Two dimensionality in quasi one-dimensional cobalt oxides

0.59 MB·

by  J. Sugiyama

APS/PRB
Two dimensionality in quasi one-dimensional cobalt oxides
5 J. Sugiyama1,∗ H. Nozaki1, J. H. Brewer2, E. J. Ansaldo3, T. Takami4, H. Ikuta4, and U. Mizutani4
0 1Toyota Central Research and Development Labs. Inc., Nagakute, Aichi 480-1192, Japan
0 2TRIUMF, CIAR and Department of Physics and Astronomy,
2 University of British Columbia, Vancouver, BC, V6T 1Z1 Canada
n 3University of Saskatchewan † and TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T 2A3 Canada and
a 4 Department of Crystalline Materials Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603 Japan
J
(Dated: February 2, 2008)
1
1 By means of muon spin rotation and relaxation (µ+SR) techniques, we have investigated the
magnetism of quasi one-dimensional (1D) cobalt oxides AEn+2Con+1O3n+3 (AE=Ca, Sr and Ba,
l] n=1,2,3,5and∞),inwhichthe1DCoO3 chainissurroundedbysixequallyspacedchainsforming
e a triangular lattice in theab-plane, using polycrystalline samples, from room temperature down to
- 1.8 K. For the compounds with n=1 - 5, transverse field µ+SR experiments showed the existence
tr of a magnetic transition below ∼100 K. The onset temperature of the transition (Tcon) was found
s
to decrease with n; from 100 K for n=1 to 60 K for n=5. A damped muon spin oscillation was
.
at observedonlyinthesamplewithn=1(Ca3Co2O6),whereasonlyafastrelaxationobtainedevenat
m 1.8 K in the other three samples. In combination with the results of susceptibility measurements,
this indicates that a two-dimensional short-range antiferromagnetic (AF) order appears below Ton
c
d- for all compounds with n=1 - 5; but quasi-static long-range AF order formed only in Ca3Co2O6 ,
n below25K.ForBaCoO3 (n=∞),asT decreasedfrom300K,1Dferromagnetic(F)orderappeared
below 53 K,and a sharp 2D AFtransition occurred at 15 K.
o
c
[ PACSnumbers: 76.75.+i,75.40.Cx,75.50.Ee

1
v I. INTRODUCTION ing face-sharing B′O6 trigonal prisms and BO6 octahe-
2 dra. Asnincreases,onlythenumberof[BO ]octahedra
6
3
increasessoastobuildthechainwithn[BO ]octahedra
2 In the two-dimensional (2D) layered cobalt ′ 6
and one B O trigonal prism.
1 6
oxides, Na CoO , [Ca CoO ] [CoO ] and
50 [Ca2Co4/3Cu2/x3O4]0.262[CoO2],2along3-r0a.6n2gema2gneticor- The n=1 compound, Ca3Co2O6, in particular, has at-
der—whichisclearlyincommensuratespindensitywave tracted much attention for the past eight years, [10, 11,
0
/ in single crystalline samples — was previously found at 12,13,14, 15,16]becauseitis consideredto be atypical
at low temperatures by positive muon spin rotation and quasi-1Dsystem. ItwasfoundthatCa3Co2O6 exhibitsa
m relaxation (µ+SR) experiments.[1, 2, 3, 4, 5] Several transition from a paramagnetic to an antiferromagnetic
- researchers reconfirmed later the existence of long-range statebelow24K(=TN),[11]althoughthemagneticstruc-
d magnetic order in the layered cobaltites by not only tureisnotfullyunderstoodevenafterneutronscattering
n µ+SR [6] but also neutron diffraction experiments.[7] studies, probably due to the competition between the
o These cobaltites share a common structural component intra-chain ferromagnetic (F) and inter-chain antiferro-
c
: as a conduction path, i.e., the CoO2 planes, in which a magnetic (AF) interactions.[11, 12] The valence state of
v two-dimensional-triangular lattice of Co ions is formed the Co ions was assigned to be +3; also, the spin config-
Xi by a network of edge-sharing CoO6 octahedra. uration of Co3+ ions in the CoO6 octahedron is the low-
spin(LS)statewithS=0andintheCoO prismthehigh-
6
ar This leads naturally to the question of the (cause and spin(HS)statewithS=2. [11,17,18]Atlowertempera-
effect) interrelationship between magnetism and dimen- tures, magnetization and 59Co-NMR measurements sug-
sionality. That is, the most stable spin configuration as gestedthe existence of a ferrimagnetic transitionaround
a function of a spin density in low dimensional systems. 10K,[12,13,19]which,however,wasnotseeninthespe-
′
Recently, a hom′ ologous series of An+2B BnO3n+3 (A= cific heat (Cp). [20] Furthermore, the Cp measurement
Ca, Sr, Ba, B and B=Co) was discovered, in which revealed an indication of either a short-range magnetic
charge carrier transport is restricted mainly to a one- order or a gradualchange in the spin state of Co ions at
dimensional (1D) [B’BnO3n+3] chain.[8, 9] Each chain is higher temperatures (100 - 200 K).[20]
surrounded by six equally spaced chains forming a tri-
angular lattice in the ab-plane. As seen in Fig. 1, the The other end member, BaCoO3 (n=∞), crystallizes
[B′BO ]chaininthen=1compoundconsistsofalternat- in the hexagonal perovskite structure, in which the face
6
sharing CoO octahedra form a 1D CoO chain. The
6 3
chains locate on a corner of the two-dimensional tri-
angular lattice separated by Ba ions.[21] Although a
†Retired weak ferromagnetic, ferrimagnetic or spin-glass-like be-
∗Electronicaddress: [email protected] havior was observed below ∼100 K in the susceptibility,
2
CoO A2+ A2+
A2+ 3 TABLEI:Composition andlattice parametersforquasi-one-
CoO3 chain CoO3 dimensionalcobalt oxides,An+2B′BnO3n+3 (A=Ca, Sr,Ba,
chain chain B′ and B=Co). Here, b=a,α=β=90o and γ=120o.
