arXiv:0707.2799v1 [cond-mat.supr-con] 18 Jul 2007
High resolution X-ray scattering studies of structural phase transitions in underdoped
Y. Zhao,1B. D. Gaulin,1,2J. P. Castellan,1J. P. C. Ruff,1S. R. Dunsiger,1G. D. Gu,3and H. A. Dabkowska1
1Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1, Canada.
2Canadian Institute for Advanced Research, 180 Dundas St. W., Toronto, Ontario, M5G 1Z8, Canada
3Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA
(Dated: February 1, 2008)
We have studied structural phase transitions in high quality underdoped La2−xBaxCuO4 single
crystals using high resolution x-ray scattering techniques. Critical properties associated with the
continuous High Temperature Tetragonal (HTT, I4/mmm) to Middle Temperature Orthorhombic
(MTO, Cmca) phase transition were investigated in single crystal samples with x=0.125, 0.095, and
0.08 and we find that all behavior is consistent with three dimensional XY criticality, as expected
from theory. Power law behavior in the orthorhombic strain, 2(a-b)/(a+b), is observed over a
remarkably wide temperature range, spanning most of the MTO regime in the phase diagram. Low
temperature measurements investigating the Low Temperature Tetragonal (LTT, P42/ncm) phase,
below the strongly discontinuous MTO→LTT phase transition, in x=0.125 and x=0.095 samples
show that the LTT phase is characterized by relatively broad Bragg scattering, compared with
that observed at related wavevectors in the HTT phase. This shows that the LTT phase is either
an admixture of tetragonal and orthorhombic phases, or that it is orthorhombic with very small
orthorhombic strain, consistent with the “less orthorhombic” low temperature structure previously
reported in mixed La2−xSrx−yBayCuO4 single crystals. We compare the complex temperature-
composition phase diagram for the location of structural and superconducting phase transitions
in underdoped La2−xBaxCuO4 and find good agreement with results obtained on polycrystalline
PACS numbers: 61.10.Nz, 64.70.Kb
The complex interplay between spin, charge, and lat-
tice degrees of freedom in the quasi-two dimensional
copper-oxide high temperature superconductors have
been the subject of intense interest since the discov-
ery of superconductivity in the La2−xBaxCuO4 sys-
tem some 21 years ago1.
La2−xSrxCuO4display a fascinating series of structural,
magnetic and superconducting phase transitions as a
function of temperature2. While La2−xBaxCuO4was the
first layered cuprate high Tc superconductor to be dis-
covered, difficulties associated with the growth of high
quality single crystals have significantly limited its study.
As a result the La2−xBaxCuO4family is much less stud-
ied than the La2−xSrxCuO4family and other high tem-
perature superconductors which have an extended his-
tory of being grown and characterized in single crystal
form2, such as the YBa2Cu3O7−δ and Bi2Sr2CaCu2O8
Recently, significant progress has been made in grow-
ing the La2−xBaxCuO4family of materials in single crys-
tal form, and this has enabled several important new
studies of this and related systems7,8,9,10. It is there-
fore timely to perform high resolution structural studies
of these new single crystals, and to compare to previous
studies on La2−xBaxCuO4in polycrystalline form11,12.
