Table Of ContentLow-frequency and shot noises in CoFeB/MgO/CoFeB magnetic tunneling junctions
Tomonori Arakawa1, Takahiro Tanaka1, Kensaku Chida1, Sadashige Matsuo1, Yoshitaka Nishihara1,
Daichi Chiba1, Kensuke Kobayashi1,∗ Teruo Ono1, Akio Fukushima2, and Shinji Yuasa2
1Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan and
2Spintronics Research Center, Advanced Industrial Science and Technology (AIST),
AIST Tsukuba Central 2, Tsukuba, Ibaraki 305-8568, Japan
(Dated: January 11, 2013)
Thelow-frequencyandshotnoisesinspin-valveCoFeB/MgO/CoFeBmagnetictunnelingjunctions
3 were studied at low temperature. The measured 1/f noise around themagnetic hysteresis loops of
1 the free layer indicates that the main origin of the 1/f noise is the magnetic fluctuation, which is
0 discussed in termsof afluctuation-dissipation relation. Random telegraph noise(RTN)is observed
2 tobesymmetricallyenhancedinthehysteresisloopwithregardtothetwomagneticconfigurations.
n We found that this enhancement is caused by the fluctuation between two magnetic states in the
a freelayer. Althoughthe1/f noiseisalmost independentofthemagneticconfiguration,theRTNis
J enhanced in the antiparallel configuration. These findings indicate the presence of spin-dependent
9 activationofRTN.Shotnoiserevealsthespin-dependentcoherenttunnelingprocessviaacrystalline
MgO barrier.
]
l PACSnumbers: 75.70.Cn,73.50.Td,73.40.Rw,72.25.Ba
l
a
h
- I. INTRODUCTION when the tunnel barrier is composed of amorphous
s
e Al2O3, electron tunneling can be explained by the con-
m ventional Julliere’s model. However, a coherent tunnel-
The magnetic tunneling junction (MTJ), which con-
. sists of a tunnel barrier sandwiched between two fer- ingviahighlyspin-polarized∆1 Blochstates13,14 playsa
t
a romagnetic electrodes, is one of the central topics in central role in MTJs with crystalline MgO barriers. Al-
m spintronics.1 MTJs exhibit tunneling magnetoresistance though information obtained by conventional I-V mea-
surements cannot directly address the coherence of elec-
- (TMR);theirresistancedependsontherelativemagnetic
d tron transport, shot noise offers further insight into the
configurations (parallel or antiparallel). Since the TMR
on effect was discovered by Julliere,2 amorphous Al2O3 has mechanism of electron transport.15–22 In fact, we re-
c beenmainlyusedasatunnelbarrier.3,4However,in2004, ported sub-Poissonian shot noise (F < 1), which is at-
[ large magnetoresistance (MR) was obtained in MTJs tributedtocoherenttunneling,inapreviouswork.20Our
with a crystalline MgO barrier5,6 supported by theo- experimentalworkisquantitativelyreproducedbythere-
v1 retical prediction.7–9 These days, MgO-based MTJs are cent theoretical work with first-principles calculations.23
Resistance fluctuations are also important, as MTJs
1 extensively studied from the viewpoints of fundamental
6 physics and device applications.
1
Although most MTJ studies have thus far been per-
2 (a)
. formed via conventional resistance measurements, noise lock-in amplifier multimeter
1 measurements can serve to further clarify the intrinsic
0 H
properties in MTJs. The noise results from the fluctu-
3 ation of the current (thermal noise and shot noise) and CoFeB (2 nm) digitizer
1 or MgO (1.05 nm)
: of the resistance such as the 1/f noise and the random CoFeB (3 nm)
v telegraphnoise(RTN).Thermalnoiseandshotnoiseare
Xi duetothethermalagitationofelectronsandthepartition VTI (2 K-300 K)
process of electrons, respectively, whereas the resistance (b) (c) 200
r 600 T = 5 K
a fluctuation in MTJs is attributed to a nonmagnetic ori-
600
gin(chargetrapinthetunnelingbarrier)andamagnetic ) AP d
othriegifnre(emaangdn/eotricfiflxuedctumaatgionnestiacnldaydeorsm).ain wallmotionin R ()400 V/dI (195 580V/dI (
d P )
Shot noise offers information on the interactions
and/or quantum correlations of conducting elec- 200 190 560
-500 0 500 -10 0 10
trons.10,11 When the average current I is fed to a tun- H (Oe) V (mV)
nel junction, the current noise S resulting from the
I
shot noise can be expressed as SI = 2eIF (in the zero- FIG. 1. (a) Schematics of measurement setup and device
temperature limit) with Fano factor F. It is well es- structure. (b) Typical MR curves of the present MTJ mea-
tablished that F = 1 in normal-insulator-normal junc- suredat5K.(c)TypicaldifferentialresistanceforP(dashed
tions,12 which means that the electron partition at the line) and AP (solid line) configurations as a function of bias
junction obeys a Poissonian process. In the MTJ case, voltage.
