New Opportunities on Phase Transitions of
Correlated Electron Nanostructures
Jinbo Cao† and Junqiao Wu†
†
Department of Materials Science and Engineering, University of California, Berkeley
and Materials Sciences Division, Lawrence Berkeley National Laboratory Berkeley, CA
94720
1.1 Introduction
Correlated Electron Materials (CEMs) exhibit rich and fascinating properties including high-TC superconductivity, colossal
magnetoresistance, and nonlinear optical behavior [4, 5]. Most of
these remarkable properties originate from the interplay between
spin, lattice, charge, and orbital degrees of freedom of the material
[4, 7]. These competing factors typically result in the coexistence of
near degenerate states and cause a spatial phase inhomogeneity or
multiple domain structures at the micro- and nanometer scale [9].
Although the spatial electronic phase separation is believed to be associated with many exotic properties of CEMs, investigation of the
fundamental properties of these materials has been hampered due to
the multiple domain structures [3-5]. For example, transport and optical measurements on devices which are much larger than the in-
2
trinsic electronic phase domains only provide an averaged response
of the inhomogeneous ensembles to external parameters. Nanoscale
materials, on the other hand, can be smaller or comparable to the
characteristic domain size of CEMs. When the electronic phases are
spatially confined, the conduction path can be better defined by precluding percolative behavior that occurs in thin film or bulk samples.
It is therefore possible to probe the properties of different electronic
phases and investigate the fundamental physical properties of CEMs
in nanoscale specimens.
The fact that multiple-phases coexistence has been observed in
many different CEMs such as manganites and cupurates near a
phase transition raises questions related to the origin of the phase inhomogeneity and its role in many interesting properties of
CEMs[10-14]. Despite decades of investigation, the question of
whether the phase separation is intrinsic or caused by external stimuli (extrinsic) still remains open[11, 15-18]. For example, in colossal
magnetoresistive manganites that undergo a phase transition from
ferromagnetic metal to antiferromagnetic insulator, these two phases
typically coexist at length scales ranging from nano- to micrometer,
displaying a spatial phase inhomogeneity[11, 12, 19]. Existing theories explain the origin of phase inhomogeneity by either an intrinsic
mechanism arising from inherent properties of such correlated electron systems[15, 16], or extrinsic mechanisms based on effects of
chemical disorder or local strain distribution[17]. In the model of
elastically mediated phase coexistence, the structural aspect will be
3
the primary reason that causes the multiphase coexistence. External
stimuli such as strain can be used to sensitively manipulate patterns
of metallic and insulating regions[17]. The recent findings that anisotropic
electronic
domains
of
La5/8-xPrxCa3/8MnO3
(x=0.3)
(LPCMO) thin film can be induced by epitaxially locking it to an orthorhombic NdGaO3 substrate suggest that the origin of phase coexistence can be strongly influenced by elastic energy rather than local
chemical inhomogeneities [20].
Continuously tuning of lattice strain in CEM nanostructures,
on the other hand, would be more desirable to uncover the origin of
the phase inhomogeneity. If phase inhomogeneity is absent in strainfree, single-crystal specimens, but can be introduced and modulated
by external strain, it would be concluded that strain is responsible
for the phase inhomogeneity in CEMs. Compared to thin films,
CEM nanostructures are dislocation-free, and can be subjected to
coherent and continuously tunable external strain. CEM phase transitions and domain dynamics can then be explored through in situ
microscopic experiments varying strain and temperature independently. Such an approach would enable, for the first time, probe
of CEMs at the single domain level under continuous tuning of their
lattice degree of freedom.
In addition to elucidating the origin of the phase inhomogeneity, the strain tuning could also be employed to modify the properties of CEMs. In contrast to conventional materials, where elastic
deformation causes minor variations in material properties, lattice
4
strain has profound influence on the electrical, optical, and magnetic
properties of CEMs through coupling between the charge, spin, and
orbital degrees of freedom of electrons. Control and engineering of
strain have become an important strategy for achieving novel functionalities and probing exotic properties of CEMs. However, bulk
inorganic materials can only sustain extremely low non-hydrostatic
strain (typically <0.1%) before plastic deformation or fracture occurs. Recent advances in synthesis of CEM nanostructures offer new
opportunities of studying the strain effect on CEMs. As these materials are typically single crystals and dislocation-free, they can sustain an extraordinary amount of uniaxial strain without fracturing
and the strain is also continuously tunable by varying the external
stress.
This chapter focuses on recent reports of vanadium dioxide
(VO2), a representative CEM that displays interesting phase transitions at convenient temperatures. Research of nanostructured VO2
has led to new discoveries and helps resolve many outstanding questions that cannot be addressed in bulk or thin film specimens. With
the contribution of nanoscale or micrometer scale VO2 samples, we
specifically focused on the following topics: 1) origin of phase inhomogeneity in VO2[3, 21, 22]; 2) domain organization and manipulation[3, 8, 23]; 3) driving mechanism of the phase transition[6, 2427]; 4) superelasticity in VO2[2]; 5) new phase stabilization under
stress[28-30]; 6) thermoelectric effects of the domain walls[31]. After discussing the application of VO2 nanostructures on above ques-
5
tions, we conclude with a short discussion of how these novel probing techniques and methods could be extended to other CEMs and
resolve the complicated questions there.
