We show that elastic currents that take into account variations of the tunnel
transmitivity with voltage and a large ratio of majority to minority spin
densities of states of the $s$ band, can account for the low voltage current
anomalies observed in magnet-oxide-magnet junctions. The anomalies can be
positive, negative or have a mixed form, depending of the position of the Fermi
level in the $s$ band, in agreement with observations. Magnon contribution is
negligible small to account for the sharp drop of the magnetoresistance with
the voltage bias.Comment: 8 pages, 3 postscript figure

Cabrera, G. G.

Garcia, N.

Applied Physics Letters

English

arXiv

We show that elastic currents, which take into account variations of the tunneling transmission with voltage and a large ratio of majority to minority spin densities of states of the conduction band at the Fermi level, can account for the low voltage current anomalies observed in magnet-oxide-magnet junctions. (C) 2002 American Institute of Physics.80101782178

Cabrera, GG

Garcia, N

Repositorio da Producao Cientifica e Intelectual da Unicamp

Low voltage I–V characteristics in magnetic tunneling junctions
G. G. Cabrera and N. Garca 
 
Citation: Applied Physics Letters 80, 1782 (2002); doi: 10.1063/1.1433168 
View online: http://dx.doi.org/10.1063/1.1433168 
View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/80/10?ver=pdfcov 
Published by the AIP Publishing 
 
