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 fasci-

nating properties including high-TC superconductivity, colossal mag-

netoresistance, and nonlinear optical behavior . Most of these re-

markable properties originate from the interplay between spin, lat-

tice, charge, and orbital degrees of freedom of the material . These

competing factors typically result in the coexistence of near degener-

ate states and cause a spatial phase inhomogeneity or multiple do-

main structures at the micro- and nanometer scale . 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 measure-

ments on devices which are much larger than the intrinsic electronic

2

phase domains only provide an averaged response of the inhomoge-

neous ensembles to external parameters. Nanoscale materials, on the

other hand, can be smaller or comparable to the characteristic do-

main size of CEMs. When the electronic phases are spatially con-

fined, the conduction path can be better defined by precluding per-

colative behavior that occurs in thin film or bulk samples. It is there-

fore 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 in-

homogeneity and its role in many interesting properties of CEMs.

Despite decades of investigation, the question of whether the phase

separation is intrinsic or caused by external stimuli (extrinsic) still

remains open. For example, in colossal magnetoresistive manganites

that undergo a phase transition from ferromagnetic metal to antifer-

romagnetic insulator, these two phases typically coexist at length

scales ranging from nano- to micrometer, displaying a spatial phase

inhomogeneity. Existing theories explain the origin of phase inho-

mogeneity by either an intrinsic mechanism arising from inherent

properties of such correlated electron systems, or extrinsic mecha-

nisms based on effects of chemical disorder or local strain distribu-

tion. In the model of elastically mediated phase coexistence, the

structural aspect will be the primary reason that causes the multi-

3

phase coexistence. External stimuli such as strain can be used to sen-

sitively manipulate patterns of metallic and insulating regions. The

recent findings that anisotropic electronic domains of La5/8-

xPrxCa3/8MnO3 (x=0.3) (LPCMO) thin film can be induced by epitax-

ially 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 .

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 strain-

free, 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 co-

herent and continuously tunable external strain. CEM phase transi-

tions and domain dynamics can then be explored through in situ mi-

croscopic 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 de-

gree of freedom.

In addition to elucidating the origin of the phase inhomogene-

ity, the strain tuning could also be employed to modify the proper-

ties of CEMs. In contrast to conventional materials, where elastic

deformation causes minor variations in material properties, lattice

strain has profound influence on the electrical, optical, and magnetic

4

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 func-

tionalities and probing exotic properties of CEMs. However, bulk in-

organic materials can only sustain extremely low non-hydrostatic

strain (typically <0.1%) before plastic deformation or fracture oc-

curs. Recent advances in synthesis of CEM nanostructures offer new

opportunities of studying the strain effect on CEMs. As these materi-

als 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 transi-

tions at convenient temperatures. Research of nanostructured VO2

has led to new discoveries and helps resolve many outstanding ques-

tions 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 inho-

mogeneity in VO2; 2) domain organization and manipulation; 3)

driving mechanism of the phase transition; 4) superelasticity in VO2;

5) new phase stabilization under stress; 6) thermoelectric effects of

the domain walls. After discussing the application of VO2 nanostruc-

tures on above questions, 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.

5

1.2 Electrical and Structural Transitions in VO2

In strain-free state VO2 undergoes a first-order metal-insulator

phase transition (MIT) at = 341 K 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, mono-

clinic, insulating phase (M1). Upon cooling through the MIT, the

vanadium ions dimerized and these pairs tilt with respect to the R-

phase c axis ( ) . It is known that the transition can be are pro-

foundly 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 in-

duced by doping with Cr or uniaxial compression perpendicular to

. In M2 only half of the vanadium atoms dimerize while the other

half form zigzag chains, therefore it can be viewed as an intermedi-

ate 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

direction by 1%. Along the tetragonal and axes, on the

other hand, the lattice expands by 0.6 and 0.1%, respectively, caus-

ing a volume shrinkage of 0.3%. The transition from M1 to M2 ex-

pands it along direction by 0.3%. Note that the lattice con-

stant is temperature dependent and the exact lattice parameters of

6

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. A triclinic phase

(T) might also derive from the M1 structure, but only with a continu-

ous change in lattice constant and angles .

1.3 Experimental Methods

Single-crystalline VO2 beams (nanometer and micrometer size

beams) were synthesized using a vapor transport method. 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 mi-

croscopy, selected area electron diffraction, etc. These VO2 beams

grow along the tetragonal axis with {110} planes as the bounding

side faces. A percentage of VO2 beams were grown one-end an-

chored on the SiO2 substrate during the synthesis, and naturally

formed cantilevers for in situ optical and SEM bending experiments.