One of the many interesting properties of the
La2−xBaxCuO4 family is the sequence of structural
phase transitions which this material displays on cool-
Both La2−xBaxCuO4 and
ing below room temperature for underdoped Ba con-
∼0.18).Previous studies on poly-
crystalline La2−xBaxCuO4 shows three different struc-
tures, which proceed from High Temperature Tetragonal
(HTT, I4/mmm), to Middle Temperature Orthorhombic
(MTO, Cmca) and finally to Low Temperature Tetrago-
nal (LTT, P42/ncm)11,12,13,14,15. The HTT→MTO and
the MTO→LTT phase transition temperatures are re-
ferred to as Td1and Td2, respectively. The HTT→MTO
transition is continuous, while the MTO→LTT transition
is known to be strongly discontinuous. These structures
are closely related to the magnetic and electronic prop-
erties of the La2−xBaxCuO4 and La2−xSrxCuO4 fam-
ilies.The phase diagram of the La2−xBaxCuO4 sys-
tem contains a dome of LTT phase, which is centred
around x=0.125. This Ba-concentration corresponds to a
steep depression of the superconducting TCas a function
of concentration, known as the 1/8 anomaly14,16. The
La2−xSrxCuO4system shows a much smaller ∼ 10% dip
in TC at x=0.125 and the absence of the LTT phase at
low temperatures17,18. The 1/8 anomaly within the LTT
phase also corresponds to strong incommensurate mag-
netic long range order at temperatures just below the
completion of the MTO-LTT phase transition7,9. Clearly,
the structural, magnetic, and superconducting properties
of the La2−xBaxCuO4 and La2−xSrxCuO4 systems are
The critical phenomena associated with the HTT-
MTO transition has been previously studied in pure
La2CuO4 as well as in La2−xSrxCuO4 in single crystal
FIG. 1: (a), High resolution longitudinal scans of the (3, 3,
0)HTT Bragg peak in single crystal La2−xBaxCuO4, x=0.125
are shown as a function of temperature. (b) Representative
longitudinal scans at T=290 K, 120 K, and 20 K from which
the color contour map in (a) was made.
and polycrystal form19,20,21,22,23,24, as single crystals of
these materials have existed for some time. These studies
show the HTT→MTO phase transition to be character-
ized with an order parameter critical exponent β vary-
ing from 0.28 to 0.3719,20,21,22,23,24. Studies on polycrys-
talline samples of La2−xBaxCuO4 by Susuki et al pro-
duced estimates for β ∼ 0.3311,12, and which are consis-
tent with expectations for 3D universality25.
In this paper, we report the successful growth of large
La2−xBaxCuO4 single crystals with x=0.095 and 0.08,
and a high resolution x-ray diffraction study on the
x=0.125, 0.095 and 0.08 compounds in this family. This
study focusses on a comparison between the structural
and superconducting phase diagrams in polycrystalline
and single crystal materials, critical phenomena associ-
ated with the HTT→MTO phase transition, and the na-
ture of the LTT phase in x=0.125 and 0.095 samples at
II. EXPERIMENT DETAILS
We studied three high quality La2−xBaxCuO4 single
crystals with x=0.125, 0.095 and 0.08. All crystals were
grown by using traveling solvent, floating zone image fur-
nace techniques. The x=0.125 sample was grown sepa-
rately, and the details of this growth have been previously
The x=0.095 and 0.08 La2−xBaxCuO4 single crystal
growths followed similar processess, and employed poly-
crystalline La2O3, BaCO3and CuO as starting materi-
als to make the initial, polycrystalline feed rod and sol-
vent.For the production of the feed rods, the start-
FIG. 2: (a), High resolution longitudinal scans of the (3, 3,
0)HTT Bragg peak in single crystal La2−xBaxCuO4, x=0.095
are shown as a function of temperature. (b) Representative
longitudinal scans at T=290 K, 120 K, and 20 K from which
the color contour map in (a) was made.
ing materials were mixed to give an initial ratio of
La:Ba:Cu=1.875:0.125:1. These materials were mixed,
ground, and annealed at 980◦C for 12 hours in air. This
process was repeated twice in order to ensure homoge-
neous feed rods. To compensate for Cu evaporation dur-
ing the crystal growth, the pre-annealed feed rods were
mixed with extra CuO. A further 1% and 2% mol CuO
was added to the starting polycrystalline materials and
thoroughly mixed to prepare the two final feed rods, re-
spectively. The final feed rods were heated to a tempera-
ture of 1190◦C, at a rate of 100◦C/hour. They were held
at this temperature for 12 hours. We also employed a sol-
vent, formed from the original polycrystalline feed rod,
with CuO added so as to reach a final ratio of constituent
atoms (La1.875Ba0.125):Cu=3:7. After mixing and sinter-
ing, small disks weighing ∼ 0.44 g were cut out and used
as solvents in the subsequent single crystal growths.
