Influence of Cr Thickness Fluctuations on Exchange Coupling in Fe/Cr/Fe(001)
Magnetic properties, such as anisotropy and coercivity, are notoriously
dependent on the physical microstructure of the material. A sensitivity to
physical microstructure was also observed recently in measurements of the
exchange coupling of two Fe layers separated by a Cr layer.
SEMPA measurements in our group found
that the periodic changes in coupling as a function of Cr thickness depend strongly on the Cr
growth temperature. The aim of this project was to obtain a microscopic picture
of the structure of the Cr layer from STM measurements and to use this
information to understand the macroscopic magnetic properties measured by SEMPA.
SEMPA magnetization images of the Fe overlayer in
Fe/Cr/Fe(001) sandwich structures are shown in Fig. 1 for Cr spacer layers
grown at Fe substrate temperatures of 30° C, 200° C, and
350° C. The Cr spacer layer is wedge-shaped, increasing in thickness
from 0 to 40 monolayers from the left to the right of the images. The
magnetization of the Fe overlayer is parallel (ferromagnetically coupled) to
the substrate in the white regions and antiparallel (antiferromagnetically
coupled) in the black regions. Which of the two clearly evident periods of
oscillation is dominant depends on the growth temperature of the Cr spacer
layer. In addition, for a fixed growth temperature the dominance of a
particular period depends on the Cr thickness as seen most clearly in the image
for the 200° C growth.
Figure 1: SEMPA magnetization images of the top Fe layer in Fe/Cr/Fe(001)
sandwich structures for different Cr growth temperatures.
Figure 2: STM images of ~5 monolayers of Cr grown on a Fe(100) whisker
held at temperatures of 50° C, 215° C, and 300° C.
The images are 100x100 nm, 200x200 nm, and 600x600 nm, respectively.
From the STM measurements we obtain a quantitative measure of the Cr film growth, shown in Fig. 2, for substrate temperatures of 50° C, 215° C, and 300° C, similar to those of the SEMPA data of Fig. 1. Layer-by-layer growth was observed for Cr deposition on an Fe substrate at a temperature of 300° C as shown in Fig. 2, where the lighter gray indicates regions higher by one atomic layer. Rougher Cr growth, limited by diffusion kinetics is observed at lower growth temperatures. The roughness in the Cr film surface is manifested as a thickness variation of the Cr film which is grown on the smooth Fe whisker surface.
To understand the exchange coupling in this trilayer structure we need to know
the Cr thickness distribution over a length scale given by the shortest length
over which the top Fe layer can change its magnetization direction. This length
scale, which is of order ~100 nm, depends on the ratio of the intralayer
exchange energy to the interlayer exchange energy. The net exchange coupling
between the top and bottom Fe systems will be then the average of the exchange
coupling at each Cr thickness, weighted by the amount of area at that thickness,
as shown schematically in Fig. 3.
Figure 3: Schematic of trilayer structure of Fe/Cr/Fe grown on Fe
whisker substrates. The roughness in the Cr growth gives rise to thickness
fluctuations in the Cr spacer layer thickness. The top layer Fe film responds
over a length scale of order 100 nm, schematically indicated by the arrow.
Therefore the exchange coupling between the two Fe layers must be averaged over
Cr thickness fluctuations which occur within this length scale.
A model for the exchange coupling at each discrete Cr thickness can be obtained
by analyzing the layer-by-layer Cr growth case. The exchange coupling J which
leads to the oscillations in the magnetization images of Fig. 1 can be
modeled as the sum of two sine waves, with periods LA and
LB. The model interaction J(n) is plotted as the solid circles in
Fig. 4(c); it only has values at each thickness nd corresponding to a
discrete number of monolayers n, each of thickness d. The strength,
J(t), of the effective interaction at any average thicknessnbsp;t, is the sum
of the interactions J(n) weighted by the fraction of the area, P(t,n), at
that average thickness having n monolayers. It is plotted as the solid
line in the lower part of Fig. 4(c) normalized to the value of J(n) for n
equals one monolayer. The model magnetization profile, the dashed line in
Fig. 4(c), is obtained by setting all positive values of the model
coupling function J(t) to the same positive magnetization value and all
negative values to a negative magnetization of the same magnitude, plotted as
M/M*=+1 or -1, respectively. The relative magnetization measured by SEMPA is
normalized to the saturation magnetization value M* in the range of Cr
thickness from 10 to 30 monolayers. The periods and amplitudes of the two
sine waves used for fitting are varied to obtain the best fit to the
experimental magnetization profile, which is obtained from the high growth
temperature curve of Fig. 1, and shown as the solid line in the upper part
of Fig. 4(c). We find LA = 2.105±0.005 d
and LB = 12.0±1 d.
Figure 4: Profiles M/M* of the normalized magnetization from the SEMPA
images of Fig. 1 are shown as solid lines in the upper parts of each panel
corresponding to Cr growth at the Fe substrate temperatures of a) 30,
b) 200, and c) 350, respectively. The dashed line is the model
magnetization given by the sign of J/J*. The solid line J/J* is the lower part
of each panel is the normalized interaction J(t) at the average
thickness t.
If the thickness fluctuations obtained from the STM measurements are taken into account, we find that the magnetization profiles measured for rough Cr growth on Fe substrates at lower temperatures can be understood in terms of the exchange coupling J(n) determined for layer-by-layer growth. For rough growth, even if the average thickness is exactly n monolayers, there may be thicknesses of n-2, n-1, n, n+1, and n+2 monolayers present in the growth front. The rms roughness of Cr films approximately 5 monolayers thick, which were grown at 50° C and 215° C and are imaged in Figs. 2, is 0.86 and 0.47 monolayers respectively. The thickness distribution at the interface is approximated well by a Gaussian width increasing with Cr thickness according to a power law, thus determining P(t,n) along the Cr wedge. The exchange coupling J(t) at each average thickness t is determined by using the exchange coupling J(n) (dots in Fig. 4(c) from fitting layer-by-layer growth) weighted by the fraction of the growth front of thickness nd contributing to the average thickness. J(t) plotted in the lower parts of Figs. 4(a) and (b) leads to the model magnetization profiles plotted as dashed lines in the upper parts.
In summary, we found that the periods of oscillation of a theoretical coupling function could be obtained by fitting to the SEMPA magnetization profile in the case of layer-by-layer growth. Using this coupling function, and taking into account the thickness fluctuations in the Cr spacer layer measured by STM, we are able to understand the origin of the strikingly different SEMPA magnetization images of Fig. 1. Thus by using the STM to understand the temperature dependent growth properties of Cr at a microscopic level, we are able to understand the macroscopic magnetic properties observed in SEMPA investigations of interlayer exchange coupling.
Influence of Cr Growth on Exchange Coupling in
Fe/Cr/Fe(100)
Influence of Thickness Fluctuations on
Exchange Coupling in Fe/Cr/Fe Structures
STM Study of the Growth of Cr/Fe(001):
Correlation with Exchange Coupling of Magnetic Layers
Homoepitaxial Growth of Iron and a Real Space
View of Reflection-High-Energy-Electron- Diffraction
The Growth of Iron on Iron Whiskers
Joseph A. Stroscio
Daniel T. Pierce
Robert J. Celotta
Supported in part by the Office of Naval Research
Online: May 1996
Last Updated: February 2008
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