lattice parameters
c n composition a(˚A) c (˚A) space group
b 1 Ca3Co2O6 9.07 10.38 R¯3c
2 Sr4Co3O9 9.35 10.57 P321
a 3 Sr5Co4O12 9.4 20.2 P3c1
(a) (b) (c) ∞5 (Sr1/2BBaa1C/2o)O7C3o6O18 59..675 340.7.25 P6P3/¯3mc1mc
FIG.1: Structuresofthequasione-dimensionalcobaltoxides
An+2B′BnO3n+3 (A= Ca, Sr, Ba, B′ and B=Co). (a) n=1,
(b) n=3 and (c) n=∞.
Here we report on a series of measurements at both
weak (relative to the spontaneous internal fields in the
[22, 23] so far there are no reported studies using neu- ordered state) transverse-field, (wTF-) µ+SR, and zero
tron scattering, NMR or µ+SR on BaCoO3. Addition- field, (ZF-) µ+SR, for polycrystalline n=1, 2, 3, 5 and
ally, a recent electronic structural calculation (LDA+U) ∞ compounds at temperatures between 1.8 and 300 K.
predictedaferromagneticgroundstateasthemoststable The former method is sensitive to local magnetic or-
configuration.[24] The structure of BaCoO3 is the same der via the shift of the µ+ spin precession frequency in
to that of CsCoCl3 and/or BaVS3, [25, 26] which are the applied field and the enhanced µ+ spin relaxation,
knownastypical1DsystemswithS=1/2. Theelectronic while ZF-µ+SR is uniquely sensitive to weak local mag-
configuration(t52g)ofCo4+ ionsinBaCoO3suggeststhat netic[dis]orderinsamplesexhibitingquasi-staticparam-
the nature of BaCoO3 is more like that of BaVS3 (with agnetic moments.
t1 for V4+) than that of CsCoCl (t6 e1 for Co2+). In
2g 3 2g g
other words, the interaction between t orbitals pre-
2g
sumably plays the dominant role for magnetism in both
BaCoO and BaVS . Also, BaVS exhibits a structural
3 3 3
phasetransitionat240K,ametal-insulatortransitionat
69 K and an AF transition at ∼30 K. [27, 28] However,
a ZF-µ+SR experiment on BaVS did not detect muon
3
spin oscillations, even at 2.2 K, but only a fluctuating II. EXPERIMENT
random field well described by a dynamic Kubo-Toyabe
relaxation function. [29]
Polycrystallinesamplesofquasi-1Dcobaltoxideswere
For the compounds with 2≤ n < ∞, there are very synthesizedatNagoyaUniversitybyaconventionalsolid
limited data onphysicalproperties,except for the struc- state reaction technique, using reagent grade Co O ,
3 4
tural data.[8, 9] Very recently, Takami et al. reported CaCO , SrCO and BaCO powders as starting mate-
3 3 3
transport and magnetic properties for the compounds rials. For BaCoO , a sintered pellet was annealed at
3
with n=2 - 5.[30] According to their susceptibility (χ) 650oCfor150hinoxygenunderpressureof1MPa. Pow-
measurements, there are no drastic changes in the χ(T) der X-ray diffraction (XRD) studies indicated that the
curve below 300 K for all these compounds, while the samples were single-phase of hexagonal structure. The
slopeofχ−1 changesataround180Kforthecompounds composition and lattice parameters of the five samples
with n=2 and 3. aresummarizedin Table I. The preparationandcharac-
terization of the samples with n=1 - 5 were reported in
As n increases from 1, the Co valence increases from
detail elsewhere.[30]
+3 and approaches +4 with increasing n up to ∞;
i.e., BaCoO . Also the ratio between prism and oc- Magnetic susceptibility (χ) was measured using a
3
tahedron in the 1D CoO chain reduces from 1/1 for superconducting quantum interference device (SQUID)
3
n=1 to 0 for n=∞.[9] Further systematic research on magnetometer (mpms, Quantum Design) at tempera-
′
A B B O isthereforeneededtoprovidemoresig- turesbetween2-600KwithmagneticfieldH ≤55kOe.
n+2 n 3n+3
nificant information concerning the dilution effect of HS Heatcapacity(C )wasmeasuredusingarelaxationtech-
p
Co3+ inthe1Dchainonmagnetism. Inparticular,muon nique(ppms,QuantumDesign)inthetemperaturerange
spinspectroscopy,asitisverysensitivetothelocalmag- between300and1.9K.Theµ+SRexperimentswereper-
netic environment, is expected to yield crucial data in formedontheM20surfacemuonbeamlineatTRIUMF.