During the electrical measurement, devices were typically fab-

ricated on as-grown, bottom-clamped VO2 beams via sputtering de-

positing 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 com-

pressive stress to VO2 beams, single-crystal VO2 beams were trans-

7

ferred to a polycarbonate or Kapton substrate and bonded by silver

Epoxy. Addition uniaxial compressive stress was achieved by three-

point 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 em-

ployed to model the domain nucleation and stabilization. In both

cases, the total energy arises from thermodynamic bulk energy, in-

terfacial energy, and strain energy. The equilibrium domain struc-

tures 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

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. On the other hand, poly-

crystalline thin films often display a broadened transition associated

with phase inhomogeneity. 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 sepa-

8

rated in a percolative manner. As discussed below, the phase inho-

mogeneity 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 forma-

tion that are widely observed in bulk and thin films, thus providing

opportunities to investigate the intrinsic properties of VO2 at the sin-

gle domain level.

Fig. 1 (a) Four-probe resistance of single-crystal VO2 beams as a function of tem-perature. The free-standing VO2 beam shows single domain behavior, whereas the clamped beam shows multiple domains during the transition. (b) Optical images of the multiple-domain devices, showing the coexistence of metallic (dark) and in-sulating (bright) domains at intermediate temperatures . 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 VO2 beam coherently strained on a SiO2

substrate. Blue and red correspond to tensile and compressive strain, respectively. “M” denotes metallic phase

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 ei-

ther 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

9

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 = 341 K (single-domain device), accompa-

nied by an abrupt change in optical reflection, with dark reflection

corresponding to metallic phase and bright reflection to insulating

phase. Different behavior was observed for the stressed beams bot-

tom-clamped on the substrate surface. The electrical resistance of

the clamped VO2 beams decreases gradually over a wide phase tran-

sition 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. 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. The electronic phase separation in VO2 beams is remi-

niscent 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 suggest that

the lattice strain be responsible to the phase inhomogeneity observed

in polycrystalline VO2 films, and shed light on the origins of phase

10

inhomogeneity in other CEMs. The broadening of phase transition in

VO2 thin films is therefore a direct consequence of the phase inho-

mogeneity across the transition, which arises from the inevitable

non-uniform local stress of the films. The above simultaneous opti-

cal 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 high-resolu-

tion optical microscopy within the transition range (Fig. 1 (c)). The

multiple domain coexistence can be understood through analysis of

energy minimization. Such a domain pattern forms spontaneously as

a result of competition between strain energy in the elastically mis-

matched 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-in-

sulating domains and domain-wall energy minimization that opposes

them. The spatial periodicity can be described quantitatively using a

model originally developed for the strained ferroelectric systems.

The total energy in unit nanobeam-substrate interface area is given

by . Here is the spa-

tial period of the domain pattern, is the volume density of the elas-

tic misfit energy, is the domain-wall energy per unit domain-wall

11

area, is the nanobeam thickness, and and are the free en-

ergy densities of the metallic and insulating phases respectively. The

equilibrium domain period for different beams can therefore be de-

termined by numerical minimization of . Figure 1(d) displays

schematic diagram of the periodic domain patterns of a VO2

nanobeam strained on a SiO2 substrate.

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 ma-

nipulate the domains at small scales. A current-driven phase oscilla-

tion and domain-wall propagation have been observed in tungsten-

doped VO2 nanobeams. 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-

ing phases along the length. The non-clamped beams on the sub-

strate were bent by pushing part of the beam with a microprobe. A

large compressive strain will result near the inner edge of the high-

curvature 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. The bent beam was in insulating phase at room tem-

12

perature. With increasing temperatures, sub-micron, periodic trian-

gular metallic domains started to nucleate at the inner edge of the

bent region where the strain was the most compressive. These do-

mains continued to grow and expand with increasing temperature,

while the triangular geometry and periodic arrangement were main-

tained. At natural phase transition temperature T~ = 341 K, the

straight, strain-free part of the beam switched abruptly to the metal-

lic 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 to-

ward 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 model-

ing, as shown in Fig. 2(b). The total energy F() is equal to the sum

of bulk thermodynamic energy, interfacial (domain wall) energy,

and strain energy,

.

The parameter denotes the phase. f() describes the relative

thermodynamic energy of the two phases and is temperature depen-

dent. 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 is the lattice mismatch between the two phases. In the

initial state, the phase distribution is random. At natural transition

13

temperature = 341 K, the equilibrium phase distribution exhibits

a periodic, triangular domain pattern, agreeing well with experimen-

tal 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 en-

ergy minimization: smaller period results in more effective strain en-

ergy relief, but at the cost of introducing more interfacial area.