2
have found broad application, such as for magnetic field
detectors,24 magnetic random-access memory,25,26 ran-
dom number generators26, and microwave oscillators.27
For these applications, the signal-to-noise ratio is crit-
ically important, where the 1/f noise and RTN limit
device performance at low frequency. There have been
manyreportsof1/f noiseandRTNinMTJswithAl O -
2 3
based,28–34 MgO-based,35–47 and other tunneling bar-
riers.22,48 Nevertheless, little is known about the noise
properties of MTJs with submicron-sized junctions with
a thin tunneling barrier,46,47 which are envisaged for
memory and oscillator applications.
In this paper, we report on noise properties, includ-
ing shot noise, 1/f noise, and RTN in well-crystalline
MgO-based MTJs with submicron-sized junctions with
thintunnelingbarriers. Thenoisemeasurementwascar-
ried out at low temperature with high experimental ac-
curacy, with a focus on the noise properties around the
magnetic hysteresis loops of the free layer. We investi-
gated each noise source systematically as a function of
magnetic field and bias voltage. The clear dependence
of the 1/f noise on the applied magnetic field indicates
that the main origin of the 1/f noise is magnetic fluc-
tuation in the free layer, which is discussed in terms of
a fluctuation-dissipation relation. Based on the bias de-
pendence ofRTN,wediscussthe originofRTN,whichis FIG.2. (a)TypicalvoltagenoisespectraldensityofourMTJs
differentfromthatofthe1/f noise. Theanalysisofshot in the AP configuration for different bias voltages: V = 12,
noise is also presented to further support our previous 22, and 55 mV at 5 K. The dashed line is a guide to the
report.20 eye. The inset shows the same spectra between 160 and 200
kHz (but note that the bottom axis is a linear scale). (b)
This paper is organized as follows: In Sec. IIA,
Measured real-time voltage fluctuations (with vertical offset
we provide information on the sample fabrication and
forclarity)forthesameconditionas(a). ThetraceforV =22
basic properties of our sample. Then the measure-
mV contains two-level fluctuations, as indicated by the two
ment system is described. In Sec. IIB, the anal- horizontal dashed lines.
ysis method to extract the frequency-dependent and
frequency-independentcomponentsisexplained. Section
III is devotedto the experimentalresults anddiscussion.
Fig.1(a)]. Thethicknessofeachlayerisindicatedin(...)
First, we show the magnetic field and bias-current de-
in nanometers. The multilayer stacks are patterned into
pendence of frequency-dependent noise in Sec. IIIA, and
ellipticpillarswith160×60nmdimensionsbymillingup
then the origin of the 1/f noise is discussed by using
to the middle of the PtMn layer. To crystallize CoFeB
the fluctuation-dissipation relation in Sec. IIIB. We es-
layers,the stack is annealedin 10,000Oe for 120 min at
timate the fluctuating magnetic moment of the RTN in 330◦C.49,50
Sec. IIIC. The bias voltage dependence of the measured
All of the results presented here were obtained at low
RTN is analyzedto obtaininformationon the excitation
temperature (3–5 K) in the variable temperature insert
mechanism in Sec. IIID, and, finally, we show the result
(Oxford VTI) in a magnetic field (H) between −40,000
ofthe white noisecomponentinSec.IIIE.InSec.IV,we
and 500 Oe. The schematic setup of our measurement
conclude our study.
system is shown in Fig. 1(a). A dc bias is applied under
a constant current condition (I) by using the dc voltage
source through a 100 kΩ resistor. The differential resis-
II. EXPERIMENT
tance (dV/dI) and the dc bias voltage (V) are measured
by a lock-in amplifier and a digital multimeter, respec-
A. Device and measurement tively. Figure 1(b) shows the typical MR curve around
the hysteresis loop of the free layer at 5 K. The clear
Multilayer stacks of MTJs were deposited in a mag- square shape of the curve without any steps indicates
netron sputtering system on a SiO layer on a silicon that there is no pinning site on a macroscopic domain
2
substrate. The order of the layer structure from the wall. The MRratio definedas (R −R )/R is 208%,
AP P P
substrate is as follows; buffer, PtMn(15), CoFe(2.5), where R and R are the sample resistances in the
P AP
Ru(0.85), CoFeB(3), MgO(1.05), CoFeB(2), and cap, parallel(P)andantiparallel(AP)configurations,respec-
where the top CoFeB layer serves as a free layer [see tively. Figure 1(c) shows the typical bias dependence
3
of the differential resistance, where the solid and dashed where α∗, f, and A are the Hooge parameter, fre-
curves correspond to the AP (−500 Oe) and P (500 Oe) quency, and junction area, respectively. The RTN is the
configurations,respectively. Inthedifferentialresistance, fluctuation between two levels, where S exhibits a
RTN
as temperature decreases below 10 K, a peak structure Lorentzian character in an ideal case.