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143.106.190.137 On: Tue, 29 Jul 2014 15:43:45
APPLIED PHYSICS LETTERS VOLUME 80, NUMBER 10 11 MARCH 2002
 This aLow voltage I – V characteristics in magnetic tunneling junctions
G. G. Cabreraa)
Instituto de Fı´sica Gleb Wataghin, Universidade Estadual de Campinas (UNICAMP), C.P. 6165,
Campinas 13083-970 SP, Brazil
N. Garcı́a
Laboratorio de Fı´sica de Sistemas Pequen˜os y Nanotecnologı´a, Consejo Superior de Investigaciones
Cientı́ficas (CSIC), Serrano 144, E-28006 Madrid, Spain
~Received 5 July 2001; accepted for publication 5 November 2001!
We show that elastic currents, which take into account variations of the tunneling transmission with
voltage and a large ratio of majority to minority spin densities of states of the conduction band at
the Fermi level, can account for the low voltage current anomalies observed in magnet–oxide–
magnet junctions. ©2002 American Institute of Physics.@DOI: 10.1063/1.1433168#g
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p-In 1975, Julliere1 proposed a simple model for tunnelin
between two ferromagnetic metals, assuming that the sp
conserved in the tunneling process and that the tunne
current is proportional to the density of states of each spi
the ferromagnetic electrodes. A magnetoresistance~MR! ef-
fect then appears when one compares the resistance for
in which the magnetization of the electrodes is antipara
~AP! and parallel~P!. However, it is only quite recently tha
tunneling ferromagnetic samples have been shown to
duce the large magnetoresistance effect~25%–30%! found,
for example, in Refs. 2–4. In addition, a remarkable dep
dence of the junction conductance on the voltage biasV)
has been observed at low voltages~of the order of a few
hundred millivolts!. In experiments reported in Refs. 3 and
the junction resistance drops significantly with applied vo
age, with a peak at zero bias~called thezero-bias anomaly!
that is more pronounced for AP alignment. The effect is a
temperature dependent, with the peak being less shar
room temperature. Finally, it is found that the junction ma
netoresistance~JMR! has a large decrease with the voltag
up to 60% at 0.5 V in some cases.4 Early theoretical calcu-
lations of tunneling currents with applied voltages
Simmons5 showed variations of the conductance that are
the order of that observed in Refs. 3 and 4, but his the
yields no structure at zero bias.
Scattering from surface magnons has been proposed
mechanism for randomizing the tunneling process and op
ing the spin-flip channels that reduce the MR.3 While the
above phenomenon may explain the JMR behavior in
immediate vicinity of the zero-bias peak~for voltages
smaller than;40 mV), estimations of magnon scatterin
cross sections show that the effect is too small to accoun
the sharp drop in resistance in the whole range
400– 500 mV observed in Refs. 3 and 4. In fact, inelas
electron tunneling spectroscopy~IETS! measurements at low
temperature4,6 showed peaks which can unambiguously
associated with one-magnon spectra at very small volta
~from 12 to 20 mV, with tails up to 40 mV!. Also, early
experiments with spin polarized photoelectrons that tun
from a ferromagnet through the surface barrier indicate
a!Electronic mail: cabrera@ifi.unicamp.br1780003-6951/2002/80(10)/1782/3/$19.00
rticle is copyrighted as indicated in the article. Reuse of AIP content is sub
143.106.190.137 On: Tueis
g
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ses
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-
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,
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inelastic electron–magnon scattering at the interfaces ca
neglected and that the spin is conserved in the tunne
process~no contribution by spin flip to the photoemissio
current!.7 In any case, the estimation of the matrix eleme
for one-magnon processes in tunneling barriers is very d
cult, while its magnitude is treated as an adjustable par
eter in Ref. 3. Even if one takes this parameter at face va
the calculation developed in Ref. 3 uses perturbation the
for one-magnon exchange, and should be valid for volta
smaller than the maximum magnon frequency, which is ty
cally of the order of 100 meV. To extend the theory beyo
this limit will imply the inclusion of multimagnon processe
which are negligible at low temperature. Contrary to t
claim made in Ref. 3, in the present letter we show that
experimental data can be explained by elastic tunneling
rents.
We propose an extension of Simmons’ tunneling theo5
that includes band structure effects onvoltage-dependen
elastic currents that conserve spin. The theory takes into
account variations of the density of states with the bias
both magnetic electrodes. This is relevant, since experim
probe depths of the order of 0.5 eV from the Fermi surfa
Several possibilities can be introduced, depending on the
sition of the Fermi level in the spin-split band picture
ferromagnetic metals.8
This latter consideration brings into question the nat
of spin polarization in transition ferromagnets. In 3d ferro-
magnets, most of the spin polarization comes from thed
band, whose density of state is typically 10 times bigger th
that of thes electrons, which in turn is poorly polarized.9 On
the other hand, tunneling currents are dominated bys and
contributions. This is so, becaused wave functions are more
localized and their effective tunneling barrier is higher. T
inclusion of s–d hybridization does not change this resu
significantly.10,11 For Ni, it has been estimated that the tu
neling probability of thes electrons is of the order of 100
times that of thed electrons, thus leading to positive sp
