Transport and magnetic properties of GdBaCo_{2}O_{5+x} single crystals: A cobalt oxide with square-lattice CoO_2 planes over a wide range of electron and hole doping

1.3 MB·English

by  A. A. Taskin

Transport and magnetic properties of GdBaCo O single crystals: A cobalt oxide
2 5+x
with square-lattice CoO planes over a wide range of electron and hole doping
2
A. A. Taskin,∗ A. N. Lavrov,† and Yoichi Ando
Central Research Institute of Electric Power Industry, Komae, Tokyo 201-8511, Japan
SinglecrystalsofthelayeredperovskiteGdBaCo2O5+x (GBCO)havebeengrownbythefloating-
zone method, and their transport, magnetic, and structural properties have been studied in detail
5
overa wide range of oxygen contents, 0≤x≤0.77. The obtained data are used to establish a rich
0
0 phasediagramcenteredatthe“parent”compoundGdBaCo2O5.5 –aninsulatorwithCoionsinthe
2 3+state. AnattractivefeatureofGdBaCo2O5+xisthatitallowsapreciseandcontinuousdopingof
CoO2 planeswitheitherelectronsorholes,spanningawiderangefromthecharge-orderedinsulator
n
at 50% electron doping (x = 0) to the undoped band insulator (x = 0.5), and further towards
a
theheavily hole-doped metallic state. This continuousdopingis clearly manifested in thebehavior
J
of thermoelectric power which exhibits a spectacular divergence with approaching x=0.5, where it
8 reacheslargeabsolutevalues(±800µV/K)andabruptlychangesitssign. Atlowtemperatures,the
2
homogeneous distribution of doped carriers in GBCO becomes unstable, as is often the case with

strongly correlated systems,and boththemagneticand transport propertiespoint toan intriguing
]
l nanoscopic phaseseparation intotwoinsulating phases(for electron-doped region) or an insulating
e anda metallic phases (for hole-doped region). Wealso findthat throughoutthecomposition range
-
r the magnetic behavior in GBCO is governed by a delicate balance between ferromagnetic (FM)
t and antiferromagnetic (AF) interactions, which can be easily affected by temperature, doping, or
s
. magneticfield,bringingaboutFM-AFtransitionsandagiantmagnetoresistance(MR)phenomenon.
t
a What distinguishes GBCO from the colossal-MR manganites is an exceptionally strong uniaxial
m anisotropy oftheCospins, which dramatically simplifies thepossible spin arrangements. This spin
- anisotropy togetherwith thepossibility of continuousambipolar dopingturnGdBaCo2O5+x intoa
d model system for studying the competing magnetic interactions, nanoscopic phase separation and
n accompanying magnetoresistance phenomena.
o
c PACSnumbers: 72.80.Ga, 72.20.Pa,75.30.Kz,75.47.De
[

1
I. INTRODUCTION ison of different systems could give a clue to the be-
v
havior of cuprates and manganites, and because those
6
less studied systems might be interesting in their own
0
Since the discovery of the high-T superconductivity
7 c right. Such exploration has indeed been proven to
(HTSC)incupratesandshortlyafterofthecolossalmag-
1 be very fruitful, resulting, for instance, in the discov-
0 netoresistance (CMR) in manganites, a great deal of ex- ery of unconventional superconductivity in a layered-
5 perimentalandtheoreticaleffortshavebeenmadetoclar- perovskite ruthenium oxide4 and recently in a layered
0 ifythenatureofthesephenomena. Theresearchhassoon cobalt oxide.5 A study of nickel and cobalt oxides has
t/ revealedthatthe unusualbehaviorofcupratesandman- also revealed the spin/charge ordering phenomena6,7,8,9
ma ganites is not limited to HTSC and CMR: These com- and nanoscopic phase separation10,11 closely resem-
pounds based on seemingly simple metal-oxygen planes
bling those in cuprates and manganites; these obser-
- turn out to possess very rich phase diagrams, originat-
d vations confirm that the charge ordering is indeed a
ing from strong electron correlations and involving spin,
n generic feature of strongly correlated electrons. By
charge, orbital, and lattice degrees of freedom.1,2,3 In
o now, probably the most rich and intriguing behavior
c particular, the strong electron correlations, which pre- has been found in cobalt oxides, which ranges from gi-
v: vent the electrons in partially filled bands from form- antMR12,13,14,15,16,17 andlargethermoelectricpowerat-
i ing conventional itinerant Bloch states, make these sys- tributed to strong electron correlations18,19,20,21 to un-
X tems prone to nanoscopic phase separation and self- conventional superconductivity.5 Apparently, the cobalt
r organization of electrons into various superstructures.
oxides, which are still much less studied than cuprates
a
The role of this electron self-organization still remains
or manganites, are meant to become the next primary
controversial. It is often argued, for example, that the
field in investigations of the strongly correlated electron
HTSC and CMR would never be possible in a homoge-
systems.
neous system,andit is the nanoscopicmixture ofphases
Unlike cuprates and manganites, the layered cobalt
that stays behind these novel phenomena.2,3
oxides have two substantially different crystallographic
Ironically,thecomplexityofmanganeseandcopperox- types: thelayeredperovskitesderivedfromsquare-lattice
ides that brings about all the fascinating physics also CoO planes, similar to HTSC and CMR compounds,
2
makes these compounds very difficult for understand- and compounds like Na CoO derived from triangular-
x 2
ing. The research thus naturally expanded towards lattice CoO planes. In both cases,the CoO planes can
2 2
other transition-metal oxides, both because the compar- be doped with charge carriers over a remarkably wide
2
range so that the effective valence of Co ions varies from
Co2+ to Co4+.1 In other words, the doping level ranges
from one electron to one hole per Co ion, if the Co3+
state withevennumberofelectronsis takenas the “par-
ent”state. Empirically,thesquare-latticeandtriangular-
lattice systems behave quite differently. For example,
the square-lattice cobalt oxides, such as La Sr CoO ,
2−x x 4
Bi Sr CoO , and RBaCo O (where R is a rare
2 2 6+δ 2 5+x
earth element), are usually reported to be non-
metallic,8,11,12,13,14,15,16,17,22,23,24,25withtheexceptionof
heavily hole-doped cubic perovskites La Sr CoO .10
1−x x 3
In contrast, the triangular-lattice cobaltites often ap-
pear to be fairly good metals,18,26,27 with the hydrated
Na CoO being even a superconductor.5 This difference
x 2
in behavior may come in part from a disparity in the
doping level, given that the latter compounds were usu- FIG. 1: Schematic picture of the RBaCo2O5+x structure for
ally studied in a more highly hole-doped region. Never- x = 0.5. It is worth noting that the oxygen ions in [ROx]
theless, the surprisingly robust non-metallic state in the layers demonstrate a strong tendency to ordering; for x =
square-lattice cobalt oxides11,25 clearly points to a more 0.5, forexample,theyform alternatingfilledandemptyrows
runningalong thea axis.12,23,28
fundamental source, which is presumably a very strong
tendency to charge ordering. In the triangular-lattice
compoundssuchtendencymightbeconsiderablyweaker.
