Table Of ContentEnhanced Spin Dependent Shot Noise in Magnetic Tunnel Barriers
Samir Garzon1∗, Yuanzhen Chen2, and Richard A. Webb1
1Department of Physics and Astronomy and USC Nanocenter,
University of South Carolina, Columbia, SC 29208, USA
2Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
7
0 We report the observation of enhanced spin dependent shot noise in magnetic tunnel barriers,
0 suggestingtransportthroughlocalized stateswithinthebarrier. Thisissupportedbytheexistence
2 ofnegativemagnetoresistance andstructureinthedifferentialconductancecurves. Asimplemodel
n oftunnelingthroughtwointeractinglocalized stateswithspindependenttunnelingratesisusedto
a explain our observations.
J
8 PACSnumbers: 72.25.Mk,72.70.+m,73.40.-c,73.40.Gk,73.40.Rw,73.50.Td,73.63.Rt,85.75.Mm
1
I. INTRODUCTION super-Poissonian shot noise is due to both charge and
]
l spin blockade.
l
a The paper is organized as follows. Section two dis-
h
Measurement of fluctuations or noise for gaining cusses enhanced shot noise in nonmagnetic tunnel barri-
-
s deeper understanding of the microscopic details of phys- ers due to two interacting localized states7 and explains
e
ical systems is not new. Shot noise measurements have a classical model that can be used to calculate the Fano
m
been successfully used to measure the transport of frac- factor for arbitrary tunnel barriers30. Section three de-
t. tional charge in two dimensional electron gas (2DEG) scribesanadditionalmechanismforenhancedshotnoise,
a Hall regime systems1,2, to study 2e charge transport particularonlytomagnetictunneljunctions,andextends
m
in superconductor-metal interfaces3,4,5, to detect local- themodeldescribedinsectiontwotoincludespindepen-
- ized states in point contact experiments in 2DEG’s6,7, dent tunneling rates. Section four describes the sample
d
n and to probe transport details of many other sys- fabrication and experimental setup, while the results of
o tems8,9,10,11,12,13,14. However, shot noise in magnetic the measurements and analysis are presented in section
c systems has received much less attention. It is only re- five. Finally, section six shows our conclusions.
[ cently that some predictions of the dependence of the
1 shot noise on parameters such as the degree of spin po-
II. SHOT NOISE ENHANCEMENT IN
v larizationhavebeenmade15,16,17,18,19,20,21,22,23,24,25,26,27.
NONMAGNETIC TUNNEL JUNCTIONS
8 Corresponding shot noise experiments in magnetic sys-
5 tems are few, and have been done in frequency regimes
4 where 1/f noise dominates28. In this paper we report Electron transport across a tunnel junction can be
1
0 theobservationofenhancedspindependentshotnoisein characterizedby asetoftransmissioncoefficients Tn, as-
magnetic tunnel junctions29. Enhancement of the shot sociated with the conducting channels across the junc-
7
0 noiseabovethePoissonianlimitinmagneticsystemscan tion. Within the Landauer-Bu¨ttiker formalism the to-
/ occur via “spin blockade” due to the presence of a local- tal noise in a tunnel junction (both thermal plus non-
t
a ized state, where a minority spin electron (with lower equilibrium excess noise) is given by
m tunneling rate) can block the transport of majority spin
- electrons (with higher tunneling rate)22,23,24,25,26,27. In 2e2
nd nsuopnemr-aPgoniestsiocntiuannnneolibsearwrihericshithiassalistos poorisgsiinbleintoaosbimseirlvaer S(f)= π¯h [2kBT Xn Tn2+
o
type of blocking behavior whenever two localized states eV
c eV coth( ) T (1 T )], (1)
v: within the barrier are available for transport. An elec- 2kBT Xn n − n