The single crystal growths were carried out using a
four-mirror image furnace (Crystal System Inc.). A small
pure La2CuO4 single crystal was employed as the seed
rod for both growths. The growths were carried out in
an O2atmosphere at pressures of 165 kPa and 182 kPa
for the two crystal growths. The growth rate was 1mm/h
with a counter-rotation speed of 25 rpm for feed and seed
rods for both growths.
Upon completion of the growths, the as-grown single
crystals were kept above 100◦C in a furnace to prevent
hydrolysis of the material, which is known to be problem-
atic for single crystal La2−xBaxCuO4. The two crystals,
which are identified in this study as being at x=0.095 and
0.08, were of almost identical dimensions of 80 mm long
by 5 mm in diameter as-grown. Within the first week
following completion of the growths, the initial ∼ 30 mm
of the crystals turned to dust as a result of hydrolysis of
the second phase. The undamaged part of both crystals
was stable. They had approximate dimensions of 50 mm
long by 5 mm in diameter for x=0.095 and 55 mm long
by 5 mm in diameter for x=0.08. These volumes are suf-
ficiently large for advanced characterization by neutron
scattering techniques, and indeed a program of neutron
measurements has been carried out on these samples26.
We note that while the two crystal growths were initi-
ated with similar starting materials, and the growths fol-
lowed similar procedures, the Ba/La ratio, as identified
by Td1and Td2, were different at the ∼ 15% level. This
originates from Cu evaporation during the growth. All
the phase transitions observed (structural, magnetic, and
superconducting) are nevertheless very sharp in temper-
ature, indicating excellent homogeneity of concentration
within the individual single crystals.
Single crystal samples with approximate dimensions 8
mm×8 mm×1 mm for x=0.125, and 5 mm×5 mm×1 mm
for x=0.095 and 0.08, were cut from large single crystals
of La2−xBaxCuO4. These were sequentially attached to
the cold finger of a closed cycle refrigerator and mounted
within a four circle x-ray diffractometer. Cu Kα1radia-
tion from an 18kW rotating anode x-ray generator was
selected using a perfect Germanium (111) single crystal
monochrometer. A Bruker Hi-Star multi-wire area de-
tector was placed on the detector arm, 76 cm from the
sample allowing an angular resolution of approximately
0.01 degrees to be achieved. All measurements focused on
(3, 3, 0)HTT Bragg peak of the samples, using notation
appropriate to the high temperature tetragonal phase.
As we were interested in critical phenomena, the sample
was mounted in a Be can and in the presence of a helium
exchange gas and the sample temperature was stabilized
to ∼ 0.005 K for all measurements.
III. EXPERIMENTAL RESULTS
A. Identification and Nature of Phases
Two dimensional maps of the scattering around the (3,
3, 0)HTTBragg peaks of all three x=0.125, 0.095 and 0.08
La2−xBaxCuO4 samples were acquired as a function of
temperature. Each data set consisted of a sample angle
rock through the Bragg peak which was integrated in the
vertical direction and plotted as a function of scattering
angle, 2θ. A longitudinal cut through this two dimen-
sional data set was performed, giving rise to the longi-
tudinal scans shown in Fig. 1b for the x=0.125 sample,
and Fig. 2b for the x=0.095 sample. Similar data sets
taken over a more restricted temperature regime for the
x=0.08 sample are of similar quality, but are not shown.
These data sets can be put together to display the
full temperature dependence of the longitudinal scans,
and this is what is shown in Figs. 1a and 2a for the
x=0.125, Td1=232.3 K
x=0.095, Td1=271.7 K
x=0.08, Td1=305.4 K
0 50 100 150 200 250
=232.3 K (*2.4)
x=0.125, Td1=232.3 K (*2.4)
x=0.095, Td1=271.7 K
x=0.08, Td1=305.4 K
FIG. 3: (a) The orthorhombic strain vs. temperature is plot-
ted for La2−xBaxCuO4 x=0.125, 0.095 and 0.08 single crystal
samples. The open and filled symbols represent warming and
cooling cycles, respectively. The orthorhombic strain is ob-
tained by fitting longitudinal scans, shown in Figs. 1 and 2.