appears around the zero bias in both P and AP config- Typical results of S for the AP configurations for
V
urations, which is consistent with the several previous V =12,22,and55mVat5KareshowninFig.2(a). In
reports.2,4,16 Interestingly, in the P configuration, addi- the data, the resistor-capacitor (RC) damping owing to
tionalsatellitepeaksseemtoappeararoundV =−5and the capacitance (760 pF) of the measurement lines has
5 mV. Such a feature may be related to the observation already been corrected for.20 In the inset of Fig. 2(a),
reported before.51 which shows the region between 160 and 200 kHz, the
To obtain the voltage noise spectral density S , we spectra are almostflat, and thus the increaseof S with
V V
measure the time-domain voltage fluctuation signal by increasing V corresponds to the shot noise. In contrast,
usingatwo-channeldigitizer(NationalInstrumentsPCI- the spectra for the low-frequencyregionstronglydepend
5922),which yields S by a fast Fourier transformation. onthefrequency,asshowninthemainpanelofFig.2(a).
V
In this process,two sets ofvoltagesignals aresimultane- ThespectraforV =55and12mVareclearlydominated
ously measured after being independently amplified by by the 1/f noise except for the high-frequency region.
two room-temperature amplifiers (NF Corporation LI- ThespectrumforV =22mVhasaclearLorentzianchar-
75A). The cross-correlationtechnique is used here to re- acter,47indicatingthatthesourceofthenoiseistwo-level
duce the external noise and amplifier noise by long-time fluctuation of the resistance, namely, RTN. Figure 2(b)
averaging.52 The frequency range of our system is 100 shows the real-time voltage signal for V = 12, 22, and
Hz to 200 kHz. In addition to S , the real-time voltage 55 mV. Apparently, the time-domain signal has a two-
V
signalis alsorecordedby the digitizerata samplingrate levelnatureonlyforV =22mV,asindicatedbythetwo
of 1 MHz. horizontal dashed lines in Fig. 2(b).
The S measurement is carefully calibrated with We performed a histogram analysis between 160 and
V
the thermal noise of several commercial resistors 200kHztoestimateS .18Toinvestigatethe1/f noise
white
(MCY100R00T, MCY250R00T, MCY350R00T, and and RTN, we first subtract the white noise component
MCY1K0000T) with a precision of 0.01%. The typi- from the measured S and then define the Hooge pa-
V
cal resolution of S for shot noise estimation is below rameter α as
V
10−20 V2/Hz. As a result, we achieved an experimental
f2 f
precision for the Fano factor well below 1%. We mea- α=A (S −S )df/I2R2ln 2 , (4)
sured three devices with the same geometry (samples 1, Zf1 V white d (cid:18)f1(cid:19)
2, and 3) which are made out of the single wafer, and
where the frequencies f and f are chosen to be 1 and
1 2
obtained consistent results.
100 kHz, respectively. The value of α thus obtained
equals the α∗ in Eq. (3) when RTN is negligibly small.
In this study, we mainly use the α that is a well-defined
B. Analysis of noise
parameter even if RTN is present.
In the present experiment, we found that the voltage
noises in MTJs consist of a white noise (Swhite), which III. RESULTS AND DISCUSSION
isafrequency-independentcomponent,1/f noise(S ),
1/f
and RTN (SRTN):53 A. Frequency-dependent noise
S =S +S +S . (1)
V white 1/f RTN
Westartwiththeexperimentalresultofthefrequency-
Thewhitenoise(Swhite)isattributedtothethermalagi- dependent noise. There have been severalstudies on the
tationofelectrons(thermalnoise)andthe partitionpro- field dependence of the 1/f noise in Al O -based28–32,34
2 3
cess of electrons (shot noise). Then Swhite is described andMgO-based35–37,39,40,43–45,47MTJs. Inthesereports,
by themeasured1/f noiseconsistsoffield-independentand
field-dependent components. The former componenthas
S =4k TR
white B d a nonmagnetic origin (charge trap in the tunneling bar-
eV
+2F eIR2coth −2k TR , (2) rier), whereas the latter component has a magnetic ori-
(cid:20) d (cid:18)2kBT(cid:19) B d(cid:21) gin (magnetic fluctuations and domain wall motion in
thefreeand/orfixedmagneticlayers). Recentstudieson
where k is Boltzmann’s constant, e is the electron
B
the 1/f noise in MgO-based MTJs have shown that the
charge,R isthedifferentialresistance(dV/dI)atagiven
d
nonmagnetic 1/f noise is no longer important owing to
V (orI), andF is the Fanofactor. The 1/f noise(S )
1/f theimprovementoftunnelingbarrierquality.43ForRTN,
in MTJs is parameterized by29
both magnetic and nonmagnetic origins were reported
α∗I2R2 in Al O -based28,30–33 and MgO-based36,38,39,46 MTJs.
