Nonlinear Dynamics of Domain Wall Propagation in Epitaxial Ferroelectric Thin Films

0.32 MB·English

by  J. Y. Jo

J. Y.Jo et al.
Nonlinear Dynamics of Domain Wall Propagation in Epitaxial Ferroelectric Thin
Films
J. Y. Jo,1 S. M. Yang,1 T. H. Kim,1 H. N. Lee,2 J.-G. Yoon,3 S. Park,4 Y. Jo,4 M. H. Jung,4 and T. W. Noh1,∗
1ReCOE & FPRD, Department of Physics and Astronomy, Seoul Nat’l University, Seoul 151-747, Korea.
2Materials Science and Technology Division, Oak Ridge National Laboratory, Tennessee 37831, USA.
3Department of Physics, University of Suwon, Gyeonggi-do 445-743, Korea.
4Quantum Materials Research Team, Korea Basic Science Institute, Daejeon 305-333, Korea.
We investigated the ferroelectric domain wall propagation in epitaxial Pb(Zr,Ti)O3 thin films
9
over a wide temperature range (3 - 300 K). We measured the domain wall velocity under various
0
electric fields and found that the velocity data is strongly nonlinear with electric fields, especially
0
at low temperature. We found that, as one of surface growth problems, our domain wall velocity
2
datafrom ferroelectric epitaxial film could beclassified intothecreep, depinning,and flow regimes

n duetocompetitionbetweendisorderandelasticity. Themeasuredvaluesofvelocityanddynamical
a exponents indicate that the ferroelectric domain walls in the epitaxial films are fractal and pinned
J
bya disorder-induced local field.

9
2 PACSnumbers: 05.45.-a,47.15.G-,64.60.F-,68.35.Rh,77.80.Dj

]
i
c The physics of surface growth in disordered media andpatternatequilibriumaswellastechnologicalappli-
s with quenched defects is of crucial importance to un- cability in multi-functional devices such as FE random
-
l derstandnumerousintriguingnaturalphenomena[1],in- access memories, actuators, and sensors [3, 4]. Quite
r
t cluding contact lines in wetting, surface of epitaxially recently, lots of piezoresponse force microscope (PFM)
m
grownfilms, and magnetic domain walls. In such media, studies have provided us microscopic aspects of FE do-
. elastic forces tend to keep surfaces flat, while defects lo- mains, including inhomogeneous nucleation process [5]
t
a cally promote the wandering, as schematically displayed and the fractal nature of their rough surfaces [6]. Note
m by Fig. 1(a). The competition between elastic and pin- that most works on FE domains have been focused on
- ning forcesleadsto acomplicatedenergylandscapewith their static properties. In spite of its scientific and tech-
d
many localminima, which affects the surface growthdy- nologicalimportance,wehavelimitedunderstandingson
n
namics under an external force. Recently, there have how the FE domain wall propagates in terms of time.
o
been extensive reports to adapt the fractal concepts to We suggestto prospectFE domainwallfromthe view
c
[ surface growth dynamics [2]. of nonlinear responses, which follow the predictions of