Indeed, the charge ordering usually gains support from of already grown RBaCo O crystals can be modified
2 5+x
theantiferromagnetic(AF)exchange,whileinatriangu- byannealingatvarioustemperaturesandoxygenpartial
lar lattice the AF spin interactions should inevitably be pressures, which may allow one to span the entire phase
frustrated. Thus far, however, non of these systems has diagram using one and the same single crystal. Further-
been systematically investigated over the entire doping more, by varying the oxygen content one can tune the
rangetorevealacoherentpictureofdopedcobalt-oxygen dopinglevelverysmoothly,whichgivesagreatadvantage
planes. in studying the critical regions of the phase diagram.
Inthis work,we undertakeasystematic study ofmag- Upon choosing a compound from the RBaCo O
2 5+x
netic and transport properties of a square-lattice cobalt group, one would prefer to have a non-magnetic R ion,
oxide over a wide doping range. For this purpose, we such as Y, La, or Lu, to avoid additional complica-
have selected the RBaCo2O5+x compounds (where R is tion coming from the rare-earth magnetism. Unfortu-
a rare earth element), which have already attracted a nately, the growth of single crystals with these non-
lot of attention owing to such fascinating features as magneticelementsturnsouttobevirtuallyimpossible.31
the spin-state and metal-insulator transitions, charge Therefore, we have selected the GdBaCo O com-
2 5+x
and orbital ordering phenomena, and giant magne- pound: Gd3+, being a 4f7 ion with zero orbital mo-
toresistance (GMR).8,9,12,13,14,15,16,17,22,23,24,28,29,30 The ment, is known to show rather simple magnetic be-
RBaCo2O5+x compoundspossessalayeredcrystalstruc- havior in transition-metal compounds, making predom-
turewhichconsistsofsquare-latticelayers[CoO2]-[BaO]- inantly paramagnetic contribution, which can be easily
[CoO2]-[ROx]stackedconsecutivelyalongthecaxis(Fig. subtracted from the overall magnetization. Also, ow-
1) – a so-called “112”-type structure.12 This structure ing to the intermediate size of Gd ion in the series of
is derived from a simple cubic perovskite R1−xBaxMO3 rare-earth elements, GdBaCo2O5+x allows a fairly wide
(where M is a transition metal), but in contrast to the range of available oxygen concentration. Recently, we
latter, the rare-earthand alkali-earth ions are located in succeeded in growing high-quality GdBaCo O single
2 5+x
their individual layers instead of being randomly mixed. crystalsusingthefloating-zone(FZ)technique,andstud-
WhatmakesRBaCo O compoundsparticularlyat- ied the magnetic and transport properties of the parent,
2 5+x
tractive for our study is a large variability of the oxygen x=0.50, composition.17
content: By changing the annealing conditions, one can Here, we present a systematic data on the evolution
modify the oxygenconcentrationin the rare-earth[RO ] of transport, magnetic, and thermoelectric properties of
x
planes (Fig. 1) in a wide range, 0 ≤ x ≤ 1 (x depends well-characterizedGdBaCo O singlecrystalsoverthe
2 5+x
alsoonthesizeofR3+ ion).12,28 Inturn,theoxygencon- entiredopingrangeavailableforthiscompound,namely,
tentcontrolsthenominalvalenceofCoions,whichvaries 0 ≤ x ≤ 0.77. This layered cobalt oxide turns out to
from 2.5+ to 3.5+, passing through 3+ (“parent” state) beareallyfascinatingfilling-controlsystemwhichallows
at x = 0.5. Ordinarily, experimental investigations of a continuous ambipolar doping: We have developed a
theT−xphasediagramsofsolidsareverytimeconsum- technique that provides an easy and precise tuning of
ing, because they require to grow many single crystals the oxygencontent in GdBaCo O single crystals and
2 5+x
of different compositions. In contrast, the composition ceramics, and succeeded in doping the parent semicon-
3

ductor (x = 0.50) with electrons (x < 0.50) or holes // // //
(x > 0.50) with steps that could be as small as 0.001 100 a axis 200
per Co ion (∆x ∼ 0.001). As a result, we could ob- (040)
serve spectacular singularities in the transport proper- x 10
ttitsmihipeteiipsnoamunocpotrbodtoeniefotrwnaainpesogepmfnriaondtlaolhtcpahehemiidsfneogcrhuortonomhltmeeposaoufgaundnnndoeddpot.pieecdelOedaccunatsrrdrtorasinttaeeusnr,,dstciyaofoennuhrdrlatdohssmetcruoecadmvogyemnpaetpalthereidece- ensity (arb. units) 010 x 50////////020x 1 0 //////// 030bx 2 5a xis //////// 040 5ensity (10 cps)1
aisrfiochunpdhatsoeidnicalgurdaemrefogriotnhsisolfayaenreidntcroigbuailntgoxniadne,oswchoipcihc Int 001 002 c axis003 004 Int0
phase separation over virtually the entire doping range. x 70 x 2 x 5 -0.2 0.0 0.2
This paper is organized as follows. In Section II, we 11 12// 23 /3/4 35 //46 47 48 qD (deg)
describe the growth of high-quality GdBaCo2O5+x sin- 2q (deg)
gle crystals by the floating-zone technique, the method
of modifying their oxygen content, and the detwinning FIG. 2: (Left) X-ray Bragg’s peaks for GdBaCo2O5+x (x =
technique used to obtain single-domain orthorhombic 0.5) crystals, which demonstrate theunit-cell doubling along
crystals. The details of magnetic and transport mea- the b and the c axis (each peak has CuKα1 and CuKα2 con-
surements are also presented in Section II. Section III tributions to the diffraction pattern). For convenience, the
starts with a brief summary of the crystal structure peak intensity is multiplied by a factor indicated near each
peak. (Right) X-ray (040) rocking curve.