Fig. 2 Domain dynamics and manipulation with strain in VO2. (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 do-

main formation in a bent VO2 beam. From top to bottom: First, initial state of ran-

dom phase distribution; Second, equilibrium phase distribution at the natural MIT

transition ; Third, equilibrium strain ( ) distribution at : yellow and

dark green denote the maximum tensile and maximum compressive strain, respec-

tively; Forth, Equilibrium strain energy density distribution: yellow denotes the

highest strain energy density: dark green denotes the lowest. (c) Uniaxial com-

pression reversibly induces a metal-insulator transition at room temperature.

Here η is the fraction of metal phase along the beam. (d) Strain engineering do-

mains 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. Compressive stress was re-

14

versibly applied along the length of a VO2 beam clamped onto a

polycarbonate substrate and the fraction of metal phase η was moni-

tored 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 reach-

ing 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), an array of metallic-insulating triangular do-

mains 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

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 cur-

vature 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 abil-

ity 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

15

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 . In

the Mott transition picture, the insulating phase is a 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 experi-

mental evidences that support both mechanisms . 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 prop-

erties. To circumvent this issue, the electrical properties of VO2

beams were investigated along the phase boundary in the stress-tem-

16

perature 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 inhomoge-

neous strain in those systems.

Figure 3 (a) Schematic view of the path for a fixed length VO2 beam moving in

the uniaxial stress-temperature phase diagram. (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 . (c) Isobaric (A),

isothermal (B), and combined sequential processes (C) in the uniaxial stress-tem-

perature 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 uncer-

tainties in determining the effective height and length of the microbeam. Also

shown is the apparent threshold resistivity from a VO2 thin film. The horizontal

line shows the constancy of in I phase.

According to Gibbs’ phase rule, the number of degrees of free-

dom (F) in a pure component system is intimately linked with the

number of components (C) and the number of phases (P) through

equation . Here C=1 for single component sys-

tem. 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),

17

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/insu-

lator 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) .

More detailed experiments to test such a constant threshold re-

sistivity over a wider range of space including both tensile and com-

pressive states were also performed . As shown in Fig. 3(c), in ambi-

ent 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-di-

mensional temperature-stress phase space by independently varying

these two external parameters. Despite of the different transition

route, the threshold resistivity ( ) of the insulating phase right be-

fore 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 all fall onto a constant line.

Such a constant has deep implications to the physics of the

MIT. In a Mott picture, the transition occurs when the density de-

18

pendent 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 resis-

tivity . 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 inter-

actions. On the contrary, a phonon-driven mechanism (Peierls transi-

tion) 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. (a) Schematic

view of bending a VO2 nano-cantilever using an AFM tip. (b) Force-displacement

curves of a VO2 cantilever measured at various temperatures. The curves are ver-

tically offset for clarity. Arrows show the position of the first kink on 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 in-

creasing stress

Superelasticity (or pseudoelasticity) has been widely observed in shape

memory alloys, where an applied stress can cause a reversible phase transforma-

19

tion between the austenitic and martensitic phases of a crystal . 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 supere-

lasticity. This effect has been recently demonstrated in the first-order MIT of VO2 .

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 . The slope of this linear part can be used to determine

the Young’s modulus of VO2. 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 temperatures that are

closer to the natural transition temperature ( ). 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-tempera-

ture phase diagram in Fig.4(c). The metal-insulator 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, con-

sistent 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 mod-

eling was also used to simulate the f-w curve and obtained qualitatively similar re-

sults, as shown in Fig. 5 (e&f).

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 distri-

bution obtained by two-dimensional phase field simulation incorporating local

20

strain relaxation for a beam of length 7.5 μm and height 0.75 μm. The applied ter-

minal 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 conden-

sation-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 liq-

uid-vapor coexisting system . In this coexisting state the compress-

ibility of the system diverges, because the decrease in total volume

is accounted for by the conversion of more vapor into much denser

liquid, rather than to increase pressure as in the pure ideal gas. The

pressure-volume curve in this system is equivalent to the f-w 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 com-

pressive 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 do-

mains start to grow in response to the increasing uniaxial compres-

21

sion 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 mea-

sured 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 tem-

perature, similar scenario exists except that now new insulating do-

mains nucleate out of the metallic phase in the top portion of the

nanobeam as a result of the maximum tensile stress there .

1.4.5. New Phase Stabilization with Strain

The role of the structural transition from the monoclinic to ru-

tile phases during the MIT in VO2 has been well documented in lit-

erature. This monoclinic phase is typically referred as M1 phase. It

is known that strain can complicate the phase transition and induce

another monoclinic structure of VO2, the M2 phase . The structure of

M1 phase is characterized by a dimerization of vanadium atoms and

a tilt of these pairs with respect to the rutile 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 . 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. In fact, the free energy of

M2 in undoped VO2 is believed to be very close to that of M1

22

around , making it difficult to stabilize a pure M2 phase . 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 . Extensive measurements using infrared scattering-

scanning near-field optical microscopy, Raman spectroscopy, and

electrical transport have been performed to probe these phase transi-

tions . The complicated phase diagram covering all three phases

(M1, M2 and R) has been mapped out using VO2 beams taking ad-

vantage of their single crystallinity and superior elastic flexibility .