Ferroelectric (FE) domains have been studied for the statistical physics on surface growth. Then, the FE
1
past decades because of scientific importance in micro- domainwallvelocityv shouldhaveanonlinearbehavior,
v
scopic aspects such as multi-domainformation, stability, showninFig. 1(b),underE. AtzerotemperatureT,the
0
9 domain wall remains strongly pinned by local disorders
5 until E reaches a threshold value E . When E ≧E ,
C0 C0
4 y it experiences a pinning-depinning transition and starts
(a) (b)(cid:88)
1. Defect to move with a nonzero velocity v, as represented with
0 creep depinning flow the red dashed line. Under this depinning regime,
9
v ∼(E−E )θ, (1)
0 C0
:
v withavelocityexponentθ. Underthe flowregime,when
i E ≫ E , v ∼ E. On the other hand, for finite T, the
X Domain wall T>0 C0
Elastic force T=0 pinning-depinning transition becomes relatively smooth,
ar x E E as represented with the green solid line. Under the low
C0 E (i.e., ≪ E ) creep regime, the domain wall motion
C0
becomes very slow and can be described by propagation
FIG. 1: (color online) (a) A schematic diagram of domain
between pinning sites due to thermal activation. Then,
wall propagation in disordered medium. Elastic forces come
fromthecurvatureofdomainwall,anddefectsworkasstrong v ∼exp[−(U/k T)(E /E)µ], (2)
B C0
pinning sites. (b) Theoretical prediction on the domain wall
velocityv vs. electricfieldE insystemgovernedbycompeti- where U is an energy barrierand µ is a dynamical expo-
tion betweendisorderandelasticity effects. EC0 representsa nent. Critical exponents of domain dynamics, including
threshold E. µandθ,canidentifytheuniversalityclassandprovidein-
formationonthe pinning forcesandthe fractalnatureof
the rough FE domain walls. Although measurements of
thesecriticalexponentvaluesfortheFEsystemsarepar-
∗Electronicaddress: [email protected] ticularly important, there are little experimental works
2

100 on SrRuO /SrTiO substrate using pulsed laser deposi-
3 3
(a)
tion [7]. X-ray diffraction studies confirmed that a high-
50
2m) quality, (001)-oriented PZT film was grown epitaxially.
C/c 0 TofabricatePZTcapacitors,we patternedthe sputtered
mP ( 35 KK Pt top electrodes with a typical area of 7.5×103 µm2.
-50 10 K Ourepitaxialfilmrevealedahighdielectricstability,suit-
20 K
40 K able to our measurements at high electric fields.
-100 300 K
Figure 2(a) shows T-dependent polarization-electric
-2 -1 0 1 2
E (MV/cm) field (P-E) hysteresis curves for a PZT capacitor, mea-
suredbetween3and300K.The saturationandremnant
1.0 (b) P values were nearly constant over a wide T range. The
systematicT variationoftheP-Ehysteresiscurvescomes
0.8
mostlyfromT-dependentchangeincoercivefieldE . At
C
pt () 0.6 3niKfic,aEntCly≈. 1MV/cm. As T increased,EC decreasedsig-
D 0.4
PFM & Current Oneofthedifficultiesinperformingthedynamicstud-
0.2 0.3 MV/cm
0.6 MV/cm ies on FE domains is to measure reliable values of v un-