of GdBaCo O over the oxygen-concentration range
2 5+x
0 ≤ x ≤ 0.77, which is followed with the experimental
results ontransport, thermoelectric, and magnetic prop-
erties of GdBaCo2O5+x, studied in this wide range of ing the ordered “112” crystal structure, and for reduc-
oxygen concentrations. The obtained data are used to ing the number of domains in the resulting crystalline
establish an empirical phase diagram presented at the rod; higher rates inevitably caused multi-domain crystal
end of this section. The implications of our observations growth. Using optical microscopy and Laue x-ray back-
are discussed in Section IV. Based on the obtained ex- reflection control, we selected single-domain parts of the
perimental results, first we propose a magnetic and elec- growncrystalrodand cut them into parallelepipedsam-
tronicstructure ofthe parentGdBaCo2O5.50 compound, ples suitable for structural, transportand magnetization
giving our explanation of its transport behavior and the measurements. All the samples’faces were carefully pol-
origin of GMR; then we discuss the effects of doping in ished and adjusted to the crystallographic planes with a
GdBaCo2O5+x;and,finally,suggestanoverallelectronic 1◦ accuracy.
phasediagramforthiscompound. SectionVsummarizes
The homogeneity and stoichiometry of the obtained
our findings.
GdBaCo O crystals were analyzed by the electron-
2 5+x
probe microanalysis (EPMA) and inductively-coupled
plasma(ICP) spectroscopywhich confirmedthatthe ac-
II. EXPERIMENTAL DETAILS
tual cation composition was uniform, corresponding to
thenominal1:1:2ratiowithintheexperimentalaccuracy.
A. Growth of GdBaCo O crystals
2 5+x Another important issue is whether Gd and Ba are well
ordered in the lattice; in fact, we found that large rare-
We have grown high-quality GdBaCo2O5+x single earth ions, such as La and Pr, easily mixed with Ba,
crystalsbythe floating-zonetechnique,usinganinfrared resulting in a disordered cubic phase R Ba CoO .
0.5 0.5 3−δ
image furnace with two halogen lamps and double ellip- InthecaseofGdBaCo O crystals,however,thex-ray
2 5+x
soidal mirrors (NEC Machinery SC E-15HD). A poly- diffraction data demonstrate that Gd and Ba are indeed
crystalline feed rod for the crystal growth was prepared well ordered into consecutive (001) layers, which results
by the solid-state reaction of Gd2O3, BaCO3, and CoO in the doubling of the unit cell along the c axis (Fig. 2).
dried powders: The mixture was successively calcined Moreover,fortheoxygenconcentrationx≈0.5,theoxy-
at 850◦C, 900◦C, 950◦C, and 1000◦C, each time for 20 gen ions are found to form alternating filled and empty
hours, with carefulregrinding after each sintering. Then chains running along the a axis; this brings about the
the obtained homogeneous single-phase GdBaCo2O5+x doublingoftheunitcellalongthebaxis(Fig. 2). Appar-
powder was isostatically pressed (at ∼70 MPa) to form ently, such long-range oxygen ordering would hardly be
a rod with typical dimensions of 7 mmφ × 100 mm. Fi- possible if considerable amount of Ba were substituting
nally,thefeedrodwasannealedat1200◦Cinairtomake Gd in GdO layers. Figure 2 shows also a typical x-ray
x
it dense and hard. rocking curve (040) for GdBaCo O , which has a full-
2 5.5
The crystal growth was performed in a flow of dried width-at-half-maximum(FWHM) oflessthan0.1◦,indi-
air, at a constant rate of 0.5 mm/h. We found that catingthatourcrystalshavefewmacroscopicdefects. An
such rather slow growth rate was essential for obtain- additional evidence for the macroscopic crystallographic
4
0.6 0.6
perfection is the ease with which the crystals could be
(a) (b)
cleaved,especially along the {001}planes, exposing per-
0.5 0.5
fectly flat, shiny surfaces.
q
nt, xe 0.4 0.4
B. Tuning the oxygen content in GdBaCo2O5+x onte 0.3 0.3 400oC
n c GdBaCoO 55 0 oC
1. Equilibrium oxygen concentration as a function of yge 0.2 oxyge2n5+x 0.2 700oC
temperature and oxygen partial pressure Ox pressure
1 bar
0.1 0.1
0.2 bar
Owing to the layered“112”crystalstructure, the oxy- 0.01 bar
gencontentinRBaCo2O5+x canbe variedwithinawide 0.0 0.0
range 0 < x < 1, where the oxygen vacancies are lo- 300 400 500 600 700 10-5 10-3 10-1 101
catedpredominantlyintherare-earthRO planes.15The T (oC) Oxygen pressure (bar)
x
mostconvenientwaytomodifytheoxygenstoichiometry
is the high-temperature annealing, yet it requires a de- FIG. 3: The equilibrium oxygen concentration xeq in
tailed knowledge of how the equilibrium oxygen content GdBaCo2O5+x. (a) Temperaturedependencesof xeq for sev-
eral values of the oxygen partial pressure. (b) Dependences
dependsonthetemperatureandoxygenpartialpressure.
Besides,oneneedstoknowthekineticsoftheoxygenex- ofxeq ontheoxygenpartialpressureatseveraltemperatures.
change: The annealing temperature should be carefully
chosen so that the oxygen exchange is quick enough for
changing remarkably with a minute (by merely 0.001)
the equilibrium state to be reachedin a reasonabletime,
modification of x. The calibrations that used the x = 0
but still slow enough to avoid unwanted oxygen absorp-
and x = 0.5 points gave the same results, which allows
tion during the subsequent cooling of the sample.
us to be confidentinabsolute values ofxinour samples.