tron which tunnels into the state with the lower tunnel-
i
X ingratescanblocktransportthroughthe otherlocalized where f, T, and V are the frequency, temperature, and
state with higher tunneling rates, due to Coulomb inter- voltagebias31. InthelimitofeV k T,Eq. (1)reduces
r B
≫
a action (“charge blockade”)7. Since in magnetic tunnel to
barriers both spin and charge blockade might occur, we
compareourmeasurementswiththeresultsfromcalcula- 4e3 V
tions using both models. Our results are consistent with S(f)= | | T (1 T ), (2)
n n
h −
the model of two interacting localized states with spin Xn
dependent tunneling rates, implying that the observed
hence the Fano factor of such a junction is given by
S(f) T (1 T )
F = n n − n . (3)
∗[email protected] ≡ 2eI P T
n n
P
2
0.0014 events, each of which is characterized by a Poissonian
probability distribution with tunneling rate Γ . The re-
2L 0.0012 i
A sultingtotalprobabilitydistributionP(t)foranelectron
p
Her 0.001 to tunnel completely acrossthe barrierat exactly a time
w t after the previous tunneling event, can be either sub-
Po0.0008
Poissonian, Poissonian, or super-Poissonian. For parti-
nt
e0.0006 cles with chargee tunneling between two reservoirswith
Curr a general probability distribution P(t), the average cur-
0.0004
e rent I is given by
s
Noi0.0002
0 e
-2 -1 0 1 2 I = (4)
t
IHnAL h i
and the Fano factor by33
FIG. 1: Noise current power as a function of current in a
2DEGpointcontactat70mKatafixedgatevoltage,together
with thecalculated full shot noise (dashed line).
t2
F = h i 1, (5)
t 2 −
h i
where for a general function g(t) the expectation value
F cannot exceed one, that is, a regular tunnel junction g(t) is defined as g(t) ∞g(t)P(t)dt.
h i h i≡ 0
exhibits only suppressed shot noise. This is equivalent For the particular case oRf tunneling through two in-
to the statement that the transport statistics of a sys- teracting localized states we assume that the tunneling
tem with multiple uncorrelated sequential and/or paral- rates associated with each site are Γ and Γ (i = 1,
iL iR
lel transport channels, each of which can be described 2). We further assume that due to Coulomb interaction
by a Poissonian probability distribution, is exclusively once an electron hops into one state the other state will
sub-Poissonian. This was verified to a very good preci- become unavailable for other electrons. The total prob-
sion in atomic size metallic tunnel junctions11. It thus ability distribution in this case is given by
came as a surprise when experimental observationof en-
hanced shot noise in a tunnel junction (which requires
super-Poissonian statistics) was first reported7. The en- P(t)= tdt′e−Γ1Lt′ e−Γ2Lt′(e−Γ2R(t−t′)Γ Γ
hancement was explained using a model of interacting Z 2L 2R
0
localized states inside the tunnel junction. Depending +e−Γ1R(t−t′)Γ Γ ). (6)
on the occupation state of one localized site, tunneling 1L 1R
throughtheothersitecouldbesignificantlymodifieddue
If the four tunneling rates are related by Γ = αΓ
tothestrongCoulombinteractionbetweenthetwosites. 1L 1R
= βΓ = βγΓ , then the Fano factor calculated from
Suchamodulatedtunnelingprocesscouldleadtolargely 2L 2R
Eqs. 5 and 6 is
enhanced shot noise, specially in small area tunnel bar-
riers where the interaction between localized states is
strongest. Ourmeasurementsintunneljunctionsformed 2β2γ2+β(1+(α γ)2)+2α2
by an electrostatic potential in 2DEG systems have also F = − . (7)
β(1+α+γ)2
shownshotnoiseenhancementduetolocalizedstates6,32.
