The hard-axis magnetization curve for a sandwich with
13Å of Cr and a total of 108Å of Fe is shown in
Fig. 1. Also shown is a theoretical
magnetization curve calculated by minimizing the total energy
of the system as a function of the orientation of the two Fe
moments, M_{1} and M_{2}. The energy density
expression is[5]

E = (1/2)(E_{1} + E_{2}) + J
cos(theta_{1} - theta_{2}), (1)

where E_{i} =
K_{1}(a_{1i}^{2}
a_{2i}^{2} + a_{2i}i^{2}
a_{3i}^{2} + a_{3i}^{2}
a_{1i}^{2}) + K_{u}
cos^{2}(theta_{i} - pi/4) - M_{i}H
(2)

with alpha_{ji} the direction cosines of
M_{i}, K_{1} the usual cubic anisotropy,
K_{u} an in-plane anisotropy which is commonly found
in very thin Fe films on GaAs or ZnSe, and
theta_{i}(H) the azimuthal angle between
M_{i} and the easy [100] direction. Here J is a
phenomenological parameter introduced to describe the
antiferromagnetic coupling between the two Fe films. The
theoretical magnetization curve found from the energy density
expression is in good agreement with the experimental data,
as Fig. 1 shows.

The transverse magnetoresistance (H perpendicular to I) trace
of the same t_{Cr} = 13Å sample is shown in Fig. 2. For all of the Fe-Cr-Fe samples
studied, the steps in the magnetoresistance data occur at the
same applied field as the steps in the magnetization curve.
In order to understand the dependence of the
magnetoresistance on the orientation of the Fe moments, two
contributions have to be considered. First, there is the
intrinsic magnetoresistance of the individual Fe layers,
which depends on the angle theta between the applied field
and the current direction.[8] Secondly, there is an
additional part of the magnetoresistance which is due to the
suppression of the antiferromagnetic alignment. One might
expect this second contribution to the magnetoresistance to
be a function of the angle, DeltaPhi = (phi_{1} -
phi_{2}), between the moments of the two Fe films.[6]

The effect of the intrinsic anisotropy of the Fe layers on
the magnetoresistance can be gauged by examining Dr/r(phi) at
a high field where the antialignment has been suppressed. Fig. 3 shows the magnetoresistance of
the t_{Cr} = 13Å sandwich as a function of the
angle between a 6 kOe applied field and the current
direction. The data have been fit to the standard form[8]

Dr/r (phi) = [Dr/r]_{long} + {[Dr/r]_{trans}
- [Dr/r]_{long}} sin^{2}(q) (3)

where [Dr/r]_{long} is the longitudinal
magnetoresistance (H || I), and [Dr/r]_{trans} is the
transverse magnetoresistance (H perpendicular to I). The fit
results in the approximately field-independent anisotropy
parameter {[Dr/r]_{trans} - [Dr/r]_{long}} =
-3.8 X 10^{-3}. This anisotropy is slightly larger
than that that of pure Fe,[8] a finding which is in agreement
with previous work on Fe-Cr-Fe sandwiches.[4]

In order to analyze the second contribution to the magnetoresistance, which is due to the suppression of the zero-field antialignment, one must assume a form for the DeltaPhi-dependence of Dr/r. Once a form has been selected, one can invert the Dr/r(H) data to obtain an "experimental" DeltaPhi (H) curve. Fig. 4 is a plot of DeltaPhi vs. H obtained from the data of Fig. 2 by assuming that the magnetoresistance has the form

Dr/r (DeltaPhi) = [Dr/r]_{sat} *
cos^{2}(DeltaPhi/2) (4)

where [Dr/r]_{sat} is the value of the transverse
magnetoresistance at magnetic saturation. The form of Eqn. 4
is suggested by the magnetization curve, which indicates that
DeltaPhi is 0o at saturation and near 180° at zero field.
The angular difference DeltaPhi calculated from Eqs. 1 and 2
is also shown in Fig. 4. The
generally good agreement between the calculated and
experimental curves in Fig. 4
indicates that the magnetoresistance does in fact vary
approximately as cos^{2}(DeltaPhi/2). Camley and
Barnas[6] previously pointed out that the transmission
coefficient of an electron propagating between the two Fe
layers will go as cos^{2}(DeltaPhi/2) when the angle
between the two Fe moments is DeltaPhi.

Wed Oct 11 09:49:01 PDT 1995