In order to establish such dependences, we have per-
Temperature dependences of the equilibrium oxygen
formed special sets of annealings, systematically varying
content x in GdBaCo O for different oxygen partial
temperature, oxygen partial pressure P , and anneal- 2 5+x
O2
pressures are shown in Fig. 3(a), which demonstrates
ing time, as exemplified by the data shown in Fig. 3.
that a large variation of x can be achieved by relatively
By measuringthe weightchangeof ∼1-g polycrystalline
simple means: by annealing in a flow of oxygen and ar-
samples,aswellaslargesinglecrystals,witha0.1-µgres-
gonmixed in different proportions. Note that the shown
olution, we couldevaluate the changein the oxygencon-
datacorrespondtotheequilibriumstate,andthatallthe
tent ∆x with an accuracy better than 0.001. Although
changesinoxygenconcentrationarethereforecompletely
alltherelativeoxygenvariationsaremeasuredveryaccu-
reversible. Our measurements haveshownthat the equi-
rately,therewouldstillbealargeuncertaintyintheabso-
libriumxvalueatagiventemperatureisroughlypropor-
lutevaluesofx,unlesswepinthisrelativescaletotheab-
tionalto the logarithmofthe oxygenpartialpressure,as
solute oxygencontentat least at one point. Fortunately,
long as x is not too close to zero [Fig. 3(b)]. Therefore,
in GdBaCo O there are two peculiar oxygen concen-
2 5+x
inorderto obtainthe lowestoxygenconcentrationx=0
trations that allow the absolute x scale to be establish
we annealed samples in a flow of argon or helium, and
unambiguously. First,inGdBaCo O crystals,similar
2 5+x
used strongly diluted (down to 10 ppm) oxygen-argon
to other RBaCo O compounds with small rare-earth
2 5+x
ions,8,9,28 the oxygen content can be reduced down to mixturestoaccessthelow-xrange,althoughprecisetun-
ing of x in this case becomes technically more difficult.
x=0byannealinginvacuum,orinertatmosphere. One
In the opposite limit, the samples with oxygen concen-
can naturally expect the x=0 composition to be stable
trations up to x = 0.77 were prepared by annealing in
overratherbroadrangeofparameters,sinceinthisphase
oxygen at high pressures (up to 70 MPa).
all the weakly-boundoxygenis removedfromGdO lay-
x
ers, while the strongly-bound oxygen in BaO and CoO
2
layers is still intact. Indeed, we observed that x satu-
rates, approaching some lowest level [see Fig. 3(b)] as 2. Oxygen intercalation kinetics
the oxygenpartialpressure is reduced andthe annealing
temperature is increased, and we attributed this satu- As we have mentioned above, there is one more point
ration value to x = 0. Much more sensitive calibration to be concerned about, upon choosing the proper an-
can be done at the x=0.5 point, which turns out to be nealing conditions, besides the equilibrium x value: it
criticalforGdBaCo O : Uponcrossingthis point,the is the oxygen-intercalation kinetics. If the oxygen diffu-
2 5+x
mixedvalencecompositionofCo2+/Co3+ ionsturnsinto sionistooslow,onewillinevitablyendupwithacrystal
theCo3+/Co4+ one,andconsequentlythetypeofcharge having a large composition gradient; if, in contrast, the
carriers switches abruptly. As we will show below, sev- oxygen uptake is too fast, it will be difficult to preserve
eral physical properties of GdBaCo O exhibit a very the achievedstate evenby very fastcooling. By measur-
2 5+x
sharp singularity in their x dependences near x = 0.5, ing how the sample’s mass evolves with time t, we have
5

0.55 0.25
(a) (b) (c)
0.6 600oC
0.50 0.20 10 - 3 bar
ceramic
1000m m x 600m m
0.4 crystal 0.45 0.15
500m m x 400m m
~X 10 - 4 bar
0.40 1 bar 0.10
0.2 300oC
1 bar 0.35 350oC 0.05
250oC
400oC 2 . 10 - 5 bar
0.0 0.30 0.00
0 10 20 30 40 50 0 2 4 6 8 10 0 2 4 6 8 10
Annealing time (h) Annealing time (h) Annealing time (h)
FIG. 4: Kinetics of the oxygen intercalation into GdBaCo2O5+x. (a) Comparison of the oxygen uptake in a ceramic sample
(with an average grain size of ∼ 10 µm) and a single crystal (with sizes in the ab plane of 500 µm×400 µm) measured in
the oxygen flow at 250◦C. Solid lines are the result of simulation, see text. (b) The oxygen uptake in a single crystal with
sizes in the ab plane of 1000 µm×600 µm measured in the oxygen flow at different temperatures (solid lines are the result of
simulation). (c) Dependenceof theoxygen-uptakekinetics in a ceramic samples at 600◦C on theoxygen partial pressure.
determined the time dependences of the average oxygen dependsonthesurfaceexchangecoefficientK,character-
content x˜(t) for different annealing conditions, as shown izing the oxygen exchange at the interface between the
in Fig. 4. Apparently, the proper duration of the heat gas and the solid, and the chemical diffusion coefficient
treatmentnecessarytoobtainahomogeneousoxygendis- D, besides the sample size. These parameterscanbe ex-
tributionshouldbeseveraltimeslongerthanthe charac- tractedbyfittingtheoreticalcurvestoexperimentaldata,
teristic time τ of the oxygenexchange processat a given as exemplified in Figs. 4(a) and 4(b). For example, the
temperature and an oxygen partial pressure. We have data shown in Fig. 4(a) provide the diffusion-coefficient
foundthatforceramicsamplesthe kineticsofoxygenin- valueofD =3×10−8cm2/sat250◦C.34 Withincreasing
tercalation in the entire studied ranges of temperature temperature, the diffusion coefficient grows rapidly and
and P follows a simple exponential law, so does the rate of the oxygen uptake, making it possi-
O2
ble to achievea homogeneousoxygendistribution in ∼1
x˜(t)=x∞−[x∞−x0]e−t/τ, (1) mmsizedcrystalalreadyafterseveralhoursannealingat
400◦C[Fig. 4(b)]. Notethattheoxygenkineticsdoesnot
wherex0 andx∞ aretheinitialandtheequilibriumoxy- show any detectable difference upon varying the sample
gen contents, τ is a time constant that depends on tem- sizealongthecaxis,implyinganessentially2Dcharacter
perature and PO2. Such simple exponential dependence of the oxygen diffusion typical for layered oxides.35
can be naturally attributed to the oxygen exchange lim-
We should note that the diffusion coefficient found in
ited by a surface energy barrier. The time constant τ
GdBaCo O is remarkable in its own right, being un-
turns out to be less than 3 hours at temperatures down 2 5+x
usually large for such low temperatures; the oxygen dif-
to 250◦C (at 1 bar oxygenpressure), so that the equilib-
fusivity appears to be comparable with that in best su-
rium state in ceramic samples can be easily achieved by
perionic conductors.34 One additional implication of the
one-day annealing [Fig. 4(a)].