0.0 der uniform E. Recently, we developed a modified PFM
-6 -5 -4 - 3 -2 -1 0
log t (s) technique for a FE thin film with a top metal electrode
[5, 8]. By combining PFM with switching current mea-
1 mm (c) surements,wewereabletotrackwallmotionsofdomains.
After applying one positive poling pulse (10 V, 50 µs)to
pole P, we switched P with a series of negative pulses.
t =15 ms t =25 ms t =30 ms t =35 ms
WethenmeasuredthePFMimagesafterallthenegative
pulses. We assumed that the PFM image obtained after
(d)
2x105 the negativepulseswouldbe nearlythe same asthatob-
tainedafterasingle pulse,with the widthbeing equalto
the sum of all the negative pulses [8]. Typically, an im-
-1t1/ (s)0 1x105 amgienuatceqsu,iswithioicnhpirsorceelsastiuvseilnygltohnegPinFMrelsaetti-ounpttoaktehseatifmewe
scale correspondingto the width of the E−pulse used in
0 these experiments. To check its validity, we calculated
0.00 0.01 0.02 0.03 theamountofnormalizedswitchedpolarization∆pfrom
u (ms-1) PFMimageswithanareaof5×5µm2. Theseareshown
as the open symbols in Fig. 2(b). We also determined
FIG.2: (coloronline)(a)P-E hysteresisloopsatdifferentT.
∆pindependently fromswitchingcurrentmeasurements,
(b)Time-dependentnormalizedswitchedpolarization,∆p(t),
which are shown as the solid symbols. The agreement
behaviors (solid symbols) from switching current and (open
between these data indicates that we could reliably use
symbols) from PFM measurements. The solid lines show the
the modified PFM techniques to study domain wall mo-
fitting results using the KAI model. (c) Scanned images of
t-dependent domain growth at E = 0.3 MV/cm. (d) Plot of tion in our FE film.
1/t0 vs. v. This relationship is linear, suggesting that 1/t0 Figure 2(c) shows typical PFM images of time-
fromswitchingcurrentstudiescanbeusedtoparameterizev. dependentgrowthforaparticularisolateddomain,which
wereobtainedatroomT withE =0.3MV/cm. As time
t increased,the domainsize increased. Eventually,it be-
gan to merge with other domains. From the area of the
on these values .
isolated domain, we determined its mean radius. By di-
In this Letter, we report our studies on the T- and
viding the change in mean radius with the change in t,
E-dependent nonlinear responses of FE domain wall dy-
we obtained the v value. We repeated these procedures
namics in epitaxial Pb(Zr,Ti)O (PZT) thin film. To
3 for more than 20 isolated domains and finally obtained
widen the accessible region of T and E, we used switch-
an average value for the given T and E. Note that our
ing current measurements, combined with direct v data
modified PFM study canprovide a way to measurev di-
determinedbyPFMimages. Wefoundthatv followsthe
rectly. However,obtainingsufficientdatatoplotallv vs.
nonlinear dynamic response, as described in Fig. 1(b).
E curves would have been too laborious. In addition, it
Wealsocouldobtainvaluesofthetwocriticalexponents,
is rather difficult to use in the low T region. Therefore,
µ and θ, from the data in the creep and the depinning
it is highly desirable to find another method to obtain v
regimes,respectively. Thisworkprovidesusnewinsights
reliably in a wide range of T and E.
on how domain walls propagate inside epitaxial FE thin
TheswitchingcurrentinaFEthinfilmshouldbeorig-
films.
inated from the P reversal, whose behavior is governed
We fabricated 100 nm-thick epitaxial PZT thin film
3
8.0x105
1.0
(a)
(a) 300 K
0.8 000...111255 MV/cm 6.0x105 1 035 KKK 0.15 -1ms)
00..46 0000....2346 -1t1/ (s)0 4.0x105 3 024000 KKK 0.10 m PFM (
0.2 01..81 2.0x105 0.05 fro(cid:88)
)
pt (
(cid:39) (b) 3 K
0.8 0.8 MV/cm 0.0 0.00
1.0 0.0 0.5 1.0 1.5
0.6 11..015 E (MV/cm)
1.2 0
0.4 1.3 (b) 3 K
1.4 5 K
1.5 10 K
0.2 1.6 -2 20 K
40 K
0.0 s) 300 K
-6 -5 -4 -3 lo-2gt (s-)1 0 1 2 3 tog () (0 -4 m) 0.0 0.1 1/0T. 2(K-1)0.3
l V/c 80
FmIeGas.u3r:em(ceonltosruonndlienre)va∆ripo(uts)Eobtvaailnueeds avtia(asw)i3t0ch0inKgacnudrre(bnt) -6 EkT/(M0B246000
U
3 K. The solid lines show the fitting results using the KAI
0 2 4 6 8 10 12
model. 1/E (cm/MV)
6.0
(c) 3 K
by domain wall dynamics. The t-dependent changes in
∆pforepitaxialFEthinfilms[9]havebeenexplainedus- -1s) 5.8
