PHYSICAL REVIEW B 84, 235144 (2011)

Spin-lattice interaction in the insulator-to-metal transition of GdBaCo2O5+δ

Mattia Allieta,1,* Cesare Oliva,1 Marco Scavini,1 Serena Cappelli,1 Ekaterina Pomjakushina,2 and Valerio Scagnoli31Dipartimento di Chimica Fisica ed Elettrochimica, Universita degli Studi di Milano, Via Golgi 19, IT-20133 Milano, Italy

2Laboratory for Developments and Methods, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland3Swiss Light Source, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland.

(Received 1 September 2011; revised manuscript received 2 December 2011; published 27 December 2011)

We use electron paramagnetic resonance spectroscopy (EPR) and synchrotron radiation x-ray powderdiffraction to study the temperature-induced insulator-to-metal transition (IMT) for GdBaCo2O5+δ samplesin the δ range 0.54(1) � δ � 0.63(1). The EPR linewidth markedly changes across IMT and its temperatureevolution can be explained considering spin state transition involving Co ions. The temperature dependencesof the EPR linewidth and of the a lattice parameter fairly overlap each other suggesting spin-lattice interactionalong the same crystallographic direction of the reported Ising-like spin anisotropy [A. A. Taskin et al., Phys.Rev. Lett. 90, 227201 (2003)]. A possible mechanism describing the interplay between this strong spin-latticeinteraction and IMT is proposed.

DOI: 10.1103/PhysRevB.84.235144 PACS number(s): 71.30.+h, 76.30.−v, 61.05.cp, 61.66.Fn

I. INTRODUCTION

LnBaCo2O5+δ layered cobalt oxides (Ln is a rare earthelement) exhibit very rich electronic and magnetic phasediagrams that involve many fascinating phenomena such asthe magnetoresistance (MR) effect.1–3 The crystal structure ofLnBaCo2O5+δ can be viewed as a sequence of square-latticelayers [CoO2][BaO][CoO2][LnOδ] stacking along the c axiswith alternation of two types of coordination environments forcobalt ions, i.e., CoO5 pyramid (Copyr) and CoO6 octahedra(Cooct). The Copyr/Cooct ratio as well as their ordering alongcrystallographic directions can be modified by tuning theoxygen concentration δ in LnOδ planes.2 More importantly,δ affects the mean valence state of cobalt ions as Co3+ canexist in low-, intermediate-, or high-spin states (LS, IS, or HS)while Co2+ and Co4+ are stable in HS and LS configurations,respectively.2 Then, the physics of these systems is driven bya complex interplay between charge, spin, orbital, and latticedegrees of freedom triggered, e.g., by temperature.

Such behavior is clearly demonstrated by the temperature-induced insulator-to-metal transition (IMT) found at TIM ≈365 K with GdBaCo2O5+δ when δ ≈ 0.5.1–5 However, despitea number of experimental and theoretical studies in layeredcobaltites, great controversy has arisen regarding the Co spinstate and the microscopic origin of IMT. In the year 2000,Moritomo et al.6 suggested that the IMT is induced bya spin-state transition (SST) from an orbital-ordered (OO)IS state to the HS state in both Copyr and Cooct sites,basing their consideration on neutron powder diffraction ofTbBaCo2O5.5. Later, a synchrotron radiation x-ray powderdiffraction (XRPD) study of GdBaCo2O5.5 ruled out any OO,suggesting that the IMT should be related to a spin-stateswitch from LS to HS states at Cooct. Conversely, the Copyr

should remain in IS state at both sides of the IMT.4 This isconsistent with ab initio calculations that verified the stabilityof pyramidal IS states in LnBaCo2O5.5 systems.7 Maignanet al.8 explained the interplay between IMT and SST using amodel based on conversion of HS to LS state in Cooct at T

< TIM which would immobilize the electron charge carriersthrough a “spin blockade” mechanism between HSCo2+ and