Shot noise in these junctions is very sensitive to micro- Parametersαandγ describetheasymmetrybetweenleft
scopic details such as the distribution of localized states and right tunneling rates for each localized state, while
in real space, as well as their energy landscape. Fig- β describes the asymmetry in tunneling rates of the two
ure 1 shows the shot noise as a function of current for localized states. Figure 2 shows F as a function of β
one of our 2DEG point contacts for a fixed gate voltage. at different values of α and γ. The Fano factor has a
The shot noise can be either enhanced or suppressed by minimum value of 0.5 when β = α and γ = 1 α. On
changingthecurrentbiasthroughthepointcontact,and γ −
the other hand, F has no upper bound. In particular,
isingeneralasymmetricwithrespecttothe bias,reflect-
F can be much larger than 1 when β is far away from
ing the asymmetry in the position of the localized state.
1, that is, when electrons dwell much longer in one site
In our measurements, Fano factors between 0.3 and 14
than in the other, effectively blocking transport through
have been observed on 25 barriers.
the faster channel. Even tunneling rates which are less
The probability distribution of tunneling events than one order of magnitude different give large values
through a tunnel barrier with an arbitrary number of of F. Since the tunneling rate depends exponentially on
either sequentialor parallel,andeither interacting orin- thedistancebetweenthelocalizedstateandthereservoir,
dependent transport channels can be constructed within even a small asymmetry in the position of the localized
a simple classical model using single channel tunneling state within the barrier will give large differences in the
3
(a) 8 8 (b) a localized state at two different rates (Γ ,Γ in the
α=9 α=0.3 1L 2L
case of 2 localized states, or Γ ,Γ for spin dependent
↑L ↓L
α=1
6 6 tunneling and a single localized state) and (ii) only one
localized state can be occupied at any time. We have
α=3
F 4 4 F assumed that an external bias is applied in such a way
α=1 α=3 thattunneling occursfromthe leftto the rightreservoir.
2 2 Assuming that Γ↑i = γi(1+p) and Γ↓i = γi(1 p) for
−
α=0.3 α=9 i = R,L, with p the spin polarization (assumed to be
the same for both magnetic electrodes) and γ the av-
0 0 i
0.1 0.2 0.5 1 2 5 10 0.1 0.2 0.5 1 2 5 10 erage tunneling rate for an electron with a definite spin
Β Β
state23, the Fano factor is given by
(c)
4γ21+p2 +γ2
L1−p2 R
F = (8)
0 1 2 3 4 5 P (2γ +γ )2
t L R
for the parallel magnetization state (P), while for the
FIG.2: Fanofactorasafunctionoftheasymmetryintunnel- antiparallel state (AP) it is
ing rates between two localized states β. Curves for different
valuesoftheleft-rightasymmetryparameteroflocalizedstate
1,α,areshownfor(a)γ=1(noleft-rightasymmetryinlocal- 4γ21+4p2−p4 +γ2
L (1−p2)2 R
izedstate2)and(b)γ=4. (c)Simulationoftunnelingevents FAP = (2γ 1+p2 +γ )2 . (9)
as a function of timeshowing bunchingof electrons. L1−p2 R
Eq. 8 agrees with the calculations of Braun et. al22 who
only give a closed form for the P state. For p = 0 Eqs.