frustrated low-dimensional system, as was the case for The experimental setup and techniques were described
the 2D layeredcobaltites. elsewhere.[31]
3
+ Aslow exp(−λslowt), (1)
0.3
wTF-µSR, H=90 Oe whereA istheinitial(t=0)asymmetry,P(t)isthemuon
0
Y
R A spinpolarizationfunction,ωµ,TF andωµ,AF arethemuon
TF
T 0.2 Larmor frequencies corresponding to the applied weak
E A
AF transverse field and the internal antiferromagnetic field,
M
A
M fast φTF and φAF are the initial phases of the two precessing
Y 0.1 Ca Co O A signals and A and λ (n = TF, AF, fast and slow) are
S 3 2 6 slow the asymmetrnies and enxponential relaxation rates of the
A (a)
four signals. The fast relaxing precessing signal has a fi-
0
niteamplitudebelow∼30Kandthetwonon-oscillatory
4 80 signals (n=fast and slow) below ∼80 K.
z) λ
H A
(Mw 3 λλTAFF 60 F and obfilFAitiyng,uχλr−en1s(m2n(=eaa)Tsu-Fr,2eA(dcF)i,nsfhafisoetwldantchdoeoslltioenwmg)pm,eaorndadteuiwnrveitehdresHepes=nu1ds0ceenkpcOteies-
o λ
λsl 2 λfast 40 faλ in the Ca3Co2O6 sample (n=1 compound). As T de-
d slow st creases from 200 K, the magnitude of ATF is nearly in-
an 1 20 (M dependent of temperature down to 100 K; then ATF de-
F (b) H creases rapidly as T is lowered further. [32] Finally ATF
T z
λ 0 0 ) levelsofftozeroattemperaturesbelowabout30K.This
indicates the existence of a magnetic transition below
60 around100K.SinceATF isproportionaltothevolumeof
ZFC
) aparamagneticphase,thevolumefractionV ofthemag-
u F
m 10 kOe netic phase below 30 K is estimated to be ∼ 100%. On
e 40
/ theotherhand,theAfast(T)curveexhibitsamaximumat
ol around30 K, probably due to the onset of even stronger
m
( 20 localfields (resulting in unobservably fastmuon spinde-

-1χ (c) polarization)below30K.ThemagnitudeofAfast reaches
the full asymmetry of ∼0.22 at the maximum. The two
0 other signals,AAF andAslow, appearbelow around20K,
0 100 200 300
whereas Afast seems to disappear below 20 K.
TEMPERATURE (K)
Both the λTF(T) and the λfast(T) curves exhibit a
broad maximum around 60 K and 30 K, respectively.
FIG.2: Temperaturedependencesof (a) An and (b)λn, and That is, λTF increases with decreasing T from 200 K to
(c) inverse susceptibility χ−1 in Ca3Co2O6 (n=1). The data 60 K, then decreases below 60 K. Meanwhile, λfast in-
wereobtainedbyfittingthewTF-µ+SRspectrausingEq.(1). creases with decreasing T from about 80 K (where it is
χ was measured with magnetic field H=10 kOe in zero field
first detected) down to 30 K, after which it decreases
cooling mode. [30]
down to the lowest temperature measured. It is note-
worthy that the highest value of λfast (∼60×106 s−1) is
III. RESULTS 20 times larger than that of λTF (∼3×106 s−1).
Inorderto elucidate magnetismbelow 30K ingreater
detail,Fig.3showsZF-µ+SRtimespectraforCa Co O
3 2 6
A. n=1 compound, Ca Co O
3 2 6 below36.7K.Thespectrumat36.7Kconsistsmainlyof
afastrelaxednon-oscillatorysignal,whilebelow23.2Ka
The wTF-µ+SR spectra in a magnetic field of H ∼ first minimum and maximum are clearly seen, indicative
of a fast relaxing oscillation. Indeed, this spectrum is
90 Oe in the Ca Co O (n=1) sample, exhibit a clear
3 2 6
reductionoftheµ+ precessionamplitude below ∼100K. reasonablywellfittedwithacombinationofanexponen-
The wTF-µ+SR spectrum below ∼100 K was well fitted tiallyrelaxedcosineoscillation(foraquasi-staticinternal
field) and fast and slow exponential relaxation functions
in the time domain with a combination of four signals;
(for fluctuating moments), given by the the last three
a slowly relaxing precessing signalcaused by the applied
terms in eq. (1). Moreover, it was very difficult to fit
field, a fast relaxing precessing signal induced by quasi-
using Kubo-Toyabe functions, which describe a random
static internal fields, a slowly non-oscillatory and a fast
fielddistribution. We thereforeconclude thatCa Co O
non-oscillatory background signals, namely: 3 2 6
undergoes a magnetic transition to a long-range ordered
A0P(t) = ATF exp(−λTFt) cos(ωµ,TFt+φTF) state below ∼30 K. Only the first minimum and maxi-
+ AAF exp(−λAFt) cos(ωµ,AFt+φAF) mum can be observed in the spectra even at 1.8 K, in-
+ Afast exp(−λfastt), dicating that the formation of the long-range order is
4
0.3
Ca Co O (a)
Y 3 2 6
R ZF-µSR
T 0.2
E
M A
AF
M
Y 0.1 Afast
S
A
A slow
0
15
)
z
H 60
M λ
λ (fast 40 λλAfaFst 10 slow (M
d λ 5 H
n 20 slow
a z)
F (b)
A
λ 0 0
20
β=0.18+_ 0.12
Hz) 15 ν ]AF1.2
M 10 og[
( l 1
F
A
ν 5 -1.2 -0.8 -0.4 0
log[(T -T)/T ](c)
N N
0
20
H=10 Oe
)
u 15
m ZFC
e
ol/ 10
m
(
F26I.G7,. 3a:ndZ3F6.-7µ+KS.RTshpeecsptreactfroaraCrea3eCaoc2hOs6hiaftted1.8u,p9w.a9r,d2s3.b2y, -1χ 5 (d)
0.08 for clarity of thedisplay. 0
0 50 100
TEMPERATURE (K)
stronglysuppressedprobablydue to geometricalfrustra-
tion in the triangular lattice.