polarization in Ni field emission experiments.12 As a net re-
sult, the contribution of thed density of states is greatly
reduced in tunneling phenomena. Within this context,
formulate a simple model with effective smooth bands
majority and minority spins using parabolic dispersions. A2 © 2002 American Institute of Physics
ject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
, 29 Jul 2014 15:43:45
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1783Appl. Phys. Lett., Vol. 80, No. 10, 11 March 2002 G. G. Cabrera and N. Garcia
 This a ub to IP:preciable variations of the density of states are attained
the top or bottom of the bands. We obtain different behavi
for the zero-bias anomaly, that is, whether the Fermi leve
located near the bottom~peak! or top of the bands~dip!, or
when the position of the Fermi level is close to the top of
majority band and the bottom of the minority one. They a
possible scenarios that we may encounter in our model.
In order to develop our calculation, one has to rewr
Simmons’ formulas with the conductance current written
the form
J(C)~V!5A (
(s,m)PC
E
EF
EF1eV
dE T~E,Ds,f,V!
3NL
(s)~E!NR
(m)~E1eV!, ~1!
whereA is a constant related to the chargee of the carriers,
T(E,Ds,f,V) is the spin independent tunneling transmiss
through the barrier for energyE, parametrized with the mea
barrier heightf and widthDs,5 the indexC5P, AP refers
to the magnetic configuration~parallel or antiparallel!, and
NL,R are the local densities of states for the left and rig
electrodes, respectively, in the regions close to the insula
The indexes (s,m) for the densities of states stand forma-
jority (M ) and minority (m) spin bands, and a sum in ex
pression~1! is made over the allowed processes for s
conserving tunneling, when the setup is in theC magnetic
configuration. We have assumed that both electrodes
made of the same ferromagnetic metal, with a symme
conductance for positive and negative bias. For not too h
temperatures, the Fermi distributions were approximated
step functions.
If the voltage is small compared to the Fermi energy,
tunneling current, as given by expression~1!, approximately
factorizes in the form of
J(C)~V!'S (
s,m5m,M
C
N(s)~EF!N
(m)~EF1eV!D J(S)~V!
5D (C)~EF ,V!J
(S)~V!, ~2!
whereJ(S)(V) is the Simmons’ tunneling current as a fun
tion of the voltage bias.5 J(S)(V) is spin independent an
carries all information concerning details of the tunneli
barrier. The structure at zero bias is produced by the t
D (C)(EF ,V) coming from the spin polarization at the Ferm
level. This approximate factorization will imply some un
versal properties in the MR. More on this later.
We denote byEM andEm the bottom~top! of the major-
ity and minority bands, respectively. In formulating th
Stoner model within naive band theory,uEm2EMu should
yield the exchange of the band. But Fermi surfaces of tr
sition metals are very intricate, having contributions fro
electron- and hole-like carriers and different shapes for m
jority and minority spin sheets. The exchange splitting is
rigid across the Brillouin zone ands–d hybridization com-
plicates this picture even more.9 In this context,Em andEM
come from the band structure andDE5uEm2EMu may be
very different from the true exchange of the band.
To parametrize our results, and denoting byEF the
Fermi energy, we define
EF
M[uEF2EMu, EF
m[uEF2Emu, EF
M[l EF
m ,rticle is copyrighted as indicated in the article. Reuse of AIP content is s
143.106.190.137 On: Tuear
s
is
e
e
t
r.
re
ic
h
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e
m
-
-
t
which includes both cases, the bottom and the top of
band. The ratio of the densities of states at the Fermi leve
given by NL
(M )(EF)/NL
(m)(EF)5Al. In Fig. 1, we display
results of our calculation for examples of typical barriers. W
have not tried an optimum fitting with experiments, becau
this depends on details of the tunneling junction which,
general, are not given in the literature~ ffective barrier
height and width: when absolute resistance is given, one
estimate the barrier height if the barrier width and the sect
of the junction are known11!, but it is clear that the experi
mental results can only be explained by assuming large
larization of the band at the Fermi level. Note that polariz
tion at the Fermi level may be inverted with respect
polarization of the whole band, as for instance in Fig. 1~c!.
The change in tunnel resistance or magnetoresista
~MR! is defined byDR/R5(RAP2RP)/RAP, and some re-
sults are displayed in Fig. 2. In Fig. 2~b!, we show a com-
parison to different experimental results found in t
literature.13
When the Fermi level lies near the top of the bands@Fig.
1~c!#, there is an increase in MR with voltage bias. Even
ally, we may reach the minority spin band edge, at which
FIG. 1. Resistance as a function of the voltage bias for the AP an
configurations and for different band structures~shown in the insets!. The
parameters for the tunneling barriers are given. As a reference, repres
tive experimental data points taken from Ref. 3 are shown in~a!, where
good agreement with our calculation is obtained withA l'2.2, the value
used in the following.~a! electron-like carriers for both majority and minor
ity spin bands;~b! hole-like majority and electron-like minority bands
~c! hole-like bands for both spins.
ject to the terms at: http://scitation.aip.org/termsconditions. Downloaded 
, 29 Jul 2014 15:43:45
of
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.
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1784 Appl. Phys. Lett., Vol. 80, No. 10, 11 March 2002 G. G. Cabrera and N. Garcia
 This adensity of states vanishes, yieldingRAP→`. Within this
limit, the system behaves as an insulator.
In our theory, the MR is just a fingerprint of variations
