Critical X-ray Scattering Studies of Jahn-Teller Phase Transitions in TbV$_{1-x}$As$_{x}$O$_{4}$

0.24 MB·

by  K. C. Rule

Critical X-ray Scattering Studies of Jahn-Teller Phase Transitions in TbV As O .
1−x x 4
K.C. Rule,1 M.J. Lewis,1 H.A. Dabkowska,1 D.R. Taylor,2 and B.D. Gaulin1,3
1Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1, Canada
2Department of Physics, Engineering Physics, and Astronomy,
Queen’s University, Kingston, Ontario, K7L 3N6, Canada
8 3Canadian Institute for Advanced Research, 180 Dundas St. W., Toronto, Ontario, M5G 1Z8, Canada
0 (Dated: February 2, 2008)
0
2 ThecriticalbehaviourassociatedwithcooperativeJahn-TellerphasetransitionsinTbV1−xAsxO4
(where x = 0, 0.17, 1) single crystals have been studied using high resolution x-ray scattering.

n Thesematerials undergocontinuoustetragonal→orthorhombicstructuralphasetransitionsdriven
a by Jahn-Teller physics at TC = 33.26(2) K, 30.32(2) K and 27.30(2) K for x = 0, 0.17 and 1
J
respectively. The orthorhombic strain was measured close to the phase transition and is shown to

4 displaymean fieldbehaviorin all threesamples. Pronounced fluctuationeffectsaremanifest in the
1 longitudinal width of the Bragg scattering, which diverges as a power law, with an exponent given
byx=0.45±0.04, onapproachingthetransitionfromeitheraboveorbelow. Allsamplesexhibited
] twinning;howeverthedisordered x=0.17 sampleshowed abroad distributionof twinswhich were
l
e stable to relatively low temperatures, well below TC. This indicates that while the orthorhombic
- strain continues to develop in a conventional mean field manner in the presence of disorder, twin
r
t domains are easily pinnedby thequenched impurities and their associated random strains.
s
.
t
a
PACSnumbers: 64.70.kp,75.40.-s,61.50.Ks
m
-
d I. INTRODUCTION transitions, the orthorhombic strain, but were not able
n
to give accurate critical property measurements for this
o
family of terbium oxides6,7. An x-ray scattering study
c
[ TbVO4 andTbAsO4 belong to a groupofcompounds of the related TbV1−xPxO4 system8 has been carried
which undergo a structural phase transition induced
out, although again, the emphasis was not on the criti-
1 by the cooperative Jahn-Teller effect. Both TbVO
4 cal regime.
v
and TbAsO exhibit a transition from the tetragonal
4 TheroleofquencheddisorderontheJahn-Tellerphase
5 I4 /amd structure at high temperatures to the twinned
4 ort1horhombicFddd phaseat temperaturesbelow 35K1. transitions in the TbV1−xAsxO4 system has more re-
0 cently been the subject of further optical birefrigence
2 At room temperature the low-lying crystal electric field studies, which also show changes in criticality induced
1. levels for the Tb3+ ions in the TbVO4 environment by the presence of impurities9. The change in criticality
consist of two singlets separated by 2.23 meV and a
0 has been discussed in the context of the Random Field
8 degenerate, non-Kramers doublet midway between the IsingModel10 andhowitmayberealizedinastructural
0 singlets2,3. TheJahn-Tellerphasetransitionchangesthe analogue of the more-familiarcase arising in magnetism
: localTb3+ environment,withaconcomitantsplitting of
v -thatofthe diluteIsingantiferromagnetinthepresence
i the doublet, and increase of the singlet separation to of a uniform magnetic field11.