S = d, (3) 2 3
1/f Af Nevertheless, there are only a few systematic studies on
4
) 600 sample 1 |dR sample 1 20
R( 400 (a) T = 5 K 1.0/dH 580 AP T = 5 K
200 0.5|/R (1 250000 OOee//mmiinn 10
H AP 0 540 1000 Oe/min
C P 0.0 O-3 )
e
2m ) 80 (b) C AP )-1 R( 500 0 slow
0
µ 205
-120 40 Peak A 200 H -2
1 C
(
α 0 195 P -4
A) -40 40 α (10 -200 H (Oe0) 200
I (µ 20 µm-12
-60 0 )2 FIG. 4. Field sweep rate dependence of dc resistance. The
solidlineisthedcresistancemeasuredwiththeslowestsweep
2m ) 30 (c) P rate (50 Oe/min) as the field was ramped from −500 to 240
µ D OeforAPand500to−300OeforP.Resultsforothersweep
12 20
- rates (200, 500, and 1000 Oe/min) are plotted as differences
0
1 10 B from the slowest one.
(
α
0
-100
α
A) 4 (1 noise outside of these peak regions, strong enhancement
I (µ -150 2µ0m-12 ogfioLnso.reTnhtzeialonwcehrapraancetlesroifsFailgws.a3y(sbs)eaenndin3(csu)cshhopweaimkargee-
-200 0 )2
plotsofαasafunctionofthemagneticfieldandthebias
-500 0 500
currentforthe APandP configurations,respectively. In
H (Oe)
these figures, the ranges of the bias current for the two
configurationsaresettobealmostthesamewithrespect
FIG.3. Themagneticfieldandbiascurrentdependenceofα
tothebiasvoltage. Thecurvesshownintheupperpanel
measuredat5Kforsample1. (a)MRcurvesofthisMTJand
of Figs. 3(b) and 3(c) correspond to the cross sections
|dR/dH|/RvaluesforP(dashedline)andAP(solidline)con-
indicated by the dashed line in each image plot.
figurations numerically estimated from the MR curves. The
vertical dashed line marks H = Hc at which |dR/dH|/R for We define Hc as the field at which |dR/dH|/R gives
AP and P have the same value. (b) The measured α for AP the same value for the AP and P configurations [see
(solid mark) configuration, where we marked the peaks of α Fig.3(a)]. The behaviorsofαand|dR/dH|/Rarefound
asAandC(upperpanel),andacolorplotofαasafunction to be well symmetric with respect to H , except for the
c
of magnetic field and bias current (lower panel). The dashed peaks. The values of α for AP and P configurations at
line corresponds to α in the upper panel. (c) Counterpart of their baselines are 3.3×10−12 and 2.7×10−13 µm2, re-
Fig. 3(b) for the P configuration, where the peaks of α are
spectively. This subtle difference is presumably due to
marked as Band D.αvaluesfor thetwo configurations were
the magnetic fluctuation of the fixed layer. Remarkably,
measured in almost the same bias voltage region.
the peak positions are roughly symmetric with respect
to H (namely, peaks A and B, and peaks C and D). Fi-
c
nally, these symmetric behaviors with respect to H are
c
the magnetic field and bias voltage dependence of RTN. always observed on all three samples. We will discuss
Herewefocusonthemagnetic1/f noiseandRTNinthe the implications of these observations later in Sec. IIID
hysteresis loop of the free layer. again.
Figure 3(a) shows the resistance and |dR/dH|/R at 5 The influence of the magnetic field sweep rate on the
K,whichisobtainedasthe fieldisrampedfrom−500to MR curve is shown in Fig. 4, where H is also a relevant
c
200OeforAPandfrom500to−240OeforPconfigura- parameter. The resistance measured by each sweep rate
tions. ThevalueofαmeasuredateachfieldforAPandP isplottedasthedifferenceofthedatafromthatobtained
configurations is shown in the upper panels of Figs. 3(b) withthe slowestsweeprate (50Oe/min),where the field
and 3(c), respectively. It is clear that the magnetic field was ramped from −500 to 240 Oe for AP and from 500
dependencies between α and |dR/dH|/R resemble each to−300OeforPconfigurations. Althoughinitiallythere
other for the two configurations:54 They increase with is no sweep rate dependence on the resistance for either
the reversal of the free layer, except for a few peaks ob- configuration, a sweep rate dependence appears as the
servedinα[peaksA,B,C,andDinFigs.3(b)and3(c)]. magnetic field crosses H . This observation strongly in-
c
Whereasthemeasuredspectraaredominatedbythe1/f dicates that the free electrode feels zero effective field at
