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~ E E ETRANSACTIONS ON MAGNETICS, VOL 35, NO 5 , S!YEMBER 1999
Modeling the Effects of Domains in Magnetic Tunnel Junctions
Pak-Kin Wong, Jan E. Evetts and Mark G. Blamire
Department of Materials Science and Metallurgy, Cambridge University, Pembroke Street, Cambridge CB2 342, United Kingdom
Abstract-A
the
electrodes
model based on the domain structure of
in
ferromagnet-insulator-ferromagnet
tunnel junctions is derived. It provides an explicit
with the model and discuss the reduction of MR by increasing temperature through randomising the domain orientations
in the FM layers.
expression of the junction magnetoresistance (MR) in
11. DERIVATION
OF MODEL
terms of the magnetization of the ferromagnetic layers.
The response in magnetic field of junctions with very
A . Notations of MR
high and very low MR are simulated, and the lack of
We define MR as the percentage difference in junction
fringing field coupling is proposed to be a reason for
resistance with respect to the resistance in high field. In our
low MR. The effect of temperature on junction MR is
discussions, three notations of MR are used: Wobs, w and w*.
discussed briefly in the context of the model.
Webs
is the MR actually observed and is a function of the ap-
plied field H. w refers to the MR of a hypothetical leakage-fi-ee
Zndex Terms-Magnetic
tunnel junctions.
tunnel junction and is also a function of H. The relation be-
I. INTRODUCTION
tween these two is wobs=sw where s called the leakage factor
In the two decades following the frst modeling work 6
as introduced in our leakage conductance model [9]. s is in-
Julliere [ 11, the magnetoresistance (MR) obtained with FM-I-
dependent of H and so Wobs and w have a fixed proportionality
FM junctions was only up to a few percent [2], which was an
in a magnetic cycle. w* is the highest possible MR between
order less than predictions. Such low MR was mainly due to
parallel and antiparallel magnetisation alignments and is by
high barrier leakage. In 1995, Moodera et a1 improved the
definition independent of H.
barrier quality by using O2 plasma oxidation and achieved
MR of over 20%, close to Julliere's predictions [3]. Shortly
after that researchers of TBM also reported similar magnitudes
of M R [4]. Based on the results of these high quality junctions, a number of models were proposed. In these models,
the FM layers are assumed to have homogeneous magnetic
property. However experimental results show that the FM
I
Fig. I . A schematic picture of the ferromagnetic electrode showing the
proportion of domains (represented by the relative areas) with magnetization in one of the orthogonal directions. In our 8x8pmZ FM electrodes, the
number of domains is in the order of 102-10'.
layers actually consist of micron and submicron domains
which do not act coherently in the magnetic reversal process
[5,6].According to Julliere and Slonczewski [1,7], the tunneling conductance is a function of the angle between the
magnetization of the hypothetically homogeneous FM electrodes, and therefore the incoherency of the domains will affect
the response of the tunneling conductance in an applied field.
We recently proposed a model of junction MR taking into
account the distribution of domains over the tunneling a&i
[SI. In this article, we show the simulations of MR-H curves
B. Derivation
We consider the FM layers to consist of a large number of
domains. The magnetization of the domains is resolved into
orthogonal components as shown schematically in Fig. 1 . a,
and b, represent the fraction of the magnetic moments, in the
directions indicated by the arrows, of the top and bottom
electrodes respectively. By considering the symmetry in Fig.
1, we take a3=a and b3=b4. We also assume no magnetic
coupling between the electrodes, so that the distributions of
Manuscriot received March 3. 1999.
the domains
P. K. Wong, fax +44 1223 334373, pkw20@hermes.cam.ac.uk
This work is support in part by a fellowship of the Croucher Foundation of
0018-9464/99$10.00 0 1999 IEEE
Hong Kong
in the layers are statistically uncorrelated. The
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2899
total field-dependent junction conductance G(H) is the sum-
than the MR peaks. The MR then decayed slowly in about 2
mation oftunneling contributions between domains of vari-
days to the lowest and steady value (point B) between
ous magnetization,
40-60% of the MR at point A. The temporal variation of the
SO
we write
zero field MR can be fiozen at any point by immersing the
G(H)=gap(aibz+azb1+2a3b3)+gp(alb I +azbz+2a3b3)
+g,(2al b3+2azb3+2bI a3+2b2a3)
junction into liquid
(1)
5
where gap,g, and g, are conductance between domains of antiparallel, parallel and orthogonal magnetization respectively.