X 6.32 meV3. The resulting magnetic groundstate for the
We have carried out a high resolution x-ray scatter-
r Tb3+ ions can then order magnetically at much lower ing study of the tetragonal to orthorhombic Jahn-Teller
a temperatures4. The structural phase transitions have
phase transitions in the TbV(1−x)AsxO4 system, with
alsobeenstudiedindisorderedsystemswhereinthenon-
particularemphasisonthe criticalregime,wheretheor-
magnetic cations are mixed. Such disordered materials
thorhombic strainis smalland fluctuations in the strain
as TbV1−xAsxO4 are characterized by the presence of may be expected to be large. This will enable a quanti-
quenched random strains introduced by the ionic radius
tativemicroscopicunderstandingofthecriticalphenom-
mismatch between V5+ and As5+, which is quite large
ena in the pure, end members of the family, and show
∼ 20%.
the extent to which the critical behaviour in the mixed
These materials and their Jahn-Teller phase transi- systemismodifiedbythepresenceofquencheddisorder.
tions have been known and studied for some time. For
example,opticalbirefrigencestudiesofthecriticalprop-
II. EXPERIMENTAL DETAILS
erties of TbVO and DyVO showed that the former
4 4
displayedmeanfieldcriticalitynearitsJahn-Tellertran-
sition, while the latter displayed3D Ising-like universal- Single crystals of TbVO andTbAsO and their solid
4 4
ity near its transition5. Early x-ray experiments mea- solutions were grown from PbO/PbF flux by the slow
2
sured the order parameter relevant to these Jahn-Teller cooling method. Pre-annealedstarting materials Tb O
2 3
2
and X O where X is either V or As were weighed
2 5
and combined with PbO and PbF , which act as high
2
temperature solvents. The mix was then melted in a
◦
Pt crucible at 1300 C and slow cooled (1-2 deg/h) to
900◦C12,13. Single crystalsin the formofelongatedrods
with typical dimensions of 5x2x2 mm were separated
fromthismelt. TheTbV As O singlecrystalstud-
0.83 0.17 4
ied was the same one previously studied by Schriemer
et al14. In that study the relative As concentration in
TbV1−xAsxO4 is given as x=0.15, in good agreement
with the value x=0.17 which we have determined from
the current x-ray measurements.
X-ray scattering measurements were performed using
a rotating-anode, Cu K x-ray source and a four circle
α
diffractometer employing a two dimensional area detec-
tor. The single crystals were mounted within a helium-
filled sample cell which was attached to the cold finger
of a closed-cycle helium refrigerator. Scattering mea-
surements werecarriedoutas a functionof temperature
with a temperature stability of ∼ 0.005 K, appropriate
forcriticalscatteringstudies. CuK radiationfromthe
α1
18 kW rotating anode x-ray generator was selected us-
ing a perfect single crystal Ge (110) monochromator.
The diffracted beam was measured using a Bruker HiS-
tar area detector, mounted on the scattering arm at a
distance of 0.7 m from the sample. This configuration
allowedforhighresolutioncharacterizationoftheBragg
peaks. The scattered intensity was measured as a func-
tionof temperature for boththe (6,6,0)Braggreflection
in the tetragonal phase, which splits into the (12,0,0)
and (0, 12, 0) reflections in the twinned orthorhombic
phase, as well as for the (8,0,0) Bragg reflection in the
tetragonal phase, which splits into (8, 8, 0) and (8, -8, FIG.1: Representativecontourmapsofthetemperaturede-
pendence of the Bragg peaks which split on going through
0) reflections in the same twinned orthorhombic phase.
the Jahn-Teller phase transitions in TbVO4, TbAsO4 and
TbV0.83As0.17O4. (a)and(b)showthesplittingofthe(8,0,
0)Braggpeakinto(8,8,0)/(8,-8,0)BraggpeaksinTbVO4.
