Table Of ContentBand edge noise spectroscopy of a magnetic tunnel junction
Farkhad G. Aliev, Juan Pedro Cascales
Dpto. Fisica de la Materia Condensada C-III,
Instituto Nicolas Cabrera (INC) and Condensed Matter Physics Institute (IFIMAC),
Universidad Autonoma de Madrid, Madrid 28049, Spain
Ali Hallal and Mairbek Chshiev
Univ. Grenoble Alpes, CNRS, INAC-SPINTEC, CEA, F-38000 Grenoble, France
Stephane Andrieu
Institut Jean Lamour, Nancy Universit`e, 54506 Vandoeuvre-les-Nancy Cedex, France
(Dated: January 23, 2015)
Abstract
5 We propose a conceptually new way to gather information on the electron bands of buried metal(semiconductor)/insulator
1 interfaces. The bias dependence of low frequency noise in Fe V /MgO/Fe (0 < x < 0.25) tunnel junctions show clear
1−x x
0
anomalies at specific applied voltages, reflecting electron tunneling to the band edges of the magnetic electrodes. The change
2
in magnitude of these noise anomalies with the magnetic state allows evaluating the degree of spin mixing between the spin
n polarized bands at the ferromagnet/insulator interface. Our results are in qualitative agreement with numerical calculations.
a
J PACSnumbers: 73.20.At,73.22.-f,72.70.+m,73.40.Gk
2
2
Buried metal (semiconductor)/insulator interfaces are or Fig.S.1(a)). Therefore, when the tunneling is tuned
] foundattheheartofelectronics1. Thecurrentintunnel- to some specific band edge in the opposite electrode, the
l
l ingdevicesisdeterminedbythebias,barrieranddensity current could acquire an extra LFN due to multiple re-
a
of states of the electrodes2,3. Electron states not allowed laxations originating from defect states contributing to
h
- inbulkcouldbecomepermittedatthesurfaceleadingto the formation of the band edge tails (Fig.S.1(b)).
s topological4,5 or interface resonant states6. For metallic
e In this Letter we investigate the bias dependence
structures the scarce knowledge on the interface bands
m of conductance and LFN in single barrier tunneling
is mainly obtained by indirect methods such as ballistic
devices in order to determine in-situ the energies of
t. electron emission spectroscopy7 or high-resolution X-ray the band edges of the buried interfaces. We unam-
a
spectroscopy8. The possibility of a reliable and down-
m biguously demonstrate the validity of the band edge
scalable in-situ methods to investigate interface electron
noise spectroscopy (BENS) concept by studying semi-
- bands remains centrally important9.
d nal Fe/MgO/Fe MTJs with partial doping of the bot-
n Tunneling magnetoresistance10–12 is extremely sensi- tom electrode (Fe) with Vanadium (V). Such substitu-
o tive to the band structures of ferromagnet/insulator tion has been shown to reduce defect states inside the
c
(FM/I) interfaces3,13–20. Despite recent attempts to un- MgObarrierduetoimprovedinterfacematchingbetween
[
derstand the nature of the electron bands which con- Fe V andMgOinFe V MgO/FeMTJs.30–32. Our
1−x x 1−x x
1 tribute to electron transport in spintronic devices21–23, numerical simulations confirm that tunneling of band-
v
the issue remains unsettled. The main tool to character- tail electrons, influenced by spin orbit interactions, are
2
ize interfaces or barriers has been inelastic electron tun- responsible for the observed LFN anomalies.
5
neling spectroscopy (IETS)23–25 analyzing the derivative
4 Our magnetic tunnel junctions were grown by Molec-
5 of the conductance as a function of bias. The resulting ular Beam Epitaxy (MBE) on MgO (100) substrates
0 IETS signals depend on the tunneling density of states under ultra high vacuum (typically 10−10 mbar) condi-
. (DOS) and inelastic scattering2,3,26 which could obscure
1 tions. Fe-V alloys were grown at room temperature by
0 the detection of the band edges in the presence of inter- co-evaporation,thelayerbeingafterwardsannealedupto
5 face disorder. The bias dependence of the conductance 900K. The barrier thickness was controlled by RHEED
1 anditslowfrequencyfluctuations couldbeanalternative
intensity oscillations. The MTJs were patterned by UV
: way to study the interface or electron confinement27,28
v photolithography and Ar etching to dimensions ranging
i DOS. from 10 µm to 50 µm. More details can be found in30.