iAncgcothrdeinKgoltmoothgeorcolva-sAsicvaralmstai-tIisshtiibcaalshthie(oKrAyIo)nmnoudcleela[t1io0]n. tg (1/) (0
and unrestricted domain growth, lo 5.6
∆p(t)=1−exp[−(t/t )n], (3)
0
5.4
where n and t are a geometric dimension and a -0.8 -0.6 -0.4 -0.2 0.0
0 log (E-E ) (MV/cm)
characteristic switching time for the domain growth, C0
respectively. In the two simplest cases, analytical
relationships between t and v can be easily obtained. FIG.4: (coloronline)(a)(Solidsymbols)T-dependentcurves
0
When the nuclei of opposite polarity are generated of 1/t0 vs. E. The dotted and solid lines are guidelines for
at a constant rate under E, t ∼ (1/v)(n−1)/n [10]. eye. (b) log(t0) vs. 1/E curves. The linear fitting indicates
Conversely, when all the nuclei 0are generated instanta- a dynamic exponent µ ∼ 1. The inset shows that UEC0/kB
neously, t ∼1/v [10]. Our previous studies on epitaxial is nearly independent of T. (c) Plot of log(1/t0) vs. log(E−
0 EC0) with the EC0 ∼1 MV/cm. From the slope of the plot,
PZT films showed that nucleation rate is approximately we found a velocity exponent θ∼0.7.
proportionalto 1/t[5],whichismuchclosertothe latter
case, so 1/t might be nearly proportional to v.
0
We investigated the relationship between v and 1/t
0
using the switching current response. Our experimental ∆p(t) occurred over a shorter timescale, i.e., a smaller
∆p(t) data were fitted using the KAI model, i.e. Eq. value of t . Conversely, at 3 K, little changes were
0
(3), as displayed by the solid lines in Fig. 2(b). This observed in ∆p(t) when E was below 0.8 MV/cm. This
prediction was closely correlated with the ∆p(t) data. implied that the FE domain was pinned by defects and
We compared 1/t values with v values, which were could not move below a threshold value of E. However,
0
directly measured by PFM. As shown in Fig. 2(d), ∆p(t) starts to change abruptly around E = 1 MV/cm.
1/t is linearly proportional to v with a small offset, This corresponded to the pinning-depinning transition.
0
indicating that the switching current response could When E increased, t rapidly decreased. The ∆p(t)
0
provide reliable values of v. data for 3 and 300 K were similar at E = 1.1 MV/cm;
Figure 3 shows ∆p(t) data with varying values of E. t ∼ 5.4 × 10−6 and 3.3 × 10−6 s at 3 and 300 K,
0
The solid symbols and lines indicate the experimental respectively. These similar t values demonstrated that
0
data and the fitting results using Eq. (3), respectively. the T-dependence of v became insignificant under very
At 300 K, a sudden change in ∆p(t) with E = 0.1 high E region.
MV/cm occurred between 0.1 and 1.0 s: namely, at Figure 4(a) shows experimental 1/t vs. E curves.
0
t ∼ 2×10−1 s. As E increased, a sudden change in Note that these 1/t − E plots resemble those in Fig.
0 0
4
1(b). In the low E region, 1/t was strongly dependent that D ≈ 1.4 ± 0.4 for our PZT thin film. Recently,
0
on T, consistent with predictions for the thermally several studies have reported non-integer dimensionality
activated creep regime. However, in the high E region, of local and static domain walls in FE thin films [6, 16].
thevaluesof1/t startedtomerge,indicatingacrossover By measuring the local switching of PZT-BiFeO sol-gel
0 3
to the flow regime. The pinning-depinning transition at thin films with liquid PFM, Rodriguez et al. reported
3 K occurred at approximately 1 MV/cm, which was that D ≈ 1.5±0.1 [6]. By measuring morphology and
close to the E value obtained from P − E hysteresis scaling of the domains in epitaxial BiFeO thin films,
C 3
curve in Fig. 2(a). Catalan et al. reported that D ≈ 1.5 ± 0.1 [16]. Our
From the experimental 1/t data, we obtained measured values of θ from the dynamic responses is
0
the value of the dynamical exponent µ for the creep consistent with these D values from the static measure-
regime. From Eq.(2), log(t ) should be proportional ments. In addition, our findings indicate that the newly
0
to (U/k T)(E /E)µ. The log(t ) vs. 1/E curves are observed fractal dimensionality of FE domains should
B C0 0
shown in Fig. 4(b). The experimental data at a given be originated from local quenched defects.