III. MEASUREMENTS OF THE (c) and (d), (e) and (f), and (g) and (h) show the splitting
ORTHORHOMBIC STRAIN of the (6, 6, 0) Bragg peak into the (12, 0, 0) and (0, 0, 12)
Bragg peaks in TbVO4, TbAsO4 and TbV0.83As0.17O4, re-
spectively. The data on the left ((a), (c), (e) and (g)) are
Figure1showsrepresentativex-rayscatteringcontour
above TC while the data on the right ((b), (d), (f) and (h))
maps taken for TbVO , TbAsO and TbV As O
4 4 0.83 0.17 4 arebelowTC. Thediagonallinein(b)indicatesthecutused
aboveandbelowtheirappropriatephasetransitiontem- for the longitudinal scans in Figure 5. A vertical line would
peratures. Figure1(a)and(b) showsdata takenaround indicate a transverse scan.
the (8, 8,0) Braggposition(in the orthorhombicphase)
in TbVO , while Figures 1 (c) and (d), (e), and (f),
4
and (g) and (h) shows data taken around the (12, 0, 0) (8, 8, 0) orthorhombic Bragg peaks in TbVO4 is shown
Bragg positions (in the orthorhombic phase) in TbVO , in Fig. 1(a) and (b), while the longitudinal splitting of
4
TbAsO , and TbV As O , respectively. All of thetetragonal(6,6,0)Braggpeaksintotwinorthogonal
4 0.83 0.17 4
these scattering data sets were acquired by integrating peaks at (12, 0, 0) and (0, 12, 0) in all three Tb-based
the Bragg scattering in the vertical direction for each oxides is seen in Figs 1(c) - (h).
sample rotation angle (Ω, plotted on the y-axis of Fig. Thesedata setscanbe analysedbyextractingthe po-
1),andthenplottingtheresultingintensityasafunction sitions for all the Bragg peaks in the field of view in
ofscatteringangle,2θ. ThedashedlineinFig. 1(c)indi- both scattering angle, 2θ, and sample orientation angle,
cates a longitudinal scan, while a vertical line on any of Ω. The scattering angle for the single crystal peaks in
thesepanelswouldindicateatransversescan. Thetrans- boththetetragonalphaseaboveT ,andthetwinnedor-
C
versesplittingofthe(8,0,0)tetragonalBraggpeakinto thorhombic phase below T , is used to extract the rele-
C
3
vantlatticeparametersandorthorhombicstrain,defined
asthedifferencebetweentheaandblatticeparameters.
qJm
The scattering angles for all of the (6, 6, 0) (tetragonal m=tanh[ ] (1)
phase)and(12, 0,0) (orthorhombicphase) Braggpeaks kBT
of all three samples are shown as a function of temper-
Figure 3 (b) shows the evolution of the splitting be-
ature in Fig. 2. Figure 3 (a) shows the correponding
tween the twin domain orientationangles, Ω, describing
orthorhombicstrainbelow T inallthree samples. Fig-
C
the (12, 0, 0) and (0, 12, 0) twin orthorhombic domains
ure 3 (b) shows the splitting in domain orientation for
below T in TbVO , TbAsO and TbV As O .
TbVO , TbAsO and TbV As O , extracted from C 4 4 0.83 0.17 4
4 4 0.83 0.17 4
Again the temperature dependence of these splittings
the difference in sample orientation, Ω positions, of the
is very well described by the full mean field solution to
Bragg peaks from the principal (12, 0, 0) and (0, 12, 0)
the order parameter, Eq. 1. This plot follows the evo-
orthorhombic twin domains below T .