X
A commonly accepted phenomenological approach re- Thenoisemeasurementssetupwasdescribedearlier33,34.
r
lates the excess low frequency noise (LFN), often in- The typical noise power spectra (S ) in the antipar-
a V
versely dependent on the frequency f, with electrons allel (AP) or parallel (P) states reveal the presence of
scatteringfromdefectscharacterizedbyabroaddistribu- 1/f noise in the frequency range between 1 and 50 Hz
tionofrelaxationtimeswithenergy29. Ifdominantdefect as S (f) ∝ 1/fβ (with 0.8 < β < 1.5, see Fig.S.1(b).
V
states are located close to the interfaces, they could cre- The bias dependence of the LFN has been determined
ate interface band edge tails (supplemental Figure 1(a) through the Hooge factor (α) from the phenomenolog-
Typeset by REVTEX 1
a ) a) 10-7
4 0 0 S (P)
) full
) F a n o 1 .0 2/Hz 100 αP Sexp(P) 10-82m)
R(%3 5 0 0 .5 ano (nV αAP 10-9 α(µ
TM F SV
3 0 0 T M R 0 10-10
0 .0 -1.0 -0.5 0.0 0.5 1.0
0 .0 0 .1 0 .2 0 .3 Bias(V)
x
b)
1.40
b ) a ) ∆ DOS
1 0 -9 a PA P 1 .4 G(0P 1 xx==04D.5D 0.5 OS
2) (0) V)/ 1.20 0.0 D
1 .2 P 1
am(m1 0 -1 0 G P(V )/G P(0 ) 1 .0 G/G G(P1.00 GP(V)/GP(0) -0.5 ∆
1 0 -1 1 -1.0 -0.5 0.0 0.5 1.0
-1 .0 -0 .5 0 .0 0 .5 1 .0
Bias(V)
B ia s ( V )
FIG. 1: (a) Dependence of the zero bias TMR and the Fano FIG. 2: (a) Bias dependence at T =4K of the Hooge factor
factor at T = 4K as a function of V content. (b) Bias de- andSNforFe V /MgO/FeMTJ.(b)Dependenceofthe
0.96 0.04
pendence, at T=4K, of the dynamic conductance in the P conductance with the applied voltage at T = 4K combined
state, and the Hooge factor α of both P and AP states for with the calculated ∆ DOS as a function of energy with
1
Fe/MgO/Fe junctions. Arrows indicate weak peaks. respecttoE . Inflectionpoints(opendots)indicate∆ DOS
F 1
band edges for 4% Vanadium for V < 0 and pure Fe (x=0)
for V >0.
ical expression: S (f)=α·(I·R)2/(A·f), where R,I, A
V
and f indicate resistance, current, area and frequency,
respectively.34. Qualitatively similar results have been in the bias range under study (Fig.2(a)). In contrast to
obtainedbyanalyzingintegratedLFN(Fig.S.1(c)). Shot what is observed for the reference sample (Fig.1), the
noise(SN)wasobtainedfromthefrequencyindependent LFN shows a clear enhancement (factor of 2) of con-
part of the LFN below 10K33. ductance fluctuations around ±0.6V. Yet a stronger en-
We begin by analyzing the electron transport and SN hancement of the LFN close to 0.6V is observed in AP
behavior at T=4K. The zero bias TMR as a function of configuration. The dynamic conductance in both states
V content shows a maximum (Fig.1(a)), confirming a re- showsanupturnaround0.6V,butappearsclearerinthe
duction of the interface mismatch reported previously at P state (Fig.2, AP state not shown for simplicity). Nu-
roomtemperature30–32. ThenearlyPoissoniancharacter merical calculations of the tunneling electron DOS indi-
of the tunneling statistics with Fano factor F =1±0.05 cate that the upturn in conductance and the noise en-
(Fig.1(a)) indicates nearly direct tunneling processes. hancement could be related with the opening of a new
Figure 1(b) shows the bias dependence of the Hooge transmission channel when the Fermi level of one mag-
factor α(V) in both P and AP states for a Fe/MgO/Fe neticelectrodecrossesoneofthebandedgesoftheother
MTJ used as reference. One observes an excess LFN be- magnetic electrode, indicated by arrows in Fig.2(b).