8 and 9 are equal and reduce to the case of nonmagnetic
leftandrighttunnelingrates(thisisspeciallytruewhen-
tunnelbarriers,withtunnelingratefromtheleft2γ and
everthelocalizationlengthissmall). Thereforewhenever L
tunneling rate to the right γ . This result shows that,
two localized states are close enough so that one chan- R
in contrast to what is typically calculated for tunneling
nel can block transport through the other, F > 1 will
between nonmagnetic reservoirs through a barrier with
be observed more often than F < 1. We performed
a localized state, the minimum Fano factor F = 1/2 oc-
numerical simulations to study the tunneling events in
curs for an asymmetric position of the localized state,
the time domain. A typical result is given in Fig. 2(c),
when γ = 2γ . Tunneling into a localized state is pro-
where the “bunching” pattern in the tunneling events, R L
portional to the total density of states in the incoming
which leads to enhanced shot noise, is clear. Unlike the
reservoirbuttunneling outofalocalizedstate is propor-
“bunching” behavior observed for bosons where quan-
tum statistics plays a role31,34,35,36, here it is purely due tional only to the density of states with spin −→S, with −→S
the spin of the electron in the localized state37. There-
to Coulomb interaction. For magnetic tunnel barriers,
fore, for a symmetric localized state the left and right
however,anothermechanismcanalsoleadto“bunching”
tunneling rates are different and give F = 1/2. Plots of
effects. This will be discussed in the next section. 6
the Fano factor as a function of the spin polarization p
are shown in Fig. 3 for (a) the P and (b) the AP states
fordifferentasymmetriesbetweenleftandrighttunneling
III. MAGNETIC TUNNEL JUNCTIONS
rates. ForlargespinpolarizationtheFanofactorintheP
state canbe muchlargerthan1, while inthe AP state it
In nonmagnetic tunnel barriersthe tunneling rates for has a maximum of 1.25 for p=1/√3 andγ γ . This
L R
≫
electrons with any spin orientation are considered to be behaviorhas been termed“spinblockade”22,23,24,25,26,27.
equal. Howeverinmagnetic tunnelbarriersthis assump- It is important to note that both P states ( and )
↑↑ ↓↓
tion is incorrect since the density of states in each of have the same Fano factor F and both AP states (
P
↑↓
the magnetic electrodes is spin dependent. Therefore and )havethe same Fano factorF . Only largespin
AP
↓↑
tunneling rates are larger for majority than for minority polarizationsproducesignificantshotnoiseenhancement.
spins. Thisprovidesadifferentmechanismforgeneration It is then natural to consider the case of two inter-
of super-Poissonian statistics. Following the procedure acting localized states, as discussed in the previous sec-
described in the previous section, we can calculate the tion, but now for magnetic tunnel barriers. This can
probability distribution for an electron to tunnel exactly be done in the same spirit as before, including spin de-
at a time t after the previous tunneling event through a pendent tunneling rates from the left reservoir to each
tunnel barrier with one localized state and spin depen- of the localized states, and from the localized states to
dent tunneling rates. It has the same form as Eq. 6, the right reservoir. Assuming equal spin polarizationfor
replacingthe indices1 and2by and . This is notsur- both reservoirs, the set of 8 rates that describe the tun-
↑ ↓
prising since in both situations (i) electrons tunnel into neling process can be reduced to 5 parameters, Γ , α,
L
4
(a) 10 1.2 (b) 8K
α=0.2
8 1
α=1
6 0.8 TB
F 4 α=5 α=5 0.6 F
0.4 LP LP
2 α=1 0.2
α=0.2 LP LP
0 0 PD
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
p p
(c)14 14 (d)
12 12
10 10 FIG.4: Schematicofmeasurementconfigurationshowingfour
F 8 8 F lowpass filtered leads with isolation resistors, a photodiode
6 6 (PD) in parallel with the tunnel barrier (TB), and the two
stages of amplification before the spectrum analyzer. Block-
4 4
ingcapacitors are used to separate theDC bias currentfrom
2 2
the100kHz noise.
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
p p
FIG. 3: Fano factor as a function of the spin polarization
by 1.4 µm. Devices with different overlapareas between
for (a) parallel (P) and (b) antiparallel (AP) magnetization
the two Co electrodes (typically between 0.005 nm2 and
states in a magnetic tunnel barrier with a single localized
0.06 nm2) are fabricated in order to achieve resistances
state. Curves with different left-right asymmetry parameter
intheproperrange. Theresistanceofthedevicesismea-
α=γL/γR are shown. (c,d) Fano factor as a function of the
spin polarization for twolocalized stateswith parameters(c) suredatroomtemperature,andsampleswithresistances
α=0.05, β=35,γ =0.15and(d)α=β =γ =5forbothP lower than 30kΩ and higher than 300kΩ are discarded.