FIG. 4: Temperature dependences of (a) A (b) λ and (c)
n n
Figures4(a)- 4(d) showthe temperaturedependences muon precession frequency νAF2π = ωµ,AF and (d) χ−1 mea-
of A , λ (n=AF, fast and slow) and muon precession sured in a zero field cooling mode with H=10 Oe [30] in
frequnencynνAF(= ωµ,AF/2π) in Ca3Co2O6. The oscillat- Cspae3cCtroa2Ous6i.ngTthheedlaatttaerwethrereoebttearimnesdinbyEqfi.tt(i1n)g. TthheeZsFol-iµd+lSinRe
ing signal has a finite intensity below 27 K, while the
in Fig. 4(c) represents the fitting curve using Eq. (2). The
slow exponential relaxedsignal disappears below around
inset of Fig. 4(c) shows the log-log plot of νAF as a function
30K. This means thatthe magnetic momentfluctuating of reduced temperature.
at high temperatures slows down with decreasing T and
thenordersbelow27K,andbecomesquasi-static(within
the experimental time scale). The T dependence of νAF, This provides νAF(0K)=14.6±0.8 MHz, β=0.18±0.12,
which is an order parameter of the transition, is in good
andT =29±5K(see,Fig.4(c)). Inspiteofthelowaccu-
N
agreementwith the T dependence of the intensity of the
racyofthe fitting, the criticalexponent(β)obtainedlies
AF magnetic diffraction peak determined by a neutron
between the predictions for the 2D and 3D Ising mod-
experiment.[11] Actually, the νAF(T) curve is well fitted els (β=0.125 and 0.3125).[33] The value of T is also in
N
by the following expression;
goodagreementwiththeresultsofχandneutrondiffrac-
tionmeasurements(T =24K).[11]Theseresultsconfirm
N
β
TN−T thatmuons experiencethe internalmagnetic fielddue to
νAF(T)=νAF(0K)× . (2)
(cid:18) T (cid:19) the long-range 2D AF order. It should be noted that
N
5
there are no marked anomalies in the ZF-µ+SR results
around 10 K corresponding to the ferrimagnetic transi-
F
tfeiorrnimteamgpneetriastmuries.[i1n2d]uTchedisbisyvtehreyerexatesornnaalbfileeblde.causethe AT An+2CoConO3n+3 (a)
D 1
E
There are two probable explanations for the decrease
Z
n=1
in ATF below 100 K. One is a conventional scenario, in LI
which a short-range 1D F order appears below 100 K A 0.5 n=2
as proposed by Aasland et al.[11] and probably com- M wTF-µSR n=3
R
pletesbelow∼40K,becausebothATF (Fig.2)andAslow O H=90 Oe n=5
(Fig. 4) seem to level off to their minimum value (∼0) N 0
below around 40 K. The long-range 2D AF order then
appears below 27 K. The other scenario is more ambi- (b)
tious; that is, a short-range 2D AF order appears below 1
)
100 K and completes below 27 K. This means that the z
H
1D F order should exist above 100 K, which is not sup- M
portedbythe presentµ+SRexperiments. Basedonly on (
F
the resultinCa3Co2O6,itis difficulttodeterminewhich λT0.1
scenario is more probable. We will therefore discuss this
problem later.
150
) FC
u
B. n=2, 3 and 5 compounds m100 H=10 kOe (c)
e
/
ol
Figure 5(a) - 5(c) show the temperature dependences m
50
of (a) normalized ATF (n-ATF), (b) λTF, and (c) χ−1 in 1 (
Ca Co O (n=1), Sr Co O (n=2), Sr Co O (n=3), χ-
3 2 6 4 3 9 5 4 12
and(Ba0.5Sr0.5)7Co6O18 (n=5). Thedatawereobtained 0
by fitting the wTF-µ+SR spectra using eq. (1) without 0 50 100 150 200
the oscillatory signal due to a static internal antiferro-
TEMPERATURE (K)
magnetic magnetic field (the AAF signal). In order to
compare the value of ATF for these samples, NATF is
defined as; FIG.5: Temperaturedependencesof(a)normalizedATF,(b)
λTF, and (c) inverse susceptibility χ−1 in Ca3Co2O6 (n=1),
ATF(T) Sr4Co3O9(n=2),Sr5Co4O12(n=3),and(Ba0.5Sr0.5)7Co6O18
NATF = , (3) (n=5). χwasmeasuredwithmagneticfieldH=10kOeinfield
ATF,max cooling mode. [30]
in which ATF,max is the maximum value of ATF. Since
ATF,max corresponds to ATF for the paramagnetic state, In spite of the large decrease in ATF below 100 K for
NATF isroughlyequivalenttothevolumefractionofthe thesampleswithn=2,3and5,theZF-µ+SRspectraex-
paramagnetic phase in the sample. hibit no oscillationsevenat1.8 K asseen inFig.6. This
indicates that the magnetic moment appears below Ton,
All four samples show the magnetic transition below c
100 K; the onset temperatures of the transition (Ton) butisstillfluctuatingat1.8K.TheZF-µ+SRspectraare
c
wellfitted by a combinationoffastandslow exponential
are estimated as 100±25 K for n=1, 90±10 K for n=2,
relaxationfunctions (for fluctuating moments)anda dy-
85±10 K for n=3 and 50±10 K for n=5, respectively.