1.2 Electrical and Structural Transitions in VO2
In strain-free state VO2 undergoes a first-order metal-insulator
phase transition (MIT) at TC0 = 341 K[32-34] with a change in conductivity by several orders of magnitude. The MIT is accompanied
by the structural phase transition from the high-temperature, tetragonal, metallic phase (rutile structure, R) to the low-temperature, monoclinic, insulating phase (M1). Upon cooling through the MIT, the
vanadium ions dimerized and these pairs tilt with respect to the Rphase c axis ( c R ) [32-34]. It is known that the transition can be are
profoundly affected by uniaxial strain as well as doping. In addition
to the aforementioned low temperature monoclinic structure M1
phase, another insulating monoclinic structure M2 phase can also be
induced by doping with Cr or uniaxial compression perpendicular to
c R [32, 33, 35]. In M2 only half of the vanadium atoms dimerize
while the other half form zigzag chains[32, 33], therefore it can be
viewed as an intermediate structure between M1 and R.
The vanadium dimerization leads to unit cell doubling in the
monoclinic M1 and M2 structures. During the MIT, the structural
transition from M1 to R effectively shrinks the specimen along c R
6
direction by  0 1%[32]. Along the tetragonal aR and bR axes, on
the other hand, the lattice expands by 0.6 and 0.1%, respectively,
causing a volume shrinkage of 0.3%[32]. The transition from M1 to
M2 expands it along c R direction by  0 0.3%[33]. Note that the lattice constant is temperature dependent and the exact lattice parameters of these three phases at the same temperature do not exist in literatures. The above numbers are approximated from the
discontinuous change from the phase diagram of Cr-doped VO2[32,
33].
A triclinic phase (T) might also derive from the M1 structure, but
only with a continuous change in lattice constant and angles [32,
33].
1.3 Experimental Methods
Single-crystalline VO2 beams (nanometer and micrometer size
beams) were synthesized using a vapor transport method[36]. The
size distribution, lattice structure and crystal orientation of these
beams were characterized by different techniques such as X-ray diffraction, scanning electron microscopy (SEM), transmission electron
microscopy, selected area electron diffraction, etc. These VO2 beams
grow along the tetragonal c R axis with {110} planes as the bounding
side faces. A percentage of VO2 beams were grown one-end anchored on the SiO2 substrate during the synthesis, and naturally
formed cantilevers for in situ optical and SEM bending experiments.
7
During the electrical measurement, devices were typically fabricated on as-grown, bottom-clamped VO2 beams via sputtering depositing adhesion layer (~20 nm Ti or V) and a Au layer (~400 nm)
onto the photolithography defined patterns. The uncovered part of
SiO2 was later etched using buffered oxide etchant to liberate the
VO2 beam into an end-end-clamping configuration. To apply compressive stress to VO2 beams, single-crystal VO2 beams were transferred to a polycarbonate or Kapton substrate and bonded by silver
Epoxy. Addition uniaxial compressive stress was achieved by threepoint concave bending bendable substrate along the length direction.
Laue diffraction was performed at the XRD end-station
(Beamline 12.3.2) in the Advanced Light Source (ALS) at Lawrence
Berkeley National Laboratory.
Both analytical model and phase field simulations were employed to model the domain nucleation and stabilization. In both
cases, the total energy arises from thermodynamic bulk energy, interfacial energy, and strain energy. The equilibrium domain structures were determined by numerical minimization of the total energy
under different conditions.
1.4 Results and Discussions
1.4.1. Phase Inhomogeneity and Domain Organization
Until the advent of VO2 single-crystal beams, measurements
on crystal bulk and polycrystalline thin films have suffered many
8
problems near the MIT. Due to the changes of the lattice parameters
associated with the transition, bulk crystals tend to crack across the
MIT and degrade upon repeated cycling[37]. On the other hand,
polycrystalline thin films often display a broadened transition associated with phase inhomogeneity[21, 38, 39]. Scanning near-field infrared microscopy was recently employed to image the metallic and
insulating phases in VO2 thin films and found that these electronic
phases are separated in a percolative manner[21]. As discussed below, the phase inhomogeneity might originate from the inevitable
non-uniform local stress in thin films and therefore prevents detailed
investigations of VO2 within the stress and temperature space. Single-crystal VO2 nanometer and micrometer size beams will avoid
the crackling of the specimens and eliminate the phase separation
and domain formation that are widely observed in bulk and thin
films, thus providing opportunities to investigate the intrinsic properties of VO2 at the single domain level.