and AP states. Within a batch, most of the samples with similar Co
overlap areas have similar resistance values. Devices are
cooleddownto 8K,andthe resistanceis measuredagain
to ascertain if they have insulator-type of behavior and
β, γ, and p, which have been already defined in sections the resistance has increased. If metallic behavior is ob-
2 and 3; however, the Fano factor is independent of ΓL. served (i.e. the resistance decreases as the temperature
In this scenario the Fano factor of the AP state can be is lowered) the sample is discarded since this shows that
much larger than 1.25 (the maximum obtainable value pinholeconductionistakingplace38 (Rowell’scriteria39).
for a single localized state). Furthermore both possibili-
Measurements are performed in a variable tempera-
ties F > F and F > F can occur, as illustrated
P AP AP P ture cryostatequipped withanaxial9 T magnet(Quan-
in Figures 3(c,d).
tum Design) and a custom built probe. For shot noise
measurements the device is dc current biased while the
noise voltageacrossthe tunnel barrieris measuredusing
IV. EXPERIMENT
a cryogenic preamplifier mounted less than 5 cm away
from the sample. A complementary room temperature
Samples are fabricated on Si wafers with 500 nm of stageisusedforfurtheramplificationafterwhichaspec-
thermally grown oxide with a standard electron-beam trum analyzer (HP89410A) samples the voltage noise in
lithography, thermal evaporation, and liftoff technique. a flat frequency band in the 100kHz range where the ef-
A bilayer of PMGI and PMMA is used to create large fects of 1/f noise can be neglected. In situ calibration of
controllable undercuts in the resist profile, which al- the measured voltage is done with a photodiode (Laser-
lowsthe use ofdouble angleevaporationtechniques, and mate, PDT-A85A30)wiredin parallelto the tunnel bar-
thereforehigherqualitytunnelbarriersthatcanbe com- rier (see Fig. 4). A photocurrent with full shot noise is
pletelydepositedwithoutbreakingvacuum,whichinour generated in the photodiode by means of an LED, while
system is typically in the 10−7 Torr range. First, 15 nm the voltage drop across the tunnel barrier is nulled by
of Co are thermally evaporated at a low rate (typically applying an external current. This ensures that all of
0.02 nm/s), after which a thin (2-4 nm) layer of Al is the currentdependent noise comes from the photodiode.
thermally evaporated at 0.01 nm/s. Then, the Al is oxi- A single calibrated measurements consists of measuring
dized at 800 to 2000 Torr-s,and the top 40 nm Co layer thephotodiodenoisevoltagepowerS atagivencurrent
pd
is deposited at a higher rate. The two Co electrodes I, the tunnel barrier noise S at the same current, and
tb
have different geometry: the bottom electrode is typi- the background noise S at zero current. Each of the
th
cally 350 nm by 1.4 µm while the top one is 120 nm noise measurements must average more than 1000 noise
5
(a) 0.24 for negative bias, (iii) the transition to a higher conduc-
tance state above 30mV,and (iv) the fact that it is non-
0.23
vanishing at zero bias. The transition to a higher con-
ductance state which occurs between 20mV and 30mV
2(cid:144)<h0.22 suggeststhatanadditionalconductancechannel,suchas
e
H20.21 a localized state, with an energy resonance width of the
V order of 2-3mV, comparable to k T = 0.69mV, has be-
d B
(cid:144)dI 0.2 come available for transport. This localized state does
not become available for transport in the negative bias
0.19
regime. This can happen if the position of the local-
izedstatewithinthebarrierisasymmetricasrepresented
0.18
-100 -50 0 50 100 by the narrow resonance localized state in Figs. 5(b,c)
VHmVL (smallellipse towardsthe rightof the barrier). However,
even in the absence of transport through this localized
(b) (c)
state, the conductance is nonzero, which means that an-
otherchannelmustbeavailablefortransportatanybias.