The magnitude of Ton is thus found to decrease with n. namical Kubo-Toyabe function GDGKT (for a fluctuating
c
random moment component).
Itshouldbenotedthattherearenomarkedanomaliesin
the χ−1(T) curve measured with H=10 kOe at Ton for
c A0P(t) = Afast exp(−λfastt)
the four compounds. Although NATF for the n=1 com- + Aslow exp(−λslowt)
pound levels off to its minimum value (∼0) below 30 K, DGKT
+ AKT exp(−λKTt) G . (4)
the NATF(T)curveforthe otherthreecompoundsnever
reaches their minimum even at 1.8 K, indicating that Thefastexponentiallyrelaxedsignal,whichcorresponds
the internal magnetic field is still fluctuating. Indeed, to the initial decay of the ZF-spectrum in Fig. 6, ap-
λTF for the samples with n=2, 3 & 5 increases mono- pears below ∼80 K for the samples with n=2 and 3.
tonically with decreasing T, whereas the λTF(T) curve The Afast(T) and λfast(T) curves increase monotonically
for Ca Co O (n=1) exhibits a sharp maximum around withdecreasingT,asexpectedfromthewTF-µ+SRmea-
3 2 6
55 K. surement. The fitted values of λfast at the lowest T
6
0.2 ZF-µSR Sr Co O
4 3 9
Sr Co O
st 5 4 12
a
Af0.1
(a)
0
80
) 60
z
H
M
40
(

st
a
λf 20 (b)
0
0 20 40 60 80 100
TEMPERATURE (K)
FIG. 7: Temperature dependences of (a) asymmetry Afast
and (b) relaxation rate λfast of a fast exponential relaxation
signal for Sr4Co3O9 (n=2) and Sr5Co4O12 (n=3). The data
wereobtainedbyfittingtheZF-µ+SRspectrumusingeq.(4).
FIG. 6: ZF-µ+SR spectra at 1.8 K for Ca3Co2O6 (n=1),
Sr4Co3O9(n=2),Sr5Co4O12(n=3),and(Ba0.5Sr0.5)7Co6O18
(n=5). Thespectraareeachshiftedupwardsby0.08forclar-
the C (T) curve, although the slope (dC /dT) increases
p p
ity of thedisplay.
slightly around 50 K with decreasing T. The lack of a
clear anomaly around 50 K in the C (T) curve suggests
p
thatthe transitionat53Kisinducedbythe 1DForder,
(=1.8 K) were 55 MHz for Sr Co O (n=2), 40 MHz for
4 3 9 as in the case for the 1D F order in Ca Co O .
3 2 6
Sr Co O (n=3) and 18 MHz for (Ba Sr ) Co O
5 4 12 0.5 0.5 7 6 18
(n=5). Since these are comparable to the value of The wTF-µ+SR experiment with 90 Oe show that, as
λAF(1.8 K)(=55 MHz) for Ca3Co2O6, the fast exponen- T decreasesfrom100K,ATF dropssuddenlydownto∼0
tialrelaxedsignalinthesampleswithn>1ismostlikely atTN,indicatingthatthewholesampleentersintoanAF
causedbyaninter-chain2DAFinteraction. Itshouldbe state. Such abrupt change in ATF is very different from
noted that λAF(1.8 K) decreases with n, suggesting that those for the other quasi-1D cobalt oxides with n=1 -
themagnitudeofthe2DAFinteractionisweakenedwith 5, which typically show a large transition width of 50 -
decreasing n. 80 K. On the other hand, the λTF(T) curve exhibits a
smallincrease below ∼50K with decreasingT,probably
associated with the complicated magnetism observed in
χ with low magnetic fields. As T decreases further from
C. n=∞ compound, BaCoO3 50 K, λTF increases rapidly below 17 K, showing typical
critical behavior towards T .
N
Figures 8(a)-8(c) show the temperature dependences The ZF-µ+SR spectrum at 1.7 K exhibits a clear but
of(a)ATF,(b)λTF,(c)χ−1,(d)specificheatCp,and(e) complex muon spin oscillation, displayed in Fig. 9(a).
its temperature derivative dC /dT for BaCoO (n=∞). The Fourier transform of the ZF-µ+SR time spectrum
p 3
Both ATF and λTF were obtained by fitting the wTF- (Fig. 9(b)) indicates that the ZF-µ+SR spectrum has
µ+SR spectra, the same way as the compounds with five frequency components (ν =14.4, 13.5, 6.4, 5.1 and
µ
n=2 - 5. The χ−1(T) curve indicates the existence of an 3.5 MHz), even though the sample is structurally single
AFtransitionat14K(=T )withH=10kOe,butaweak phase at room temperature and there is no indication of
N
Forferrimagneticbehaviorbelow53KwithH=100Oe. any structuralphase transitiondown to 77 K in resistiv-
Also, the C (T) curve shows a sharp maximum at 15 K, ity (ρ) and thermopower (TEP) measurements;[22] nor
p
indicating the existence of a magnetic transition. How- are there any anomalies in the χ(T) curve down to 4 K,
ever, at around 53 K, there are no clear anomalies in except around T . The ZF-spectra were well fitted by
N
7
0.3
0.2
BaCoO
TF 3
A wTF-µSR
0.1
(a)
H=90 Oe
0
) 0.4 BaCoO
z 3
H wTF-µSR
M
( 0.2 H=90 Oe

F
T (b)
λ
0
150
) 10 kOe BaCoO
u 3
m ZFC
100
e FC
/
ol 100 Oe
m
( 50 ZFC (c)

-1χ FC
0
9
)
K
m BaCoO
to 6 ZF 3 FanIGd.(9b:) (Fao)uZriFer-µt+raSnRsfsopremctroufm(af)o.rBTahCeoOso3lid(nl=in∞e)inatF1i.g7.K7
a
- represents theresult of fitting using eq.(5).