LSCo3+. In strong contrast with SST, a muon-spin relaxationstudy on LnBaCo2O5+δ δ ≈ 0.5 suggested that the HSstate of Co3+ is retained at T < 300 K.9 Recently thermalexpansion measurements on GdBaCo2O5.5 confirmed the SSTas the driving force for IMT excluding the occurrence ofstepwise SST at lower temperatures.5 Another model basedon density functional theory calculations10 and supported byphotoemission11 and isotope-effect neutron diffraction data12

suggested that the IMT is due to hole delocalization in theCo3+ HS state rather than to SST.10,12

In this paper we present a EPR study on GdBaCo2O5+δ

combined with synchrotron XRPD as a function of δ and of thetemperature across the IM transition. EPR spectroscopy allowsdirect access to the spin-environment interactions through theinvestigation of the spin relaxation behavior.13 The EPR signalmarkedly changes with increasing temperature for δ = 0.54(1)and δ = 0.57(1) samples, indicating that the spin exchangefrequency increases above TIM in both cases. By comparingEPR and XRPD T -dependent experimental results we clearlydemonstrate that the interplay between Co spin state andcrystal lattice plays a central role in the IM mechanism ofthis layered cobaltite.

II. EXPERIMENTAL PROCEDURES AND RESULTS

GdBaCo2O5+δ was synthesized by a conventional solid-state reaction technique14 and the desired oxygen content wasadjusted on three aliquots according to annealing conditionsand thermal treatments reported by Taskin et al.2 The oxygencontent was determined by the procedure described in Ref. 15;δ = 0.54(1), δ = 0.57(1), and δ = 0.63(1) were found for thethree prepared samples.

XRPD patterns were collected at the ID31 beamline of theEuropean Synchrotron Radiation Facility (ESRF) in Grenoble.For each sample, 40 diffraction patterns were collected inthe 0 < 2 ϑ < 20◦ range from 300 to 400 K selecting awavelength of λ = 0.39620(5) A. Moreover, some high-qualitydiffraction patterns were collected at λ = 0.35422(1) A for atotal counting time of 1 h at selected T between 300 and

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MATTIA ALLIETA et al. PHYSICAL REVIEW B 84, 235144 (2011)

(a) (b)

FIG. 1. (a), (b) Selected region of XRPD patterns as collected atdifferent temperatures for the δ = 0.54(1) and δ = 0.57(1) samples,respectively. The black dots are the experimental data while thecontinuous lines are the results from Rietveld refinements. The Millerindexes of the diffraction peaks are also reported. Typical agreementfactor R(F 2) between observed and calculated XRPD patterns rangefrom 0.06 to 0.08.

400 K depending on sample composition. Data were analyzedusing the Rietveld method as implemented in GSAS softwaresuite.16 All the data sets have been refined against the Pmmmmodel derived from the cubic perovskite by doubling alongthe b and c axes (ac × 2ac × 2ac unit cell, where ac standsfor the cell parameter of the cubic perovskite lattice).4 Toaccount for the actual δ values in structural models, welocated the extra oxygen ions (with respect to δ = 0.5)at the 1c (0,0,1/2) position considering the 1g (0,1/2,1/2)fully occupied. This is equivalent to considering an orderedalternation of Copyr and Cooct along the [010] direction forδ = 0.5.1,4,6,17 The Rietveld refinements in selected portionsof the diffraction patterns collected at various temperatures forδ = 0.54(1) and δ = 0.57(1) samples are shown in Fig. 1.Refined lattice parameters are shown for all the samplesin Fig. 2.

The presence of splitting in the diffraction profile of (040),(020), and (002) peaks is evident for δ = 0.54(1) and δ =0.57(1) in a narrow T range ( ∼7–8 K) below TIM ≈ 365 K1–5

as shown in Fig. 1. This phase transition in the proximity ofIMT is well known to occur in LnBaCo2O5.5

4,6,12,18 and thepresence of peak splitting in the XRPD patterns is related tocoexistence of the low- and high-T structural phases. The latterfinding provides evidence for the first order of the transition.18

