
Fe/Cr system (see Giant Magnetoresistance) led to
enhanced interest in the magnetic coupling of tran-
sition metal ferromagnets, because of the many ap-
plications of GMR.
1. Theoretical Models
Interlayer exchange coupling is believed to be an in-
direct exchange interaction mediated by the conduc-
tion electrons of the spacer layer. It is closely related
to the Ruderman–Kittel–Kasuya–Yoshida (RKKY)
interaction between localized moments mediated by
the conduction electrons of a host metal. The essen-
tial ingredients of the RKKY interaction, a localized
spin-polarized perturbation and a sharp Fermi sur-
face, lead to the well-known coupling oscillations.
Like the exchange coupling in the rare earth metals
themselves, the magnetic coupling of gadolinium,
dysprosium, holmium, and erbium through yttrium
and lutetium spacer layers has been described by the
RKKY interaction.
For transition metal ferromagnets separated by
paramagnetic interlayers, the description of the cou-
pling needs to be modified. A phenomenological
description of the coupling proposed to explain the
Figure 1
Coupling between magnetic films across metallic
interlayer (dark shaded). Encircled arrows indicate
moments in monolayer sheets parallel to the interfaces.
The arrows indicate ferromagnetic coupling across the
interlayer in (a) and antiferromagnetic coupling in (b).
The magnetic coupling of films with a helical magnetic
structure shown in (c) leads to a phase angle c.
955
Multilayers: Interlayer Coupling