high oxygen mobility, which is important to the present
Inthecaseofsinglecrystals,however,theoxygeninter-
study,isthattheoxygenionsmaybecapableofrearrang-
calation deviates from the simple exponential behavior,
ing even at room temperature or below, and one should
andgoesatanoticeablyslowerrate,asillustratedinFig.
expect the oxygen to form ordered superstructures or to
4(a). We have found that for ∼ 500 µm sized crystals,
participate in mesoscopic phase separation.
two days of annealing at 250◦C is far from being enough
toreachtheequilibriumoxygenconcentration[Fig. 4(a)]; After the homogeneous oxygen distribution in a crys-
suchannealingturnsouttobeinsufficientevenfor∼100 tal is reached, an important issue to be concern about
µmsamples. Thisdifferenceinthekineticsofoxygenab- is the cooling procedure, which must be as fast as pos-
sorptionisapparentlycausedbyanadditionallimitation sible to avoid any further oxygen uptake. To obtain the
imposed by the bulk oxygen diffusion: While the crystal most homogeneous samples we used the following rules
surface layer is readily filled with oxygen, it takes much upon selecting the annealing conditions. The anneal-
more time for oxygen to diffuse towards the inner part ing temperature and the partial oxygen pressure were
ofthe crystal. For rectangular-shapecrystalsthe oxygen selected so that: i) they provided the required oxygen
exchange kinetics has an analytical solution,32,33 which content in the crystal, and ii) the annealing time nec-
6
essary to reach the equilibrium oxygen distribution was electric contacts were obtained by drawing with a gold
in the range from several hours to several days. After paint on polished crystal surfaces, and subsequent heat
the annealing was completed, the samples were quickly treatment. For current contacts, the whole area of two
quenched to room temperature without changing the opposing side faces was painted with gold to ensure a
atmosphere. Upon quenching, the crystal temperature uniform current flow through the sample. In turn, the
droppedby100−200◦Cinseveralseconds,guaranteeing voltagecontactsweremadenarrow(∼50µm)inorderto
the blocking of any further oxygen exchange. The huge minimize the uncertainty in absolute values of the resis-
differenceinthetimescales–hoursanddaysformodify- tivity. Itisimportanttonotethatthegoldcontactswere
ing the oxygen concentration and seconds for quenching prepared before all the heat treatments that were used
– ensured us that the unwanted oxygenuptake could af- to vary the oxygen content. After the required oxygen
fect no more than a fraction of percent of the crystal’s concentrationwas set by annealing, thin gold wires were
volume. An important point to be specially emphasized attached to the contact pads using a room-temperature-
is that the oxygenexchangeat the interface between the dryingsilverpaste(DuPont4922),whichelectricallyand
gas and the solid is strongly suppressed at low oxygen mechanicallyboundthe wireto the sample. As the mea-
partialpressures. AsillustratedinFig. 4(c),byreducing surements were completed, the wires were removed and
theoxygenpartialpressureonecanarrangeaslowoxygen the crystal was reannealed to get the next x value.
uptake in a ceramic sample even at 600◦C. This feature The MR measurements were done either by sweeping
turns out to be very useful in obtaining homogeneous the magnetic field between ±14 T at fixed temperatures
samples within the low oxygen concentration range. stabilized by a capacitance sensor with an accuracy of
∼1 mK,37 or by sweeping the temperature at a fixed
magnetic field. Both ∆ρ /ρ and ∆ρ /ρ have been
c c ab ab
C. Detwinning of crystals measured for Hkab and Hkc.
The Hall resistivity was measured using a standard
The oxygen ordering is indeed observed in six-probetechnique by sweeping the magnetic field Hkc
GdBaCo O at x ≈ 0.5, where the oxygen ions to both plus and minus polarities at fixed temperatures;
2 5+x
in GdO planes order into alternating filled and empty the electric currentwas alwaysalong the ab-plane. After
x
chains, causing a tetragonal-to-orthorhombic (T-O) the symmetric (MR) contribution coming from a slight
transition and doubling of the unit cell along the b axis misplacement of the contacts was subtracted from the
(Fig. 2). Usually, this T-O transition is accompanied raw data, the Hall resistivity appeared to be perfectly
by heavy twinning of crystals that mixes the a and b linear in magnetic field for all measured temperatures,
orthorhombic axes; one therefore needs to perform a de- implying that the anomalous Hall effect was negligible.
twinning procedure to get a single-domainorthorhombic In order to determine the thermoelectric power (See-
crystal for studying the in-plane anisotropy. To detwin beckcoefficient)S,wegeneratedaslowlyoscillatingther-
crystals, we slowly cooled them under a uniaxial pres- malgradientalongthe sample (within ∼1 K),and mea-
sure of ∼ 0.15 GPa from 260◦C, using a polarized-light sured an induced periodic voltage. This allowed us to
optical microscope to control the twin removing.36 We get rid of thermoelectric contributions generated in the
should note, however, that the GdBaCo2O5+x crystals remaining circuit. A chromel-constantan thermocouple
are very fragile, and it was virtually impossible to employed for measuring the thermal gradient was at-
completethedetwinningprocedurewithouthavingthem tached to the heat source and to the heat sink, which
cleavedinto two or more pieces. These pieces were fairly were fixed to the sample by a silver paste. To obtain
well detwinned (according to x-ray measurements, the the absolute value of the thermoelectric power, a contri-
remaining fraction of misoriented domains usually did bution from the gold wires (∼ 2 µV/K) used as output
not exceed 4-5%) and suitable for magnetization mea- leads was subtracted. Thermopower measurements were
surements. Thus far, however, we have not succeeded in mostlyperformedonlong(>2mm)samplesbyapplying
detwinning the crystals with already prepared electrical a temperature gradient along the a or the b axis.
contacts (see below), which are necessary for transport
Magnetization measurements were carried out using a
measurements.