the electronic density of states with voltage for both s
bands. This result comes about when one assumes facto
tion ~2!, implying that DR/R is almost independent of th
tunneling mechanism~insensitive to details of the tunnelin
barrier!, ~being just! a density of states effect. This fact ma
be tested experimentally if one is able to prepare a family
‘‘good’’ tunneling junctions with the same magnetic ele
trodes but changes some parameters of the insulating ba
~for instance, the barrier width!. As expected, the resistanc
~P or AP! will change, but our prediction is that the MR wi
behave as a universal function of the voltage, and will ha
the same value as the absolute MR. Deviation from t
value may be used as a criterion for the quality of the ju
tion, and may indicate the presence of barrier shorts
pinholes.14 It was also suggested in Ref. 15 to locally modi
the density of states at the tunneling interface in a contro
manner in order to monitor the tunnel resistance and MR
Temperature (T) effects can also be taken into accou
through relation~1! with the broadening of the Fermi distr
butions, but a rough estimate shows that the effect shoul
similar to that of applied voltage ofeV'2kBT, with effec-
tive lowering of the barrier height, smaller resistance, a
softening of the zero-bias anomaly, in agreement with
periments.
The following conclusions are pertinent:~i! the overall
variation of the tunneling current with voltage can be e
plained by elastic tunneling for spin conserving currents.
propose that this variation is just a density of states eff
Inelastic scattering is not needed to explain the experime
In any case, the large variations shown in the present ca
FIG. 2. Magnetoresistance, as defined in Ref. 3, for cases~a! and~b! in Fig.
1. The densities of states are adjusted to the zero-bias value of the MR o
experimental results, which are taken from Ref. 3 in Fig. 2~a! and from
Ref. 4 in Fig. 2~b!.rticle is copyrighted as indicated in the article. Reuse of AIP content is sub
143.106.190.137 On: Tueza-
f
ier
e
is
-
r
d
t
be
d
-
-
e
t.
ts.
u-
lation have to be considered in any alternative model;~ii ! for
the data in Refs. 3 and 4, the anomalies in the currents
the magnetoresistances can be explained within this sim
framework, provided that the ratio of majority to minorit
spin electrons is of the order of 2.2–2.5, at the Fermi leve
one is allowed to choose an appropriate configuration of
bands~see Fig. 1!, a maximum, a minimum or a mix of both
can appear at the anomaly~as was observed in Ref. 8!; ~iii !
the results may be sample dependent, since oxidation s
inside the metal, at the interface, and in the oxide layer m
contribute to polarization of the current, thereby induci
local changes in the densities of states. Alternatively, it m
also, happen like suggested in Refs. 11, 16, and 17, tha
current has contributions from conduction paths~pinholes!
that provide large values of magnetoresistance18 due to do-
main wall scattering.19 In this last case, the contribution from
d electrons may be important, and the density of states
have mixed contributions froms andd electrons, and a va
riety of topologies in the MR.20
This work was supported by EU Project No. IST-200
26011. One of the authors is a visiting scientist at the La
ratorio de Fı´sica de Sistemas Pequen˜os y Nanotecnologı´a,
Consejo Superior de Investigaciones Cientı´ficas ~CSIC!,
Madrid, Spain. He is grateful to the LFSPN for hospitali
and support. He also acknowledges partial financial sup
from Fundac¸ão de Amparo a` Pesquisa do Estado de Sa˜o
Paulo~Brazil! through project No. FAPESP 2000/09434-3
1M. Julliere, Phys. Lett.54A, 225 ~1975!.
2T. Miyazaki and N. Tezuka, J. Magn. Magn. Mater.139, L231 ~1995!; J.
S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, Phys. Rev. L
74, 3273~1995!.
3S. Zhang, P. M. Levy, A. C. Marley, and S. S. P. Parkin, Phys. Rev. L
79, 3744~1997!.
4J. S. Moodera, J. Nowak, and R. J. M. van de Veerdonk, Phys. Rev.
80, 2941~1998!.
5J. G. Simmons, J. Appl. Phys.34, 1793~1963!; J. Phys. D4, 613 ~1971!.
6Y. Ando, J. Murai, H. Kubota, and T. Miyazaki, J. Appl. Phys.87, 5209
~2000!.
7U. Bänninger, G. Busch, M. Campagna, and H. C. Siegmann, Phys. R
Lett. 25, 585 ~1970!.
8M. Sharma, S. X. Wang, and J. H. Nickel, Phys. Rev. Lett.82, 616~1999!.
9V. L. Moruzzi, J. F. Janak, and A. R. Williams,Calculated Electronic
Properties of Metals~Pergamon, New York, 1978!.
10J. A. Hertz and K. Aoi, Phys. Rev. B8, 3252~1973!.
11N. Garcı́a, Appl. Phys. Lett.77, 1351~2000!.
12R. Meservey and P. M. Tedrow, Phys. Rep.238, 173 ~1994!.
13It is interesting to note that the MR found in Ref. 4 is symmetrical
relation to the polarity of voltage, in spite of the fact that the resistan
are highly asymmetric@therefore the data were not shown in Fig. 1~b!#.
The MR does not show either any indication of the magnon peaks fo
with IETS at small bias~after Ref. 4!.
14J. J. Ȧkerman, J. M. Slaughter, R. W. Dave, and I. K. Schuller, Appl. Ph
Lett. 79, 3104~2001!.
15P. LeClair, J. T. Kohlhepp, H. J. M. Swagten, and W. J. M. de Jonge, P
Rev. Lett.86, 1066~2001!.
16C. L. Platt, A. S. Katz, R. C. Dynes, and A. E. Berkowitz, Appl. Phy
Lett. 75, 127 ~1999!
17B. J. Jönsson-Ȧkerman, R. Escudero, C. Leighton, S. Kim, and I. K
Schuller, and D. A. Rabson, Appl. Phys. Lett.77, 1870~2000!.
18N. Garcı́a, M. Muñoz, and Y.-W. Zhao, Phys. Rev. Lett.82, 2923~1999!.
19G. G. Cabrera and L. M. Falicov, Phys. Status Solidi B61, 539~1974!; G.
Tatara, Y.-W. Zhao, M. Mun˜oz, and N. Garcı´a, Phys. Rev. Lett.83, 2030
~1999!
20N. Garcı́a, H. Rohrer, I. G. Saveliev, and Y.-W. Zhao, Phys. Rev. Lett.85,
2030 ~2000!.
theject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
, 29 Jul 2014 15:43:45