As shown in Fig. 2, with increasing T toward IMT, both theb and c lattice parameters exhibit a steplike increase while a

suddenly shrinks for both δ = 0.54(1) and δ = 0.57(1) samples.No phase coexistence was evidenced by the XRPD patterns ofthe δ = 0.63(1) sample, since b and c linearly increase in300 � T � 400 K range and a decreases up to T ∼ 325 K.The anisotropic thermal expansion of the unit cell parametersresults in a variation of the unit cell volume. By comparingunit cell volume values as a function of T and δ reported inthe insets of Fig. 2, we note that the discontinuity which holdsfor first-order transition is apparent only for δ = 0.54(1). Thisprovides an indication that the order of the structural phase

(a)

(b)

(c)

FIG. 2. (a)–(c) Lattice parameters a (filled squares), b/2 (emptycircles), and c/2 (filled circles) as a function of temperature aredisplayed for δ = 0.54(1), 0.57(1), and 0.63(1), respectively. Insets:the temperature dependence of the unit cell volume for selectedtemperature range.

transition may change from the first to second order uponincreasing δ.

EPR measurements were performed on a Bruker ELEXSYSspectrometer equipped with an ER4102ST standard rectangu-lar cavity at X band (9.4 GHz) frequency in the temperaturerange 305–450 K every 5 K. Powdered samples were placedinto quartz tubes and the derivative dP/dH of power P

absorbed was recorded as a function of the static magneticfield H .

In Fig. 3 we show EPR spectra as a function of temperaturefor δ = 0.54(1) sample, as an example. The signal consistsof a single broad resonance line. It is well known that theCo3+ EPR signal cannot be observed because of a too-shortrelaxation time19 so that the EPR signals in GdBaCo2O5+δ canbe originated from the shift and/or broadening of the Gd3+resonance caused by exchange interaction Jf sS·s betweenlocalized 4f electron spin (S) and the spins (s) of the transitionmetal.13

At each T , the spectra were well fitted by a single Dysonianlineshape20 shown as a solid line in the inset of Fig. 3. However,meaningless negative dispersion-to-absorption α contributionswere evaluated in these EPR features. By comparing ourspectra with the Dysonian line reported in the literaturefor other perovskitic systems,21 we found that the EPRfeatures measured by us correspond only to a part of theliterature-reported line.21 In particular, the left lobe of theEPR spectrum shown in the inset of Fig. 3 is too broad tobe fully observable. This leads to unreliable numerical valuesof the x0 (peak position), α, or w (linewidth) parameters.Another possible reason could be the presence of multiple

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FIG. 3. (Color online) EPR spectra of the δ = 0.54(1) sampleas a function of temperature. The arrow outlines their trend withincreasing temperature and in particular at the critical temperatureTc ≈ 365 K. In the inset an example of fit using a Dysonian line shapeis shown (open circles: observed data; solid line: fit).

signals as reported for other Co-based oxides.22 However,attempts by linear combinations of Lorentzian and Gaussianfunctions gave no improvement to the lineshape description.We decided to extract the peak-to-peak linewidth (�Hpp) bydirect observation of the experimental patterns as indicated inthe inset of Fig. 3. The trend of �Hpp with temperature isshown in Figs. 4(a)–4(c) for all the samples. It should be notedthat in our spectra the base line is not well defined and, hence,we cannot determine directly the peak position.

�Hpp shows three different temperature-dependent regionsfor δ = 0.54(1) and δ = 0.57(1): (i) It is roughly constant ordecreases smoothly between 300 and 330 K; (ii) it decreasessteeply with increasing T toward a critical temperature Tc for∼330 < T < ∼ 360 K; (iii) it exhibits a distinct kink at Tc =360 ± 5 K, then approaches constant values up to T = 450 K.The behavior of �Hpp is rather different for the δ = 0.63(1)sample, showing a smaller �Hpp value at T = 300 K withjust a weak decrease at Tc ∼ 325 K. All the samples displaya similar �Hpp value at T > Tc. In Fig. 4(d) we compare theTc with the TIM values determined by Taskin et al. for δ =0.50 and δ = 0.65 from resistivity measurements.2 The goodagreement between the two critical temperatures as a functionof δ indicates that the EPR linewidth change at Tc is consistentwith the IM transition. Tc = TIM will be considered hereinafter.