SQUID magnetometer at fields up to 7 T applied along
one of the crystallographic axis. Measurement modes
included taking data upon heating the sample after it
D. Details of measurements wascooleddownto2Kinzerofield(ZFC),uponcooling
the sample inmagnetic field from400K (FC), andupon
To characterize the physical properties of sweeping the field at fixed temperatures. Throughout
GdBaCo O , we have carried out resistivity, mag- this paper, the magnetization coming from Co ions is
2 5+x
netoresistance (MR), Hall, thermopower, and magneti- determined by subtracting the contribution of Gd ions,
zation measurements within the 2-400 K temperature assuming their ideal paramagnetic (PM) behavior with
range. total spin S = 7/2; the latter is a good approximation
Thein-plane(ρ )andout-of-plane(ρ )resistivitywas sincenoorderingofGd3+ momentsinanyofthesamples
ab c
measured using a standard ac four-probe method. Good is detected down to 1.7 K.
7
III. RESULTS We should keep in mind, however, that this dividing is
based only on the macroscopic symmetry, and thus it
A. Crystal structure should not be taken too literally; the behavior of the
local structure may in fact be much more tricky. For
example, it is quite likely that oxygen ordering or meso-
Figure 5 shows the evolution of the GdBaCo O
2 5+x scopic phase separation takes place at small x values as
crystal structure as a function of the oxygen concentra-
well, but the ordered domains are too small to be dis-
tionx. We canclearlydistinguishthreedifferentcompo-
cernible by conventional x-ray diffraction. The same is
sition regions:
alsotrue forhighoxygencontentswhereone mayexpect
• 0 ≤ x < 0.45, the system keeps a macroscopically fairly ordered phases at x ≈ 2/3;3/4, as well as various
tetragonal structure, where the unit cell smoothly mesoscopic phase mixtures.
expands in the c direction and shrinks in the in-
plane directions with increasing x;
B. Resistivity
• 0.45 < x < 0.60, the oxygen ions order into alter-
nating filled and empty chains running along the
Inperovskitecompounds,the electron-bandfillingcan
a axis,which results in the orthorhombicstructure
be modified by a partial substitution of cations with el-
andinthe doublingoftheunitcellalongthebaxis
ements having a different valence, as in the case of the
(see Fig. 2);
La Sr MO compounds(M isatransitionmetal),and
1−x x 3
byintroducingcationoranionvacanciesandinterstitials
• x>0.60,the system evolvestowards a macroscop-
as in V O , LaTiO , and YBa Cu O .1 At in-
icallytetragonalsymmetry,thoughinquite acom- 2−y 3 3+δ 2 3 6+x
teger filling (integer number of electrons per unit cell)
plicatedway. Forcrystalslocatedattheloweredge
these compounds are usually band or Mott insulators,
ofthis compositionrange,weobservedatthe same
yetametallic stateoftenemergesuponchangingthe fill-
time the x-ray diffraction peaks corresponding to
ing level, that is, when electron or holes are doped into
the orthorhombic structure with the unit cell dou-
the parent insulator.
bling,andthoserelatedtothetetragonalstructure.
This two-phase state is clearly intrinsic and unre- In GdBaCo2O5+x, it is obviously the x = 0.5 com-
latedtoamacroscopicoxygen-concentrationgradi- position that is the parent compound, where all the Co
ent that would emerge if crystals were improperly ions are nominally in the 3+ state. The limiting phases
annealed. Indeed, the signs of the two-phase state x = 0 and x = 1 should correspond to the 1:1 mixtures
were reproducibly observed only in a quite narrow Co2+/Co3+ and Co3+/Co4+, respectively, or in other
range of x and disappeared as the oxygen content words to the doping levels of 0.5 electrons and 0.5 holes
wasfurtherincreased. Atthehighestachievedoxy- per Co ion. It would not be surprising, therefore, if the
gen concentration, we could distinguish only the x = 0.5 composition were insulating, and a metallic be-
tetragonal,albeit somewhat broadened, diffraction havior were emerging when the oxygen content deviates
peaks. from x = 0.5 towards lower or higher values. The ac-
tual behavior of GdBaCo O , however, turns out to
2 5+x
be more complicated: In contrast to the naive expec-
4.0 tations, it never becomes a true metal (Fig. 6), even
axes thoughwe changethe doping levelina verybroadrange
a from 0.5 electrons per Co (x = 0) up to 0.27 holes per
a=b b/2 b Co (x = 0.77).38 At low temperatures, the in-plane re-
)
os (A 3.9 c tshisetiwvihtyoleρaabcceexshsiibbiltesraanngiensouflxat.inMgobreeohvaevri,obrythlorookuignhgouatt
r
e
et the low-temperature region (T < 150 K) in Fig. 6, one
m may easily find out that the resistivity even increases as
a
ar the oxygen content is reduced below 0.5 (“electron dop-
p
Cell 3.8 c/2 ifnrogm”);wchleaatrloyn,ethuesuoablsleyrveexdpeecvtosluttoiosneediuffperosnredmopairnkgabalny
insulator.
Although GdBaCo O never behaves as a normal
2 5+x
metal,thetemperaturedependenceofitsresistivitydoes
3.7 not follow that of a simple insulator or semiconductor
0.0 0.5 1.0 either. As the temperature increases above 200−250 K,
x the in-plane resistivity ρ (T) shows a gradual crossover
ab
(for x ≤ 0.44) or a sharp transition at T ≈ 360 K
FIG.5: Room-temperatureparametersoftheGdBaCo2O5+x (for x close to 0.5) into a metal-like state, see inset of
unit cell as a function of theoxygen content. Fig. 6. This sharp “metal-insulator” transition (MIT)
8
10-1 x ≥ 0.70. In addition to the MIT, a clear, albeit small,
kink is seenonthe ρ(T)curvesinthe temperature range
104 100-260 K, which is related to a magnetic transition as
103 m ) 10-2 will be discussed below.
c To make it more transparent how the resistivity in
102 W ( ab GdBaCo2O5+x evolves with oxygen content, in Fig. 7
m ) r 10-3 wReegpalrodtleρsasboaftthseevteermalpteermatpuerrea,ttuhreesxa-dseapefnudnecnticoenooffrxe-.