eV eV
Furthermore, the conductance of this other channel in-
creases linearly with the applied voltage. Models for di-
rect tunneling do not agree with the linear increase in
FIG. 5: (a) Differential conductance in units of 2e2/h mea-
conductance since they predict a parabolic dependence
sured by calculating the derivative of resistance data at 8K.
on voltage. However, a reasonable scenario where this
The line is a fit to the negative bias data, and has been
can happen is tunneling through an additional localized
symmetrically extended to the positive bias region. (b,c)
state above the Fermi energy which has a very wide res-
Schematics of the asymmetric configuration of the localized
onance [large ellipsoid in Figs. 5(b,c)].
states for negative (b) and positive (c) bias.
The resistance as a function of the in plane field par-
allel to the geometrical easy axis of the Co electrodes
was then measured at different biases (Fig. 6 shows the
spectra to give a good signal to noise ratio. From these magnetoresistance at a current of -0.627 µA). Sharp re-
averagednoisevoltagepowersitispossibletoextractthe sistancechangeswheneverthe magnetizationofeither of
Fano factor of the tunnel barrier at a current I. In the the Co electrodes reverses are evident. The smoother
limit eV k T, where thermal and excess noise can be transition is due to the slower reversal of the wider Co
B
well separ≫ated, the Fano factor is given by electrode, in which the effect of a magnetic easy axis
not aligned with the geometrical easy axis is more ev-
ident. Two traces in both directions of magnetic field
Stb Sth sweep illustrate that the transitions can occur at some-
F(I)= − . (10)
S S what different fields, showing that the domain structure
pd th
−
configuration after each demagnetization process can be
Each of these calibrated measurements is performed 10- different. However, there are ranges of magnetic field at
20 times and the results are again averaged. This in- which the device has a definite magnetization configura-
creases the signal to noise ratio while minimizing the ef- tion and by applying a magnetic field any of the states
fects of drifts due to, for example, temperature changes , , , can be obtained.
↑↑ ↑↓ ↓↑ ↓↓
in the electronics which affect the gain of the setup. Us- An essential observation regarding Fig. 6 is that the
ing this method it is possible to measure the shot noise value of the magnetoresistance,
from currents smaller than 1 nA, which produce voltage
R R
fluctuations of the order of 1 nV/Hz1/2. This is more MR= ↑↓− ↑↑ (11)
than 20 times smaller than the thermal noise from the R↑↓+R↑↑
isolation resistors (Fig. 4), which is the main source of
is negative. Negative magnetoresistance was expected
noise in the system. From now on we will discuss the
and has been observed in Co-SrTiO 40, Py-Ta O , and
results of the measurements of one of our devices, which 3 2 5
Py-Ta O /Al O 41 systems, and reflects the importance
shows the largest enhancement of the shot noise. 2 5 2 3
of the compound effect of spacer and magnetic materi-
als. However,negativeMRhasalsobeenobservedinsys-
tems which typically exhibit positive MR, and has been
V. RESULTS AND DISCUSSION
attributed to inversion due to pinhole transport38, or to
resonant tunneling through a localized state in the tun-
The differential conductance of one of our devices is nel barrier42. From the insulator-like temperature de-
shown in Fig. 5(a), together with a symmetric lin- pendenceoftheresistancewecanruleoutthe possibility
ear fit. The most important features of the differen- of pinhole conduction. This result, together with the
tial conductance are (i) its asymmetry, (ii) its linearity differential conductance data presented earlier, provide
6
0.5
64. (a)
2L
A0.4
p
H
63.8 er
w
LW Po0.3
Hk nt
R63.6 urre0.2
C
e
ois0.1
63.4 N
0
-1.5 -1 -0.5 0 0.5 1 1.5
-160 -80 0 80 160
IHuAL
BHmTL
FIG.6: NegativemagnetoresistanceofaCo-Al2O3-Cotunnel (b) 7
barrier at 8K showing two consecutivesweeps.
