^{59}Co NMR evidence for charge ordering below T_{CO}\sim 51 K in Na_{0.5}CoO_2

0.25 MB·English

by  F. L. Ning

APS/123-QED
59Co NMR evidence for charge ordering below TCO ∼ 51 K in Na0.5CoO2
F. L. Ning1, S. M. Golin1, K. Ahilan1, T. Imai1,2, G.J. Shu3, and F. C. Chou3,4
1Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada
2Canadian Institute for Advanced Research, Toronto, Ontario M5G1Z8, Canada
3Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan and
4National Synchrotron Radiation Research Center, HsinChu 30076,Taiwan
(Dated: February 2, 2008)
TheCoO2 layersinsodium-cobaltatesNaxCoO2 maybeviewedasaspinS = 21 triangular-lattice
doped with charge carriers. The underlying physics of the cobaltates is very similar to that of the
8 high Tc cuprates. We will present unequivocal 59Co NMR evidence that below TCO ∼ 51 K, the
0 insulating ground state of the itinerant antiferromagnet Na0.5CoO2 (TN ∼ 86 K) is induced by
0 charge ordering.
2
PACSnumbers: 71.27.+a,71.30.+h,76.60.-k
n
a
J
The discovery of unconventional superconductivity in riodic Coulomb potential on the CoO triangular-lattice
2
0 sodium-cobaltate Na CoO [H O] (T ∼ 4.5 K) [5, 14,15, 16, 17,18]. Inthe caseofNa CoO , electron
1/3 2 2 4/3 c 0.5 2
2
[1,2,3]hasgeneratedmajorexcitementinthecondensed and neutron diffraction measurements have suggested

matter community. Co ions in the CoO layers take that Na+ ions form zigzag chains [5, 14, 15]. This re-
] 2
l a mixed valence state Co+4−x, and form a triangular- sults in the presence of two structurally inequivalent Co
e
lattice. Since Co4+ and Co3+ ions nominally have spins sites,eachformingachainstructure[15]asshowninFig.
-
r of S = 1 and S = 0, respectively, one may consider 1. One of the nearest neighbor sites of Co(1) is occu-
t 2
s the CoO layers as a S = 1 triangular-lattice doped pied by a Na+ ion, while Co(2) has no Na+ ions in the
. 2 2
t with charge carriers, in analogy with the doped CuO nearest neighbor sites [15]. Since the Coulomb poten-
a 2
m square-lattice in the high Tc cuprate superconductors. tial from Na+ chains attracts electrons, the valence of
ThefingerprintsofCospinsareeverywhereinNa CoO : Co(1)sites,Co+3.5−δ,issmallerthanthatofCo(2)sites,
d- Na0.82CoO2 isanitinerantantiferromagnet(TN ∼x21K2) Co+3.5+δ. The average valence of Co ions in Na0.5CoO2
n [4];Na CoO isa “CurieWeiss metal”withlargepara- is +3.5. The valence of Co(2) sites is closer to Co+4
0.7 2
o magneticsusceptibility[5];Na CoO isanitinerantan- (S = 1), hence Co(2) exhibits strong spin fluctuations
0.5 2 2
[c tiferromagnet (TN ∼ 86 K) [5], and undergoes a myste- above TN ∼= 86 K [19], and develops a sizable ordered
rious metal-insulator transition below ∼51 K [5]. magnetic moment ∼ 0.26µB within the CoO2 plane be-

2 In the case of the cuprates, doped holes tend to segre- low TN [9, 20]. On the other hand, Co(1) sites have
v gatethemselvesfromtheunderlyingS = 1 square-lattice much weaker spin fluctuations above TN[19]. The upper
3 to form static charge stripes [6]. Whether2the charge or- bound of the ordered moment at Co(1) sites is as small
2
dering in stripes is related to or competing against the as ∼0.04µB at 8 K and too small to be detected by po-
0
4 mechanism of high Tc superconductivity is controversial larized neutron scattering techniques [9]. 59Co zero field
. [7]. A major question we address here is whether or not NMRisaverypowerfultechniquefordetectingsmallhy-
1 the cobaltates also exhibit a similar phenomenon in the perfine magnetic field Bhf, which is proportional to the
1
triangular-lattice geometry. The insulating ground state orderedmagnetic moments. Yokoi et al. took advantage
7
0 of Na0.5CoO2 below ∼ 51 K has attracted considerable ofthishighsensitivity,anddemonstratedthepresenceof
: attention because of speculation that it may be charge small ordered moments at Co(1) sites along the crystal
v ordered [5, 8, 9, 10]. However, earlier 23Na NMR mea- c-axis below TN ∼ 86 K. This led them to propose two
i
X surementsinNa CoO showednoevidenceoftheemer- possible spin structures as shown in Fig.1 [20].