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 tempera-

tures. (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.

(c) AFM image of the clamped VO2 beam at 333 K, showing periodic surface cor-

rugation 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, single-crystal VO2

beams grow on molten SiO2 surface and could be clamped in differ-

ent 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 mi-

crobeams revealed new information, as shown in Fig. 6(a&b). The

23

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 direction at a period of ~150 nm. At room temperature

these stripes distribute over the entire length of the beam. With in-

creasing 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 am-

plitude of 0.7 nm, corresponding to a corrugation angle of ~ 0.6o.

XRD was employed to elucidate the crystal structure of the sub-mi-

cron sized domains along the VO2 microbeams. For free-standing

beams with no surface corrugation, Laue pattern of XRD shows

M1 structure at T < and R structure at T > as expected. For

the bottom-clamped beams that show striped phase, however, a split-

ting 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 ob-

served in, for example, polysynthetic twins in ferroelectric Rochelle

salts and twinning superlattices recently found in doped InP

nanowires.

24

The appearance of M2 phase during the transition was also

demonstrated by Raman spectroscopy. 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: M1M1+RM2+RR. While those crystals initially in

the M2 phase will transform to R phase directly without passing the

M1 phase as: M2M2+RR. By simultaneously performing trans-

port experiments and Raman spectroscopy on the same VO2 speci-

men, 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. By direct injection of charge into clamped

devices, a metallic monoclinic phase was also produced. This

demonstrates that electrical and structural phase transitions in VO2

can be decoupled, and a “true” Mott metal-insulator transition can be

revealed.

The complex stress-temperature phase diagram were determ-

ined through a combination of in situ optical microscope and SEM.

Enabled by the superior mechanical properties of single-crystal

beams, the uniaxial stress-temperature phase diagram of VO2 was

expanded more than an order of magnitude wider than that was pre-

viously achieved. Electrical resistance across the insulating M1 and

25

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 plat-

form to investigate the thermoelectric effect of Schottky junctions.

High-performance thermoelectric materials are currently one of the

focuses in materials research for energy conversion technologies . A

good thermoelectric material should have a relatively high ther-

mopower (Seebeck coefficient) . Interfacing different materials has

been proposed as a strategy to enhance 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 de-

termination of the small change in the Seebeck coefficient. Accom-

panied 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 ther-

moelectric 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.

26

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 ( ) of

the middle segment of the VO2 beam was measured as a function of

in a four-probe geometry. in the pure insulating phase

(namely, < 323 K) is and was fitted using the standard equation

for semiconductors, . This fitted was

extrapolated to higher temperatures, from which the fraction of the

insulating phase in the middle segment was calculated using

.

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 tempera-

ture. 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 VO2 beam measured as a func-

tion 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 was measured directly and agreed well with the

values in bulk VO2. In the phase coexisting regime, the Seebeck co-

27

efficient can be either measured directly from the devices or pre-

dicted 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 equa-

tion , where is extrapolated

from the pure insulating phase regime and is constant over

the temperature range. The measured and expected were

plotted in Fig.7 (c). It can be seen that in the multiple metal-insulator

domain regime, the measured 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.

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. Prob-

ing the transition and domain physics in vast phase spaces allows

one to reveal many fundamental mechanisms underlying the transi-

tion. Despite decades of investigations, there are still many unre-

solved questions in VO2 that are largely associated with the elec-

tronic phase separation and multiple domain structures near the

28

phase transition. The unique size and extremely flexible mechanical

properties of VO2 beams (nanometer or micrometer size beams) of-

fer a platform to investigate many fundamental properties of VO2. It

is demonstrated that lattice strain is responsible for the phase inho-

mogeneity 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 proper-

ties of VO2 beams can be used to probe the superelasticity of the

solid-state phase transition and expand the uniaxial stress-tempera-

ture 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 junc-

tions.

Research on nanostructured VO2 has revealed many interesting

new aspects that cannot be achieved in its bulk or thin film counter-

parts. The probing methods and techniques in VO2 beams can be ex-

tended to other CEMs upon the successful synthesis of desired

nanostructures. Systematic investigations, especially in situ experi-

ments, 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 fer-

roelectrics, and many other unique properties in CEMs. CEM nanos-

tructures can sustain an extraordinary amount of uniaxial strain as

well as be subjected to continuously tunable external stress, making

29

them suitable for a variety of in situ experiments. The methods dis-

cussed 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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