ol
m 3
/
J (d)
( the following equation;
p
C 0
)2 0.2 5
K
m A0P(t) = AAF,i exp(−λAF,it) cos(ωµ,it+φ)
ato Xi=1
ol- 2
m 0.1 + A exp(−λ t), (5)
J/ i i
T ( Xi=1
d (e)
C/p 0 where A0 is the empirical maximum experimental muon
decay asymmetry, A and λ (i = 1 - 5) are the
d 0 20 40 60 80 100 AF,i AF,i
asymmetries and exponential relaxation rates associated
TEMPERATURE (K) with the five oscillating signals, and A and λ (i = 1
i i
and 2) are the asymmetries and exponential relaxation
FIG.8: Temperaturedependencesof(a)weaktransversefield ratesofthetwonon-oscillatingsignals(forthemuonsites
asymmetry ATF, (b) exponential relaxation rate λTF, (c) in- experiencing fluctuating magnetic fields).
pveerrsaetusurescdepertiivbailtiitvyeχd−C1p,/(ddT)spfoerciBficaCheoaOt3C(pn,=an∞d)(.e)AitTsFteamnd- The internal magnetic fields of the five signals, i.e.,
λTF were obtained by fitting the wTF-µ+SR spectra with νµ,i with i = 1 - 5, exhibit a similar temperature depen-
ATFexp(-λTFt)cos(ωµ,TFt+φTF).@χwasmeasuredwithmag- dence,asseeninFig.10(a). Thatis,asT decreasesfrom
netic field H=10 kOe and 100 Oe in both zero-field cooling 20 K, each ν suddenly appears below 15 K, at which
µ,i
(ZFC) and field cooling (FC) mode. the C (T) curve shows a typical behavior for the AF
p
transition (Fig. 10(b)), and increases with a decreasing
slope dν /dT, then levels off to a constant value below
µ,i
5 K. Here, it is worth noting that the ν -vs.-T curve
µ,i
indicates the change in an order parameter of the tran-
sition. Thus, the rapid temperature dependence of ν
µ,i
8
curve between 300 - 600 K using the Curie-Weiss law.
16 The solid line in Fig. 11(b) represents the Meff(n) curve
for the charge and spin distribution on the CoO chain
BaCoO 3
3 in Table II; that is, one Co3+ in the CoO prism (Co3+)
z) 12 ZF-µSR withtheHSstate(S=2)andoneCo3+ an6d(n-1)Co4+priin
H
M 8 the CoO6 octahedra(Co3o+ct andCo4o+ct) with the LS state
( (S=0 and 1/2). The relationship between M and n is
eff
µ,i given by;[34]
ν 4
(a)
1 n−1
M2 = M2 + M2 , (6)
0 eff n+1 eff,S=2 n+1 eff,S=1/2
(cid:16) (cid:17)
1.5
K) 2K)0.06 where Meff,S=2 and Meff,S=1/2 are Meff for Co ions with
-atom 1 T ( J/mol 00..0042 eStiqo=n(27o)a,fnmtdheeSas=aub1ro/evd2eM(sCpeoiffn3p+rbiaenaldonwdchnCa=rog4o5e+cti)cs.onwfiSeglilnucreeaxtpitolhaneinievndartibhaye-
mol C/p 0 CoO3 chainis the most probable one. This also suggests
0.5 0 100 200 that the oxygen deficiency in the samples with n ≤ 5
(J/ T2 (K2) (b) is very small. For BaCoO3 (n=∞), Meff is estimated
Cp as 2.45 µB, whereas it is Meff = 1.73 µB for Co4o+ct with
0
S=1/2. This discrepancy was also reported by another
0 5 10 15 20
group (M ∼ 2.3 µ ) and was explained using a large
eff B
TEMPERATURE (K) g factor (=2.2) for the Co ions, [22] although g=2.0 for
Fe-doped Ca Co O was found in an ESR study. [35]
3 2 6
FIG. 10: Temperature dependences of (a) νµ,i and (b) Cp
for BaCoO3 (n=∞). The data of νµ,i were obtained by fit- ForCa3Co2O6(n=1),Θp=36.1±0.8K,andthisiscon-
ting the ZF-spectrum with eq. (5). The inset of Fig. 10(b) sistentwithpastwork.[12,13]Asnincreasesfrom1to3,
shows the dependenceof Cp/T on T2. Since Cp/T decreases Θp changesitssignfrompositivetonegativeandrapidly
roughly in proportion to T2 below T2, the magnetic contri- decreasesdownto-180K,thenincreaseswithfurtherin-
N
butionshould notbeignored evenat thelowest T measured. creasingnandapproaches∼0atn=∞. Alargenegative
ThismeansthatitisextremelydifficulttodeterminetheDe- paramagnetic Curie temperature for the samples with
byetemperatureand/orsubtractthelatticecontributionfrom n=2and3obviouslyindicates thatthe transitionatTon
c
theexperimental data.