C
lution of the domain orientation for both the majority
Figure2(a)showsthesplittingof(12,0,0)and(0,12, andminoritydomainspresentwithinthe field-of-viewof
0) Bragg peaks in all three systems in absolute units of our scattering experiments, for which typical data sets
scattering angle, while Fig. 2 (b) shows the same data, are shown in Fig. 1. For TbVO4 and TbAsO4, a single
butnowrelativetothescatteringangleoftheBraggpeak majority and minority domain is visible at most tem-
in the high temperature tetragonal (HTT) phase. This peratures. However the TbV0.83As0.17O4 data sets are
data shows quite clearly that all three samples display qualitatively different with many domains visible even
continuous phase transitions, as was known previously at temperatures well removed from TC. For example,
forTbVO46 andTbAsO415,andthattheircriticalprop- thedatasetforTbV0.83As0.17O4 atT=26.3K(TC-4K)
erties are similar. The scattering in Fig. 2 (a) however, showsatotalof5twindomains;2majoritytwindomains
also shows that within the high temperature tetragonal athigh scattering angleand 3 minority twin domains at
phase, the lattice parameter (identified by its scatter- low scattering angle. Moreover the dynamic range in
ing angle) for TbV As O lies ∼ 17% of the way domain orientation angle spanned by the multiple twin
0.83 0.17 4
between TbVO and TbAsO , as given by a linear vari- domains is considerably larger than is found in either
4 4
ation in lattice parameter between the end members of TbVO4 or TbAsO4 below TC. Figure 3 (b) quantifies
the series, TbVO and TbAsO . Such a linear variation this behaviour, following the splitting of the majority
4 4
is observed in the TbV1−xPxO4 system8. This estab- and minority twin domain orientation angles (Ω) below
lishesanaccurateconcentrationfortheTbV0.83As0.17O4 TC. The extrapolated, low temperature Ω splitting is
single crystal by microscopic means. very similar for TbVO4 and TbAsO4, but considerably
larger for TbV As O , where the splitting between
0.83 0.17 4
Figure 3 (a) shows the corresponding orthorhombic the orientation angle, Ω, of the most intense minority
strains, defined as the difference in lattice parameters a twin and most intense majority twin domain is plotted.
and b, as a function of temperature below T for each The order parameter data shown in Fig. 3, along
C
ofTbVO ,TbAsO andTbV As O . Relatedmea- with the fits to full mean field behaviour, Eq. 1, allow
4 4 0.83 0.17 4
surements of the orthorhombic strain have been mea- a precise determination of the critical temperature TC,
sured previously as a function of temperature for the in these systems. Fitting both the orthorhombic strain
TbV1−xPxO4 system8. However, the present measure- shown in Fig. 3 (a) and the twin domain orientation
mentsaretakensufficientlyclosetothephasetransitions splittingshowninFig. 3(b),weobtainTC =33.26(2)K,
such that an accurate determination of TC and a quan- 30.32(2)Kand27.30(2)KforTbVO4,TbV0.83As0.17O4
titative study of the critical properties of these phase and TbAsO , respectively. In itself, this is a somewhat
4
transitions is possible. It is clear from the data that surprisingresult,asitshowstheTC forTbV0.83As0.17O4
the order parameter,the orthorhombicstrain, rises very to lie midway between that of TbVO and TbAsO , de-
4 4
sharply with decreasing temperature, such that little of spite only 17% of the V ions being replaced by As ions.
this data would reside in the asymptotic criticalregime, This is very likely a manifestation of the quenched im-
where the order parameter is small compared with its purities on the Jahn-Teller driven phase transition in
saturation value. Therefore we fit this data to a full TbV0.83As0.17O4.
mean field solution, Eq. 1, rather than simply to the The behaviour of the twin domains below T in
C
asymptotic expression for small values of the order pa- TbV As O can be qualitatively understood in
0.83 0.17 4
rameter. This gives a mean field critical exponent for terms of pinning of the twin domains by randomstrains
the order parameter, β =0.5, but the full data sets are due to the quenched impurities. Clearly, this does not
accurately described. This description of the order pa- influence the critical properties of the order parame-
rametersasafunctionoftemperatureusingthe solution ter, the orthorhombic strain, which remains well de-
to the transcendental Eq. 1 below, is shown as the solid scribed by mean field behaviour at all temperatures, as
lines in Fig. 3 (a) and (b). Clearly the full mean field is the case for both TbVO and TbAsO . The influ-
4 4
solution provides an excellent description of this data. ence of quenched impurities on twin domain interfaces
4
FIG.2: Thetemperaturedependenceofthepeakpositionin FIG. 3: Figure 3a (top) shows the measured order
2θ for each of the three samples: TbVO4 (closed symbols), parameters, the orthorhombic strains (a-b), in TbVO4,
TbAsO4 (opensymbols)andTbV0.83As0.17O4 (crossedsym- TbV0.83As0.17O4, and TbAsO4. These have been fit to the
bols). The structural phase transition is indicated by the mean field solution (Equation 1) for the order parameter as
splitting of thesingle Bragg intensity into two with decreas- a function of temperature, which is shown as the solid lines.