Low voltage I-V characteristics in magnetic tunneling junctions

3 pages, 2 figures.We show that elastic currents, which take into account variations of the tunneling transmission with voltage and a large ratio of majority to minority spin densities of states of the conduction band at the Fermi level, can account for the low voltage current anomalies observed in magnet–oxide–magnet junctions.This work was supported by EU Project No. IST-2000-
26011. One of the authors is grateful to the LFSPN for support. He also acknowledges partial financial support
from Fundaçao de Amparo à Pesquisa do Estado de Sao
Paulo (Brazil) through project No. FAPESP 2000/09434-3.Peer reviewe

García García, Nicolás

Digital.CSIC

APPLIED PHYSICS LETTERS VOLUME 80, NUMBER 10 11 MARCH 2002Low voltage I – V characteristics in magnetic tunneling junctionsG. G. Cabreraa)Instituto de Fı´sica Gleb Wataghin, Universidade Estadual de Campinas (UNICAMP), C.P. 6165,Campinas 13083-970 SP, BrazilN. Garcı´aLaboratorio de Fı´sica de Sistemas Pequen˜os y Nanotecnologı´a, Consejo Superior de InvestigacionesCientı´ficas (CSIC), Serrano 144, E-28006 Madrid, Spain~Received 5 July 2001; accepted for publication 5 November 2001!We show that elastic currents, which take into account variations of the tunneling transmission withvoltage and a large ratio of majority to minority spin densities of states of the conduction band atthe Fermi level, can account for the low voltage current anomalies observed in magnet–oxide–magnet junctions. © 2002 American Institute of Physics. @DOI: 10.1063/1.1433168#In 1975, Julliere1 proposed a simple model for tunnelingbetween two ferromagnetic metals, assuming that the spin isconserved in the tunneling process and that the tunnelingcurrent is proportional to the density of states of each spin atthe ferromagnetic electrodes. A magnetoresistance ~MR! ef-fect then appears when one compares the resistance for casesin which the magnetization of the electrodes is antiparallel~AP! and parallel ~P!. However, it is only quite recently thattunneling ferromagnetic samples have been shown to pro-duce the large magnetoresistance effect ~25%–30%! found,for example, in Refs. 2–4. In addition, a remarkable depen-dence of the junction conductance on the voltage bias (V)has been observed at low voltages ~of the order of a fewhundred millivolts!. In experiments reported in Refs. 3 and 4,the junction resistance drops significantly with applied volt-age, with a peak at zero bias ~called the zero-bias anomaly!that is more pronounced for AP alignment. The effect is alsotemperature dependent, with the peak being less sharp atroom temperature. Finally, it is found that the junction mag-netoresistance ~JMR! has a large decrease with the voltage,up to 60% at 0.5 V in some cases.4 Early theoretical calcu-lations of tunneling currents with applied voltages bySimmons5 showed variations of the conductance that are ofthe order of that observed in Refs. 3 and 4, but his theoryyields no structure at zero bias.Scattering from surface magnons has been proposed as amechanism for randomizing the tunneling process and open-ing the spin-flip channels that reduce the MR.3 While theabove phenomenon may explain the JMR behavior in theimmediate vicinity of the zero-bias peak ~for voltagessmaller than ;40 mV), estimations of magnon scatteringcross sections show that the effect is too small to account forthe sharp drop in resistance in the whole range of400– 500 mV observed in Refs. 3 and 4. In fact, inelastic-electron tunneling spectroscopy ~IETS! measurements at lowtemperature4,6 showed peaks which can unambiguously beassociated with one-magnon spectra at very small voltages~from 12 to 20 mV, with tails up to 40 mV!. Also, earlyexperiments with spin polarized photoelectrons that tunnelfrom a ferromagnet through the surface barrier indicate thata!Electronic mail: cabrera@ifi.unicamp.br1780003-6951/2002/80(10)/1782/3/$19.00Downloaded 09 Mar 2010 to 161.111.180.191. Redistribution subject tinelastic electron–magnon scattering at the interfaces can beneglected and that the spin is conserved in the tunnelingprocess ~no contribution by spin flip to the photoemissioncurrent!.7 In any case, the estimation of the matrix elementsfor one-magnon processes in tunneling barriers is very diffi-cult, while its magnitude is treated as an adjustable param-eter in Ref. 3. Even if one takes this