Fig. 1 (a) Four-probe resistance of single-crystal VO2 beams as a function of temperature. The free-standing VO2 beam shows single domain behavior, whereas the
clamped beam shows multiple domains during the transition[3]. (b) Optical images of the multiple-domain devices, showing the coexistence of metallic (dark) and
insulating (bright) domains at intermediate temperatures [3]. The scale bar is 5
μm. (c) Optical image of clamped VO2 at 338 K showing periodic metallic and insulating domains. The width of the VO2 beam is around 1.5 μm. (d) Schematic diagram showing the periodic domain pattern of a VO 2 beam coherently strained on
a SiO2 substrate[8]. Blue and red correspond to tensile and compressive strain,
respectively. “M” denotes metallic phase
9
Depending on whether a stress is imposed on the sample or not,
VO2 beams show rather distinct optical and electronic properties. By
adjusting the synthesis conditions, VO2 beams can be grown with either a weakly coupled beam-substrate interface where the stress can
be easily released, or a strongly coupled, clamped interface that pins
the beam to the substrate. In the latter case thermal stress is imposed
on the beams after cooling from the growth temperature to room
temperature. Both types of beams were incorporated into four- probe
devices using lithography for transport measurement. As shown in
Fig. 1(a), devices made from un-strained sample display a sharp
drop of resistance at TC0 = 341 K (single-domain device), accompanied by an abrupt change in optical reflection, with dark reflection
corresponding to metallic phase and bright reflection to insulating
phase[3]. Different behavior was observed for the stressed beams
bottom-clamped on the substrate surface. The electrical resistance of
the clamped VO2 beams decreases gradually over a wide phase transition temperature range, showing an effective second-order phase
transition. High-magnification optical imaging of the clamped
beams in Fig. 1(b) revealed multiple metallic and insulating domains
appearing during the transition, where dark domains nucleated in the
bright phase and grew with increasing temperature, finally merging
into a single metallic phase[3]. The broadening of transition therefore is a direct consequence of the nucleation and growing/shrinking
of metallic/insulating domains as a function of temperature in
stressed VO2 beams[3]. The electronic phase separation in VO2
10
beams is reminiscent of the phase inhomogeneity observed in other
CEM thin films, although the domain patterns in VO2 beams are
more regular due to the lateral confinement and more coherent strain
imposed on them. That the multiple phase coexistence can be observed in stressed VO2 beam but not in free-standing specimens[3]
suggest that the lattice strain be responsible to the phase inhomogeneity observed in polycrystalline VO2 films[21], and shed light on
the origins of phase inhomogeneity in other CEMs[17]. The broadening of phase transition in VO2 thin films is therefore a direct consequence of the phase inhomogeneity across the transition, which
arises from the inevitable non-uniform local stress of the films. The
above simultaneous optical and electronic experiments also established a direct correlation between optical contrast and the electronic
phases in VO2 beams, where bright and dark reflection indicates the
insulating and metallic phase, respectively.
A fully coherently strained VO2 beam bottom clamped on the
substrate exhibits periodic metal-insulator domains in highresolution optical microscopy within the transition range (Fig. 1 (c)).
The multiple domain coexistence can be understood through analysis of energy minimization[8]. Such a domain pattern forms spontaneously as a result of competition between strain energy in the elastically mismatched VO2/substrate system and domain wall energy in
the VO2. The period of the pattern is determined by the balance between the strain-energy minimization that favors small, alternating
metallic-insulating domains and domain-wall energy minimization
that opposes them[8]. The spatial periodicity can be described quan-
11
titatively using a model originally developed for the strained ferroelectric systems[40]. The total energy in unit nanobeam-substrate interface
E ( ) 
area
is
given
by
[8,
40]
  1  e2(2 j 1) t /   t ( f M  f I )t
. Here  is the spatial

 
 3 j 0 (2 j  1)3

2
period of the domain pattern,  is the volume density of the elastic
misfit energy,  is the domain-wall energy per unit domain-wall area, t is the nanobeam thickness, and f M and f I are the free energy
densities of the metallic and insulating phases respectively. The
equilibrium domain period for different beams can therefore be determined by numerical minimization of E ( ) . Figure 1(d) displays
schematic diagram of the periodic domain patterns of a VO2 nanobeam strained on a SiO2 substrate[8].
1.4.2. Domain Dynamics and Manipulation
The dynamics of domains in response to external stimuli are
also attractive as they provide an effective route to control and manipulate the domains at small scales. A current-driven phase oscillation and domain-wall propagation have been observed in tungstendoped VO2 nanobeams[23]. The domain oscillation occurs through
the axial drift of a single metallic-insulating domain wall driven by a
combined effect of Joule heating and Peltier cooling.