ing temperature. Figure 2a shows the true 2θ splitting for Figure 3b (lower) shows the domain orientation Ω splitting
each of the compounds, while Figure 2b shows the splitting of the (12, 0, 0) and (0, 12, 0) Bragg peaks and fits to the
relativetothescatteringinthetetragonalphaseathightem- same mean field solution. The TbV0.83As0.17O4 Ω splitting
peratues. wastakenasthedifferencebetweenthemajority andminor-
ity domains with the strongest Bragg intensity. This was an
issueforTbV0.83As0.17O4 aloneasthetwinneddomainscol-
lapsed intoasingle dominantmajority andminority domain
has been investigated by light scattering techniques14,
peak within a few degrees of TC for thepurematerials.
whichisexpectedtobesensitivetosuchlargescalestruc-
ture. The present results are qualitatively consistent
with these results, showing stable multi-domain twin
ening in the vicinity of T . Representative longitudinal
states in TbV As O , distinct from TbVO and C
0.83 0.17 4 4
scans near the (6, 6, 0) Bragg position in the tetragonal
TbAsO , and therefore a larger volume fraction taken
4
phaseand(12,0,0)Braggpositionsintheorthorhombic
up by domain interfaces in TbV As O . However,
0.83 0.17 4
the changein criticalproperties previously reported9 on phase of TbVO4 are shown in Fig. 4. Very similar data
was obtained for TbAsO , but it is not displayed. Fig-
introduction of quenched impurities is not observed. 4
ure4(a)showsalongitudinalscanthrough(6,6,0)well
aboveT atT=47.05K(T + 13.8K),while Fig. 4(d)
C C
showsa longitudinal scanthrough(12, 0,0) atT=26.75
IV. MEASUREMENTS OF FLUCTUATIONS OF
K, 6.51 K below T . Both of these scans have approx-
C
THE ORTHORHOMBIC STRAIN
imately the same intrinsic width, and we consider them
to be resolution limited. Figures 4 (b) and (c) however,
Close examination of the scattering data sets at the showlongitudinalscansmuchclosertoT . Figure4(b)
C
(12,0,0)/(0,12,0)Braggpositions inbothTbVO and shows data just above T at T=33.58 K (T + 0.32 K)
4 C C
TbAsO revealed a very interesting longitudinal broad- while Fig. 4 (c) shows the same scan just below T , at
4 C
5
Data of the form shown in Fig. 4 was fit to an
Ornstein-Zernike form, Eq. 2, convoluted with the res-
olution function appropriate to the measurement. We
employed the scattering well above T , at T ∼ 50 K,
C
as the resolution function, assuming that all fluctuation
effects are gone at such high temperatures. The results
of fitting the TbVO data is shown as the solid lines in
4
Fig. 4, and this clearly provides an excellent descrip-
tion of the longitudinal scans at all temperatures, Simi-
lar quality fits to the TbAsO were also obtained. The
4
resulting intrinsic widths to the longitudinal scans are
shown as a function of temperature for TbVO in Fig.
4
5 (a) and for TbAsO in Fig. 5 (b). Data is shown
4
forbothindependentwarmingandcoolingrunsforboth
materials,althoughno significanthistorydependence to
thewidthsofthescatteringwereobserved. Fortempera-
tures below T , longitudinalscansthroughboth major-
C
ity and minority twin domains were investigated. Over
the narrow range of temperature below T for which a
C
finite width can be observed, the intrinsic widths of the
majority and minority twin domain peaks differ, with
theminoritytwinpeakshowingagreaterintrinsicwidth
than the majority twin domain, consistent with the in-
terpretationof the minority twin domains as being rela-
tivelysmall. ArelatedsetofdatanearT wasacquired
C
for TbV As O , however the relevant longitudinal
0.83 0.17 4
lineshapesweremorecomplicatedthanthoseobservedin
TbVO andTbAsO ,andtheseresultsarenotdiscussed
4 4
here.