III. DISCUSSION AND CONCLUSION

According to magnetization measurements performed byRespaud et al.17 on a GdBaCo2O5.54(3) sample, a drasticchange in the Weiss-Curie temperature �WC and effectivecobalt magnetic moment was observed above TIM. In orderto estimate the strength of the magnetic interactions involved,we calculated the value of the isotropic exchange constants (J )

(a)

(b)

(c)

(d)

FIG. 4. (a)–(c) �Hpp against temperature for δ = 0.54(1), δ =0.57(1), and δ = 0.63(1), respectively. (d) The Tc (filled circles)highlighted in panels (a)–(c) are compared with TIM reported byTaskin et al. (Ref. 2) (open squares).

using the molecular field theory for three-dimensional (3D)systems. To compute J from the molecular field equation,23

we assumed the model proposed by Taskin et al.1,2 in whichthe magnetic interactions are generated by IS-Co3+ and weused the modulus of the values of �WC reported below andabove the IMT.17 By considering S = 1 for IS-Co3+ and Z =3, i.e., by counting only for nearest neighbors, we estimated|Jins|/kB ≈ 69 K and |Jmet|/kB ≈ 150 K in the insulatingand metallic phases, respectively. This corresponds to a ratioof |Jmet|/|Jins| ∼ 2 indicating that the isotropic exchangeinteractions between cobalt ions increase above TIM.

In the case of strong isotropic exchange interactions theGaussian EPR linewidth is narrowed into a Lorenztian linewith �Hpp given by 23–25

�Hpp = hM2

gμBωex, (1)

where ωex ≈ J /h is the frequency of the isotropic exchangeinteractions caused by the Heisenberg Hamiltonian H

ijex

(=J si · sj ) between neighboring spins si and sj . It should be

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noted that, in the case of an asymptotic regime as observedat T →300 K and at T →TIM for δ = 0.54(1) and δ =0.57(1) samples, both the second moment M2 and the exchangefrequency ωex are temperature independent. Basically, Eq. (1)can be employed to explain that the �Hpp asymptotic value atT > TIM in the metallic phase is smaller than that reachedat T →300 K in the insulating phase. According to theequation, above TIM the decreasing of �Hpp can be justifiedby an increase of the frequency of the isotropic exchangeinteractions ωex and/or by a decrease in the second momentM2. As a matter of fact, M2 parameter depends on anisotropicexchange interactions and can be determined by measuringthe angular dependence of EPR linewidth or g factor as afunction of several orientations of a single crystal samplein the external magnetic field.26 As we deal with powderedsamples, we cannot resolve the anisotropy of the EPR spectraand, hence, we cannot say anything about the influence ofsuch parameter to explain the strong narrowing. On the otherhand, from ωex ≈ J /h we can scale the J ratio accordinglyand deduce that ωmet

ex > ωinsex . Thus, the observed temperature

decreasing of the �Hpp above TIM is compatible with anenhancement of the isotropic exchange frequency term in themetallic phase.

According to the model proposed by Maignan et al.,8 theincrease of spin-spin exchange frequency observed at T >

TIM in δ = 0.54(1) and δ = 0.57(1) samples can be easilyunderstood as an increasing of hopping probability of 3d

electrons between nearest-neighbor Co ions. The metallic stateis interpreted as the motion of an extra electron from an excitedHSCo2+ ion to a HS or to an ISCo3+ ion.8 However, thismodel does not explain how Co2+ ions are created and doesnot consider that a motion of one eg electron from HSCo3+

to ISCo3+ would generate an unstable non-LSCo4+. To avoidthe production of such cobalt species, we suppose that theCo3+

oct sites in the metallic phase of an ideal δ = 0.5 sampledisplay the IS state together with a T -independent ISCo3+

pyr.4 It

should be noted that an eg electron hopping from an ISCo3+oct

to the next ISCo3+oct along the a and c axes and/or to the next

ISCo3+pyr along the b axis generates, in any case, a couple of

LSCo4+ and HSCo2+ stable species. For example, the electrontransfer along the b axis from Copyr to Cooct and vice versa canbe sketched as t5