Through actively bending single VO2 beams, it has been
shown that strain can produce ordered arrays of metallic and insulat-
12
ing phases along the length[3]. The non-clamped beams on the substrate were bent by pushing part of the beam with a microprobe. A
large compressive strain will result near the inner edge of the highcurvature regions of the bent beam and a tensile strain will occur
near the outer edge. Figure 2(a) shows the development of an array
of triangular domains along a bent VO2 beam imaged at different
temperatures[3]. The bent beam was in insulating phase at room
temperature. With increasing temperatures, sub-micron, periodic triangular metallic domains started to nucleate at the inner edge of the
bent region where the strain was the most compressive. These domains continued to grow and expand with increasing temperature,
while the triangular geometry and periodic arrangement were maintained. At natural phase transition temperature T~ TC0 = 341 K, the
straight, strain-free part of the beam switched abruptly to the metallic phase as expected, while the bent part of the beam showed a
nearly 50-50% coexistence of metallic and insulating phases. As
temperature was further increased, the metallic phase expanded toward the outer edge and finally completely eliminated the insulating
phase.
The domain nucleation and organization in a bent beam can be
successfully captured through two-dimensional phase-field modeling, as shown in Fig. 2(b)[3]. The total energy F() is equal to the
sum of bulk thermodynamic energy, interfacial (domain wall) energy, and strain energy,
13


2
1
2
F ( )    f   
  Cijkl  ij   ijT  kl   klT  dA .
2
2





The parameter  denotes the phase. f() describes the relative
thermodynamic energy of the two phases and is temperature dependent. The second term reflects the interfacial energy. The last
term is the elastic energy where C is the elastic modulus tensor,  is
the strain, and  T is the lattice mismatch between the two phases. In
the initial state, the phase distribution is random. At natural transition temperature TC0 = 341 K, the equilibrium phase distribution exhibits a periodic, triangular domain pattern, agreeing well with experimental observations. This pattern nearly completely relieves the
strain energy in the bent beam, with some remnant strain at the triangular tips (Fig. 2(b)). The period varies for different interfacial
energy density and elastic constants. Specifically, the period is determined by competing effects of strain energy relaxation and interfacial energy minimization: smaller period results in more effective
strain energy relief, but at the cost of introducing more interfacial
area.
Fig. 2 Domain dynamics and manipulation with strain in VO 2[3]. (a) Optical images of an array of triangular metallic domains nucleated and co-stabilized by
tensile and compressive strain along a bent microbeam. (b) Phase-field modeling
of domain formation in a bent VO2 beam. From top to bottom: First, initial state
of random phase distribution; Second, equilibrium phase distribution at the natural MIT transition
TC0 ; Third, equilibrium strain (  xx ) distribution at TC0 : yel-
14
low and dark green denote the maximum tensile and maximum compressive strain,
respectively; Forth, Equilibrium strain energy density distribution: yellow denotes the highest strain energy density: dark green denotes the lowest. (c) Uniaxial compression reversibly induces a metal-insulator transition at room temperature. Here η is the fraction of metal phase along the beam. (d) Strain engineering
domains in a flexible VO2 microbeam. Scale bars in (a), (c), and (d), 10 μm
Strain was also used to lower the temperature of the transition
from its bulk value of 341 K to room temperature, which paves the
way for future potential applications[3]. Compressive stress was reversibly applied along the length of a VO2 beam clamped onto a
polycarbonate substrate and the fraction of metal phase η was monitored as a function of applied stress. As shown in Fig. 2(c), VO2
beam remained entirely insulating (η=0) until stressed to a total
strain of approximately -1.9%, then entered a strain regime where
periodic metallic and insulating domains coexisted, ultimately reaching a full metallic state (η=1) at total strain of approximately -2.1%.
As the resistance of the VO2 beam changes by several orders of
magnitude across the MIT, this strain-controlled, room-temperature
phase transition can be used as a “srain-Mott” transistor.Enabled by
the sensitivity of the electronic phases to local strains, external stress
was used to manipulate and engineer these functional domains. As
displayed in Fig. 2(d)[3], an array of metallic-insulating triangular
domains are created and eliminated by simply modulating the local
strain state of a bent VO2 beam. Initially the beam was strain-free,
and therefore in pure insulating phase at room temperature and pure
15
metallic state at 343 K. When the beam was locally bent at 343 K,
an array of triangular insulating domains was created in the high
curvature region in response to the local tensile strain. These domains were highly mobile and could be driven to different location
along the beam by slight modifications of the bending geometry.
The ability to engineer phase inhomogeneity and phase transition
with strain in VO2 opens opportunities for designing and controlling
functional domains for device and sensor applications. As distinctly
different physical and chemical properties are associated with the
metallic and insulating phases, interfacing strain-engineered VO2
with other molecular, nano- or polymeric materials may provide new
assembly strategies to achieve collective and externally tunable
properties. Similar approaches can be applied in other CEMs and
may lead to new revolutions of strain engineering solid state materials to achieve collective functionalities.
