2. II. EXPERIMENT
All samples were prepared on Ni–P coated, polished
Al–Mg substrates using the BPS Circulus M12 sputter-
deposition tool. The amorphous SUL ͑a-SUL͒ consisted of
60 nm thick antiferromagnetically coupled CoTaZr on a Ta
adhesion layer. Two types of IL schemes were employed. In
the first scheme ͑I͒, Fig. 1͑b͒, the IL stack consisted of a 5
nm thick Ta seed layer, 7.5 nm thick Ru growth layer, and
IrMn segregation layer of varying thickness. In the second
scheme ͑II͒, Fig. 1͑c͒, a 10 or 20 nm thick crystalline SUL
͑c-SUL͒ made from CoFe alloy was added on top of the
a-SUL. For achieving the desired fcc ͑111͒ crystallographic
growth of the c-SUL, a 5 nm thick Ta seed and 4–10 nm
thick Ru growth layer was employed in that order. In this
scheme, the IL consisted of a single layer of IrMn of varied
thickness. For both schemes, the RL was sputtered from a
composite CoCrPt–SiO2 target with 5 mol % of SiO2, and
both the IrMn IL and the RL were sputtered at high pressures
to induce a granular microstructure. The thickness of the RL
was about 13 nm unless otherwise specified. For purposes of
comparison, a reference media sample having optimized
structural and magnetic properties was prepared using Ru as
IL. For this sample, the IL stack consisted of 5 nm Ta seed,
7.5 nm Ru growth layer, and 5 nm Ru segregation layer. The
films were characterized by x-ray diffraction ͑XRD͒, trans-
mission electron microscope ͑TEM͒, vibrating sample mag-
netometer ͑VSM͒, and a polar magneto-optical Kerr effect
͑MOKE͒ magnetometer. For grain size analysis by TEM, the
entire stack of layers with the exception of the relatively
thick SUL was sputtered on carbon-coated Cu grids.
III. RESULTS AND DISCUSSION
In the atomic stoichiometric ratio of Ir:Mn of about 1:3,
IrMn has the L12, or AuCu3 prototype crystal structure. As
depicted in Fig, 1͑a͒, the lattice parameter of 3.778 Å trans-
lates into a distance of 2.671 Å along the close-packed ͑111͒
plane. This distance compares more favorably with the 2.51
Å for the a-lattice parameter of hcp Co than the correspond-
ing 2.72 Å of hcp Ru. Since the stacking of atoms along the
L12 ͑111͒ and hcp ͑00•2͒ planes are equivalent, IrMn when
grown with out-of-plane ͑111͒ texture can support the het-
eroepitaxial growth of hcp ͑00•2͒ Co. In addition, IrMn is a
well-known antiferromagnet with a Neel temperature of 690
K ͑417 °C͒ in the bulk, and the antiparallel aligned spins lie
in the ͑111͒ plane.25
This may have implications for the ther-
mal stability of the media, as also the SUL noise properties,
and is discussed below.
A. Media scheme „I…
Information on the crystallographic and magnetic prop-
erties of scheme ͑I͒ media can be found in Ref. 24. As the
thickness of the IrMn segregation layer was increased from 3
to 7.5 nm, the ⌬50 of the IrMn ͑111͒ and that of the Co
͑00•2͒ decreased, and coercivity Hc increased. The normal-
ized slope at coercivity ␣ dropped significantly, whereas the
nucleation field Hn increased only marginally. Hc–Hn, which
is indicative of the strength of the intergranular ͑IG͒ ex-
change coupling interactions, increased from 1200 to 2200
Oe, which indicates that the IG exchange interactions in the
RL reduce upon increasing the IrMn segregation layer thick-
ness. For medium with 7.5 nm thick IrMn segregation layers,
⌬50 of Co ͑00•2͒ perpendicular texture of 4.1°, coercivity
Hc of 4300 Oe, and negative nucleation field -Hn of 2100 Oe
could be obtained. On the whole, the IrMn segregation layer
can induce segregated grains with coercivity and nucleation
fields that are comparable to that in the reference media
sample.
Figure 2 is a plot of the thermal stability factor, SF
which was obtained from fitting the dynamic coercivity to
the Sharrock model.26
Modified values of the Sharrock coef-
ficients, namely, the flip frequency value of 2ϫ1011
Hz and
the exponent value of 0.7 were used here.27
When the thick-
ness of the IrMn segregation layer was increased from 3 to
7.5 nm, SF increased from 73 to 88. Even with different
values of the coefficients, the trend in the SF was the same.