FIG. 4: Representative fits to the longitudinal scans for
TbVO4. Thisdataistakenfromlongitudinalcutstothefull
A
datasets,asshowninFig. 1(c). (a)and(d)weretakenwell S(2θ)= (2)
above and below TC=33.26(2) K, respectively, and are res- (2θ−2θpeak)2+κ2
olution limited. (b) and (c) are relatively close to TC and The most striking and interesting result is that the
show substantial broadening in the longitudinal direction.
intrinsic width of the Bragg peaks, interpreted as an
The resolution-corrected longitudinal widths of the profiles
inverse correlation length, displays a pronounced peak
were extracted and are plotted as a function of temperature
at T , reminiscent of λ anomolies in the heat capac-
in Figs. 5 and 6. C
ity of systems undergoing continuous phase transitions.
Thetemperaturedependenceofthedivergenceofthein-
trinsic width, or inverse correlation length, is examined
T=32.82 K (T - 0.44 K). It is clear that both of these
C on a log-log plot in Fig. 6, wherein data above T in
C
longitudinalscansnearT areappreciablybroaderthan
C TbVO and TbAsO is plotted vs reduced temperature
4 4
those well removed from T , and therefore are not res-
C (T-T )/T . Again independent warming and cooling
C C
olution limited.
runs are shown, with no history dependence observed.
We associate this broadening with fluctuations in the Thisplot, whichemploysthe sameT susedtodescribe
C
order parameter, similar to that observed near continu- the critical properties of the order parameter shown in
ous magnetic phase transitions. However,in the present Fig. 3, clearly brings out the power law nature of the
case, fluctuations in the orthorhombic strain lead to a divergenceof the intrinsic width of the scattering as T
C
longitudinal broadening of Bragg peaks of the form (6, is approached from above. Figure 6 (a) shows this data
6, 0) in the tetragonal phase. Rather than narrowing for both TbVO and TbAsO , and it is clear that both
4 4
in angle or reciprocal space as the phase transition is materials display a very similar power law divergence
approached, these peaks broaden and decrease in peak over at least one and a half decades in reduced tem-
intensity as T is approached from above. Broadening perature. Figure 6 (b) shows the intrinsic width of the
C
is also observed below T , but the widths of the Bragg longitudinalscaninTbAsO alone,whereasinglepower
C 4
peaksfalloffquickly,suchthatallthescatteringinboth lawdescribesitsdivergenceoveralmostthreedecadesin
TbVO and TbAsO is resolution limited for tempera- reduced temperature. The exponent characterizing the
4 4
tures more than 2 K below T . divergence is x=0.45 ± 0.04.
C
6
Whilewehavecharacterizedthepowerlawdivergence
of the inverse correlation length, or intrinsic width, at
T ,wedo nothavea preciseinterpretationforthis crit-
C
ical phenomenon. In their high-resolution gamma-ray
diffraction experiments on TbVO , Smith and Tanner7
4
observeda broadening in the rocking-curvewidths, that
is the transversewidth of the Bragg peaks, as the phase
transitionwasapproachedfromabovethatsomewhatre-
semblesthebroadeningthatwemeasured. Theydidnot
analyzeit in detail, but suggestedthat it arosefromthe
strainsassociatedwithrandominternalstressesrelaxing
as the elastic constant C tends to zero. While such
66
a mechanism could contribute in our case, it is difficult
to believe that it would exhibit critical behaviour over
such a wide range and with such well defined power law
behaviour as we observe.