parameter at face value,the calculation developed in Ref. 3 uses perturbation theoryfor one-magnon exchange, and should be valid for voltagessmaller than the maximum magnon frequency, which is typi-cally of the order of 100 meV. To extend the theory beyondthis limit will imply the inclusion of multimagnon processes,which are negligible at low temperature. Contrary to theclaim made in Ref. 3, in the present letter we show that theexperimental data can be explained by elastic tunneling cur-rents.We propose an extension of Simmons’ tunneling theory5that includes band structure effects on voltage-dependentelastic currents that conserve spin. The theory takes intoaccount variations of the density of states with the bias atboth magnetic electrodes. This is relevant, since experimentsprobe depths of the order of 0.5 eV from the Fermi surface.Several possibilities can be introduced, depending on the po-sition of the Fermi level in the spin-split band picture offerromagnetic metals.8This latter consideration brings into question the natureof spin polarization in transition ferromagnets. In 3d ferro-magnets, most of the spin polarization comes from the dband, whose density of state is typically 10 times bigger thanthat of the s electrons, which in turn is poorly polarized.9 Onthe other hand, tunneling currents are dominated by s bandcontributions. This is so, because d wave functions are morelocalized and their effective tunneling barrier is higher. Theinclusion of s – d hybridization does not change this resultsignificantly.10,11 For Ni, it has been estimated that the tun-neling probability of the s electrons is of the order of 100times that of the d electrons, thus leading to positive spinpolarization in Ni field emission experiments.12 As a net re-sult, the contribution of the d density of states is greatlyreduced in tunneling phenomena. Within this context, weformulate a simple model with effective smooth bands formajority and minority spins using parabolic dispersions. Ap-2 © 2002 American Institute of Physicso AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp1783Appl. Phys. Lett., Vol. 80, No. 10, 11 March 2002 G. G. Cabrera and N. Garciapreciable variations of the density of states are attained nearthe top or bottom of the bands. We obtain different behaviorsfor the zero-bias anomaly, that is, whether the Fermi level islocated near the bottom ~peak! or top of the bands ~dip!, orwhen the position of the Fermi level is close to the top of themajority band and the bottom of the minority one. They arepossible scenarios that we may encounter in our model.In order to develop our calculation, one has to rewriteSimmons’ formulas with the conductance current written inthe formJ (C)~V !5A ((s ,m)PC EEFEF1eVdE T~E ,Ds ,f ,V !3NL(s)~E !NR(m)~E1eV !, ~1!where A is a constant related to the charge e of the carriers,T(E ,Ds ,f ,V) is the spin independent tunneling transmissionthrough the barrier for energy E, parametrized with the meanbarrier height f and width Ds ,5 the index C5P , AP refersto the magnetic configuration ~parallel or antiparallel!, andNL,R are the local densities of states for the left and rightelectrodes, respectively, in the regions close to the insulator.The indexes (s ,m) for the densities of states stand for ma-jority (M ) and minority (m) spin bands, and a sum in ex-pression ~1! is made over the allowed processes for spinconserving tunneling, when the setup is in the C magneticconfiguration. We have assumed that both electrodes aremade of the same ferromagnetic metal, with a symmetricconductance for positive and negative bias. For not too hightemperatures, the Fermi distributions were approximated bystep functions.If the voltage is small compared to the Fermi energy, thetunneling current, as given by expression ~1!, approximatelyfactorizes in the form ofJ (C)~V !’S (s ,m5m ,MCN (s)~EF!N (m)~EF1eV !D J (S)~V !5D (C)~EF ,V !J (S)~V !, ~2!where J (S)(V) is the Simmons’ tunneling current as a func-tion of the voltage bias.5 J (S)(V) is spin independent andcarries all information concerning details of the tunnelingbarrier. The structure at zero bias is produced by the termD (C)(EF ,V) coming from the spin polarization at the Fermilevel. This approximate factorization will imply some uni-versal properties in the MR. More on this later.We denote by EM and Em the bottom ~top! of the major-ity and minority bands, respectively. In