0.5 2
r genceofachargeorderedstatebelow∼51K [11,12,13]. Although the existence of multiple Co sites in
a
InthisLetter,wetakeamoredirectapproachtoprob- Na CoO is sometimes referred to as a consequence of
x 2
ingthechargeenvironmentinCoO2layers,bymeasuring charge ordering persisting up to room temperature, it
the EFG (Electric Field Gradient) of Co sites with zero- is important to realize that these distinct behaviors of
field59CoNMR.TheEFGtensoristhesecondderivative Co(1) and Co(2) sites in Na CoO are directly linked
0.5 2
of the Coulomb potential, and hence is directly related with the periodic Coulomb potential arising from Na+
to the local charge density. We will present unequivocal zigzagchains. Moreover,chargesonthe Cosites aremo-
evidence that the insulating ground state of Na0.5CoO2 bile, and Na0.5CoO2 is metallic above TCO ∼ 51 K [5].
below TCO ∼ 51 K is indeed the consequence of charge Incontrast,strongelectron-electroncorrelationeffectsin
ordering. highT cupratesinduceaself-organizedpatternofdoped
c
A major distinction between cobaltates and cuprates carriersintheformofchargestripes[6]. Thespatialperi-
is that the Na+ ions in cobaltates can spatially or- odicity of the charge ordered state is different from that
der for certain values of Na concentration, x. Be- of the Coulomb potential of the underlying lattice. It
sides donating electrons, ordered Na+ ions exert a pe- is this type of self-organized charge pattern that we are
2
searching for in Na CoO . to the crystalc-axis. Inthe paramagneticstate at110K
0.5 2
In Fig.2, we present typical zero-field 59Co (nuclear (> TN), we deduced from the 59Co NQR lineshape that
spin I = 7) NMR lineshapes from a piece of electro- νc =2.799(5)MHzandη =0.300(1)forCo(1)sites,and
2 Q
chemicallydeintercalatedNa CoO singlecrystal(mass νc =4.040(5) MHz and η =0.400(1) for Co(2) sites.
0.5 2 Q
∼ 25mg) [21, 22]. The observed lineshapes are similar
The second term in the Hamiltonian represents the
to Yokoi’s[20]. Below T ∼ 86 K, we observe 7 NMR
N Zeeman interaction between Co nuclear spins and the
peaks of Co(2) sites for transitions between nuclear spin local magnetic field, B, at the position of the observed
Iz = 2m2+1 and Iz = 2m2−1, where integer −3≤m≤+3. nuclear spin. γn = 2π×10.054 MHz/Tesla is the 59Co
In the frequency range above 5 MHz, we have also suc-
nuclear gyromagnetic ratio. In our zero-field NMR mea-
cessfully detected Co(1) zero-field NMR signals for the
surements, we apply no external magnetic field. Hence
m = 0 to m = +3 transitions. The intensity of NMR B=B ,whereB isthehyperfinemagneticfieldfrom
hf hf
signals decreases in proportion to the square of the fre- orderedCo moments. B is proportionalto the sublat-
hf
quency, and measurements below 5 MHz are formidable. tice magnetization, M(T), of Co sites [20]. The m = 0
We summarize the temperature dependence of the ob-
transition frequency depends primarily on the Zeeman
served peak frequencies fm of Co(1) sites in Fig.3. A term,f ∼γ |B |. At60K,f =6.659MHzand19.780
0 n hf 0
remarkable feature of Fig.2 and Fig.3 is that all 4 peaks
MHz for Co(1)andCo(2)sites,respectively,because the
ofCo(1)sitessplit intotwo preciselybelowTCO ∼51K. hyperfine magnetic field is |B | ∼ 0.6 Tesla at Co(1)
hf
In contrast, Co(2) sites show no anomalies. In what fol-
sites, and ∼1.9 Tesla at Co(2) sites. The separationbe-
lows, we will refer to the two inequivalent Co(1) sites
tween adjacent peaks, (f −f ), depends primarily
m+1 m
as Co(1a) and Co(1b). In passing, the comparison be- on the EFG. For Co(1) sites, (f −f ) ∼ νc ∼ 2.8
m+1 m Q
tween the zero-field and low-field NMR lineshapes indi-
MHz, since the ordered moments point along the c-axis.
