Tuning the structural instability of SrTiO_3 by Eu doping: The phase diagram of Sr_1-xEu_xTiO_3

0.44 MB·English

by  Z. Guguchia

preprint(October 14, 2011)
The phase diagram of Sr Eu TiO : Crossover from displacive to order-disorder
1−x x 3
dynamics
Z. Guguchia,1 A. Shengelaya,2 H. Keller,1 J. K¨ohler,3 and A. Bussmann-Holder3
1Physik-Institut der Universita¨t Zu¨rich, Winterthurerstrasse 190, CH-8057 Zu¨rich, Switzerland
2Department of Physics, Tbilisi State University, Chavchavadze 3, GE-0128 Tbilisi, Georgia
3Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany
The phase diagram of Sr Eu TiO is determined experimentally by EPR measurements and
1−x x 3
analyzed theoretically in terms of the self-consistent phonon approximation (SPA) as a function of
x (x=0.0, 0.03, 0.25, 0.5. 0.75, 1.0). It is observed that the oxygen octahedral tilting instability
temperatureT increasesnonlinearlywithx. Thetheoreticalanalysisdemonstratesthatacrossover
S
1
from displacive to order-disorder dynamics takes place for x ≥ 0.25, signaled by a change in the
1
local double-well potential and the soft mode temperature dependence.
0
2
PACSnumbers: 74.20.Mn,74.25.Ha,74.70.Xa,76.75.+i

t
c
O
The Eu and Sr titanites have a variety of aspects in goustothepurecompoundsasdescribedinRef. [7]. The
3 common which might enlarge their potential applica- values of x are x=0.03, 0.25, 0.5, 0.75, 1, which is suffi-
1 tional properties as mixed crystals or as layered mate- cient to characterize the phase diagram. The polycrys-
rials. Since Eu and Sr have the same ionic radii and the tallinesampleshavebeenmeasuredbymeansofelectron

]
i samevalenciesintheperovskiteABO3structure,alsothe paramagnetic resonance (EPR) techniques with the em-
c
lattice constants are the same. In addition, both com- phasis on investigating and characterizing the structural
s
- pounds show an incipient ferroelectric instability which instability in detail. EPR measurements were performed
l
r is suppressed by quantum fluctuations [1], where the ex- inaBrukerEMXspectrometeratX-bandfrequencies(ν
t
m trapolated values for the polar instability are 37K for ≈9.4GHz)equippedwithacontinuousHegas-flowcryo-
SrTiO (STO) [2–4] and less than -150K for EuTiO stat in the temperature range 4.2 < T < 300 K. In this
. 3 3
t (ETO) [5, 6]. Very recently we have shown theoretically paper we restrict the discussion to temperatures T > 50
a
m and experimentally [7] that a novel analogy exists be- K.EPRdetectsthepowerPabsorbedbythesamplefrom
tweenbothcompounds,namely,anoxygenoctahedraro- the transverse magnetic microwave field as a function of
-
d tationalinstabilityrelatedtothesofteningofanacoustic the static magnetic field H. The signal-to-noise ratio
n phononmode. TherespectivetransitiontemperaturesT of the spectra is improved by recording the derivative
S
o
differ distinctively, however, namely, T =105K in STO, dP/dH using a lock-in technique with field modulation.
c S
[ andTS=282KinETO.ThelargegapinTS betweenETO That the EPR method is very powerful for the detection