formulating theStoner model within naive band theory, uEm2EMu shouldyield the exchange of the band. But Fermi surfaces of tran-sition metals are very intricate, having contributions fromelectron- and hole-like carriers and different shapes for ma-jority and minority spin sheets. The exchange splitting is notrigid across the Brillouin zone and s – d hybridization com-plicates this picture even more.9 In this context, Em and EMcome from the band structure and DE5uEm2EMu may bevery different from the true exchange of the band.To parametrize our results, and denoting by EF theFermi energy, we defineEFM[uEF2EMu, EFm[uEF2Emu, EFM[l EFm,Downloaded 09 Mar 2010 to 161.111.180.191. Redistribution subject twhich includes both cases, the bottom and the top of theband. The ratio of the densities of states at the Fermi level isgiven by NL(M )(EF)/NL(m)(EF)5Al . In Fig. 1, we displayresults of our calculation for examples of typical barriers. Wehave not tried an optimum fitting with experiments, becausethis depends on details of the tunneling junction which, ingeneral, are not given in the literature ~effective barrierheight and width: when absolute resistance is given, one canestimate the barrier height if the barrier width and the sectionof the junction are known11!, but it is clear that the experi-mental results can only be explained by assuming large po-larization of the band at the Fermi level. Note that polariza-tion at the Fermi level may be inverted with respect topolarization of the whole band, as for instance in Fig. 1~c!.The change in tunnel resistance or magnetoresistance~MR! is defined by DR/R5(RAP2RP)/RAP, and some re-sults are displayed in Fig. 2. In Fig. 2~b!, we show a com-parison to different experimental results found in theliterature.13When the Fermi level lies near the top of the bands @Fig.1~c!#, there is an increase in MR with voltage bias. Eventu-ally, we may reach the minority spin band edge, at which theFIG. 1. Resistance as a function of the voltage bias for the AP and Pconfigurations and for different band structures ~shown in the insets!. Theparameters for the tunneling barriers are given. As a reference, representa-tive experimental data points taken from Ref. 3 are shown in ~a!, wheregood agreement with our calculation is obtained with A l’2.2, the valueused in the following. ~a! electron-like carriers for both majority and minor-ity spin bands; ~b! hole-like majority and electron-like minority bands;~c! hole-like bands for both spins.o AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp1784 Appl. Phys. Lett., Vol. 80, No. 10, 11 March 2002 G. G. Cabrera and N. Garciadensity of states vanishes, yielding RAP→‘ . Within thislimit, the system behaves as an insulator.In our theory, the MR is just a fingerprint of variations ofthe electronic density of states with voltage for both spinbands. This result comes about when one assumes factoriza-tion ~2!, implying that DR/R is almost independent of thetunneling mechanism ~insensitive to details of the tunnelingbarrier!, ~being just! a density of states effect. This fact maybe tested experimentally if one is able to prepare a family of‘‘good’’ tunneling junctions with the same magnetic elec-trodes but changes some parameters of the insulating barrier~for instance, the barrier width!. As expected, the resistance~P or AP! will change, but our prediction is that the MR willbehave as a universal function of the voltage, and will havethe same value as the absolute MR. Deviation from thisvalue may be used as a criterion for the quality of the junc-tion, and may indicate the presence of barrier shorts orpinholes.14 It was also suggested in Ref. 15 to locally modifythe density of states at the tunneling interface in a controlledmanner in order to monitor the tunnel resistance and MR.Temperature (T) effects can also be taken into accountthrough relation ~1! with the broadening of the Fermi distri-butions, but a rough estimate shows that the effect should besimilar to that of applied voltage of eV’2kBT , with effec-tive lowering of the barrier height, smaller resistance, andsoftening of the zero-bias anomaly, in agreement with ex-periments.The following conclusions are pertinent: ~i! the overallvariation of the tunneling current with voltage can be ex-plained by elastic tunneling for spin conserving currents. Wepropose that this variation is just a density of states effect.Inelastic scattering is not needed to explain the experiments.In any case, the large variations shown in the present calcu-FIG. 2. Magnetoresistance, as defined in Ref. 3, for cases ~a! and ~b! in Fig.1. The densities of states are adjusted to the zero-bias value of the MR of theexperimental results, which are taken from Ref. 3 in Fig. 2~a! and fromRef. 