catesthatthe NMRsignalsnear6MHz, showningreen, For Co(2) sites, the separation is (f −f ) ∼ νa,b ∼
are not related to Co(1) sites [13]. We tentatively at- m+1 m Q
νc/2 ∼ 2 MHz or less, because the ordered magnetic
tribute these unidentified signals to defect sites caused Q
moments pointwithin the ab-plane. The observedpeaks
by slight deviation of Na concentration from 0.5 and/or
f arenotevenlyspaced,becausethenuclearquadrupole
minordisorder. We alsoconfirmedthatbothCo(1a)and m
and Zeeman interactions are comparable in the present
Co(1b) lines split in weak magnetic field applied along
case. This means that we must diagonalize the Hamil-
thec-axis[13]. ThismeansthatbothCo(1a)andCo(1b)
tonian in eq.(1) exactly to fit the lineshapes. By relying
sites have up-spins as well as down-spins.
on inaccurate second-order perturbation analysis, Yokoi
To understand the effects of the EFG on NMR line-
et al. not only misidentified the peaks of Co(2) sites but
shapes, we need to theoretically compute the resonance
werealsounabletodeducethecriticallyimportantinfor-
frequencyf ofthem-thtransitionasf =(E −
m m (2m+1)/2 mation associated with the Co(1) sites [20].
E(2m−1)/2)/h,wheretheenergylevelsEn areeigenvalues
Basedontheexactdiagonalization,wematchedallthe
of the standard 59Co nuclear spin Hamiltonian,
observed zero-field NMR peaks with theoretically calcu-
hνZ lated values of fm as shown by vertical lines in Fig.2.
H = Q{3I2 −I(I+1)+η(I2 −I2)}−γ hB·I. (1) This allowedus to deduce the relevantNMR parameters
6 Z X Y n of eq.(1), i.e. νc, η, the magnitude of B , and the rel-
Q hf
The first term of the Hamiltonian represents the nuclear ative polar angle (θ, φ) between Bhf and the c-axis. We
quadrupole interaction [23] between the EFG and the found that η shows no temperature dependence across
59Conuclearquadrupolemoment. Thediagonalizedten- 51K,and(θ, φ) changeless than2degreesfromthe val-
◦ ◦
sor of the nuclear quadrupole interaction (νX, νY, νZ) ues at 60 K (θ = 9±1 , φ = 0 ). Hence we focus our
Q Q Q attentiononthe temperature dependence ofνc andB
is proportional to the EFG tensor (dφ2/dX2, dφ2/dY2, Q hf
dφ2/dZ2), where φ is the total Coulomb potential seen of Co(1a) and Co(1b) sites.
by59Conuclei,andX,Y andZ representthreeorthogo- Co(1a) and Co(1b) have different values of νc, as
Q
nal,principalaxes(byfollowingtheconvention,wedefine showninFig4b. Thisisdirectproofthatlocalchargeen-
|νX| < |νY| < |νZ|). From the comparison of zero-field vironment is different between Co(1a) and Co(1b) sites.