c 101
sistivity splits into roughly the same three composition
W ( ab100 300 T3 5(K0) x400 regions as were observed in the behavior of the crystal
r structure (Fig. 5). For both low (0 ≤ x < 0.45) and
0.165
10-1 0.440 high (x>0.7) oxygen concentrations, the resistivity ap-
0.450 pears to be almost x-independent, while in the region
0.500
10-2 0.510 0.45 < x ≤ 0.7 it changes rather steeply, by orders of
0.525 magnitude. This step-like resistivity drop, taking place
0.650
10-3 0.700 upon goingfrom “electron-doped”to “hole-doped”com-
positions, tends to hide the singularity expected for the
0 100 200 300 400 parentcompound. Onlyverydetaileddatacollectedwith
T (K) a step of δx ≤ 0.01 make this singularity discernible on
thelow-temperatureρ −xcurves,whereitismanifested
ab
FIG.6: In-planeresistivity ρab(T) of GdBaCo2O5+x crystals as a narrow peak in the vicinity of x=0.50.
with different oxygen concentrations. Inset: expanded view
Infact,themostunusualandintriguingfeatureinFig.
of ρ (T) in the vicinity of the “metal-insulator” transition.
ab 7istheasymmetrywithrespecttotheoxygenconcentra-
tionx=0.50. Theresistivityevolutionatx≥0.50looks
104 rather conventional: Indeed, doping of ∼ 2.5% of holes
(x=0.525),whichturnsCo-ionsintoamixed3+/4+va-
103 lence state, dramatically improves the conductivity. As
T (K) can be seen in Fig. 7, the in-plane resistivity at 100
102
100 K drops by more than two orders of magnitude as x
101 150 increases from ≈ 0.50 to 0.525, and by three orders of
m ) 250 magnitude more upon further increasing x. In contrast,
c 100 370 upon electron doping (reducing x below 0.50), an initial
W ( ab 10-1 daercerseiastsieviotfytghreowretshis.tiMviotryeoavlmero,sitniamwmieddeiarteegliyontuxrn≤s0in.4to4
r
boththeabsolutevalueoftheresistivityanditstempera-
10-2
ture dependence arevirtually independent of the oxygen
10-3 content (Figs. 6, 7). Such insensitivity of the conduc-
tivity to doping is very unusual, and may only be pos-
0.0 0.5 1.0 sible if the electrons released upon removing the oxygen
X do not participate in the charge transport. This clearly
speaks against the “rigid-band” picture, where electrons
FIG. 7: Doping dependencesof ρab in GdBaCo2O5+x at sev- are expected to fill the lowest-energy unoccupied states.
eral temperatures. Apparently, the electron doping is accompanied by de-
veloping of microscopic insulating states or mesoscopic
regions, where the electrons are immediately trapped.
at x ≈ 0.5 is similar to what has been reported for air- At this point it is useful to remind that the insulating
sintered RBaCo O ceramics.12,13,14,15 Although the nature of the limiting x = 0 composition has been al-
2 5+x
resistivity ρ ∼ 400−600 µΩcm on the metal side of ready understood as coming from the charge ordering of
ab
the MIT is still relatively large, in transition-metal ox- electrons in CoO2 planes into a unidirectional charge-
ides such resistivity values are actually more consistent densitywave.8,9 Itisthereforereasonabletosuggestthat
with a metallic, rather than a hopping transport.1 As therobustinsulatingbehaviorobservedinthewiderange
can be seen in the inset of Fig. 6, the metal-insulator 0≤x≤0.44 is also associated with some kind of charge
transition is the sharpest and takes place at the highest ordering among the doped electrons.
temperature T ≈ 364 K for x = 0.50, while any de- Itisinterestingtoanalyzethelow-temperaturebehav-
MIT
viation from this stoichiometry blurs the MIT and shifts ior of the resistivity, which can give information on the
it to lower temperatures. This is particularly clear for transportmechanismsoperatinginthe system. Data fit-
high oxygen contents: T is reduced to ∼ 325 K for ting has shown that a crystal with the precisely tuned
MIT
x = 0.65, and no distinct transition can be found for x=0.50compositionexhibitsasimple activationbehav-
9
T (K) T (K) T (K)
400 100 75 50 400 100 5 0 25 10 400 200 100
105
(a) (b) (c)
104
103
102
m) 101
c
W( 100 X X X

r 0.500 0.450 0.165
10-1 0.480 0.250
0.505 0.330
10-2 0.510 0.440
0.525
10-3
0.005 0.010 0.015 0.020 0.2 0.3 0.4 0.5 0.6 0.04 0.06 0.08 0.10 0.12
T -1 (K -1) T -1/4 (K -1/4) T -1/2 (K -1/2)
FIG.8: Low-temperatureresistivity inGdBaCo2O5+x: (a)activation behaviorfor x=0.50; (b)3Dvariable-rangehoppingfor
x=0.45−0.525; and (c) Efros-Shklovskii behavior for x=0.165−0.440.
ior ρ ∝exp(∆/T) with ∆≈70 meV [Fig. 8(a)], which better fitted by the Efros-Shklovskii expression for the
ab
is well consistent with the understanding of this com- hopping conductivity,40 ρ ∝ exp[(T′/T)1/2], see Fig.
ab 0
position as a parent insulator (narrow-gap semiconduc- 8(c). The latter behavior is usually observed when the
tor). However, when the oxygen content deviates some- Coulomb interaction starts to play a key role in carriers
what from x = 0.50, the resistivity behavior almost im- hopping, bringing about a strong depletion in the den-
mediately switches into the 3D variable-range hopping sity ofstates (Coulombgap)near the Fermienergy. The
(VRH) mode,39 ρ ∝ exp[(T /T)1/4], as shown in Fig. data in Fig. 8 imply that the Coulomb-repulsion effects
ab 0
8(b). This type of conduction is typical for disordered in GdBaCo O gain strength as the oxygencontent is
2 5+x
systems where the charge carriers move by hopping be- reduced below ≈0.45.