(b) The same orthorhombic strain vs. temperature as in (a)
but now plotted vs T/Td1 and the strain has been scaled (for
the x=0.125 sample, by a factor of 2.4) to emphasize universal
behavior for T/Td1 greater than 0.8.
x=0.125 and x=0.095 samples, respectively. These data
sets clearly show the bifurcation of a single Bragg peak
into two, and then back into one, as the temperature is
decreased from room temperature to 20 K, signifying the
sequence of phase transitions HTT→MTO→LTT. The
fact that two Bragg features can be seen in a single longi-
tudinal scan within the MTO phase is indicative of twin-
ning within the orthorhombic phase, although the two
twin domains which are observed do not possess equal
volume fraction within the crystal; one Bragg feature is
considerably stronger in intensity than the other. A mi-
nority and majority twin domain is clearly present, but
the relevant volume fraction can change from one ther-
mal cycle to the next. For example, the x=0.095 data
set shown in Fig. 2(a) shows data from two independent
thermal cycles, one ending with a lowest temperature of
∼ 200 K, while the next beginning a new thermal cycle
at 200 K. In the first of these, the high angle Bragg peak
x=0.125, Td1=232.3 K
x=0.095, Td1=271.7 K
x=0.08, Td1=305.4 K
-0.04-0.02 0 0.02
-0.1 -0.08 -0.06
temperature, (T-Td1/Td1) for the x=0.125, 0.095, and 0.08
La2−xBaxCuO4 samples at small values of reduced tempera-
ture, near Td1. The open and filled symbols show data from
warming and cooling cycles, respectively. Fits of the data to
the form of the order parameter squared vs reduced tempera-
ture, Eq. 1, used to extract values of β are shown as the solid
The orthorhombic strain is plotted vs reduced
is the majority domain, while in the second cycle, the
lower angle Bragg peak is the majority domain.
The fact that we observe both twin domains in the
MTO phase means that the peak positions, the lattice
parameters, and consequently the orthorhombic strain,
2(a-b)/(a+b), can be determined as a function of tem-
perature. This is shown for all three samples in Fig. 3a.
The single (3, 3, 0)HTT Bragg peak breaks into (6, 0,
0)MTO and (0, 6, 0)MTO near Td1=232 K, 272 K and
305 K in the x=0.125, 0.095, and 0.08 samples, respec-
tively, before reforming into a single (3, 3, 0)LTT Bragg
peak near Td2=60 K, 45 K, and 35 K, respectively.
Examination of Figs 1-3 shows two qualitative features
of the evolving structures. Note that for ease of compari-
son, the 2θ range of the scattering in Figs. 1 and 2 is the
same. First, the orthorhomic strain decreases quite sub-
stantially with increasing Ba concentration. The lowest
temperature strain, for example, in the x=0.125 sample
is roughly half that of the x=0.095 sample. Secondly
and more importantly, the longitudinal profile of the (3,
3, 0)LTT peak at the lowest temperatures measured, well
within the LTT phase, is considerably broader than the
corresponding profile of (3, 3, 0)HTT. This is true for
both the x=0.125 sample and the x=0.095 sample as
can be seen by comparing the top and bottom panels
of Fig.1b (for x=0.125) and Fig.
This shows that the LTT phase is either an admixture
of a tetragonal and an orthorhombic phase, as was sug-
gested by electron microscopy on an earlier generation of
La2−xBaxCuO4crystals27, or that it is itself othorhom-
bic with a very small orthorhombic strain. In either case
it is not as “tetragonal” as the HTT phase, and is consis-
tent with the “less orthorhombic” low temperature struc-
2b (for x=0.095).