1.4.3. Investigation of Phase Transition at the Single Domain Level
By investigating the electrical and optical properties of VO2 at
the single domain level, it is possible to discover new aspects of its
phase transition in unprecedented detail. For example, it has been a
topic of debate for decades that whether the MIT is fundamentally
driven by electron-electron correlation, therefore is a Mott transition,
or by electron-lattice interaction, therefore a Peierls transition [21,
24-26, 41-43]. In the Mott transition picture, the insulating phase is a
16
Mott insulator where the bandgap opens because of Coulomb blockade between strongly localized d electrons at the vanadium sites. In
the Peierls transition picture, the bandgap exists because of lattice
potential modulation by the vanadium dimerization. There are many
experimental evidences that support both mechanisms [21, 24-26,
41-43]. The controversy is largely due to the poorly understood
near-threshold behavior in thin films or bulk crystals, where phase
separation and domain formation prevent direct measurements of intrinsic electronic and optical properties. To circumvent this issue, the
electrical properties of VO2 beams were investigated along the phase
boundary in the stress-temperature phase space at the single domain
level. Such an electrical measurement precisely along the phase
boundary is not possible in thin films or bulk because of percolative
conduction and inhomogeneous strain in those systems.
Figure 3 (a) Schematic view of the path for a fixed length VO 2 beam moving in
the uniaxial stress-temperature phase diagram[1]. (b) Resistivity of the insulating
phase of VO2 as a function of temperature. A constant resistivity (at 60-100 oC) is
observed when the system moves along the phase boundary [6]. (c) Isobaric (A),
isothermal (B), and combined sequential processes (C) in the uniaxial stresstemperature phase diagram of VO2 showing phase transition from the insulating
(I) phase to metallic (M) phase. Green dots show schematically the position
where the transition threshold is defined. (d) Measured resistivity of VO2 beams at
300 K, at the threshold, and in M-phase, respectively. The error is mostly from
uncertainties in determining the effective height and length of the microbeam. Also
shown is the apparent threshold resistivity from a VO 2 thin film. The horizontal
line shows the constancy of
 th in I phase.
17
According to Gibbs’ phase rule, the number of degrees of
freedom (F) in a pure component system is intimately linked with
the number of components (C) and the number of phases (P) through
equation F  C  P  2  3  P .
Here C=1 for single component
system. Under a single phase (P=1) condition, two variables (F=2)
such as temperature and stress can be controlled to any selected pair
of values. However, if the system enters the two phase region (P=2),
the temperature and stress cannot be varied independently any more.
When VO2 beam is clamped onto a substrate at its two ends with
fixed length, the system will be forced to move along the metal/insulator phase boundary in the stress-temperature phase space, as
shown in Fig. 3 (a). A constant resistivity of the insulating phase
was observed when the system moves along the phase boundary Fig.
3 (b) [1, 6].
More detailed experiments to test such a constant threshold resistivity over a wider range of space including both tensile and compressive states were also performed [27]. As shown in Fig. 3(c), in
ambient conditions VO2 is in insulating state. The metallic state can
be reached either following the route A at constant stress (akin to the
isobaric process for a liquid-vapor transition), or following the route
B at constant temperature (isothermal process). Moreover, routes A
and B can be combined to form sequential processes following the
routes C. The devices allow investigation of the MIT in the two-
18
dimensional temperature-stress phase space by independently varying these two external parameters. Despite of the different transition
route, the threshold resistivity (  th ) of the insulating phase right before the system switches to metallic phase stays constant over a wide
range. As shown in Fig. 3(d), the systems have different transition
temperature and room-temperature resistivity under different strain
states. However, the values of  th all fall onto a constant line.
Such a constant  th has deep implications to the physics of the
MIT. In a Mott picture, the transition occurs when the density dependent screening reaches a critical strength. As suggested by Mott
theory, the density is the maximum semiconducting carriers coming
from the insulating side, which is proportional to the threshold resistivity  th . The observation that a constant critical free carrier density
has to be reached to trigger the insulator to metal transition indicates
that the transition is fundamentally driven by electron-electron interactions. On the contrary, a phonon-driven mechanism (Peierls transition) would not be expected to be sensitive to the carrier density in
the insulator.
