structural response (throughdI 30 2 anddI 31 3 ),
which is temporally correlated with the delayed
response inRVO2.Wedonotfindanyevidence
of theRphase in this incubation state to with-
in the experimental detection limits, which
suggests that the direct electric field–induced
transformation is small and that thermal ef-
fects are dominant ( 26 ) [see additional mea-
surements and electrothermal simulations in
( 25 ) and fig. S6]. To understand the dynamics
ofdI 220 , we first note that the (220) peak is
present in both equilibrium phases. Structure
factor calculations predict that the intensity of
the (220) peak in theRphase is higher than
that in theM1phase (fig. S4A). To investigate
whether this equilibrium transformation com-
pletely describes the observed positive changes
indI 220 , we performed static electron diffrac-
tion measurements while heating the sample
slowly (fig. S7). A broad transition beginning
at 340 K was observed, with a width of ~20 K.
In fig. S7B, we plot the temperature-dependent
ratios of the normalized intensity changes
dI 220 =jjdI 30 2 anddI 220 =jjdI 31 3. Evaluating these
at a temperature well above the transition
temperatureTc—where the entire sample must
transform to theRphase—enables us to quan-
tify the maximum relative change in (220) in-
tensity that can be caused by the equilibrium
M1→Rtransition. In Fig. 3G, we calculate
these relative normalized intensity changes
for the time-resolved E-IMT and compare them
with the equilibrium limits, which are indi-
cated by the dashed lines. Notably, at time
delays smaller than 100ms, we find that the
structural transformation under electrical ex-
citation cannot be described solely by the for-
mation of theRphase. At longer times, the
relative peak changes tend toward their equi-
librium values, which suggests the eventual
completion of theM1→RSPT. For additional
analysis, see figs. S8 to S10 and ( 25 ).
To gain further insight into the unusual
behavior of the (220) peak, we turn to the op-
tical pump experiments. As shown in Fig. 3H,
photoexcitation triggers the ultrafastM1→RSPT within ~0.5 to 0.7 ps, as indicated by a
quenching of the 30ðÞ 2 and 31ðÞ 3 peaks. In
marked contrast, the (220) peak intensity in-
creases on a much slower time scale of ~2.9 ps.
These observations of dissimilar time scales
for the evolution of different peaks are con-
sistent with previous optical pump–UED probe
experiments, which showed that the slower
response ofdI 220 is related to a purely elec-
tronic (i.e., isostructural) transition fromM1
into the metastablemMphase ( 7 , 8 , 25 ). In
particular, these experiments correlateddI 220
with changes in the terahertz conductivity and
to symmetry-preserving charge reorganiza-
tion, showing that the fluence-dependent
ratiodI 220 =jjdI 30 2 serves as an indicator of the
M1→mMtransition. This is consistent with the
analysis of our P-IMT data, where, in a man-
ner similar to E-IMT (Fig. 3G), we compute
the relative normalized intensity changes and
compare them with the thermally driven SPT
(Fig. 3H, inset). The changes are larger than
can be explained purely by theM1→Rtransi-
tion. Taken together, our photoexcitation
measurements provide clear evidence for the
creation of amMphase on picosecond time
scales. Returning to the analysis presented in
Fig. 3G, this interpretation of P-IMT dynamics
reveals an important discovery: Electrical exci-
tation creates, on microsecond time scales, a
transientmMphase in addition to the stable
Rphase. This causes the peak intensity ratios
dI 220 =jjdI 30 2 anddI 220 =jjdI 31 3 to exceed their
equilibrium values. As the voltage is main-
tained, themMdomains convert fully to the
thermodynamically stableRphase on a time
scale of ~100ms. This represents a direct ob-
servation of this transient isostructural state
during the electrically triggered IMT in VO 2.
Furthermore, this similarity between the path-
ways of E-IMT and P-IMT involving the inter-
veningmMphase is exemplified by the close
correspondence between their structural dy-
namics across eight orders of magnitude in
time scale (Fig. 2).
To gain insight into the phase coexistence
and conditions leading to the emergence of
themMphaseduringE-IMT,weperform
time-dependent phase-field simulations of a
VO 2 device under an electric field ( 27 , 28 )
[Fig. 4A and ( 25 )]. The state of the material
is characterized by the structural and elec-
tronic order parameters,h(r,t) andm(r,t),
respectively, whereris the spatial coordinate
andtis time. TheM1phase is characterized
byh=m=1andtheRphase byh=m=0.The
nucleation and growth of new domains is
described by the spatiotemporal evolution of
handm, free carrier density, and temper-
ature, driven by the free energy reduction that
includes contributions from the bulk chemical
energy, interfacial energy, and the free energy
density of electrons and holes. To capture
the intrinsic heterogeneity of the material,354 16 JULY 2021•VOL 373 ISSUE 6552 sciencemag.org SCIENCE
Time delay (ps)0.01 0.1 1 1000.51220-1× 302
-1× 313(^0610)
1
8
A
B
0
Time delay (ms)
123
0
1
2
3
0
1
2
3
0
1
2
3
0
Time delay (μs)
25 50 75 100
0
0.5
1
0
0.5
1
0
0.5
1
3
10
1
30
3
10
1
30
3
10
R
VO2
(kΩ)
R
VO2
(kΩ)
R
VO2
(kΩ)
1
30
C
D
E
F
(^0406080100)
0.3
0.6
0.9
1.2
Time delay (μs)
G
H
(i)(ii) (iii)
V V
4.8 V
5.6 V
5.0 V
7.4 V
4.0 V 4.4 V
220
-1× 302
-1× 313
220
-1× 302
-1× 313
0.7 ps
0.5 ps
2.9 ps
(normalized)
(%)
(%)
(%) (%)
(%)
(%)
220
/|
hkl
|
220 /| 302 |
220 /| 313 |
Electrical: M1 mM + R
Optical: M1 mM + R
Equilibrium limit: M1→R
Fig. 3. Phase transformation dynamics and evidence of a transient metallic monoclinic (mM) phase.
(AtoC) Normalized intensity changes in the 30 2
, 31 3
, and (220) peaks during and after electrical excitation
with a 500-ms voltage pulse of magnitude 4 V (A), 4.8 V (B), and 5.6 V (C) on device 1 (channel width = 40mm,
length = 20mm). (DtoF) Normalized intensity changes in the 30 2
, 31 3
, and (220) peaks on short time
scales after the application of a step voltage att=0,withmagnitude4.4V(D),5V(E),and7.4V(F)ondevice
2 (channel width = length = 20mm). The transient device resistanceRVO2is measured simultaneously (purple). In
(A) to (F), the curves for 30 2
and 31 3
are inverted. (G) Ratio of normalized intensity changes of the (220)
and 30 2
peaks (green triangles) and of the (220) and 31 3
peaks (red squares) corresponding to the data shown
in (F). Green and red dashed lines indicate the equilibrium limits for theM1→RSPT. (H) Normalized intensity change
after photoexcitation with an ~100-fs optical pulse at a fluence of ~27 mJ cm−^2. Solid lines are single exponential
fits, and the shaded areas represent 95% confidence intervals. The curves for 30 2
and 31 3
are inverted.
The inset shows the ratio of normalized intensity changesdI 220 =dI 30 2
(^) anddI 220 =dI 31 3
(^) compared with the
equilibrium limits indicated by the dashed lines. Data in (G) and in the inset of (H) have been smoothed by three-
point adjacent averaging for better visualization. All the data were taken at a stage temperature of 300 K.
RESEARCH | REPORTS