2ge1g − ISCo3+

pyr + t52ge

1g − ISCo3+

oct → t52ge

0g −

LSCo4+pyr + t5

2ge2g − HSCo2+

oct (Fig. 5). This process justifies

high ωex above TIM since the presence of LSCo4+pyr and HSCo2+

oct

implies double exchange (DE) interaction between LSCo4+pyr

and HSCo2+oct and ISCo3+

oct/pyr ions occurring along the b axis.At the same time, the formation of eg conduction band of IScharacter gives rise to the observed metallic ground state sinceDE paths formed by the 3D network of ISCo3+

oct/pyr account forelectronic delocalization in all directions. Upon cooling belowTIM, a SST from IS to LS state can occur solely at Co3+

oct whilethe Co3+ in pyramid remains in IS state.4 Within this spinconfiguration, t2g electron hopping from LSCo3+

oct to ISCo3+pyr

produces a couple of LSCo4+oct and HSCo2+

pyr. Conversely eg

electron hopping from ISCo3+pyr to LSCo3+

oct ions generates stable

LSCo4+pyr but unstable ISCo2+

oct (Fig. 5). This latter processaccounts for the decreased ωex value since the above sketchedmodel to produce Co4+-Co2+ pairs would be no longer valid.

(a)

(b)

FIG. 5. Schematic electronic level diagram of Co in GdBaCo2O5.5

showing the processes of eg electron hopping. On the left-hand side of(a), (b) the eg electron transfers from pyramidal to octahedra Co sitesare displayed in the metallic and insulating phases, respectively. Onthe right-hand side of the same panels the diagram related to cobaltspecies generated after the hopping processes are shown.

Hence, we can say that the proposed mechanism identifies theSST from LSCo3+

oct to ISCo3+oct as a possible origin for the IMT.

The temperature-induced SST is corroborated by the suddenunit cell volume expansion observed for δ = 0.54(1) sample.Indeed the transition to a higher spin state in Co3+ impliesbigger ionic radius with respect to LSCo3+.4,5

Dealing with δ > 0.5 samples, the role of the increasedamount of LSCo4+ induced by increasing δ must be takeninto account in the above mechanism. As suggested by Taskinet al.,2,3 the presence of LSCo4+ can imply double exchange(DE) interaction between LSCo4+, ISCo3+, and LSCo3+.These exchange channels are active even at room temperatureand can be considered to enlighten the gradual improvementin the conductivity that blurs the IMT with increasing δ.2,3

We argue that the δ dependence of EPR results reported herecan be understood considering the interplay between SST andDE. Looking at the �Hpp temperature dependences, distincttransitions were found for δ = 0.54(1) and δ = 0.57(1) samplesand we can suggest that the DE contribution is negligible forδ � 0.57 (i.e., Co4+/Co3+ � 7.5%). Conversely, the weakeffect observed in the temperature dependence of �Hpp for δ =0.63(1) (i.e., Co4+/Co3+ ≈ 15%) can be explained consideringa strong contribution of DE that accounts for high ωex valueeven at room temperature. Moreover we observe a gradualdecrease of �Hpp value increasing δ above 0.54(1) at 305 K.This is a further confirmation that the narrowing of the EPRline with increasing Co4+ concentration can be fully explainedby the DE channel between LSCo4+ and LS/ISCo3+ active atT < TIM.

To compare the XRPD and EPR results, in Fig. 6(a)we plot the normalized change of �Hpp, δ�Hpp/�Hpp =[�Hpp(305)–�Hpp(T )]/�Hpp(305), together with the nor-malized changes of the lattice constants for δ = 0.54(1) sample,

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(a)

(b)

FIG. 6. (Color online) (a) The normalized �Hpp (open squares)values are reported together with the normalized a (filled circles), b/2(open circles), and c/2 (filled squares) axes for δ = 0.54(1) sample.(b) The normalized data (a axis and �Hpp) are reported for δ =0.57(1). The activation model proposed (solid line) is superimposedin panels (a), (b) to experimental data.