1.4.4. Superelasticity in Phase Transition
Fig. 4 Superelastic metal-insulator phase transition in VO2 beams[2]. (a) Schematic view of bending a VO2 nano-cantilever using an AFM tip. (b) Forcedisplacement curves of a VO2 cantilever measured at various temperatures. The
curves are vertically offset for clarity. Arrows show the position of the first kink on
19
each curve. (c) Calculated stress at the root of the VO2 beam at the measured first
kink of the force-displacement curves plotted in the stress-temperature phase
space. Solid squares and empty triangles represent the stress in the loading and
unloading process, respectively. The dashed line is the phase boundary calculated
from the Clapeyron equation using a latent heat of 1020 Cal/mol. (d) Optical images of side-bending a wide VO2 beam, showing the nucleation of new domains
with increasing stress
Superelasticity (or pseudoelasticity) has been widely observed in shape
memory alloys, where an applied stress can cause a reversible phase transformation between the austenitic and martensitic phases of a crystal [44]. The superelasticity originates from the reversible creation and motion of domain boundaries
during the phase transformation rather than from bond stretching or the introduction of defects in the crystal lattice. CEMs are typically brittle and can only be
stretched or compressed for an extremely small percentage. In CEMs with phase
transitions, control of the domain wall motion may provide an effective way to realize superelasticity. This effect has been recently demonstrated in the first-order
MIT of VO2 [2]. An AFM tip was used to bend a VO2 nano-cantilever and the
force-displacement (f-w) curves was recorded, as shown in Fig. 4(a&b). At small
deflections, the f-w curve is linear as expected [2]. The slope of this linear part can
be used to determine the Young’s modulus of VO 2. At large deflections (but still
within the reversible, elastic regime), VO2 beam shows superelasticity, as evidenced by the appearance of kinks and nonlinearity. These kinks are reproducible
upon repeated bending of the VO2 nanobeams and occur at lower displacements at
0
temperatures that are closer to the natural transition temperature ( TC ). At the
same degree of deflection, no such kinks were observed when bending nanobeams
with similar size but made of materials without phase transition, such as ZnTe
nanowires. The critical stress from the first kink on the f-w curve is calculated and
plotted on the stress-temperature phase diagram in Fig.4(c). The metal-insulator
20
phase boundary is calculated from the Clapeyron equation using a latent heat of
the MIT of 1020 Cal/mol. The measured critical stress points are distributed along
the phase boundary line, consistent with the Clapeyron equation. Figure 4(d)
shows optical images of side-bending a wider VO2 beam, which suggests that the
nonlinearity and kinks in the f-w curve is related to the creation and motion of new
domains. Phase-field modeling was also used to simulate the f-w curve and obtained qualitatively similar results, as shown in Fig. 5 (e&f)[2].
Fig. 5 (a) Simulated force-displacement curves for a beam demonstrating the
slope change that occurs at the onset of new domain formation. (b) Domain distribution obtained by two-dimensional phase field simulation incorporating local
strain relaxation for a beam of length 7.5 μm and height 0.75 μm. The applied
terminal load force is 20 μN, for temperature below and above the natural transition temperature, respectively. (c) Residual strain energy distributions corresponding to the parameters in part (b) illustrating how new domains relieve strain
energy
The superelastic behavior observed during the MIT in VO2
provides a new route to investigate the solid-solid phase transitions
in general. The dynamics of force-displacement curve during the
transition can be easily understood by comparing it with the condensation-evaporation process between a liquid and its vapor. When the
vapor is compressed isothermally below the critical temperature, the
pressure first increases following the ideal gas law, then reaches a
plateau where liquid droplets nucleate out of the vapor forming a
liquid-vapor coexisting system [45]. In this coexisting state the
compressibility of the system diverges, because the decrease in total
volume is accounted for by the conversion of more vapor into much
21
denser liquid, rather than to increase pressure as in the pure ideal
gas. The pressure-volume curve in this system is equivalent to the fw curve in VO2 nanobeam. At temperatures lower than the natural
transition temperature, the bottom edge at the root of the nanobeam
will be compressively stressed with increasing bending. At a critical
compressive stress, new metallic domains start to nucleate out of the
original insulating phase, and the bottom portion of the nanobeam
root enters a metal-insulator phase coexisting state. As the nanobeam is further bent beyond the critical stress, the metallic domains
start to grow in response to the increasing uniaxial compression and
a vanishing Young’s modulus is expected from the metal-insulator
coexisting part (bottom portion) of the nanobeam. The top portion of
the nanobeam is under tension and therefore remains in the original
insulating phase. The overall Young’s modulus measured is the effective Young’s modulus of the “composite” beam and therefore a
lower but non-zero slope of the f-w curves is observed in this region.
At temperatures higher than the natural transition temperature, similar scenario exists except that now new insulating domains nucleate
out of the metallic phase in the top portion of the nanobeam as a result of the maximum tensile stress there [2].
1.4.5. New Phase Stabilization with Strain
The role of the structural transition from the monoclinic to rutile phases during the MIT in VO2 has been well documented in literature. This monoclinic phase is typically referred as M1 phase. It
22
is known that strain can complicate the phase transition and induce
another monoclinic structure of VO2, the M2 phase [35]. The structure of M1 phase is characterized by a dimerization of vanadium atoms and a tilt of these pairs with respect to the rutile c R axis. In M2
structure, however, only half of the vanadium atoms dimerize while
the other half form zigzag chains. M2 structure has been widely observed in Cr-doped samples [32, 33, 46]. However, due to the difficulty in accessing the undoped M2 phase, it has not been established
how conductive it is and what role it plays in the MIT of VO2[32]. In
fact, the free energy of M2 in undoped VO2 is believed to be very
close to that of M1 around TC0 , making it difficult to stabilize a pure
M2 phase [35]. Recent experiments show more evidence that under
certain strain state M2 can act as a transitional structure for the
phase transition from M1 to the R phase [22, 28-30, 47]. Extensive
measurements using infrared scattering-scanning near-field optical
microscopy, Raman spectroscopy, and electrical transport have been
performed to probe these phase transitions [22, 28, 30]. The complicated phase diagram covering all three phases (M1, M2 and R) has
been mapped out using VO2 beams taking advantage of their single
crystallinity and superior elastic flexibility [30].