T falls approximately into a linear line, indicating that We want to point out future studies and possible im-
µ is close to 1.0. Considering experimental errors, we plications of our works: (i) in order to fully understand
found µ=0.9±0.1. This µ value agreeswith previously the domain wall dynamics in epitaxial FE thin films,
reported values for epitaxial and polycrystalline PZT we need to measure other critical exponents, related
films [11, 12]. The inset shows the value of UE /k T to the divergence of the correlation length, the local
C0 B
calculated from lines of best fit for several values variance of the domain wall position, and so on [2]; (ii)
of T. The straight line indicates that the value of domain dynamic responses in systems with different
UE /k is nearly independent of T and is about 300 structural conditions such as polycrystalline FE thin
C0 B
K·MV/cm, close to previously reported value of around films and ultrathin films should be investigated and
400 K·MV/cm from local domain switching data using comparedwiththoseinepitaxialfilms;(iii)thecomplete
PFM at room T [11]. understanding on FE domain dynamics is necessary for
The value of µ reflects the nature of the pinning numerous practical applications, including optimizing
potential in our PZT films. Under a pinning potential operation speed of miniaturized FE devices.
with a short range (the so-called random bond), one- In summary, we investigated domain wall motions of
and two- dimensional domain walls should have the µ epitaxial PZT film over a wide range of temperature
values of 0.25 and 0.5, respectively [13]. However, under and applied electric field. We found that the motions
apinning potentialwithalongrange(the randomfield), were likely to be governed by the nonlinear dynamics of
µ = 1.0 regardless of dimensionality [13]. Recently, two surface growth in a disordered medium with quenched
conflicting µ values were reported for epitaxial PZT defects. We determined two critical exponents for
thin films; 1.0 and 0.5-0.6 [11, 14]. Our study confirms domain wall propagation dynamics, which indicate the
that µ = 0.9±0.1 over wide range of T. This µ value random field nature of the defects and fractal nature
suggests that the defects in our PZT thin film induce a of domain walls. Our works provide us a new future
long-rangedlocal field and pin FE domain walls [15]. direction of studies on the domain wall motions in
From our experimental 1/t data, we also obtained ferroelectric materials.
0
the value of the velocity exponent θ near the pinning- We acknowledge valuable discussions with B. Khang.
depinning transition. By Eq.(1), log(1/t ) should be This study was financially supported by the Creative
0
proportionalto θ·log(E−E ). As shown in Fig. 4(c), Research Initiatives (Functionally Integrated Oxide
C0
this is approximately the case when T =3 K. The slope Heterostructures) of the Ministry of Science and Tech-
of the line for best fit was θ ≈0.71±0.05. We could not nology (MOST), the Korean Science and Engineering
find any earlier studies with which compare this θ value Foundation (KOSEF), and the laboratory Directed
for FE thin films. Research and Development Program of Oak Ridge
The θ-value should reflectthe dimensionalityD of the National Laboratory (H.N.L). J.Y.J. acknowledges the
surface for an elastic object in a disordered medium, as financial support, in part, of Brain Korea 21.
θ = (5+D)/9 [13]. Using this relationship, we found
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5
[11] T. Tybell et al., Phys.Rev.Lett. 89, 097601 (2002). withoutdefects.However,basedonelectrostatic calcula-
[12] J.Y. Jo et al.,Phys.Rev. Lett.99, 267602 (2007). tions for domain wall motion in a periodic potential, it
[13] P.Chauve,T.Giamarchi, andP.LeDoussal, Phys.Rev. hasbeenreportedthatthecalculatedvaluesfortheacti-
B 62, 6241 (2000). vation field (i.e., UE0/kBT) and critical length of nuclei
[14] P.Paruch,T.Giamarchi,andJ.-M.Triscone,Phys.Rev. disagree with experimental values for thin films [11].
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[15] Electrostatic calculations resulting in a value of µ = 1
have also been obtained for a periodic lattice potential