In order to verify the improvement in the thermal stabil-
ity, viscosity measurements were performed. Figure 3͑a͒ is a
plot of the field-dependent viscosity coefficient S, obtained
from fitting the time decay t of the magnetization to the
FIG. 1. ͑Color online͒ ͑a͒ The crystal lattice structures and parameters of
interest for hcp Co, hcp Ru, and L12 IrMn. The shaded planes are the
respective close-packed planes. ͑b͒ Proposed media scheme ͑I͒ using IrMn
IL. ͑c͒ Media scheme ͑II͒.
FIG. 2. ͑Color online͒ Change in thermal SF and intrinsic coercivity Ho,
plotted as a function of the IrMn layer thickness for samples from scheme
͑I͒.
07B738-2 Srinivasan et al. J. Appl. Phys. 105, 07B738 ͑2009͒
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
3. expression, M͑t͒=M͑0͒+S ln͑t͒ for different values of the
reverse field after the sample has been saturated with a posi-
tive field. S peaks near the nucleation field in PMR media,
where the demagnetization fields are strong compared to at
the coercivity point.28,29
The peak value of S is closely re-
lated to the degree of IG exchange-coupling interactions in
the RL. Strong exchange interactions lead to significant co-
operative reversal and large thermal decay near Hn, and thus
large peak values of S. In this context, it is interesting to note
that with the increase in the thickness of the IrMn segrega-
tion layer, the peak value of S decreased and shifted toward
higher field values, As far as S is a measure of the propensity
of the magnetization for reversal by thermal effects, the re-
duced value of S confirmed that the thermal stability is im-
proved.
To further investigate on the source of the improved SF,
torque magnetometry was used to determine the effective
magnetic anisotropy Ku
eff
of the RL. For this set of measure-
ments, media stack without the SUL was studied, because the
high moment SUL obscures the RL signals. Ku
eff
is equal to
Ku
ani
−2MS
2
where Ku
ani
is the magnetic anisotropy energy
constant and MS is the saturation magnetization. Ku
eff
was
obtained from the second harmonic of the magnetic torque
curve ͑not shown here͒ which was measured as a function of
the angle between the fixed applied field and the normal to
the film plane. The torque curve was then evaluated at dif-
ferent applied fields, and Ku
eff
was extracted at each field
point. Figure 3͑b͒ shows the plot of Ku
eff
of the RL, as a
function of the inverse applied field for different IrMn layer
thicknesses. At small external fields, the torque curve is dis-
torted by the large demagnetizing fields near the hard-axis
͑in-plane͒ point, which leads to different values of Ku
eff
. How-
ever, at large external fields that can overcome the demagne-
tization effects, the Ku
eff
values begin to converge. For all
samples, the value of Ku
eff
when extrapolated to zero inverse
field, i.e., infinite applied field was ϳ2.6ϫ106
ergs/cm3
.
For an MS value of ϳ500 emu/cm3
, evaluated by means of
VSM, Ku
ani
was ϳ4.2ϫ106
ergs/cm3
for all samples, and
not changing within experimental error. Consequently, the
origin of the improved thermal stability does not appear to be
due to any improved magnetic anisotropy.
The increase in SF is unlikely to be due to an increase in
the activation volume of reversal either, since large IG ex-
change interactions are associated with large activation vol-
umes. When the strength of the IG exchange interaction re-
duces, it also leads to a decrease in the activation volume
which, in turn, could affect the thermal stability.30
This is
especially so as thicker segregation layers have been reported
to provide superior templates for the columnar growth and
segregation of the RL grains.8,9,16
In order to eliminate the
possibility of improvement in the thermal stability coming
from the improved growth of the IrMn segregation layer, SF
was evaluated for media samples incorporating an IrMn cap-
ping layer.24
RL with high oxygen content and on dual Ru
ILs was capped with 7.5 nm IrMn layer. While the sample
without the IrMn cap layer exhibited SF value of 60, the
sample with the IrMn cap layer had SF value of 72.
The above important observations point out the principal
role of IrMn in improving the thermal stability of the RL.