iscausedbyaninter-chain2DAFinteraction. Consider-
ing the structural similarity among the quasi 1D cobalt
oxides, Ton for the samples with n=1 and 4 are there-
c
just below TN suggests that the transition is likely to be foremostlikelydue totheappearanceofthe short-range
continuous. Actually,theCp(T)curvealsosupportsthat 2D AF order. The magnitude of the 1D F interaction
the transition at 15 K is continuous. The five frequen- would be strongly affected by n, because not only the
cies are therefore unlikely to be caused by inequivalent structureofthechainbutalsotheCovalencearealtered
muon sites in the crystal lattice (compositional inhomo- by n (see Table II). Compared with the the intra-chain
geneities), but most likely reflect the intrinsic behavior 1D F interaction, the inter-chain 2D AF interaction is
of BaCoO3. expected to be insensitive to n, as the geometrical ar-
rangementof the chainsin the ab plane is essentially the
sameforallthecompoundswithn=1-∞. Thisindicates
thattheinter-chainAFinteractionplaysasignificantrole
IV. DISCUSSION for determining the magnetism detected by the current
µ+SR measurements. Here we wish to emphasize that
Ton is not caused by the change in the spin state of Co
A. Ton for the compounds with n=1 - 5 c
c ionsproposedbyHardyetal.,[20]becausethedecreasein
A confirms the appearance of a magnetically ordered
TF
In order to understand the common features of the phase. On the contrary, it was found that not ATF but
macroscopic magnetism of the quasi-1D compounds λTF exhibit an anomaly at the spin state transition in
taken collectively, Fig. 11 shows the average valence of the layered cobaltites.[3]
Co (V ) ions, the effective magnetic moment of Co ions
Co Since each chain is considered to act as a single spin,
(M ) and the paramagnetic Curie temperature (Θ ) as
eff p we ignore the intra-chain 1D F interaction. Within the
a function of n. The V (n) curve is calculated from the
Co mean field theory, T is expressed by;
N
nominal composition of the 1D system; that is, we ig-
nored a possible oxygen deficiency in the samples. The 1 S(S+1)
T = 2z |J | , (7)
values of Meff and Θp were obtained by fitting the χ(T) N 2 AF 3kB
9
TABLE II: Composition and nominal charge and spin distribution in theCoO3 chain for quasi-one-dimensional cobalt oxides,
An+2Con+1O3n+3 (A= Ca, Sr, Ba). Here, Copri and Cooct denote the Co ion in a CoO6 prism and in a CoO6 octahedron.
For the compounds with n= 2 - 5, mixed valence state would exist in the neighboring CoO6 octahedra to minimize electronic
repulsion.
n composition charge distribution spin distribution
1 Ca3Co2O6 Co3p+ri, Co3o+ct 2, 0
2 Sr4Co3O9 Co3p+ri, Co3o+ct, Co4o+ct 2, 0, 1/2
3 Sr5Co4O12 Co3p+ri, Co3o+ct, Co4o+ct, Co4o+ct 2, 0, 1/2, 1/2
5 (Sr1/2Ba1/2)7Co6O18 Co3p+ri, Co3o+ct, Co4o+ct, Co4o+ct, Co4o+ct, Co4o+ct 2, 0, 1/2, 1/2, 1/2, 1/2
∞ BaCoO3 Co4o+ct 1/2
der. Assuming thatTon (orTmid) =T′ andz=6,we can
c c N
|| estimateJAFforthecurrentsamplesusingthespindistri-
4 bution in Table. II. Here, Tmid denotes the temperature
E c
C (a) at which NATF=0.5. Figures 12(a) and 12(b) show the
N
E
L 3.5
A
V n=1
on
o T
C n=2 c
3 || 100 n=3 T mid
c
)
4 || K
(
n=5
(b) Tc 50
) 3 (a)
µB n=8
( A Co O
M eff 2 0 n+2 n+1 3n+3
30
S=1/2 (g=2)
1 ||
100 || K) 20
(
(c) B
k
0
/
K) |AF 10
( J
Θ p -100 | (b)
0
-200
|| 5 5.2 5.4 5.6 5.8
o
1 10 100 8 d (A)
inter-chain
n in AE Co O
n+2 n+1 3n+3 FIG. 12: The relationship between the inter-chain distance
dinter−chain and (a) Tc and (b) JAF in the quasi 1D system,
FIG. 11: (a) Average Co valence, (b) effective magnetic An+2Con+1O3n+3. The solid and open circles in Fig. 12(a)
moment of Co ions (Meff) and (c) paramagnetic Curie representTconandTcmidandthoseinFig.12(b)corresponding
temperature (Θp) as a function of n in the 1D system, JAF; Tcmid definedas thetemperature at which NATF=0.5.
An+2Con+1O3n+3. variation of T and J as a function of the inter-chain
c AF
distance dinter−chain in An+2Con+1O3n+3. Although Tc
where z is the number of the nearest neighboring spins, decreases with dinter−chain (and/or n), the magnitude of
J /k is roughly the same (∼20 K or 10 K) for all the
J is the 2DAF couplingconstantandk is the Boltz- AF B
AF B samples. ThissuggeststhatTon isinducedbythe2DAF
mann constant. Although T =29±5 K for Ca Co O c
N 3 2 6 interaction not only for the compounds with n ≥2 but
from the ZF-µ+SR measurement, we introduce a virtual
T (T′) to explain the behavior of the A (T) curve, also for Ca3Co2O6.