�L/L = [L(305)–L(T )]/L(305) where L = a, b, c. In thebiphasic region we considered an average lattice parametervalue calculated as F1L1 + F2L2, where L is the latticeparameter and F is the relative phase fraction. Indices 1 and 2stand for low-T and high-T phases, respectively.

As shown in Fig. 6(a), it is clear that the tempera-ture dependences of δ�Hpp/�Hpp and �a/a fairly over-lap each other and the change of �Hpp is much largerthan that of the latter parameter; e.g., at T = 400 K,δ�Hpp/�Hpp ≈ 15% and �a/a ≈ 0.5%. In particular, �a/a

is the only normalized lattice parameter that increases as afunction of T and saturates above TIM in a manner remarkablysimilar to δ�Hpp/�Hpp. This could give evidence that theCo-O-Co interatomic distances along the [100] directioncontract with increasing T giving rise to the enhancementof the spin-spin exchange frequency along this direction andthe decreasing of �Hpp. These results suggest spin-latticeinteraction along the a axis.

Anisotropic interactions involving Co3+ spin and crystalstructure are not new in the GdBaCo2O5+δ system. Inparticular, Taskin et al.1 found Ising-like behavior of spinsalong the a axis in the ferromagnetic (FM) phase of

GdBaCo2O5.5 single crystal below the Curie temperature TCurie

∼275 K.1,2 According to the proposed model,1 the insulatingFM ground state is generated from the interaction of ISCo3+ions forming two-leg ladders extended along the a axis.1,2

These ladders are separated from each other, along the b axis,by ac CoO2 layers composed by nonmagnetic LSCo3+.1,2

Above TCurie a clear FM-to-paramagnetic (PM) transitionis observed in the magnetization curve of δ ≈ 0.5 samplecomposition.1 Basically, two contrasting explanations can begiven for such transition: (1) Cobalt spins keep their spin easyaxis in the direction of the a axis but the interaction betweenFM ladders becomes weaker than the PM contribution ofGd3+; (2) the orientation FM order of Co3+ Ising-like spins iscompletely destroyed above TCurie.

Ising-like behavior of spins and the observed δ�Hpp/�Hpp

and �a/a scaling behavior shows that the a axis is thepreferred crystallographic direction for distinct phenomenarelated to the FM and the PM phases. According to Taskinet al.1,2 in the FM phase the a axis is the preferred directionfor magnetization which precludes the formation of magneticmoments along the b and c axes. Above TCurie, in the PMphase, the a axis is the preferred direction for the spin-lattice interaction which is connected mainly to spin-spinexchange channels. In order to make a link between the twodistinct phenomena occurring along the same crystallographicdirection, we might suggest that something related to the natureof spins of the FM phase is retained along the a axis evenwhen the phase is PM. This could support explanation (1)given above and, more importantly, the bridge between FMand PM could be useful to figure out the interplay betweenthe spin-lattice interaction and SST. Indeed, with increasingT and by approaching the IMT from the FM phase, theSST from LS to ISCo3+ occurs in the octahedral ac layersstacked along the b axis. On the other side, we suggest that thegeneration of the ISCo3+ state, holding to lattice deformation,can be significantly influenced by the nature of spins of theFM phase along the a axis. Hence, strong coupling betweenspin-spin exchange interactions and the a lattice parametercan be made explaining the observed �a/a and δ�Hpp/�Hpp

scaling.In our model the SST is linked with an increasing of

spin-spin exchange frequency which is the driving force ofIMT. The formation of the metallic phase could be thenexplained by thermally activated hopping of spins betweenneighboring Co sites where the SST from t6

2ge0g-LS state to

a cobalt high-spin state enhances the number of electronsin the eg conduction band.4 To account for such behaviorwe consider that the change of �Hpp can be described byδ�Hpp/�Hpp ≈ Kexp[–E(T )/kBT ] where K is a constantand E(T ) is a temperature-dependent energy gap. The energyE(T ) is given by the parametrized power function E(T ) =E0[1–(T /TIM)3.39] used to model the temperature dependenceof energy splitting between ground and excited spin states ofCo in GdCoO3 system.27 Using the optical band-gap widthEg = 0.26 eV given in Ref. 28, we calculated the solidlines shown in Figs. 6(a) and 6(b). The good agreementbetween model and observed data proves the role of excitedCo spin states and, thus, SST in the IMT dynamics of the δ =0.54(1) sample. These considerations are still valid for the δ =0.57(1) sample, as shown in Fig. 6(b). Conversely, just a weak