Given that SF increased with the thickness of the IrMn seg-
regation layer, but Ku
ani
did not significantly change, IG ex-
change interactions decreased, viscosity coefficient S showed
decreased peak values, and even an IrMn cap layer was able
to increase SF, it appears doubtful that the enhanced thermal
stability could be strictly attributed to just the film texture or
the IG exchange interaction factors. In this scenario where
the origin of the thermal stability is not clearly understood,
we offer certain conjectures on the possible sources that
could be further investigated. While the IrMn is likely to be
superparamagnetic at a thickness of 3 nm, it is demonstrably
antiferromagnetic ͑see Sec. III C͒ at 7.5 nm. As mentioned
earlier, the antiferromagnetically coupled spins lie in the
͑111͒ plane which is also the plane of texture for these
samples. It may then happen that these spins couple via an
interlayer coupling mechanism to the perpendicularly ori-
ented spins of the RL. Interlayer exchange coupling of hard-
soft stacked media has been shown to improve the thermal
stability in exchange-coupled composite media31
and
coupled-granular continuous media.32
The antiferromagnetic
IrMn segregation layer may also help to stabilize the initial
growth layers of the RL through an exchange-bias interaction
effect. It should be emphasized here that due to the lack of
direct evidence, the above model is only hypothetical and
more experiments are necessary to understand the mecha-
nism behind the thermal stability improvement. However, if
the above hypothesis is confirmed, it potentially offers the
opportunity to shrink the grain size of the RL while still
maintaining the thermal stability.
B. Evolution of RL grains on IrMn segregation layers
The evolution of the magnetic properties and microstruc-
ture of the RL grains on the IrMn segregation layer is dis-
cussed in this section. Figure 4͑a͒ shows the MOKE hyster-
FIG. 3. ͑Color online͒ ͑a͒ Field-viscosity coefficient S
plotted as a function of the applied field, and ͑b͒ Ku
eff
plotted as a function of the inverse applied field, for
samples from scheme ͑I͒.
07B738-3 Srinivasan et al. J. Appl. Phys. 105, 07B738 ͑2009͒
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
4. esis loops and Fig. 4͑b͒ shows the change in the Hc, -Hn, and
loop squareness Sء
, for different thicknesses of the RL. For
all samples, the rest of the media stack consisted of 7.5 nm
IrMn segregation layer, 7.5 nm thick Ru growth layer, and 5
nm Ta seed layer on Al–Mg substrate. It is interesting to note
that the sample with the 3 nm thick RL exhibits superpara-
magnetic behavior and the sheared hysteresis is indicative of
IG exchange-decoupled grains. This is in contrast to the
highly IG exchange-coupled grains that are usually observed
for the initial growth layer of the RL on Ru segregation
layers.33,34
As the thickness of the RL is increased and the
RL grains grow in columnar fashion Hc and -Hn increase due
to the increased switching volume. Sء
also increases with the
increased RL thickness, which implies that the RL grains
become progressively more exchange coupled. This is again,
in contrast to the growth of the RL on Ru segregation layers,
where the RL grains become progressively less exchange
coupled with increased thickness.
Figures 5͑a͒–5͑d͒ show the TEM micrographs of the RL
from the above media samples. At all thicknesses, including
at the relatively thin 3 nm in ͑a͒, the RL shows well-
segregated grains with distinct grain boundaries. This obser-
vation corroborates the conclusions regarding the initial
growth layer of the RL on the IrMn segregation layer. The
estimated grain diameter for these samples are ͑a͒
7.5Ϯ1.7 nm, ͑b͒ 7.7Ϯ1.7 nm, ͑c͒ 7.5Ϯ1.5 nm, and ͑d͒
7.8Ϯ1.8 nm. The width of the grain boundary was about
1.1–1.2 nm. It should be pointed out here that TEM micro-
graphs of the IrMn segregation layer did not show a segre-
gated microstructure which confirms that the microstructure
observed above in Fig. 5͑a͒ is actually from the RL.