N N TF
indicating the appearance of the short-range 2D AF or- For BaCoO , the lowest Ton and the sharp transition
3 c
10
widtharecharacteristicfeaturescomparedwiththosefor
the compounds with n ≤5 (see Figs. 5 and 8). Also, a
clearmuonoscillationis observedonly inBaCoO3 below K)0.3
15 K. These suggest a smaller fluctuation and/or distri-
u
bution of the internal magnetic field in BaCoO3 than in m
0.2
the compounds with n ≤5. As seen in Table II, Co4+ e Ca Co O
/
ions with S=1/2 (Co4+) are stable in BaCoO , while ol 3 2 6
both Co3+ ions with oSct=2 and S=0 (Co3+ and3 Co3+) m0.1 H=10 kOe
pri oct (
ZFC
coexist in Ca Co O and Co3+, Co3+ and Co4+ in the T
3 2 6 pri oct oct d
compounds with n=2 - 5. A mixed valence state is ex- 1/ 0
pected in the neighboring Co3+ and Co4+ ions for min- -χ
oct oct d
imizing electronic repulsion, indicating the existence of -0.1
a fluctuating magnetic field. Also, the spin and charge 0 50 100 150 200 250
distribution in the compounds with n ≤5 would induce TEMPERATURE (K)
a large distribution in the internal magnetic field. These
are most likely to be the reasons for the difference be- FIG. 13: Temperature dependence of the slope of χ−1
tween BaCoO3 and the compounds with n=1 - 5. (dχ−1/dT)forCa3Co2O6. χarethedatashowninFig.2(c).
andneutrondiffractionmeasurements,butthelattercan
B. Ferromagnetic order along the chain be relatively easily observed by µ+SR.
As seen in Fig. 8, the χ−1(T) curve for BaCoO ex-
3
hibits a weak F or ferrimagnetic behavior below 53 K
C. Multi-frequency components in BaCoO
3
only under low magnetic fields. Reflecting this change,
λ increases slightly below ∼50 K with decreasing T,
TF
while there are no anomalies in the A curve down to In order to evaluate the critical exponent (β) for the
TF
15K.Itisthereforemostreasonabletoconcludethat,as AFtransition,Fig.14showstherelationshipbetweenthe
T decreases,the 1D F order completes below 53 K, then normalizedoscillationfrequencyν /ν (0K)andthere-
µ,i µ,i
the 2D AF order becomes stable below 15 K. In other duced temperature (T -T)/T . Here, ν (0K) and T
N N µ,i N
words, the F order in the chain is easily observed by are obtained by fitting the ν (T) curve (Fig. 10) with
µ,i
χ measurements but looks very complex in µ+SR. This eq. (2). We obtain β=0.191±0.009 and T =14.5±0.2.
N
situation is similar to the case for the typical 1D anti- The evaluated β for BaCoO also ranges between the
3
ferromagnet CsCoCl , in which the short-range 1D AF predictionsforthe 2Dand3DIsingmodel(β=0.125and
3
order appears below 75 K.[36] This corresponds to the 0.3125) , and is roughly the same as that for Ca Co O
3 2 6
maximum in the χ(T) curve. Nevertheless, moving soli- (β=0.18±0.12). This indicates a strong 2D character
tons alongthe chain[37] induce a largefluctuation of the of the AF transition in BaCoO , in contrast to β=0.31
3
internal field at the muon sites. As a result, µ+SR was for the 1D antiferromagnet CsCoBr . [40] Here β of
3
abletodetectthe2DAForderbutunabletoobservethe CsCoBr was evaluated using the neutron diffraction
3
short-range 1D AF order.[38] data in the vicinity of T (5×10−4 ≤ (T −T)/T ≤
N N N
0.08), whereas β of BaCoO the µSR data at 0.03 ≤
Forthecompoundswithn=1-5,weproposethatTon 3
(orTmid)=T′ iscausedbythe2DAFinteraction. Hencce, (TN −T)/TN ≤ 0.9. According to Ref. [40], however β
c N of CsCoBr looks almost the same value (0.31) even us-
there shouldexist a transitioninto the short-range1D F 3
ing the data at 0.03 ≤ (T −T)/T . The result that
ordered state above Ton. For Ca Co O , this require- N N
c 3 2 6 β[BaCoO ]<β[CsCoBr ] is therefore reliable. This dis-
ment is very consistent with the indication of a short- 3 3
crepancyisprobablyduetothedifferenceofthedorbitals
rangemagneticorderbelow∼200Kdetectedbyaspecific
heatmeasurement.[20] The χ−1(T)curvefor the current contributing to the magnetism; that is, t2g for Co4+ in
BaCoO ande forCo2+ inCsCoBr . Theoverlapofthe
Ca Co O also exhibits a deviation from the linear rela- 3 g 3
3 2 6 former between the neighboring chains is expected to be
tionshipbelow∼ 150K(see Fig.13),[13]presumablyin-
smaller than that of the latter.[41]
dicatingtheappearanceofthe1DForder. Furthermore,
recent χ measurements for the compounds with n=2 - 5 The simple hexagonal structure of BaCoO (and the
3
showed a field dependence even at 300 K.[39] This may lack of structural phase transitions at low T) and good
beduetotheappearanceofshort-range1DForderalong quality of our sample suggest the difficulty for explain-
the chain. The overallscenario for the quasi-1D systems ing five frequencies by multi-muon sites and/or inhomo-
is therefore that the 1D F ordered state exists even at geneity of the sample. In addition the fact that the five
∼200 K, while the 2D AF ordered state appears below frequencies show a sharp transition at the same temper-
∼100 K. The former is very difficult to detect by µ+SR ature indicates that these are the intrinsic behavior in