low 200 mV, where FeO35 and Fe/MgO2 interface defect Even clearer signs of the band edges in LFN are seen
states have been predicted to influence the conductance. with an 8% of V where the lowest background LFN
FortheMTJwithanon-optimisedFe/MgOinterfaceone and the maximum TMR (Fig.1) are achieved. Figure
observesastrongsuppressionofLFNwithbiaswithweak 3 shows α(V) dependence in Fe V /MgO/Fe MTJs
0.92 0.08
anomaliesintheα(V)around0.5V,indicatedbyarrows. weretheoptimumrelationbetweentwocompetingeffects
The doping of Fe with V improves the interface mis- is reached: FM/I interface relaxation on the one side
match and decreases the Fe/MgO interface defect states and still not essential suppression of the magnetization
density30–32, which allows the implementation of the and the induced Fe-V structural disorder on the other
BENS method. Figure 2(a) shows the α(V) and SN(V) side30–32. We estimate the TMR from our simulations
dependencesforFe V /MgO/FeMTJs. TheSN(V) using the Julli`ere model10 (Fig.S.2) which indicates the
0.96 0.04
givesaFanofactorclosetoone, provingdirecttunneling optimumvaluesarereachedfor9%ofV,i.e. ratherclose
2
a ) 1 0 - 1 0 T = 1 0 K P b ) 1 0 -9 T =10K A P statailtewsesamkleyarinofluutetnhceeIsEITESTSsig(ninaslesr.tToufnFniegl.iSn.g1(tco)t)hreebflaecntd-
T =0.3K T =0.3K
2) 2) ing only the derivative of the DOS close to EC. On the
m m1 0 -10 other hand, much stronger changes in LFN vs. bias are
m( m( seen due to a strong change of excited defect relaxation
a a
1 0 -11 1 0 -11 times38 whentunnelingclosetoEC, activatinganexcess
of the low frequency conductance fluctuations. There-
-1 0 1 -1 0 1
B ia s ( V ) B ia s ( V ) fore, interface defect states dominate the LFN, and not
c ) d ) T = 300K the derivative of the conductance (insert of Fig.S.1(c)).
)1 .0 PA P 2)4 x 1 0 -11 TTT === 61000.3KKK oriTgihneatfeosllofrwoimngdaisrogrudmere/ndtesfeicntdsiccaltoesethtoatthLeFNFMm/aIininly-
S m terface: (i) direct tunneling (Fig.1); (ii) the metallic na-
(m0 .5 m(2 x 1 0 -11
G a ture of the electrodes, with resistance a few thousand
times below the barrier resistance, ensuring that electric
0 .0 0
-1 0 1 -0 .6 -0 .4 -0 .2 signals and their fluctuations mainly come from regions
B ia s ( V ) B ia s ( V ) in the barrier and interfaces; (iii) by analyzing LFN at
higherbiasesweavoiddirectresonantexcitationoflocal-
izedFeOorO interfacedefectlevelspredictedbelow200
FIG. 3: Bias dependence at T =4K of the Hooge coefficient mV35.
forthe(a)Pstateand(b)APstateinFe V /MgO/Fe
0.92 0.08
A simplified physical picture explaining the variation
MTJs. (c) Bias dependence at T = 4K of the dynamic con-
ductance for the P and AP state. (d) Low frequency noise of LFN when tunneling to three different energies E1,2,3
peaks gradually disappear with increasing temperature. around EC (Fig.4(a) and Fig.S.1) is as follows. When
electrons tunnel to energies E > E , their relaxation
1 C
time is fast due to the delocalized character of the band
to what is experimentally observed. We have found that statesnearE1 withacorrespondinglysmallcontribution
the Fe0.92V0.08/MgO/Fe MTJs show clear anomalies in to LFN. For tunneling to electron states E3 < EC the
the Hooge factor for biases around 1V and around 0.6V LFN is also expected to be small due to low probabil-
for the P state only, as shown in Fig. 3(a,b). Fig.3(d) ity of these tunneling events. However, when electrons
demonstrates how the anomaly in the P state around tunnel to the energies E2 (cid:46) EC, the tunneling current
0.6V gradually disappears with temperature, probably could be affected by multiple trapping-type relaxations
due to thermal excitations. originatingfromshallowdefectstatescontributingtothe
Qualitatively similar effects were seen for formation of the band edge tails. We estimate that the
Fe V /MgO/Fe and Fe V /MgO/Fe MTJs LFNpeakwidthisroughlydeterminedbytheenergydif-
0.83 0.17 0.75 0.25
with the latter being the most robust to electrical ferencebetweenthemobilityedgeandthebottomofthe
breakdown (standing up to 2.5V). In the high V con- band tail.