According to the observations made above, the IrMn
segregation layer can promote segregated, islandlike growth
of the RL right from the beginning, which is not the case for
the RL on Ru segregation layers. A comparison of the surface
energy of the plane of texture for these two segregation lay-
ers i.e., the IrMn ͑111͒ and the Ru ͑00•2͒, may help in un-
derstanding the reason behind the different growth mecha-
nisms of the RL. The surface energy data for IrMn ͑111͒ are
not available in the literature; however those of Ir ͑111͒ and
Mn ͑111͒ are available. These values are ϳ3.0 and 1.6 J/m2
,
respectively.35
As a rough guide, if we assume the effective
surface energy as the weighted sum of the individual com-
ponents, the surface energy of IrMn ͑111͒ is 1.88 J/m2
. In
comparison, the surface energy of Co ͑00•2͒ is
2.55–3.08 J/m2
and that of Ru ͑00•2͒ is ϳ3.05 J/m2
. Ac-
cording to the thermodynamics of thin-film growth, when the
deposit has lower surface energy than the substrate it grows
on, it tends to wet the substrate and form two-dimensional
structures.36
This is the case for the growth of the Co-based
RL on the Ru segregation layer where the RL wets the Ru
layer and initially grows in a layer-by-layer mode. On the
other hand, when the deposit has higher surface energy than
the substrate, three-dimensional island growth occurs accord-
ing to the Volmer–Weber growth mode. This could be the
case for the Co-based RL on the IrMn segregation layer,
where islands are observed right from the start.
The above observations, taken together, imply that the
IrMn segregation layer can lead to a uniform, columnar, is-
landlike microstructure for the RL, which can be beneficial
in terms of reduced media noise.
C. Media scheme „II…
When incorporated judiciously in PMR media, antiferro-
magnetic IrMn segregation layers also raise the possibility of
concurrently reducing the thickness of the IL stack. The
scheme ͑II͒ for PMR media, which was illustrated in Fig.
1͑c͒, is an example of a media stack where the total IL thick-
ness could be reduced to below 10 nm. The type of SUL
combination used here, referred to as hybrid SUL, consists of
an amorphous a-SUL and a crystalline c-SUL. The a-SUL
acts to mirror the write head and close the head-field circuit,
whereas the c-SUL channels the write head flux lines onto
the a-SUL while at the same time serving as a growth layer
for the RL.14,37
We have previously reported on the structural
and magnetic properties of RL on hybrid SUL, and where the
FIG. 4. ͑Color online͒ ͑a͒ MOKE hysteresis loops, and
͑b͒ change in Hc, -Hn, and Sء
, for samples from scheme
͑I͒, with different thicknesses of the RL as noted.
FIG. 5. ͓͑a͒–͑d͔͒ TEM micrographs for samples from scheme ͑I͒, with dif-
ferent thicknesses of the RL as noted.
07B738-4 Srinivasan et al. J. Appl. Phys. 105, 07B738 ͑2009͒
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
5. segregation layer for the RL was Ru. Micromagnetic simu-
lations have shown that enhanced head field and head-field
gradients can be obtained on hybrid SUL when the nonmag-
netic IL thickness is less than 10 nm.37,38
However, the draw-
back in using crystalline SUL is that the grain sizes in the RL
are rather large, and noise due to domain wall motion in the
c-SUL hinders the read-back signal.39
In this section, we
discuss how an IrMn segregation layer may potentially help
to resolve some of these issues.
XRD scans ͑not shown here͒ showed that even for me-
dium with the Ru layer thickness of 4 nm, the ⌬50 of the
CoFe ͑111͒ and of the Co ͑00•2͒ was 4.6°. For thicker 10 nm
Ru layer, the ⌬50 of these respective peaks dropped to 3.6°
and 3.8°. As a result, good crystallographic growth could be
obtained for the RL. Hysteresis loops obtained by MOKE
͑not shown here͒ appeared sheared, indicating exchange-
decoupled RL grains, and nucleation fields were small, pos-
sibly due to small RL grains. The remanent coercivity Hc
rem
,
obtained from dc-demagnetization measurements increased
slightly from 4100 to 4300 Oe upon increasing the Ru layer
thickness, and the normalized slope at coercivity ␣ was
ϳ2.7ϫ10−4
/Oe for all samples. These values compare well
with modern commercial PMR media. Thus, Ru growth lay-
ers as thin as 4 nm are sufficient to grow CoFe with ͑111͒
texture. On this type of hybrid SUL, with IrMn as the seg-
regation layer, well-oriented and magnetically isolated RL
can be obtained.