1 and STO has motivated us to construct the phase dia- ofTS hasbeenprovenearlyonforSTOwhereabroaden-
gram of Sr Eu TiO as a function of Eu content x. ingoftheEPRlinewidthofaFe3+-oxygenvacancypair
v 1−x x 3
2 Since our previous analysis of the dynamical properties (V O) center at TS has been observed [9]. In the present
2 of both systems has been based on the same lattice dy- experiment due to the large Eu spins and the fact that
9 namical parameters, with the distinction that the self- polycrystalline materials were used, only the change of
2 consistently derived double-well potentials are very dif- the EPR line width with temperature was studied.
.
0 ferent, i.e. STO is in the displacive limit whereas ETO Figure1showstheEPRspectraofSr Eu TiO with
1−x x 3
1 obeys order-disorder dynamics, we use the same param- 0.03≤x≤1 at T=300 K. For all x one observes a single
1
eters also for the mixed crystals. As data for the soft weaklyasymmetricresonancelinewhichiswelldescribed
1
mode temperature dependence are missing, we employ by a Dyson shape [10],
:
v x-dependent averages of the nonlinear potential for the
Xi in between lying compounds. In order to obtain agree- P(H)= (cid:52)H +α(H −Hres) (1)
(H −H )2+(cid:52)H2
mentwiththeexperimentalphasediagram, thecoupling res
r
a between the oxygen octahedra is varied to reproduce the i.e.,aLorentzlineatresonancefieldH withhalfwidth
res
experiment. The experimental phase diagram has been at half maximum ∆H and a contribution 0 ≤ α ≤ 1 of
determined by electron paramagnetic resonance (EPR) dispersiontotheabsorption, resultinginacharacteristic
where the structural transition temperature T appears asymmetry. ThedispersioncontributiontotheEPRline
S
as a distinct line width anomaly. shape evidences that the samples are conducting, since
The low temperature antiferromagnetic transition of theasymmetricsignalistypicalformetalswheretheskin
ETO at T =5.5K [8] is also x-dependent, but this will effectdriveselectricandmagneticcomponentsofthemi-
N
not be discussed here where the focus is exclusively on crowave field out of phase. The parameter α depends on
the x-dependent structural instability. sample size, geometry, and skin depth. If the skin depth
Samples of Sr Eu TiO have been prepared analo- is small as compared to the sample size, α approaches
1−x x 3
2
S r E u T iO 3 2 0 0 S r E u T iO T s
1-x x 3 1 -x x 3
2 8 0 0 x = 1
T
x = 1 2 4 0 0 s
.) x = 0 .7 5
.u x = 0 .7 5 2 2 5 0
a
l ( x = 0 .5 T
na e)22 22 00 00 s
sig x = 0 .2 5 (O x = 0 .5
R th1 6 0 0
P d
E x = 0 .0 3 i
w
e1 5 0 0
n
T = 3 0 0 K R li1 0 8 0 x = 0 .2 5 T
0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 P s
E
H ( O e ) 1 0 4 0
4 0 0 x = 0 .0 3
FfoIrG0..013:≤(Cxo≤lo1raotnTlin=e3)0E0PKR. spectraofEu2+inSr1−xEuxTiO3 3 6 0 T s
3 2 0
5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0
T ( K )
1. From Fig. 1 it is obvious that the EPR signal broad-
ens with increasing Eu concentration. This effect can be FIG.2: (Coloronline)TemperaturedependenceoftheEPR
explained by an increasing magnetic dipolar interaction linewidth for Sr Eu TiO samples with 0.03≤x≤1. The
1−x x 3
between Eu2+ ions as their average distance is reduced arrows indicate the structural phase transition temperature.
with increasing Eu concentration. The Lorentzian line
shape is a signature of the exchange narrowing process
due to strong exchange coupling between the magnetic abruptly and an almost linear decrease with decreasing
Eu2+ ions. The fine and hyperfine structures, which are T is seen. For the compositions x=0.75 and 0.5 an anal-
expected for the single Eu2+ ions, are not observed in ogousbehaviorisobservedwithTS movingtolowertem-
oursamples. Thisimpliesthatstartingfromthesmallest peratures. The results are shown in Fig. 2. It is inter-
Euconcentrationx=0.03studiedhere,theexchangenar- esting to note that the maximum of the EPR line width
rowing process is sufficient to merge the entire spectrum changes to minimum as a function of temperature be-
into a single EPR line. Figure 2 shows the temperature low x=0.25. Although the reason for this is not clear at
dependence of EPR line width in Sr Eu TiO sam- present, tentative explanations are given below.
1−x x 3
ples with 0.03≤x≤1. For x=1 and in the temperature ThephasediagramasdeducedfromFigure2isshown
interval 50-285 K, the EPR line width broadens linearly in Figure 3. Obviously TS depends nonlinearly on x.
withaslopeofapproximately0.2mT/K.Thelineartem-
perature dependence is characteristic for the Korringa
3 0 0
mechanism of relaxation where localized Eu2+ moments
couple to charge carriers through an exchange interac-
tion [10]. In this case the slope of the linear broadening
2 5 0
is proportional to (J N(E ))2, where N(E ) is the
Eu−CE F F
conductionelectrondensityofstatesattheFermienergy,
and J is the exchange coupling constant of the Eu
Eu−CE )2 0 0
spins with the conduction electron (CE) spins [10]. It is (K
obvious from Fig. 2, that the EPR line width exhibits s
T
an anomaly at 285K. This temperature coincides with
1 5 0
specific heat anomaly due to the structural phase transi-