tures proposed previously for La2−xSrx−yBayCuO4 sin-
B. Critical Phenomena at the HTT→MTO Phase
Longitudinal scans of the form shown in Fig. 1b and
2b were fit for the purpose of extracting the peak posi-
tions in 2θ and therefore the d spacings associated with
the MTO phase.This is straightforward for data far
removed from the HTT→MTO phase transition, as the
two peaks are well defined and separated, as can be seen
in the middle panels of Fig. 1b and 2b. Closer to the
phase transition, one peak may appear as a shoulder to
the other, and it is more difficult to ascribe unique val-
ues to the two lattice parameters. We fit these data in
two different ways in order to attain robust values for
the lattice parameters close to the transition. One of
these was to simply fit the longitudinal scans to sums of
Lorentzians or Lorentzians raised to an adjustable expo-
nent, while a second technique was to look for zeros in
the derivatives of the intensity as a function of 2θ. These
gave consistent results for the lattice parameters, giving
us confidence that the orthorhombic strain could be es-
timated accurately close to the transition. However, this
technique also gives non-zero values for the orthorhom-
bic strain, albeit relatively small ones, within the HTT
Previous work on the HTT→MTO phase transition in
polycrystalline La2−xSrxCuO4and La2−xBaxCuO4sam-
ples show the orthorhombic strain to scale as the square
of the order parameter11,12,19,21. Consequently we ex-
amined the critical behaviour of the orthorhombic strain
in our La2−xBaxCuO4single crystals by fitting the mea-
sured strain as a function of temperature to:
∆ = ∆0× (Td1− T
)2β+ Background (1)
where the square of the order parameter, ∆, is the or-
thorhombic strain, 2(a-b)/(a+b), and the background
accounts for finite strain within the HTT phase intro-
duced by the fitting process described above. The results
of this fitting is shown in Fig. 4, which shows the or-
thorhombic strain as a function of reduced temperature,
(T-Td1)/Td1, in the region of small reduced temperature
close to Td1. Clearly this description of the data is very
good. It results in accurate estimates for both β and
Td1. These are Td1=232.3 ± 0.7 K, 271.7 ± 1 K, and
305.4 K ± 1 K for the x=0.125, 0.095, and 0.08 samples,
respectively. The extracted values for β are 0.35 ± 0.03,
0.34 ± 0.04 and 0.28 ± 0.06, respectively.
Using these values of Td1for each of the three samples,
we can scale the plot of orthorhombic strain vs temper-
ature, Fig. 3a, so as to give scaled orthorhombic strain
vs T/Td1, which is shown in Fig. 3b. We see that above
T/Td1∼ 0.8 the orthorhombic strains for all three sam-
ples collapse to a single curve. We therefore expect uni-
234 234 235 236 237
231 231 232 233
274 274 275 276 277
308 309 310
270 271 272 273
304 305 306 307
FIG. 5: The dependence of critical exponent β and goodness-
of-fit parameter χ2are shown as a function of the assumed
value of Td1 for x=0.125 (upper panel), x=0.095 (middle
panel) and x=0.08 (lower panel) La2−xBaxCuO4 single crys-
tal samples. The uncertainty in β is largely determined by
the uncertainty in critical temperature Td1.
versal behaviour in this regime, which is borne out by the
similarity in the extracted values for the critical exponent
β at all three Ba concentrations.
The uncertainties associated with the critical exponent
β are largely determined by the uncertainties in the criti-
cal temperature, Td1, derived from the fits to the critical
behaviour. We performed fits to Eq. 1 using Td1set to
a range of values around the approximate phase transi-
tion temperature, and then allowed the fit to adjust the
other parameters in Eq. 1. This gives a monotonically
increasing estimate for β as a function of increasing Td1.
Best estimates for β and Td1are given by the minimum
in the goodness-of-fit parameter χ2which we define as:
FIG. 6: The orthorhombic strain is plotted as a function of
reduced temperature, (Td1-T)/Td1, on a log-log scale for the
x=0.125, 0.095 and 0.08 single crystal La2−xBaxCuO4 sam-
ples. The open and filled symbols show results from warming
and cooling cycles, respectively. For comparison power law
behavior showing β=0.35, indicative of the theoretically ex-
pected 3D XY universality class, is indicated as the straight
line on this log-log plot.
where N is the number of data points.