Nz.
4
i
h
5 3
a,bj is the probability of tunneling between domains indicated
by a, and b, in Fig. 1. At a high enough field, al=bl=l and
$ 2
1
all others vanish, giving a total conductance of G(H)=g,.
O-3
Therefore w(H), defined as [g,-G(H)]/G(H), becomes
Fig. 2. Initial MR-H curves. X, A and B correspond to MR values of Omin
20min and 2 days after the previous magnetic cycle.
By writing the maximum possible MR between single do-
The temporal variation of the initial curves can be ex-
mains as w*=(gp-gaP)/gap,
we have gadgp=(l + ~ * ) - ' ;and fiom
plained by (3) and (4) in view of the minimisation of the total
the dependence of MR on the angle between the magnetiza-
magnetostatic energy of the system. In Fig. 2, point X corre-
tion [7], we have g,/gp=( l+w*/2)( l+w*)-'. By putting the
sponds to partially parallel magnetization, i.e. O<M,, Mb<l.
expressions of gaP/gpand g,/g, into (2), we obtain
The system frstly reduced its energy by forming antiparallel
magnetization, i.e. M,Mb=-l, giving the highest MR of w*
w(H)=( I+w*)(uw*+ l)-'-l
( 3)
from (3). This antiparallel alignment is possibly promoted by
u=a3+al(bl+b3)+az(bz+b3)=( 1+MaMb)/2.
(4)
the fringing field coupling of the electrodes suggested by
In (4), Ma=al-az and Mb=bl-bZ are the magnetization of the
Tsuge et a1 [lo], whose junctions have similar nominal
FM electrodes normalised to their saturation values. There-
structure as ours. To eliminate further the fringing flux, the
fore (4) gives explicitly the relation between junction MR and
domains in each FM layer reorganised to form closed flux
the magnetization of the constituent FM electrodes.
loops, i.e. M,=Mb=O, giving w(H)=w*(w*+2)"=0.41~* (or
where
41% of w*). This is calculated with w*=46.3% for Fe-CoFe
111. COMPARISONS WITH EXPERIMENTS
A . Initial MR-H Curves
We have observed temporal variations of MR in our
8pmxSpm Fe/A1203/CoFe mesa junctions with multiply
oxidised barriers [8,9]. Apart from the usual hysteretic MR-H
peaks, the junctions showed initial curves, starting from zero
to high field (Fig. 2), similar to those seen in spin valve
multilayers. The MR of the initial curves at zero field depend
on the duration of waiting after the previous magnetic cycle.
In Fig. 2, point X on the hysteretic curve is the MR immediately after a magnetic cycle. That zero field MR rose in 20-30
min to its highest value (point A)'which was 0-9% higher
junctions predicted by Julliere's formula [ 11. This agrees well
with the ohervation that the steady zero field MR is 40-60%
of the highest value.
B. Simulation of MR-H Curves
With (3) and (4) the MR-H curves of a FM-I-FM junction
can be simulated with the normalised magnetization of the
electrodes. As examples, we simulated the results of
CoFe/A1203/Cojunctions in [3] and Ni/A1203/Cojunctions
in [ l l ] , which are examples of very high and very low M R
respectively. From Fig. 3, the simulation agrees very well
with the low MR results except by a proportionality factor
explainable by the leakage factor mentioned in IIA. For the
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2900
high MR case, the anisotropy magnetoresistance (AMR) d
room temperature. Increasing temperature tends to 'randomise
the FM layers quoted in [3] are used instead of the magnetiza-
the alignment of domains along H and therefore lowers the
tion (M), and we assume a proportionality between AMR(H)
MR shown by the junction. This is consistent with a recent
and M(H). Good agreement is obtained in regions beyond the
theory that MR is lowered by temperature rise through effects
coercivities of the individual FM layers. In between the coer-
on the FM-I interfacial magnetism [ 121.
civities, the measured MR increased sharply to beyond the
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Iv. DISCUSSIONS
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