tion recently observed in EuTiO [7]. Qualitatively the
3
sensitivity of the EPR line width to the structural phase 1 0 0
transition can be understood as stemming from either 0 .0 0 0 .2 5 0 .5 0 0 .7 5 1 .0 0
band structure modifications N(E ) or from changes of x in S r E u T iO
F 1 - x x 3
J . AscanbeseeninFig. 2,theEPRlinewidthin
Eu−CE
EuTiO starts to increase with decreasing temperature FIG.3: (Coloronline)TemperaturedependenceoftheEPR
3
above TS suggestive of conductivity changes above the linewidth for Sr1−xEuxTiO3 samples with 0.03≤x≤1. The
structural phase transition. At T this behavior changes arrows indicate the structural phase transition temperature.
S
3
- 3 .0 - 3 .0 thesoftopticmodefrequency. Thelackofdatafromthe
( a ) mixed crystals does not admit to follow the same proce-
- 2 .5 - 2 .5 dure. Thex-dependentdouble-wellpotentialparameters
aregivenintermsofthebarrierwellg /g andareshown
2 4
- 2 .0 - 2 .0 ) in Figure 4a. Obviously, around x ≥ 0.25 the barrier
2
) m heightbecomesindependentofx, whereasforx≤0.25a
2m- 1 .5 - 1 .5 8 c strong x-dependence sets in. Since ETO is in the order-
rg c -1 0 disorder limit and STO in the displacive limit, x=0.25
’ e(- 1 .0 - 1 .0 1(4 represents the border where a dynamical crossover be-
f /g tweenbothtakesplace. Thiscanalsobeenseenfromthe
2
- 0 .5 - 0 .5 g temperature and x-dependence of the long wave length
softopticmode(Figure4b)whereforx>0.25allmodes
0 .0 0 .0
fall almost on the same line and follow the same tem-
0 .0 0 .5 1 .0
perature dependence. Since at the same Eu composition
x in S r E u T iO
1-x x 3 also the line width anomaly changes from peak to dip,
1 2
we identify this crossover as its origin. Details will be
x = 1
x = 0 .7 5 ( b ) given elsewhere. With the double-well defining parame-
1 0
x = 0 .5 ter values and the temperature dependence of the long
x = 0 .2 5
wave length optic mode frequencies it is possible to de-
8 x = 0 .0 3
duce the temperature dependence of the zone boundary
x = 0
) related acoustic mode energy corresponding to the octa-
0 6
= hedral rotational instability [13]. This alone is, however,
q
2(TO 4 notenoughtoreproducetheexperimentaldataforTS. It
w is necessary to also correct for the spin-phonon coupling
which - as has been shown previously [7] - strongly sup-
2
presses the zone boundary acoustic mode frequency. We
infer this correction indirectly by modifying the second
0
0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 nearest neighbor coupling f(cid:48) such as to yield the correct
T ( K ) TS. Interestingly, we find that this coupling follows the
x dependence of T (Figure 4a).
S
FIG. 4: (Color online) (a) The x-dependence of the octa-
hedral coupling f(cid:48) (triangles) and the double-well potential
height g /g (squares). (b) Temperature and x-dependence
2 4 To summarize, the phase diagram of Sr Eu TiO
1−x x 3
ofthesoftopticmodefrequencywherethecolorcodeforthe
has been determined experimentally by EPR measure-
different x-values is given in the figure.
ments with focus on the structural instability related to
oxygenoctahedraltilting. Itisfoundthatthisinstability
depends nonlinearly on the Eu composition x. The the-
For x ≤ 0.25 TS increases sharply to become almost pro- oretical analysis is based on the nonlinear polarizability
portional to x between 0.25 ≤ x ≤ 0.75 followed by a model and predicts a crossover in the critical dynam-
steep increase for x ≥ 0.75. This nonlinear dependence ics around x=0.25. The experimental phase diagram
isratherunexpectedsincetheionicsizesofSrandEuare is reproduced by assuming that the double-well poten-
thesame,andtheseionsarenotinvolvedintheTiO6 ro- tial represents a doping and x dependent average of the
tational instability. However, as we have shown recently end member potentials and by adjusting the next near-
[7], the dynamics of the phase transitions of STO and est neighbor interactions which are found to follow the
ETOdifferconsiderably,beingalmostdisplaciveforSTO x-dependenceofT . Fromthecalculationsitisexpected
S
and of order-disorder type for ETO. It can thus be as- thatforx≤0.25alsoanomaliesintheacousticmodedis-
sumedthatacrossoverbetweenbothdynamicsispresent persion appear which can be detected experimentally by
inthemixedcrystalswhichcausesthenon-monotonicde- resonant ultrasound spectroscopy and as precursor dy-
pendence of TS on x. namics in local probe experiments, analogous to STO.
In order to model the phase diagram of STO-ETO
weadoptthesamenonlinearpolarizabilityframeworkas
previously used [7, 11–13], and employ x-dependent av- This work was supported by the Swiss National Sci-
erages of the double-well defining quantities g ,g where enceFoundation,theSCOPESgrantNo. IZ73Z0 128242,
2 4
g istheattractiveharmonicelectron-ioninteractionpa- the NCCR Project MaNEP, the EU Project CoMePhS,
2
rameterandg thenonlinearfourthorderrepulsiveterm. and the Georgian National Science Foundation grant
4
These values are typically derived self-consistently from GNSF/ST08/4-416.
4
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