6
5
4
F
evidence for conduction through localized states.
3
By applying a magnetic field, the sample is set to one
2
ofthefourdifferentidentifiablemagnetizationstates, ,
, , or , and the shot noise voltage power is m↑ea↑- 1
↑↓ ↓↑ ↓↓
suredas described before. Figure 7a showsthe results of 0
such measurements as a function of the current through -100 -50 0 50 100
VHmVL
the device, together with a dashed line representing the
correspondingvalue offull shotnoise (givenbythe noise
FIG. 7: (a) Measured shot noise current power as a function
from the photodetector). Figure 7(b) shows the mea-
of current at 8K for different magnetization alignments. The
sured Fano factor F as a function of the voltage across
dashed line represents the expected full shot noise. (b) Fano
the tunnel barrier, calculated using the data from Fig.
factor calculated from thedata in (a).
7(a) and Eq. 10.
For positive bias the Fano factor is about 0.9, close to
the full shot noise Fano factor of 1. The weak suppres-
sion of the shot noise can happen if electron tunneling section3iscompatiblewiththepositivebiasFanofactor
through the barrier occurs in a sequential way through behavior.
localized states within the barrier or via parallel chan- However, the most interesting result of our measure-
nels. For example, tunneling through a localized state mentscomesfromthenegativebiaspartoftheshotnoise
will give a Fano factor between 0.5 and 1 (Eq. 8 in the data (Fig. 7), which show a very enhanced voltage de-
limit p = 0), depending on the particular values of the pendent shot noise that varies strongly with the magne-
tunneling rates, which themselves depend on the partic- tization state of the contacts. As the voltage bias is de-
ularbias conditions,the shapeofthe tunnel barrier,and creased from zero the shot noise increases until it peaks
thepositionandenergyofthelocalizedstate. Thesedata at -13 mV. While the Fano factor for the state has a
↓↑
further supports the claim for the existence of localized peakvaluecloseto7, onlyincreasesto3.6. Inaddition
↓↓
states within the barrier, which we used to explain the the state , which has a similar resistance to , shows
↑↓ ↓↑
results of the differential conductance and magnetore- a peak Fano factor of only 4.8. After -13 mV the shot
sistance measurements. An important observation also noisedecreasesandby-58mVitisalreadybelowthefull
regardingthe positivebiasregionofFig. 7(b)isthatthe shot noise value. At -80 mV the Fano factors for both P
Fano factor is very similar for the four different magne- and AP states are close to their positive bias value and,
tization configurations. This can be explained by Eqs. withinexperimentaluncertainty,theyareequivalent. We
8 and 9 if there exists a large left-right asymmetry. For have already explained the suppressed positive bias shot
example, if γ /γ = 6 and p = 0.1, the Fano factor is noisevaluesasduetotransportthroughalocalizedstate.
L R
0.875 for the P state and 0.877 for the AP state, which In order to understand the negative bias data we must
agreewiththe datawithin theexperimentaluncertainty. explainfirstthe existence ofpeaksin the shotnoise,and
Even for higher values of the spin polarization it is pos- second, their spin state dependence.
sible to find ratios γ /γ which give similar F for both The simple model of section 3 does not contain any
L R
P and AP states. For example γ /γ = 28 gives 0.877 explicit voltage bias dependence, but it can be included
R L
(0.838)fortheP(AP)forp=0.4. Hencethesimplemodel by introducing voltage dependent tunneling rates,which
of tunneling througha single localizedstate describedin requireassumptionsaboutthepositionandenergyofthe
7
12 state can be not only larger than 1.25 (the maximum
value in the case of transport through a single localized
10
state) but even larger than the Fano factor for the P
state. ThedashedlinesinFig. 3(c)illustratethatvalues
8
of the asymmetry parameters and the spin polarization
F 6 (forexample,p=0.47)canbechoseninordertogiveFano
factors which agree (F 7, F 4.7) with the mea-
AP P
≃ ≃
4 sured peak values. Similar Fano factors can be obtained
for both larger and smaller values of the spin polariza-
2 tionbychoosingdifferentcombinationsoftheasymmetry
parameters α,β, and γ.