Fig. 6 (a) Top-viewed high-resolution SEM image of a free-standing VO2 beam at
298 K showing featureless surface. No change was observed at elevated temperatures. (b) SEM images of a bottom-clamped VO2 beam at 298, 323, 333 and 368 K
(left to right), showing diminishing of the striped phase at elevated temperatures.
23
(c) AFM image of the clamped VO2 beam at 333 K, showing periodic surface corrugation of the striped phase. (d) Typical room-temperature XRD pattern of a
bottom-clamed VO2 beam indexed as a twinned monoclinic M2 phase (M2 /M2).
The brightest spots come from the Si substrate, while the remaining ones showing
splitting are from the VO2 beam. The scale bar is 1µm in (a&b).
During the vapor-transport synthesis[36], single-crystal VO2
beams grow on molten SiO2 surface and could be clamped in different strain states varying from beam to beam, depending on local
conditions during the cooling process. High-resolution scanning
electron microscopy (SEM) imaging of these two types of microbeams revealed new information, as shown in Fig. 6(a&b). The
free-standing beams always have smooth, featureless surface that
does not change as temperature increases. The bottom clamped
beams, however, often show periodic stripes well aligned in parallel
to the cR direction at a period of ~150 nm. At room temperature
these stripes distribute over the entire length of the beam. With increasing temperature, new domains with featureless surface start to
nucleate out of the striped phase and eventually eliminate the stripes
at high temperatures. Atomic force microscopy (AFM) shows that a
weak surface corrugation is responsible for the striped contrast in the
SEM images. Figure 6(c) shows the morphology of the beam surface
obtained at 333 K using AFM. The surface corrugation has an amplitude of 0.7 nm, corresponding to a corrugation angle of ~ 0.6 o.
XRD was employed to elucidate the crystal structure of the submicron sized domains along the VO2 microbeams. For free-standing
24
beams with no surface corrugation, Laue pattern of XRD shows
M1 structure at T < TC0 and R structure at T > TC0 as expected. For
the bottom-clamped beams that show striped phase, however, a splitting of the XRD spots was observed in the Laue pattern, as shown
in Fig. 6(d). The VO2 spots were indexed to the M2 structure with
two polysynthetic twins identified and labeled as M2α and M2β as
shown in Fig.2 6(d). This configuration resembles the structures observed in, for example, polysynthetic twins in ferroelectric Rochelle
salts [48, 49] and twinning superlattices recently found in doped InP
nanowires[50].
The appearance of M2 phase during the transition was also
demonstrated by Raman spectroscopy[22, 28]. The three structural
phases (M1, M2 and R) of VO2 can be differentiated by Raman
spectra through the distinct phonon modes at 608 cm-1 (M1 only),
645 cm-1 (M2 only), or featureless spectrum (metallic, R). With increasing temperature, it is found that VO2 beam initially in M1
phase will convert to M2 phase before the final conversion to full
metallic phase as: M1M1+RM2+RR. While those crystals initially in the M2 phase will transform to R phase directly without
passing the M1 phase as: M2M2+RR[22]. By simultaneously
performing transport experiments and Raman spectroscopy on the
same VO2 specimen, it is possible to deduce the electrical properties
of different phases and associate the structural domain formations
with the MIT. The activation energy is reported to be 0.09 eV for
M1 phase and 0.43 eV for M2 phase[28]. By direct injection of
25
charge into clamped devices, a metallic monoclinic phase was also
produced[28]. This demonstrates that electrical and structural phase
transitions in VO2 can be decoupled, and a “true” Mott metalinsulator transition can be revealed.
The complex stress-temperature phase diagram were determined through a combination of in situ optical microscope and
SEM[30]. Enabled by the superior mechanical properties of singlecrystal beams, the uniaxial stress-temperature phase diagram of VO2
was expanded more than an order of magnitude wider than that was
previously achieved. Electrical resistance across the insulating M1
and M2 and metallic R phases was measured over the extensive
phase diagram, and the M2 phase was found to be more resistive
than the M1 phase by a factor of three. The approach can be applied
to other strongly correlated electron materials to explore remote
phase space and reveal and engineer new properties.