The use of crystalline SULs raises the question of
domain-motion induced noise and how to control it. To this
effect, we demonstrate that the c-SUL can be pinned by
exchange-bias interaction with the antiferromagnetic IrMn
segregation layer above it. Figure 6 is a plot of the in-plane
VSM hysteresis loops obtained along a set of antiparallel
directions, from sample with media structure ͑II͒. For this
sample, the Ru growth layer was 10 nm thick, the CoFe
c-SUL was 20 nm and the IrMn segregation layer was 7.5
nm. The two in-plane hysteresis loops, which belong to the
CoFe c-SUL, exhibit features typical of the ferromagnet-
antiferromagnet exchange-bias interaction, such as shifted
and asymmetric hysteresis.25
The exchange-bias field
strength, estimated from the shift of the hysteresis from the
origin, was ϳ50 Oe. It should be pointed out here that there
was no external field applied during sputtering, apart from
that originating from the sputter magnetron targets. Since the
loops are only partially shifted, the domains in the CoFe also
will only be partially pinned. A dedicated process, such as
one that uses an externally applied magnetic field during
sputtering, could possibly help to achieve larger exchange-
coupling fields and thus completely domain-free SUL. In ad-
dition, antiparallel coupled CoFe layers will also help to
overcome this problem.11,12
However, through media scheme
͑II͒, we have established the proof of principle for the con-
cept of pinning the c-SUL with the IrMn segregation layer
above it.
IV. CONCLUSIONS
The potential advantage of antiferromagnetic IrMn seg-
regation layers for PMR media was discussed. The IrMn has
a superior lattice matching with Co than even Ru, and sup-
ports good perpendicular crystallographic texture, large co-
ercivity, and small, exchange-decoupled grains for the RL.
The thermal stability of the RL was also enhanced on the
antiferromagnetic IrMn segregation layers. If this effect
arises due to an interlayer exchange interaction between the
IrMn layer and the RL, then it offers the opportunity to po-
tentially further reduce grain size in media without sacrific-
ing thermal stability. The IrMn segregation layers can pro-
mote the formation of segregated, islandlike grains even
during the initial stages of the growth of the RL which can
help to reduce media noise. When incorporated in a scheme
using hybrid SULs, the antiferromagnetic IrMn can help to
pin the SUL, while also lowering the total IL thickness to
below 10 nm. With further optimization, this scheme could
help to reduce crystalline SUL noise and also improve writ-
ability.
1
S. Oikawa, A. Takeo, T. Hikosaka, and Y. Tanaka, IEEE Trans. Magn. 36,
2393 ͑2000͒.
2
G. A. Bertero, D. Wachenschwanz, S. Malhotra, E. M. T. Velu, B. Bian, D.
Stafford, Y. Wu, T. Yamashita, and S. X. Wang, IEEE Trans. Magn. 38,
1627 ͑2002͒.
3
T. Oikawa, M. Nakamura, H. Uwazumi, T. Shimatsu, H. Muraoka, and Y.
Nakamura, IEEE Trans. Magn. 38, 1976 ͑2002͒.
4
H. Uwazumi, K. Enomoto, Y. Sakai, S. Takenoiri, T. Oikawa, and S.
Watanabe, IEEE Trans. Magn. 39, 1914 ͑2003͒.
5
K. Krishnan, T. Takeuchi, Y. Hirayama, and M. Futamoto, IEEE Trans.
Magn. 30, 5115 ͑1994͒.
6
K. W. Wierman, T. J. Klemmer, B. Lu, G. Ju, K. J. Howard, A. G. Roy,
and D. E. Laughlin, J. Appl. Phys. 91, 8031 ͑2002͒.
7
M. Zheng, G. Choe, K. E. Johnson, L. Gao, and S.-H. Liou, IEEE Trans.
Magn. 38, 1979 ͑2002͒.
8
R. Mukai, T. Usumaki, and A. Tanaka, J. Appl. Phys. 97, 10N119 ͑2005͒.
9
J. Z. Shi, S. N. Piramanayagam, C. S. Mah, H. B. Zhao, Y. S. Kay, and C.
K. Pock, Appl. Phys. Lett. 87, 222503 ͑2005͒.
10
S. H. Park, S. O. Kim, T. D. Lee, H. S. Oh, Y. S. Kim, N. Y. Park, and D.
H. Hong, J. Appl. Phys. 99, 08E701 ͑2006͒.
11
B. R. Acharya, J. N. Zhou, M. Zheng, G. Choe, E. N. Abarra, and K. E.
Johnson, IEEE Trans. Magn. 40, 2383 ͑2004͒.
12
K. Tanahashi, R. Arai, and Y. Hosoe, IEEE Trans. Magn. 41, 577 ͑2005͒.
13
520 Gbits/in.2
demonstration by Western Digital in October 2007 ͑see
press release at www.wdc.com͒.