As mentioned previously, our observed longitudinal
broadening of the (6, 6, 0) (tetragonal) and the (12,
0, 0)/(0, 12, 0) (orthorhombic) Bragg peaks in Fig.
5 greatly resembles heat capacity anomolies associated
with continuous phase transitions. This may be a natu-
ralexplanationofthe intrinsic width, asthe width isin-
versely proportional to the fluctuating domain size, and
thus proportionalto the volume fractionof the material
occupied at any one time by interface. The energy of
such a system would scale as the amount of interface,
andalongitudinalBraggpeakwidthscalingasaderiva-
tive of the energy, the heat capacity, seems physically
resonable. The critical exponent x may be close to that
FIG. 5: Resolution-corrected longitudinal widths, or inverse
describing fluctuations near a mean field, or mean field
correlation lengths, showing critical fluctuations around the
tricriticalpoint,forwhichalargeheatcapacityexponent
(6, 6, 0) (tetragonal phase) and (12, 0, 0) and (0, 12, 0) (or-
characteristic of a divergence is appropriate. At present
thorhombic phase) of TbVO4 (top) and TbAsO4 (bottom).
wecannotbemoreprecise,buthopethattheobservation
BelowTC opendatapointsrefertothemajoritytwindomain,
and characteriozation of this critical behaviour informs while closed data points refer to the minority twin domain.
and motivates further work and understanding. Square and circle data points refer to independent cooling
and warming cycles.
V. COMPARISON TO RELATED
STRUCTURAL PHASE TRANSITIONS AND well described by three dimensional universality. The-
FLUCTUATIONS
oretical expectations for these systems are for 3D XY
critical behaviour18, and this is consistent with what
We can compare the present results on the order pa- is observed16,17. Even qualitatively, it is clear that
rameterandfluctuationsneartheJahn-Tellertetragonal the growth in the orthorhombic strain with decreasing
to orthorhombicstructural phase transitions in TbVO4, temperature in TbVO4, TbAsO4 and TbV0.83As0.17O4
TbAsO4 and TbV0.83As0.17O4, to those in related sys- is different from that observed in La2−xBaxCuO4 and
tems. Theprincipalcharacteristicsofthepresentresults La2−xSrxCuO4 . Comparing to a recent high resolution
are mean field critical behaviour for the orthorhombic x-ray scattering study on the La2−xBaxCuO4 system17,
strain, andthe observationof clear fluctuation effects in we can see that the orthorhombic strain grows in a
the vicinity of T . relatively gentle manner with decreasing temperature
C
Two topical and well studied systems which un- compared with what is observed in TbVO4, TbAsO4
dergo tetragonal to orthorhombic structural phase and TbV0.83As0.17O4. Figure 3 shows that the lat-
transitions are the high temperature superconductors ter orthorhombic strains grow to ∼ half of their satu-
La2−xBaxCuO4 andLa2−xSrxCuO4 . Criticalx-rayand ration values at 0.9 × TC. The same growth in the
neutronscatteringonthese materialsdo notshow mean La2−xBaxCuO4 systemrequireslowertemperaturesand
field behaviour,but rather the orthorhombicstraingoes half of saturation is only achived by ∼ 0.7 TC.
like the square of the order parameter16,17, which is Therearedifferencesofcourse,betweenthe hightem-
7
at low temperatures. These have been interpreted as
fluctuations above a very low temperature Jahn-Teller
phase transition, which is either never realized, or only
realized at unattainably low temperatures. Indeed, to
our knowledge,the present work is the only other study
of structural phase transitions which show such critical
broadening of the Bragg peaks in the vicinity of T .
C
The temperature scale overwhich these fluctuations are
observed is quite different in Tb Ti O as compared
2 2 7
with TbVO , TbAsO and TbV As O . In the
4 4 0.83 0.17 4
presentcase,the broadeningoftheBraggpeaksappears
as critical phenomena and the strongest fluctuation ef-
fects fall off within a few degrees of T . In contrast,
C
the Jahn-Teller-like fluctuations in Tb Ti O occur co-
2 2 7
incident with the formation of a spin liquid state, and
aremeasureableoveranextendedregimeoftemperature
from 20 K to 0.3 K.