tent range, the LFN is strongly influenced by random In the MTJs under study, electron tunneling mainly
telegraph noise at positive biases around 1V, reflecting occursbetweenpolarizedbandswithdifferentBlochstate
a strongest asymmetry in interface defect states previ- ∆ symmetries spin filtered by the MgO barrier14–19.
1,5
ously visualized with scanning electron microscopy for This allows a rough estimation of the interband mixing
Fe V /MgO/Fe MTJs32. attheinterfacebyanalyzingvariationofBENS response
0.8 0.2
Fig.4(a) qualitatively explains the BENS method. As with relative alignment of the electrodes. Let us discuss
long as tunneling through the barrier is coherent, the qualitatively the reasons why BENS could provide LFN
main source for LFN are conductance fluctuations due peaks both in the P and AP states (Figs. 2,3). For sim-
to atomic defects affecting ∆ and ∆ interface states. plicity, we shall use the majority and minority Fe elec-
1 5
Resultinglocalizedstatesclosetothebandedges36 could tronbandstunnelinginFe/MgO/Fejunctions(Fig.4(c)).
contribute, as reported for bulk semiconductors37,38, to When the MTJ is in the AP state, then in accordance
the enhanced LFN. The key new feature of the BENS withBENS arguments∆5↑ ⇒∆5↓ and∆1↑ ⇒∆1↓ band
is the versatility in displacing the Fermi level (E in edge tunneling could provide a peak in LFN (AP) at
F
Fig.4(a)) of the ejector electrode with respect to the dif- different biases from 0.4 to 1.3 V if conductance fluctua-
ferent band edges (or mobility edge, E in Fig.4(a)) by tionsoriginatefromelasticscatteringevents. Experimen-
C
simply varying the applied bias. The right panel shows tally, however, we observe LFN peaks in the P state too
how the conductance and its derivatives are expected to (Fig.2(a)), which we link with the presence of spin-orbit
change when a new electron channel with a band edge coupling induced ∆ ⇐⇒∆ interband mixing at
1(↑↓) 5(↓↑)
opens at E . In order to clearly detect inelastic re- theFe/MgOinterface39. Indeed,largelateralmomentum
F
laxation through IETS, some well defined defect states transferandinterbandscatteringcouldbedominantonly
should relax energy through coupling to a well-defined close to the interfaces40. Within such scenario, the rela-
set of phonon energies. We believe that the random in- tionbetweenamplitudesofthepeaksLFN(P)/LFN(AP)
terface potential and the absence of well-defined defect provides an evaluation of the degree of interband mix-
3
a) b) a)fffffffffffb)
E
DOS DOS Ecρ(E) EEE231 I V) 1 Theory∆∆∆51mmmaiinnj
EF VBias MgO dI/dV Vbias E(eF 0 Experim∆51enmtaj
EF E- -1 FFeeV
c) Fe spin↑ d2I/dV2 Vbias
2.0 Fe spin↑ 0.0 0.1 0.2 0.3
y (eV) 10..00 Δ1 Δ5 Δ1 21..00 Ene LFN Vbias ffffffffffffffc) 1.0 x
erg-1.0 ↑ ↑ ↑ 0.0 rgy ng
En-2.0 Δ2 Δ2 Δ5 --12..00 (eV) Vbias offmixi0.5
ef
e
gr
FIG. 4: (a) Sketch of the principle behind BENS, presented e
D
fortheAPstate,whereE correspondstothemobilityedge. 0.0
C -1.0 -0.5 0.0 0.5 1.0
(b) The energies of these defect states can be inferred from
E-E (eV)
the IV curve of the sample, and its first (dynamic conduc-
F
tance) and second (IETS) derivatives, but they are detected
inamuchclearerwaythoughlowfrequencymeasurements.(c)
Sketchofabandedge(∆ ,∆ )contributiontothetunneling FIG. 5: (a) Schematic of the calculated crystalline structure
1 5 √ √
at ∼−1.2V. for a 2× 2 unit cell of (Fe V ) /MgO . (b) Calcu-
1−x x 11 5
lated changes in the energies of the band edges in Fe V
1−x x
compared to the experimental data of low frequency noise
ing between majority ∆ band and the minority ∆ of anomalies for the P state. Fully open experimental points
1↑ 5↓
roughly 0.2-0.3. indicate a weak peak (increase of noise in less than 10%).