5
sample 1 where Sm, µ0, and χ′m′ denote, respectively, the spectral
T = 5 K 200 density of magnetic fluctuation, the vacuum permeabil-
80 AP 100 ity,andtheimaginarypartofthemagneticsusceptibility.
Then by using a typical equation of 1/f noise [Eq. (3)]
0 and the Kramers-Kronigrelation, Eq. (5) reduces to30
)
2m 0 1
2µ α∗ = kBTA∆R 1 dR , (6)
-10 2mµ0Rln(fmax/fmin)(cid:18)RdH(cid:19)
1
(α 40 where2mand∆Raretherespectivechangesofthemag-
P neticmomentandresistanceassociatedwiththereversal
of the free layer. Thus, the measured linear relation be-
tween α and |dR/dH|/R for the P state in Fig. 5 can
be explained by Eq. (6); namely, the origin of 1/f noise
is thermal agitation of the magnetic moment of the free
0 electrode. ThedashedlinecorrespondstoEq. (6),where
0.0 0.5 1.0
we take the saturation magnetization M of CoFeB to
|dR/dH|/R (10-3 Oe-1) S
be1.3×106 A/m.43 Fromroughestimation,weobtained
f /f ∼ 1010±2, which is consistent with the result
max min
FIG.5. αatseveralbiascurrentsvs|dR/dH|/RforP(open f /f ∼109 that Ingvarsson et al.30 reported. The
max min
symbols) and AP (solid symbols). The inset shows the full nonlinear behavior with |dR/dH|/R beyond ∼1 mOe−1
scale of the same data for AP. The dashed line is a guide to
is possibly caused by deviation from the thermal equi-
theeye.
librium state of the free layer. In fact, the measured
dc resistance corresponding to this region strongly de-
pends on the field sweep rate (see Fig. 4). According to
H . TheshiftofH fromzerofieldisexplainedbytaking
c c previous works,43,55,56 the linear relation between α and
a magnetic interaction between the free and fixed layers
|dR/dH|/Rcorrespondsto constantmagnetic lossesand
into account.
has been shown by Stearrett et al.54 in the P and AP
configurations.
B. 1/f noise
C. Random telegraph noise
Now, we discuss what we can learn from the 1/f
noise. Previously, Ingvarsson et al.30 scaled α ver- Previously magnetic RTN have been observed in
sus |dR/dH|/R and explained the result in terms of Al2O3-based30,31 and MgO-based38,39,46 MTJs, which
a fluctuation-dissipation (FD) relation. The scaling aretypicallysensitivetothemagneticfieldandbiasvolt-
of the 1/f noise by the FD relation has been tested age. AlthoughitisdifficulttodealwiththeRTNsystem-
againstAl O -based30,31andMgO-based43,54MTJswith atically in general, a few authors successfully estimated
2 3
micron-sizedjunction areas. Here,we testthe scaling by the effective magnetic moment of the fluctuator and dis-
the FD relation on the free layer of MgO-based MTJs cussedpossibleoriginsofmagneticRTN.InAl2O3-based
withsubmicron-sizedjunctionsfollowingIngvarssonetal. MTJs with micron-sized junctions, Ingvarsson et al.30
We replot the data in Figs. 3(c) and 3(d) andobtain the and Jiang et al.31 suggested a small rotation of a single
relation between α and |dR/dH|/R as shown in Fig. 5. domain or domain wall hopping between pinning sites.
Remarkably,thevaluesofαforthePconfiguration(open Recently, Herranz et al.46 reported that the magnetic
symbols)arealmostproportionalto|dR/dH|/R. Forthe RTNis causedby magneticinhomogeneities anddomain
AP configuration, the α values (solid symbols) first de- walls in free and fixed layers.
viate from the dashed line (drawn to guide the eye) be- We observed a strong enhancement of the Lorentzian
cause of peaks A and C, and then fall onto the dashed components in regions with specific bias voltages and
line again. Inthe insetofFig.5, αfor the AP configura- magneticfields. HereweconsiderpeaksA,B,C,andDin
tion is shown over the wider range of |dR/dH|/R. After Fig. 3(b) as typical examples. Generally, the Lorentzian
droppingontothedashedline,αforAPrapidlyincreases component in the noise spectral density indicates that
with |dR/dH|/R beyond ∼1 mOe−1. In this region, the thenoiseiscausedbythe fluctuationbetweentwolevels,
measured spectra exhibit a complicated enhancement of namely, RTN. The real-time voltagesignals near peak A
Lorentzian character possibly from several RTNs. for H =−300, −320,and −360 Oe are shown in the left
If one assumes thermal equilibrium, then the FD rela- panel of Fig. 6(a); the rightpanel shows the correspond-
tion for this magnetic system is given by30 ing histograms for the voltagesignals (2×105 points for
200 ms). These signals have two distinct voltage levels,
2k T andhence we attribute the measuredLorentziancompo-
S = B χ′′ (f), (5)
m πµ f m nents to RTN. The histograms are fitted by a double-
0
6
(a) where E, ∆m, and 1/τ are the field-independent acti-
H = -300 Oe sample 1 0
T = 5 K vation energy, the total magnetic moment of the fluctu-
20 ator, and an attempt frequency, respectively (where we
) H = -320 Oe take + for the 1 state and − for the 2 state). To esti-
V
µ matetheeffectivemagneticmomentparalleltoH (∆m ),
( 0 k
V we take the ratio of each dwell time:30,31,46 τ /τ ∝
∆ 1 2
H = -360 Oe exp −2∆m H/k T . By a linear fit ofln(τ /τ ) versus
k B 1 2
-20 H [s(cid:0)ee Fig. 6(b)], w(cid:1)e estimated the effective magnetic
moment ∆m to be 1.6×103µ for both positive and
0 0.5 1.0 0 300 600 k B
Time (ms) Counts negative currents (I = ±42 µA), where µB is the Bohr
magneton. This value corresponds to 0.08% of the total
(b)
-240 J) Hmoawgneveteirc, mthoemcehnatnogfetihnerferseiestaelneccetro∆dRe (r2e.s0ul×tin1g06fµrBom).