β and χ2are shown as a function of Td1for the x=0.125
(top panel), x=0.095 (middle panel), and x=0.08 (bot-
tom panel) samples in Fig.
is determined by the corresponding uncertainty in Td1,
and it is roughly 10% for the x=0.125 and 0.095 samples
where we have an extended data set throughout the MTO
phase, and roughly 20% for the x=0.08 sample where the
data set is restricted to temperatures close to Td1.
pated 3D XY universality on the basis of a Landau
expansion appropriate to this ferroelastic system. These
early results on polycrystalline systems were consistent
with the β=0.35 expected from 3D XY universality29,30.
However, these earlier estimates for β spanned the range
from 0.28 to 0.37, ignoring uncertainties associated with
the estimates, which covers all standard 3D universality
classes: Heisenberg (∼0.37), XY (∼0.35), Ising (∼0.32)
and which begins to approach values consistent with
tricritical phenomena (0.25)25.
Figure 6 shows the orthorhombic strain, 2(a-b)/(a+b),
plotted as a function of the reduced temperature, (Td1-
T)/Td1, on a log-log plot in order to identify the expected
power law regime. For comparison a straight line appro-
priate to β=0.35 and 3D XY universality is also plotted.
For each sample, two data sets are plotted, one for a
warming run and one for a cooling run. We observe very
similar power law behaviour in all three samples, and
behaviour which is very much consistent with 3D XY
universality as anticipated theoretically. We also see, at
least for the x=0.125 and 0.095 samples for which we have
data over the entire MTO phase regime in temperature,
5. The uncertainty in β
TABLE I: Summary of structural and superconducting phase
transition temperatures in single crystal La2−xBaxCuO4
0.35 ± 0.03
0.34 ± 0.04
0.28 ± 0.06
aFrom Ref. 7.
bFrom Ref. 26.
that a single power law is a remarkably good descriptor
of the data over a very large temperature regime. There
appears to be a slight increase in slope for reduced tem-
peratures greater than ∼ 0.2, but overall, power law-like
growth of the orthorhombic strain is observed over almost
two decades in reduced temperature. This is in contrast
to most critical phenomena, wherein asymptotic critical
behaviour is expected to cross over to a mean field-like
regime, as one moves away from the critical temperature.
Taken together our orthorhombic strain measurements
show critical behaviour at the HTT→MTO phase transi-
tion in single crystal La2−xBaxCuO4over a broad range
of concentration which is characterized by β=0.34 ±
0.04. This result clearly demonstrates 3D universality,
and is consistent with 3D XY universality which is ex-
pected based on Landau theory. It is also largely con-
sistent with previous experimental work on single crys-
tal and polycrystal La2−xSrxCuO4 and polycrystalline
La2−xBaxCuO4, much of which centred on measurements
of superlattice Bragg peak intensities within the MTO
structure, as opposed to measurements of the orthorhom-
bic strains22,24. Superlattice Bragg peak intensities near
continuous phase transitions can be difficult to interpret,
as they can be influenced by extinction and by fluctua-
tions above the phase transition. This latter effect mani-
fests itself in upwards curvature and difficulty identifying
a precise phase transition temperature, which in turn can
lead to uncertainty in critical exponents.
C. Phase Diagram and Comparison to
It is of interest to compare the La2−xBaxCuO4phase
diagram known to characterize pre-existing polycrys-
talline samples with that determined for the high qual-
ity single crystals in the present studies. A rather de-
tailed comparison can be carried out, as two structural
and one superconducting transition temperature charac-
terize La2−xBaxCuO4 samples in this underdoped con-
centration range. The phase transitions measured for
the single crystals in this study are summarized in Table
1. The critical exponent β relevant to the HTT→MTO
structural transition is also shown in the same table for
The superconducting transition temperatures were de-
0.15 0.15 0.2 0.25 0.3
0 0.05 0.1
FIG. 7: Phase boundaries identifying structural and super-
conducting phases of La2−xBaxCuO4 single crystals are plot-
ted on the phase diagram derived from previously studied
polycrystalline samples.The structural transitions at Td1
and Td2 are indicated by filled squares, while superconduct-
ing TC’s are indicated by open circles. The first order tran-
sition at Td2 is indicated by a bar ∼ 10 K wide, showing the
onset to completion of the phase transition. Solid lines show-
ing phase boundaries from polycrystalline La2−xBaxCuO4are
taken from Adachi et al.15
termined from SQUID magnetometry as reported by
Dunsiger et al.26for the x=0.095 and x=0.08 samples,
and by Fujita et al.7for the x=0.125 sample.