4 in Fig. 2~b!.Downloaded 09 Mar 2010 to 161.111.180.191. Redistribution subject tlation have to be considered in any alternative model; ~ii! forthe data in Refs. 3 and 4, the anomalies in the currents andthe magnetoresistances can be explained within this simpleframework, provided that the ratio of majority to minorityspin electrons is of the order of 2.2–2.5, at the Fermi level. Ifone is allowed to choose an appropriate configuration of thebands ~see Fig. 1!, a maximum, a minimum or a mix of bothcan appear at the anomaly ~as was observed in Ref. 8!; ~iii!the results may be sample dependent, since oxidation statesinside the metal, at the interface, and in the oxide layer maycontribute to polarization of the current, thereby inducinglocal changes in the densities of states. Alternatively, it mayalso, happen like suggested in Refs. 11, 16, and 17, that thecurrent has contributions from conduction paths ~pinholes!that provide large values of magnetoresistance18 due to do-main wall scattering.19 In this last case, the contribution fromd electrons may be important, and the density of states willhave mixed contributions from s and d electrons, and a va-riety of topologies in the MR.20This work was supported by EU Project No. IST-2000-26011. One of the authors is a visiting scientist at the Labo-ratorio de Fı´sica de Sistemas Pequen˜os y Nanotecnologı´a,Consejo Superior de Investigaciones Cientı´ficas ~CSIC!,Madrid, Spain. He is grateful to the LFSPN for hospitalityand support. He also acknowledges partial financial supportfrom Fundac¸a˜o de Amparo a` Pesquisa do Estado de Sa˜oPaulo ~Brazil! through project No. FAPESP 2000/09434-3.1 M. Julliere, Phys. Lett. 54A, 225 ~1975!.2 T. Miyazaki and N. Tezuka, J. Magn. Magn. Mater. 139, L231 ~1995!; J.S. Moodera, L. R. Kinder, T. M. Wong, and R. Meservey, Phys. Rev. Lett.74, 3273 ~1995!.3 S. Zhang, P. M. Levy, A. C. Marley, and S. S. P. Parkin, Phys. Rev. Lett.79, 3744 ~1997!.4 J. S. Moodera, J. Nowak, and R. J. M. van de Veerdonk, Phys. Rev. Lett.80, 2941 ~1998!.5 J. G. Simmons, J. Appl. Phys. 34, 1793 ~1963!; J. Phys. D 4, 613 ~1971!.6 Y. Ando, J. Murai, H. Kubota, and T. Miyazaki, J. Appl. Phys. 87, 5209~2000!.7 U. Ba¨nninger, G. Busch, M. Campagna, and H. C. Siegmann, Phys. Rev.Lett. 25, 585 ~1970!.8 M. Sharma, S. X. Wang, and J. H. Nickel, Phys. Rev. Lett. 82, 616 ~1999!.9 V. L. Moruzzi, J. F. Janak, and A. R. Williams, Calculated ElectronicProperties of Metals ~Pergamon, New York, 1978!.10 J. A. Hertz and K. Aoi, Phys. Rev. B 8, 3252 ~1973!.11 N. Garcı´a, Appl. Phys. Lett. 77, 1351 ~2000!.12 R. Meservey and P. M. Tedrow, Phys. Rep. 238, 173 ~1994!.13 It is interesting to note that the MR found in Ref. 4 is symmetrical inrelation to the polarity of voltage, in spite of the fact that the resistancesare highly asymmetric @therefore the data were not shown in Fig. 1~b!#.The MR does not show either any indication of the magnon peaks foundwith IETS at small bias ~after Ref. 4!.14 J. J. A˙ kerman, J. M. Slaughter, R. W. Dave, and I. K. Schuller, Appl. Phys.Lett. 79, 3104 ~2001!.15 P. LeClair, J. T. Kohlhepp, H. J. M. Swagten, and W. J. M. de Jonge, Phys.Rev. Lett. 86, 1066 ~2001!.16 C. L. Platt, A. S. Katz, R. C. Dynes, and A. E. Berkowitz, Appl. Phys.Lett. 75, 127 ~1999!17 B. J. Jo¨nsson-A˙ kerman, R. Escudero, C. Leighton, S. Kim, and I. K.Schuller, and D. A. Rabson, Appl. Phys. Lett. 77, 1870 ~2000!.18 N. Garcı´a, M. Mun˜oz, and Y.-W. Zhao, Phys. Rev. Lett. 82, 2923 ~1999!.19 G. G. Cabrera and L. M. Falicov, Phys. Status Solidi B 61, 539 ~1974!; G.Tatara, Y.-W. Zhao, M. Mun˜oz, and N. Garcı´a, Phys. Rev. Lett. 83, 2030~1999!20 N. Garcı´a, H. Rohrer, I. G. Saveliev, and Y.-W. Zhao, Phys. Rev. Lett. 85,2030 ~2000!.o AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp

Low voltage I–V characteristics in magnetic tunneling junctions

G. G. Cabrera

N. Garcı́a

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Low Voltage I-V Characteristics in Magnetic Tunnel Junctions

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