1 100
( RTN was estimated from the real-time voltage signal to
) τ2 be 0.13 Ω, which is about 0.035% of the total resistance
/τ1 0 I =-42 µA change for the reversal of the free layer, which is con-
(
Tln I =+42 µA sistent with the above value (0.08%). This observation
k B -100 strongly suggests that the observed RTN is responsible
-
-350 -300 for the magnetic fluctuator. The bias dependence of the
H (Oe) estimated ∆m is shown in Fig. 6(c). With increasing
(c) k
bias current, ∆m is monotonically decreased for both
k
bias polarities. This means that as the injection current
2000 gets higher, smaller magnetic fluctuations are allowed.
)
µB The ∆m values in the previous reports30,31,46 are
( k
m || 1500 larger than those in our result by at least two orders
∆ of magnitude. Here we discuss the origin of the fluctu-
ator that contributes to the measured magnetic RTN. If
1000
one assumes full reversal of a single domain in the free
-50 -40 -30 30 40 50
I (µA) layer, a typical area size of the magnetic fluctuator is
5.9×10−6µm2,wherethejunctionareais7.4×10−3µm2.
FIG.6. (a)Magneticfielddependenceofthevoltagefluctua- Thissmallvalue andthe absenceofanystepinthe mag-
tions(offsetforclarity)measuredaroundpeakAinFig. 3(b) netic hysteresis loops in Fig. 4 indicate that the contri-
(leftpanel)andthecorrespondinghistograms(dots)(2×105 bution of a macroscopic domain wall can be ruled out.
points)(rightpanel). Thesolidanddashedcurvesarethefit- The estimated ∆m and ∆R for the AP configuration
k
ted curves (double Gauss function) and each Gaussian com- have almost the same percentages against the full rever-
ponent. (b) Logarithm of the rate of the dwell times for sal of the free layer. Finally, enhancement of magnetic
I =−42 µA (open circle) and 42 µA (solid circle) as a func-
RTNisobservedforbothconfigurations. Basedonthese
tion of H. The dashed and solid lines are the results of the
results, we attribute the fluctuator to two quasistable
linear fitting. (c) Bias dependence of estimated fluctuation
single-domainstateswith some strainin the free layer.26
magnetic moments.
Gaussian function, which is shown in the same panel by D. Crossover from the 1/f noise to RTN
the dashed lines. Let us call the two states “1” and “2.”
Fromthe areaofeachGaussian,whichisproportionalto To understand the excitation mechanism of the RTN
the dwell time of each state (τ and τ ), we estimate the we focus on the bias dependence of the noise property
1 2
ratioofthedwelltimesbetweenthesestates(τ /τ ). Fig- at peak A. Figure 7 represents the frequency-dependent
1 2
ure 6(b) shows a logarithmic plot of τ /τ versus H for component of measured spectra at −300 Oe (AP config-
1 2
I =±42µA.Remarkably,logτ /τ isproportionaltothe uration) for V = 12, 23, 30, and 50 mV. Although pure
1 2
magnetic field. The strong dependence of the dwell time 1/f noise is observed in the low-bias region as shown in
for each state as a function of magnetic field indicates Fig. 7(a), RTN is dominant at V = 23 mV, resulting
that the RTN is due to a magnetic fluctuator. in the strong enhancement of the Lorentzian component
We assume that two states with dwell times of τ and (“RTN1”) [Fig. 7(b)]. The characteristic frequency of
1
τ have activation energies of E ±∆m·H. By further the RTN is given by the full width at half maximum of
2
assuming the Arrhenius relation, we express the dwell the Lorentzian(fc). Forexample, fc =20kHzforRTN1
times τ and τ as inFig.7(b). Withincreasingbiasvoltage,the character-
1 2
isticfrequencyofRTN1increasesandanotherLorentzian
1 1 E±∆m·H component (“RTN2”) with different f appears [Fig.
= exp − , (7) c
τ (H) τ (cid:18) k T (cid:19) 7(c)]. Finally, the 1/f noise becomes dominant again
1,2 0 B
7
)
2m
20 (a)
-120 10
1 V
( C
0
(b)
2000
0.10 m
sample 1 1000 || (
0.05 H = -300 Oe
T = 5 K B )
0.00 0
(c)
RTN1
5
10
fitted
)
z 3
H 10
(
f c
RTN2
1
10
0 10 20 30
V (mV)
FIG. 8. Bias dependence of the parameters characterizing
the RTN at −300 Oe for AP. (a) Bias voltage dependenceof
α. (b) The triangle is the resistance change of RTN1. The
opendiamondistheestimatedfluctuatingmagneticmoments
in Fig. 6(c). (c) fc for RTN1 (circle) and RTN2 (triangle).