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(a) (b)

FIG. 7. (Color online) (a), (b) The ab planar bond lengthdifference (Dab) values as a function of T for δ = 0.54(1) (circles),to δ = 0.57(1) (squares) and δ = 0.63(1) (triangles) are reported inthe octahedral and pyramidal environment, respectively.

correlation between the �a/a and δ�Hpp/�Hpp trends wasfound for δ = 0.63(1) up to ∼325 K.

Co3+ in IS state is a Jahn-Teller (JT) active ion, so thatwe expect an increased JT distortion across TIM. Aimingto account for Q2-type JT distortion, we calculated thedifferences between ab-planar long and short Co-O bondlengths10 (Dab) obtained by Rietveld refinements against thehigh-quality XRPD data.29 In Fig. 7 the Dab values related tooctahedra and pyramids are plotted as a function of T for allthe samples.

In the former case, Dab increases linearly with increasingtemperature for δ = 0.54(1), indicating that the Q2-typedistortion of the basal plane increases when heating aboveTIM. Interesting features come out with increasing δ. At T ≈300 K, the Dab values are very similar for δ = 0.54(1), δ =0.57(1), and δ = 0.63(1). This indicates that increasing δ wellabove 0.5 does not significantly affect the Co-O distances inthe octahedra. Dab seems to increase linearly with increasingT for δ = 0.57(1), approaching a constant value aboveTIM. Conversely, Dab remains practically unchanged for δ =0.63(1). In the pyramid, the Dab parameters were weakly δ

dependent and they did not change significantly with T . Thisis in agreement with the assumption of T -independent ISCo3+

pyrstates.

The increasing of Dab distortion observed by the XRPDanalysis of the δ = 0.54(1) sample corroborates the occurrenceof the proposed SST through the gradual population of theJT-active IS state. On the other hand we have suggested thatthe DE interactions between LSCo4+ and LSCo3+

oct and ISCo3+pyr

(Ref. 1) strengthens with δ increasing above δ � 0.54(1)giving rise to a blurred IMT.2 We then expect that the strongDE contribution can also restrain the temperature-inducedSST by making the LSCo3+

oct species less available for thetransition. This leaves the high-temperature ISCo3+ states lesspopulated and destroys the JT effect at Co3+

oct sites. Such effectsare supported by the absence of a sudden unit cell volumeexpansion across IMT and the saturation of Dab above TIM forδ = 0.57(1) sample as shown in Fig. 7. In addition, the lack ofphase coexistence and the temperature-independent behaviorof the Dab parameter for δ = 0.63(1) further confirms theremoval of the JT with increasing δ. These structural effectsgive evidence to the occurrence of a transition from low-spinto JT-active intermediate spin state and should support themechanism proposed to explain IMT.

In conclusion, the increasing of electron hopping probabil-ity between Co in different spin states can be indentified asthe main driving force for IMT in GdBaCo2O5+δ system. EPRdata are consistent with this model and the increasing of ωex

with increasing T can be explained by taking into account theSST from LSCo3+

oct to ISCo3+oct . XRPD and EPR results give

evidence about a strong coupling between the SST and thecrystal structure. To figure out the nature of this couplingand its connection with IMT two ingredients are needed:(i) spin-lattice interaction along the a axis; (ii) JT distortioninduced by ISCo3+

oct which is removed with increasing δ givingrise to a blurred IMT.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the European Syn-chrotron Radiation Facility for provision of beam time andDr. Adrian Hill for assistance in using the ID31 beamline andan anonymous reviewer for fruitful comments.

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29See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.84.235144 for diffraction patterns and tablescontaining refined structural parameters obtained from the high-quality XRPD collected at λ = 0.35422(1) A at selected tempera-tures between 300 and 400 K.

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