Finally we return to the issue of mean field criticality
vs criticality associated with random fields. We did not
observe a departure from mean field criticality associ-
ated with random fields in TbV As O . This may
0.83 0.17 4
be because the random fields associated with the disor-
der are too weak to influence the critical behaviour in
the rangeof reducedtemperaturesthat we couldaccess.
Ameasureofthestrengthofthedisorderandassociated
random fields is the extent to which they depress the
transitiontemperature. The observedT for our mixed
C
sample was 30.32 K, lower than the value 32.25 K ex-
pected from a linear variation in T between the two
FIG.6: (top)Critical behaviourofthelongitudinalwidth,κ C
end members. This depression in T confirms that dis-
C
fromEq. 2,aboveTC forTbVO4andTbAsO4areshownasa
order is relevant and that associated random fields are
functionofreducedtemperature. ThesamedataforTbAsO4,
present. Insomerelatedsystemsthathavebeenstudied,
along with a fit to a power law divergence characterized by
theexponent x=-0.45 ± 0.04. DyAsxV1−xO420,21 and KH2AsxP1−xO422, however, as
well as dilute antiferromagnetic systems11 the depres-
sions in T were larger and random-field critical be-
C
haviour was clearly observed.
peraturesuperconductingcopperoxidesandtheterbium
basedoxideswereporthere. Thecupratesarequasi-two-
dimensional, for example, while TbVO , TbAsO and
4 4
VI. CONCLUSIONS
TbV As O are three dimensional. Most notably
0.83 0.17 4
however the magnetic Cu2+ ion in La2−xBaxCuO4 and
La2−xSrxCuO4 is not Jahn-Teller active - a single hole We have studied the critical properties near Jahn-
residesinanon-degeneratedorbital. Thiswouldappear Teller,tetragonaltoorthorhombicstructuralphasetran-
to be the most likely source for the difference in critical sitions in TbVO , TbAsO and TbV As O using
4 4 0.83 0.17 4
behaviour. TbVO4, TbAsO4 and TbV0.83As0.17O4 pos- high resolution x-ray scattering. These results show the
sess Tb3+ ions whose orbitals and the occupation of the order parameter, the orthorhombic strain, in all three
orbitals change on going through TC, likely generating materials to exhibit mean field criticality. The disor-
longrangestrainfieldswithconcomittantmeanfieldbe- dered member of this series, TbV As O is distin-
0.83 0.17 4
haviour. guishedonlyinsofarasitexhibitsawidedynamicrange
Another interesting comparison is to other Tb3+- ofmajorityandminorityorthorhombictwindomainori-
based transition metal oxides. Here an interesting com- entations,and these are stable to low temperatures. We
parisoncanbemadewithaveryrecenthighresolutionx- ascribe this to the pinning of the domain structure by
rayscatteringstudyofthecubicpyrochloreTb Ti O 19. random strains arising from the quenched disorder in
2 2 7
This geometrically-frustrated magnetic material does TbV0.83As0.17O4.
not undergo a structural phase transition at finite tem- We also observe very interesting fluctuation effects in
perature, but recent x-ray scattering measurements ob- TbVO and TbAsO in the vicinity of T . These are
4 4 C
serve broadening of the allowed structural Bragg peaks manifestinlongitudinalbroadeningofthe(6,6,0)Bragg
8
peaksinthetetragonalphase,whichsplittobecome(12, critical exponent, x=0.45 ± 0.04. We hope that this
0,0)and(0,12,0)Braggpeaksintheorthorhombiclow latter work informs and motivates a full theoertical un-
temperature phase. This broadening exhibits a power derstanding of this fluctuation phenomena.
law divergence at T , in TbVO and TbAsO , with a This work was supported by NSERC of Canada.
C 4 4
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