0
-120 -100 -80 -60 -40 -20 0 Detailed data from a different cooldownin which only
VHmVL and were measured in the negative bias region are
↑↓ ↑↑
showninFig. 8. Although the size ofthe peaks is differ-
FIG. 8: Detailed Fano factor curves as a function of voltage ent, the voltage at which they occur is unchanged. The
for the same device shown in Fig. 7 in a different cooldown
different peak size can be due to differences in the mag-
to 8K.
netic states of the electrodes, as well as to differences in
the properties of the localized states after thermal cy-
cling.
localized state, as well as information on the properties
of the tunnel barrier (in the simplest approximation the
widthandheightofthebarrier). CalculationsbyBulka23
VI. CONCLUSIONS
for magnetic tunnel barrierswith a single localized state
have shown that as the voltage bias across the barrier is
increased, the shot noise (after subtracting the thermal We have made differential conductance, magnetoresis-
noise) can increase quickly from zero up to a maximum tance, and shot noise measurements in small area mag-
super-Poissonianvalueandthendecreasewithlargerbias netic tunnel barriers, which give evidence for transport
to sub-Poissonian values. An asymmetry between posi- through two competing localized states. The shot noise
tive andnegativebias canbe justified foranasymmetric is enhanced above its Poissonian value at certain volt-
position of the localized state [Fig. 5(b,c)] by observ- ages and it is in these regions of super-Poissonian be-
ing Fig. 3(a), since for a fixed value of p (say p=0.8), havior that a strong dependence of the Fano factor on
γ /γ =5 gives F=0.88 but γ /γ =1/5 gives F=3.77. the magnetization state of the ferromagnetic electrodes
R L R L
Thisqualitativelyexplainstheexistenceofthepeaksand isobserved. Suchbehaviorisexplainedbyusingasimple
why they appear only for the negative bias region. probabilistic model for tunneling through two strongly
However,the large peak values of the Fano factor and interacting localized states, taking into account the spin
their dependence onthe spin state can not be accounted dependence of the tunneling rates. The enhancement of
for within the simple model of transport through a sin- theFanofactorisduetoacombinationof“spinblockade”
gle localized state since it predicts, on the one hand, whereminority spinelectronsblock the transportofma-
a maximum Fano factor of 1.25 for the AP state and, jorityones,and“chargeblockade”whereanelectronthat
on the other hand, the same shot noise for both of tunnels into a localized state with small tunneling rate
the P states (F =F =F ) and both of the AP states (slow channel) blocks transport through the other faster
P ↑↑ ↓↓
(F =F =F =F ). As pointed out by Tserkovnyak channeldue toCoulombinteraction. Thevoltagedepen-
AP ↑↓ ↓↑ P
(private commun6 ication), the difference in Fano factor dence of the Fano factor (both the existence of a peak,
betweenthe twoPstatesandbetweenthe twoAPstates and the positive/negative bias asymmetry) can be qual-
could be due to structural differences between these itatively understood as a change in the tunneling rates
states. The magnetoresistance data (Fig. 6) already when the resonant energies of the localized states move
showedadditionalstructurewhichmightsuggestthat with respect to the chemical potentials of eachreservoir.
and , as well as and , are not equivalent state↑s↑. However, a complete model which includes explicit volt-
The↓la↓rge AP state↑F↓ano fa↓c↑tor can be explained assum- age dependence of the conductance and the shot noise is
ing that two localized states contribute to transport, as missing.
illustrated in Fig. 3(c), where the Fano factor in the AP We thank Y. Tserkovnyakfor helpful discussions.
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