The solid curveis the fit to fc for RTN1
FIG. 7. (a)–(d) The frequency-dependent component of the
spectrum for V = 12, 23, 30, and 50 mV, respectively. The
Figure 8(c) shows that, although the estimated f for
solidcurvesarethefittedcurvesobtainedbysummingthe1/f c
RTN1andRTN2exhibitsalmostanexponentialincrease
noise, RTN1, and RTN2, where each component is shown as
with the bias for their whole curves, there is a kneelike
a dashed curve.
structureinthecurveforRTN1atV . Wefitf forRTN1
c c
to f = f exp(−E/k T∗) using the Arrhenius relation
c 0 B
in the spectrum [Fig. 7(d)]. To fit the obtained spectra and taking Joule heating into account, where f0 is an
asasummationof1/f noise(S )andafewLorentzians attempt frequency. We also assume that the activation
1/f
(S ), weuse β/fγ andβ∗/[1+(f/f )2],respectively. energyE is independent ofthe bias voltageandthat the
HeRrTeNγi and f are the spectiral exponecnit and character- effective temperature T∗ = T +ζV2. The solid curve
ci
istic frequency of the Lorentzian for “RTNi” (i = 1 and in Fig. 8(c) corresponds to the fitted curve, where the
2). Outside the peak region, the estimated γ is close to estimatedE andζ are1.3×10−21 Jand1.3×104 K/V2,
1,whereasitis reducedfrom1asthe Lorentziancompo- respectively. Comparingthisresulttothepreviousone,33
nents are enhanced. By taking the Dutta-Dimon-Horn in which the activation energy for nonmagnetic RTN in
model,57 in which the 1/f noise is the result of a su- Al2O3-basedMTJswasfoundtobe0.3×10−19 J,wesee
perposition of many RTNs with a broad distribution of that our value is much smaller. This is consistent with
activationenergies,thissuppressionofγ accompaniedby the absence of nonmagnetic RTN in high-quality MTJs
the enhancement of RTN can be explained by a change in the low-temperature, low-bias regime.
of the energy distribution of the magnetic fluctuators. Returning to the magnetic configuration dependence
The bias dependence of the parameters characterizing oftheRTN,oneseesthatαvaluesforpeaksAandBare
RTNat−300OefortheAPconfigurationissummarized enhancedatroughlysymmetricpositionswithrespectto
in Fig. 8. V ∼ 21 mV is the bias voltage where α H [see lower panels in Figs. 3(b) and 3(c)]. The values
c c
shows its maximum. The effective magnetic moment of of α for peaks A and B have their maxima at almostthe
the fluctuator, ∆m , and the change in resistance, ∆R, same bias voltage, whereas the amplitude of the maxi-
k
are compared in Fig. 8(b). The behaviors of α, ∆m , mum for peak A is almost seven times as large as that
k
and∆R are similarto eachother inthat they havetheir ofpeakB.Weassumethatthe samemagneticfluctuator
maxima at V andthen decrease as the bias is increased. contributestothesetwopeaks. Thesymmetrichysteresis
c
Finally, both ∆m and ∆R become almost half of their loopofthefreelayerwithrespecttoH alsosupportsthis
k c
maxima at the bias at which the peak of α disappears. assumption (see Fig. 4). Here, the difference in the peak
8
(a) rities within the barrier is assumed. In this theoretical
10 model,F stronglydependsontheasymmetryoftheeach
)zH 4 AH P= -400 Oe sTa =m 3p lKe 2 α tunneling and can be 0.5 to 1.
2V/ (10 Full shot noise in MgO-based MTJs was reported by
-1810 2 (Ff i=tt e1.d00) 5 µ m-12 pGaupeerrreirno eextpaelr.imanendtssowmheeroef tthhee aMugthOorbsaorrfietrhsewpereresenast
(
S V )2 thick as 3 and 1.5 nm, respectively.17,18 This indicates
0 0 thatMgO-basedMTJsarefreefromtheprocessthrough
1.0 impurity sites, possibly resulting from the high quality
P
1.0 H = 500 Oe of the crystallizedMgO. Later, we reported the suppres-
sion of the Fano factor for the P configuration (typi-
0.5 cally 0.91) with a 1.05-nm-thick MgO barrier, whereas
fitted
0.5 (F = 0.89) the F for the AP configuration is almost unitary (typi-
cally0.99).20ToexplainthissubtlereductionofF within
theabovesequentialtunnelingmodel,wehavetoassume
0.0 0.0
-10 0 10 averyasymmetricbarrier(1:100),whichisunrealisticas
V (mV) the barrier of our MTJ is thin. Moreover, by using this
(b) model,wecannotexplainthe magneticconfigurationde-
1.0
P sample 3 pendence of the reduced F, and hence we can rule out
)
2z/H 1.0 H = -40000 Oe T = 3 K α (1 tshuilstsscfoernaFriov.alWueesninotcelutdhinagt atlhleofthtihcek-ebxaprreireirmceanstealcraen-
V 0
-180 0.5 (Ff i=tt e0.d92) 0.5 µ -12 bpreinecxippllaeisnecdalcbuylarteicoenn.t23thNeaomreetliyc,althweorFkanboasfeadctoonr,awfihriscth-
1 m
S (V )2 icslurseidouncpedrinfrcoimple1,,siisgnaadliinregctthcaotnstehqeureenacreeocfothheerePnatuclhiaenx--
0.0 0.0
-10 0 10 nelswithhightransmissionprobabilitiesthroughtheepi-
V (mV)
taxial MgO barriers. Thus, our result on the shot noise
gives unique evidence for coherent tunneling through a
FIG.9. (a)Whitenoisecomponentandαmeasuredat3Kin
crystallized MgO barrier.