strongly first order MTO→LTT transition is measured
both by the abrupt change in the orthorhombic strain
seen in Fig. 1 and 2, for the x=0.125 and x=0.095 sam-
ples, respectively, as well as by the appearance of the (0,
1, 0) superlattice Bragg peak intensity as again reported
by Dunsiger et al.26for the x=0.095 and x=0.08 samples,
and by Fujita et al. for the x=0.125 sample7.
Figure 7 shows the La2−xBaxCuO4 phase diagram
with HTT, MTO, and LTT phases indicated.
HTT→MTO and MTO→LTT transitions are shown as
filled squares for the three Ba concentrations measured.
The discontinuous transition at Td2is indicated as a bar,
in order to show the onset to completion of the transition,
which is ∼ 10 K wide. Td2 in Table 1 is the midpoint
of the transition. The superconducting transitions are
given by the open circles, and they indicate the onset of
the superconductivity, which is also what is listed in Ta-
ble 1. Previous results for these same phase boundaries
as determined for polycrystalline La2−xBaxCuO4 sam-
ples are shown as the solid lines in Fig. 7. These results
were extracted from Adachi et al.15and are reproduced
As can be seen on inspection of Fig. 7, the agree-
ment between the structural and superconducting phase
boundaries in polycrystalline La2−xBaxCuO4 and the
new floating zone image furnace grown single crystals is
remarkably good. The absolute values for Td2 are sys-
tematically high, at the 10% level for the polycrystalline
materials as compared to the single crystals, but overall
the full level of agreement is excellent. In particular we
see that good agreement between the two for Td1means
that this transition can be used as an accurate marker for
the Ba concentration in single crystal La2−xBaxCuO4,
as Td1has such strong Ba dependence. The image fur-
nace single crystals were grown without crucibles, and
are expected to be of higher purity than the correspond-
ing polycrystalline materials grown from a flux melt in
a crucible. The similarity between the overall phase dia-
grams in polycrystalline and image furnace grown single
crystal La2−xBaxCuO4, implies an insensitivity of these
phase boundaries to this level of imperfection.
We have successfully grown large single crystals of
La2−xBaxCuO4 with x=0.095 and 0.08 using floating
zone image furnace techniques. These single crystals are
sufficiently large so as to enable neutron scattering stud-
ies, which will be reported separately26. High resolution
single crystal x-ray diffraction measurements were carried
out on these samples, as well as on a high quality x=0.125
single crystal. These measurements focus on the (3, 3,
0)HTT Bragg peak and show the HTT→MTO→LTT se-
quence of structural phase transitions known to be rele-
vant to underdoped La2−xBaxCuO4. The measurements
also clearly show anomolous longitudinal broadening of
the (3, 3, 0)LTTBragg peaks in the x=0.095 and x=0.125
samples at low temperatures, indicating that the LTT
phase is not a simple tetragonal phase, but rather an
admixture of tetragonal and orthorhombic phases, or an
orthorhombic phase with very small orthorhombic strain.
Critical orthorhombic strain measurements near the con-
tinuous HTT→MTO phase boundary show clear 3D uni-
versality, with universal behavior observed in the or-
thorhombic strain vs T/Td1for the three x=0.125, 0.095
and 0.08 samples. The best estimate for a common crit-
ical exponent β for these samples is β=0.34 ± 0.04,
which is consistent with 3D XY universality expected
theoertically for such ferroelastic transitions. A detailed
comparison of the La2−xBaxCuO4phase diagram incor-
porating structural and superconding phase boundaries
at this underdoped concentration regime indicates excel-
lent agreement with pre-existing data based on polycrys-
It is a pleasure to acknowledge the contributions of
Ms. Ann Kallin to the single crystal growth. This work
was supported by NSERC of Canada. Gu was supported
by the US Department of Energy under contract number
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