(c)Calculateddegreeofmixingbetween∆ and∆ interface
In order to examine quantitatively the applicability of 1 5
Bloch state character in (Fe V ) 1/MgO for x=0.091.
our model we have performed ab−initio calculations of 1−x x 1 5
√ √
2× 2 unit cell of Fe V /MgO (x=0, 0.045, 0.091,
1−x x
0.182) with a 5 monolayers (ML) of MgO and 11 ML
of Fe V . Our first-principles calculations are based ferencebetweenbottomandtopinterfaces32. Ontheex-
1−x x
on density functional theory (DFT) as implemented in perimental side, measurements on MTJs with the least
theViennaabinitiosimulationpackage(VASP)42within Vanadiumweredonebelow1Vduetotheirvulnerability,
the framework of the projector augmented wave (PAW) makingthemdifficulttocomparewiththecalculationre-
potentials43 todescribeelectron-ioninteractionandgen- sults above 1V.
eralized gradient approximation (GGA)44 for exchange- Finally, in order to better understand the influence of
correlation interactions. A 13×13×3 K-point mesh was spin mixing at the interface, we have also analyzed the
used in our calculations. A plane wave energy cut-off Bloch state character of the interfacial Fe atom in the
equalto500eVforallcalculationswasusedandisfound presence of SOI as a function of the energy difference to
to be sufficient for our system E . Fig.5(c) presents this analysis for ∆ and ∆ inter-
F 1 5
Fig.5 compares the experimentally observed LFN face states in Fe V /MgO structure, mainly par-
0.909 0.091
anomalies in the P state (open dots) with the band edge ticipating in the electron tunneling through MgO. When
positions (closed dots) estimated from inflection points the degree of mixing at certain energy is equal to zero,
in the DOS simulations for the majority and minority it means that there is no mixing between different ∆
∆ and ∆ states of Fe V /MgO (x=0, 0.045, 0.091, channels and there is only one ∆ Bloch state character
1 5 1−x x
0.182)structures(asindicatedbyarrowsintheFig.2(b)). that dominates the tunneling at this energy tunneling.
We have also indicated by horizontal dotted lines the es- Thechannelmixingismorepronouncedatbiasesaround
timatedpositionsofthebandedgesoftheFe/MgOstruc- −(0.4÷0.5)V and not above ±1V, i.e. close to the in-
ture. tervalswhereLFNanomaliesofdifferentmagnitudewere
A reasonable agreement between simulations and the observed in both magnetic states (Fig.5(c)). We believe
experimentisobserved,especiallyfortheVanadiumcon- that ∆5↑ ⇒∆5↓ and ∆1↑ ⇒∆5↓ mixing could be due to
tent between (0.04 < x < 0.17) with reduced lattice surface induced band crossings and explains the appear-
mismatch, the lowest background LFN and the highest ance of peaks in LFN both in the P and AP states.
TMR. Tosummarize,wehaveintroducedthebandedgenoise
A few factors could contribute to some difference be- spectroscopy concept which permits an investigation of
tween experimental results and calculations. First of all, the electron band edges in a wide class of tunneling de-
calculations do not consider the presence of dislocation vices. We demonstrated successfully BENS approach
induced mismatch as well as the structural disorder dif- in epitaxial magnetic tunnel junctions. The dependence
4
of the BENS on the relative magnetic alignment of the characterizing buried interfaces.
electrodes allows us to estimate the importance of in-
terband hybridization and spin flips at the FM/I inter- TheauthorsacknowledgeA.Gomez-Ibarlucea,D.Her-
faces. Given the crucial importance of buried interfaces ranz and F. Bonell for their help with the experiments
in solid-state devices, the clear need to understand their andsamplegrowth. Thisworkhasbeensupportedbythe
electronic structure, and the limited options available, SpanishMINECO(MAT2012-32743)andComunidadde
our work presents a substantial advance in the field of Madrid (P2009/MAT-1726) grants.
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5