14
S. N. Piramanayagam, J. Appl. Phys. 102, 011301 ͑2007͒.
15
U. Kwon, R. Sinclair, E. M. T. Velu, S. Malhotra, and G. Bertero, IEEE
Trans. Magn. 41, 3193 ͑2005͒.
16
S. N. Piramanayagam, C. K. Pock, L. Lu, C. Y. Ong, J. Z. Shi, and C. S.
Mah, Appl. Phys. Lett. 89, 162504 ͑2006͒.
17
Y. Inaba, T. Shimatsu, T. Oikawa, H. Sato, H. Aoi, H. Muraoka, and Y.
Nakamura, IEEE Trans. Magn. 40, 2486 ͑2004͒.
18
M. Zheng, B. R. Acharya, G. Choe, J. N. Zhou, Z. D. Yang, E. N. Abarra,
FIG. 6. ͑Color online͒ In-plane VSM hysteresis loops along a set of anti-
parallel directions for sample from scheme ͑II͒.
07B738-5 Srinivasan et al. J. Appl. Phys. 105, 07B738 ͑2009͒
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
6. and K. E. Johnson, IEEE Trans. Magn. 40, 2498 ͑2004͒.
19
H. Nemoto, R. Araki, and Y. Hosoe, IEEE Trans. Magn. 42, 2336 ͑2006͒.
20
A. Hashimoto, S. Saito, and N. Itagaki, Appl. Phys. Lett. 89, 262508
͑2006͒.
21
S. N. Piramanayagam, H. B. Zhao, J. Z. Shi, and C. S. Mah, Appl. Phys.
Lett. 88, 092506 ͑2006͒.
22
S. N. Piramanayagam, H. B. Zhao, J. Z. Shi, and C. S. Mah, Appl. Phys.
Lett. 88, 092501 ͑2006͒.
23
K. Srinivasan, S. K. Wong, S. N. Piramanayagam, and Y. S. Kay, J. Appl.
Phys. 103, 093912 ͑2008͒.
24
K. Srinivasan, S. N. Piramanayagam, and R. Sbiaa, Appl. Phys. Lett. 93,
072503 ͑2008͒.
25
J. Nogues and I. K. Schuller, J. Magn. Magn. Mater. 192, 203 ͑1999͒.
26
M. P. Sharrock, J. Appl. Phys. 76, 6413 ͑1994͒.
27
M. Igarashi and Y. Sugita, IEEE Trans. Magn. 42, 2399 ͑2006͒.
28
A. Lyberatos, J. Earl, and R. W. Chantrell, Phys. Rev. B 53, 5493 ͑1996͒.
29
K. Srinivasan, S. N. Piramanayagam, R. Sbiaa, and R. W. Chantrell, J.
Magn. Magn. Mater. 320, 3041 ͑2008͒.
30
J. D. Dutson, K. O’Grady, B. Lu, Y. Kubota, and C. L. Platt, IEEE Trans.
Magn. 39, 2344 ͑2003͒.
31
R. H. Victora and X. Shen, IEEE Trans. Magn. 41, 537 ͑2005͒.
32
K. K. Tham, Y. Sonobe, and K. Wago, IEEE Trans. Magn. 43, 671 ͑2007͒.
33
H. S. Jung, M. Kuo, S. S. Malhotra, and G. Bertero, Appl. Phys. Lett. 91,
212502 ͑2007͒.
34
H. S. Jung, M. Kuo, S. S. Malhotra, and G. Bertero, J. Appl. Phys. 103,
07F515 ͑2008͒.
35
H. L. Skriver and N. M. Rosengaard, Phys. Rev. B 46, 7157 ͑1992͒.
36
J. A. Venables, in Thin Films: Heteroepitaxial Systems, edited by W. K.
Liu and M. B. Santos ͑World Scientific, Singapore, 1999͒, pp. 1–63.
37
S. N. Piramanayagam, K. Srinivasan, R. Sbiaa, Y. Dong, and R. H. Vic-
tora, J. Appl. Phys. 104, 103905 ͑2008͒.
38
Y. Dong and R. H. Victora, IEEE Trans. Magn. 44, 3527 ͑2008͒.
39
J. Z. Shi, S. N. Piramanayagam, S. Y. Chow, S. J. Wang, J. M. Zhao, and
C. S. Mah, IEEE Trans. Magn. 42, 2369 ͑2006͒.
07B738-6 Srinivasan et al. J. Appl. Phys. 105, 07B738 ͑2009͒
Author complimentary copy. Redistribution subject to AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