the P (H = 500 Oe) and AP (H = −400 Oe) configurations
WeshowinFig.9thetypicalresultsofthewhite-noise
on sample 2 as a function of V. The solid curve is the fitted
componentS andαat3Kasafunctionofbiasvoltage.
curve between V =−10 and 10 mV. (b) Counterpart of Fig. V
In Fig. 9(a), S is nicely fitted by Eq. (2) for |V| ≤ 10
9(a) in theP configuration (H =−40,000 Oe) on sample 3. V
mV. For |V| > 10 mV, α increases due to enhancement
of RTN for both configurations, and, as a result, S de-
V
amplitude between A and B cannot be accounted for by viates fromthe fitted curve. Itis notedthat the effect of
conventional Joule heating. That is, because the Joule the1/f noiseonSV isnegligiblysmallinthisbiasrange.
heatingeffectisproportionaltothebiascurrentatafixed The above observation indicates that to accurately esti-
bias voltage, this effect for peak A is only 1/3 that for matetheFanofactorimmunetothefrequency-dependent
peak B. These results may imply a spin-dependent heat- noise, it is necessary to analyze the noise in the low-bias
ing process of a localized spin system in the free layer regime at low temperature. Experimentally, we cansup-
depending on the magnetic configurations. press magnetic RTN by stabilizing the magnetizationby
applying a large magnetic field for the P configuration.
In fact, in Fig. 9(b), the enhancement of RTN is sup-
E. Shot noise pressed, and thus SV is almost perfectly fitted by the
shot-noise formula with F =0.92.
Finally, we discuss the shot noise to connect our pre-
vious work with the present one and to support fur-
ther evidence of our claim made before. The frequency- IV. CONCLUSION
independentcomponentofthespectrumiswelldescribed
by Eq. (1). F describes how the noise deviates from The low-frequencynoise properties insubmicron-sized
the Poissonianvalueandthuscharacterizesthe partition CoFeB/MgO/CoFeB-based MTJs with thin tunneling
process of the electron tunneling. Conventional tunnel barriers are systematically investigated. The measure-
junctions exhibit F = 1, reflecting the Poissonian pro- ments are carried out at low temperature by controlling
cess. RegardingAl O -basedMTJs,afterthefirstreport the magnetic field and bias current (voltage), where we
2 3
of the full shot noise (F ∼ 1),31 reduced Fano factors focus on the noise properties on the magnetic hystere-
rangingfrom0.45to1werereported.15,16 Thisreduction sis loops of the free layer. A clear correlation between
can be explained by the sequential tunneling model,16 α and |dR/dH|/R is observed. The nice scaling of the
where the process of two-step tunneling through impu- observation by the FD relation indicates that the main
9
origin for the 1/f noise is thermal magnetic fluctuation ofMTJsispossiblebyusingdeviceswithwell-crystallized
of the free layer. RTN is observed inside the magnetic thinMgObarriersandbymeasuringthenoiseatlowtem-
hysteresis loops for both configurations. We found that peratureandlowbias. Furtherstudyofthenoiseproper-
this is due to the magnetic fluctuation between two qua- tiesinMgO-basedMTJswithvariousbarrierthicknesses
sistable single-domainstates withsome straininthe free isnecessarytosystematicallyelucidatethemechanismof
layer. Although the 1/f noise is almost independent of the noise and improve the device properties.
themagneticconfiguration,RTNisremarkablyenhanced
for the AP configuration and at specific bias voltages.
Suchresultsindicateaspin-dependentactivationprocess ACKNOWLEDGMENT
ofRTN.Shotnoisemeasurementgivesusquantitativein-
formation for coherent tunneling. This work was partially supported by the JSPS Fund-
ing Program for Next Generation World-Leading Re-
Our study shows that a systematic study on the noise searchers.
∗ [email protected]; Present address: Tiusan, Phys.Rev.Lett. 109, 066601 (2012).
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