tween localized electronic states. The formation of such
The unusual resistivity behavior at high oxygen con-
localizedstatesmay be rathersimply conceivedof inthe
centrations (Fig. 6) is also worth mentioning. For both
following way: Initially, at the oxygen composition of
the x = 0.65 and x = 0.70 crystals, ρ smoothly in-
ab
x=0.50,GdBaCo O possessesawell-orderedcrystal
2 5+x creases by 2 − 3 orders of magnitude upon decreasing
structure, where the oxygen ions form perfect filled and
temperature,andreachesapparentlynon-metallic values
emptychainsalternatingalongthebaxis(Fig. 1). When
of the order of 1 Ωcm. Nevertheless, it becomes also
theoxygenconcentrationdeviatesfromx=0.50,thisre-
clear from Fig. 6 that, at least in the temperature range
sults either in vacancies emerging in the filled chains, or
studied,theresistivitytendstosaturateatafinitevalue,
inoxygenionsthatgointotheemptychains. Whilethese
instead of diverging at T = 0; such behavior would in-
oxygen defects inevitably generate electrons or holes in
dicate a metallic ground state, if the resistivity values
the CoO planes, they also produce a poorly screened
2 were not that large. A possible solution of this puzzle is
Coulomb potential that may well localize the generated
anintrinsicmesoscopicphaseseparation,thatmakesthe
carriers, so that some of the adjacent Co ions acquire carriers to move along filamentary conducting paths.41
the Co2+ or Co4+ state. Then the conductivity oc-
Inthiscase,thezero-temperatureconductivity,beingde-
curs through hopping (tunneling) motion of such local-
termined by the topology of the metallic phase, may be
ized Co2+ or Co4+ states. As can be seen in Fig. 8(b), arbitrary small and can easily violate the Mott limit39
theslopeoftheresistivitycurvesmonotonicallydecreases
that sets the minimum metallic conductivity for homo-
with increasing x, implying that the localization length
geneoussystems. Thispictureisquiteplausible,since,as
of holes (Co4+ states) is noticeably larger than that of
we have mentioned above, the crystal structure at these
electrons.
high oxygenconcentrations actually bears signs of phase
separation.
Upon further decreasing the oxygen content below
x ≈ 0.45, the temperature dependence of the resistiv- Thus far we discussed the resistivity behavior along
ity becomes steeper than expected for the Mott’s VRH the CoO planes, which is however not the full story,
2
regime, ρ ∝ exp[(T /T)1/4], and we find that it is since one might anticipate a strong electron-transport
ab 0
10
105 25
GdBaCoO X
104 2 5.5
0.165
r 20
103 r c 00..235300
ab
0.440
102 0.500
15
m) 101 b
c a
W ( 100 r / c 10
r r
10-1
5
10-2
(a) (b)
10-3
0
100 200 300 400 100 200 300 400
T (K) T (K)
FIG.9: TheresistivityanisotropyinGdBaCo2O5+x. (a)ResistivityofGdBaCo2O5.50 measuredalongthecaxisandalongthe
ab plane. (b) The resistivity anisotropy ratio ρc/ρab for x=0.165−0.440 and 0.500.
anisotropy to be brought about by the layered crys- this system that is responsible for the appearance of
tal structure of GdBaCo O . Indeed, many lay- conductivity anisotropy.
2 5+x
ered transition-metal oxides, such as high-T cuprates,42
c
manganites,43 or even cobaltites built from triangular-
lattice CoO planes,18,26 exhibit huge anisotropy val- C. Thermoelectric power
2
ues and contrasting temperature dependences of the
in-plane and out-of-plane resistivity. In the case of Among the features that currently attract a lot of
GdBaCo2O5+x, where the GdOx layers with variable attention to transition-metal oxides are their unusual
oxygen content are located in between the CoO2 planes andpotentiallyusefulthermoelectricproperties.18,19,44,45
(Fig. 1),itwouldbenaturaltoexpectakindof3D-to-2D The peculiar thermoelectric behaviorin TMoxidesis of-
transition to occur upon reducing x from 1 to 0, that is, tenattributedtostrongelectroncorrelations,20,21though
astheoxygenionsbindingtheCoO2 planesareremoved. the picture still remains far from being clear. In this
However, a comparison of the in-plane and out-of-plane respect, the RBaCo O compounds, being capable of
2 5+x
resistivityinFig. 9showsthatthisisnotreallythecase. smoothlychangingthedopinglevelinaverybroadrange,
The anisotropy ρc/ρab indeed increases slightly as the appeartoprovideagoodtestinggroundforstudyingthe
oxygen concentration is reduced from x ≈ 0.44 towards problem.
zero [Fig. 9(b)], but remains rather moderate. In fact, a The thermoelectric power S(T) measured on both
considerable anisotropy is observed only at intermediate single-crystal and ceramic GdBaCo O samples46
2 5+x
temperatures, while at both high and low temperatures throughout the available oxygen-concentration range is
GdBaCo2O5+x tends to become virtually isotropic. It presented in Fig. 10. Following the usual approach in
turnsoutthereforethattheoxygen-depletedGdOxlayers analyzing the behavior of semiconductors, we have plot-
donotconstituteaseriousobstacleforthec-axiselectron ted the data in the inverse-temperature scale, since in
motion. semiconductors the thermoelectric power is expected to
Somewhat different behavior of the parent belinearin1/T withaslopereflectingtheactivationen-
GdBaCo O compound provides a clue to un- ergyforchargecarriers∆ ,S(T)≈A±(k /e)(∆ /k T).
2 5.50 s B s B
derstand the mechanism responsible for resistivity It becomes immediately clear from Fig. 10 that the only
anisotropy. As can be seen in Figs. 9(a), 9(b), the compositionthatexhibitsaconventionalsemiconducting
in-plane and out-of-plane resistivities stay virtually behaviorisx=0.500,withtheactivationenergy∆ ≈70
s
indistinguishable from each other down to T ≈ 260K, meV being in good agreement with that deduced from
where the FM-AF transitiontakesplace.17 Upon further the resistivity data in Sec. IIIB. Just a subtle deviation
decreasing the temperature, the curves sharply diverge of the oxygen concentration from x = 0.500 (by merely
and ρ /ρ grows from ≈ 1 at T ≥ 260K up to ≈ 22 0.001)qualitativelychangesthethermoelectricbehavior:
c ab
at 100 K. This indicates that the charge motion in S becomes almosttemperature independent at≈100K,
GdBaCo O is very sensitive to the arrangement indicating that the electron transport is no longer gov-
2 5+x
of Co spins, and it is the peculiar spin ordering in ernedby the band gap. It is worthnoting that the resis-