1.4.6. Thermoelectric Across the Metal-Insulator Domain Walls
The metal-insulator domain walls in VO2 beams offer a platform to investigate the thermoelectric effect of Schottky
junctions[31]. High-performance thermoelectric materials are currently one of the focuses in materials research for energy conversion
technologies [51-54]. A good thermoelectric material should have a
relatively high thermopower (Seebeck coefficient) [51, 55]. Interfacing different materials has been proposed as a strategy to enhance
26
the Seebeck effect from that of the constituent materials alone. Effect of single or a few Schottky junctions on the Seebeck coefficient
has not been experimentally tested, mainly due to the lack of materials suitable for accurate determination of the small change in the
Seebeck coefficient. Accompanied with formation of the multiple
metal-insulator domains in VO2 microbeams, one or a few Schottky
junctions can be reversibly created and eliminated in the plane perpendicular to the current and heat flow direction. This offers a material platform where the thermoelectric effect can be measured from
the same specimen with or without the Schottky junction, so that an
accurate extraction of the net junction effect becomes possible[31].
As schematically shown in Fig. 7(a), the VO2 beam is in pure
insulating phase at low temperatures (< 323 K), and pure metallic
phase at high temperatures (> 373 K). At intermediate temperatures
(323 ~ 373 K), both phases coexist. The total resistance ( Rtotal ) of the
middle segment of the VO2 beam was measured as a function of T
in a four-probe geometry. Rtotal in the pure insulating phase (namely,
T < 323 K) is RI and was fitted using the standard equation for sem-
iconductors, RI T   RI0  exp  Ea kBT  . This fitted RI T  was extrapolated to higher temperatures, from which the fraction of the insulating
phase
in
the
x T   Rtotal T  RI T  .
middle
segment
was
calculated
using
27
Figure 7 (a) Schematics of multiple M-I domains forming along the device at
intermediate temperatures, showing the creation and elimination of one or a few
Schottky junctions on the same specimen. (b) Four-probe resistance of a VO2
beam taken right after the Seebeck voltage measurement at each global temperature. Solid line is a fit of the resistance in pure I phase with standard equation and
extrapolated to 393 K. (c) Seebeck coefficient of a VO 2 beam measured as a function of temperature. Solid blue line is the Seebeck coefficient expected from the
measured resistance in (b).
In the pure insulating or metallic phase regimes, the Seebeck
coefficient S T  was measured directly and agreed well with the
values in bulk VO2[31, 56]. In the phase coexisting regime, the Seebeck coefficient can be either measured directly from the devices or
predicted by a linear combination of contributions from the insulating and metallic domains. If one neglects the contribution from the
metal-insulator domain walls, the total Seebeck voltage is expected
to be a sum of contributions from both domains following the equation Stotal T   x T   S I T   1  x T    S M , where SI T  is extrapolated
from the pure insulating phase regime and SM T  is constant over
the temperature range. The measured and expected Stotal T  were
plotted in Fig.7 (c). It can be seen that in the multiple metal-insulator
domain regime, the measured Stotal T  is significantly lower than the
expected value, differing by up to a factor of 2. The exact reason is
still under investigation but is believed to be related to the correlated
electron nature of the system[31].
28
1.5 Conclusions
In this chapter, we have presented a comprehensive review of
recent reports on VO2 nanostructures. VO2 is a prototypical CEM
that exhibits coupled electrical and structural phase transitions. Probing the transition and domain physics in vast phase spaces allows
one to reveal many fundamental mechanisms underlying the transition. Despite decades of investigations, there are still many unresolved questions in VO2 that are largely associated with the electronic phase separation and multiple domain structures near the phase
transition. The unique size and extremely flexible mechanical properties of VO2 beams (nanometer or micrometer size beams) offer a
platform to investigate many fundamental properties of VO2. It is
demonstrated that lattice strain is responsible for the phase inhomogeneity in VO2 and can be employed to control and manipulate metal-insulator domains. The fundamental driving mechanism of the
phase transition in VO2 is more electron-electron correlations related
than electron-phonon interactions. The superior mechanical properties of VO2 beams can be used to probe the superelasticity of the solid-state phase transition and expand the uniaxial stress-temperature
phase diagram. Stress was employed to stabilize M2 phases of VO2
that is otherwise thermodynamically inaccessible. In the end, we
demonstrate that the unique ordered domain patterns in VO2 can be
used to investigate the thermoelectric properties of Schottky junctions.
29
Research on nanostructured VO2 has revealed many interesting new aspects that cannot be achieved in its bulk or thin film counterparts. The probing methods and techniques in VO2 beams can be
extended to other CEMs upon the successful synthesis of desired
nanostructures. Systematic investigations, especially in situ experiments, are key components to resolve many complicated questions
such as the origin of phase inhomogeneity in manganites, flux quanta in high-TC superconductors, domain wall conductivity in ferroelectrics, and many other unique properties in CEMs. CEM
nanostructures can sustain an extraordinary amount of uniaxial strain
as well as be subjected to continuously tunable external stress, making them suitable for a variety of in situ experiments. The methods
discussed in this chapter offer new insights and opportunities to the
study of materials system in condensed matter physics community.
Acknowledgements
We greatly acknowledge the financial support of National Science
Foundation under Grant No. EEC-0425914.
30
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