Q Q Q
NQR (Nuclear Quadrupole Resonance) results at 110 K Inprinciple,adifferentiationoftheEFGbetweenCo(1a)
(seeFig.2)andhigh-fieldNMR,wefoundthatthe main- and Co(1b) sites could arise if a structural phase tran-
principal axis Z coincides with the crystal c-axis within sition doubles the unit cell of Na+ zigzag chains. To
experimental uncertainties (∼ 5 degrees). This means rule out such a scenario, we deduced νc(Na) at two
Q
that the other principal axes, X and Y, lie within the structurally inequivalent Na sites, Na(1) and Na(2) [15],
CoO plane. Poisson’s relation for the Coulomb inter- from the measurements of +1 to −1 central transition
2 2 2
action sets a constraint, νX +νY +νZ = 0. Hence we and ±3 to ±1 satellite transitions of 23Na NMR in the
Q Q Q 2 2
have only two independent parameters in the first term same crystal [13]. As summarized in Fig.4a, we found
of eq.(1), νc (we now denote Z = c) and the anisotropy no hint of additional splitting or extra broadening for
Q
parameterη =(νQY−νQX)/νQZ. ηisameasureofthedevia- νQc(Na) below TCO. The upper bound of the potential
tionfromaxialsymmetryoftheEFGtensorwithrespect splitting of νc(Na) at 4 K is less than ∼ 1%, while
Q
3
the splitting of νc between Co(1a) and Co(1b) sites, have only spin ordering and show no anomalies either
Q
∆νc =νc, Co(1b)−νc, Co(1a),reachesasmuchas∼6%,as in NMR lineshapes or νQ across 51 K. In Fig.1, we
Q Q Q show the possible charge ordering patterns with the
showninFig.4d. Thereforewe conclude thatCo(1) sites
smallest possible unit cell. Our observation of a striped
undergo a charge ordering transition at T ∼51 K.
CO configuration of the charge ordered state, consisting
The observed differentiation of B between Co(1a)
hf of Co(1) chains with charge and spin ordering and
and Co(1b) sites in Fig.4c is also understandable as a
Co(2) chains with spin ordering only, is consistent with
consequence of charge ordering. Since the valence state
the two-fold symmetry observed for in-plane magne-
is different below T ∼ 51 K, the number of electrons
CO toresistance by Balicas et al. [8]. The splitting of νc
fillingthet orbitalsofCo(1a)andCo(1b)siteswillalso Q
2g
(and hence EFG) reaches as much as ∼ 6 % between
be different. This naturally results in a different magni-
Co(1a) and Co(1b) sites. We recall that νc at 63Cu
tude of ordered moments at Co(1a) and Co(1b) sites, Q
sites increases by ∼ 10% in high T cuprates when the
and hence separate values of B . In Fig.4d, we plot c
hf
hole concentration x changes by 0.15 in the CuO plane
the splitting of B between Co(1a) and Co(1b) sites, 2
hf
∆B = BCo(1a) − BCo(1b). ∆B shows an identical of La2−xSrxCuO4 [24]. If we assume that the charge
hf hf hf hf doping effects on the EFG are comparable between
temperaturedependenceas∆νc withinexperimentalun-
Q cobaltates and cuprates, we can crudely estimate the
certainties. This is not surprising, because to a good
differentiationofthevalencebetweenCo(1a)andCo(1b)
approximation, both ∆νc and ∆B should be propor-
Q hf sites as ∼ 0.1. It is worth noting that t-U-V model
tional to the difference of the number of electrons occu-
calculations [10] showed that a differentiation of valence
pying the Co 3d orbitals. Thus we may consider ∆νc
Q of Co(2) sites as little as ∼ 0.03 may be sufficient to
and ∆B as the order parameter of charge ordering be-
hf drive CoO planes into insulating. On the other hand,
low 51 K. By fitting the temperature dependence down 2
none of the charge orderedpatterns proposed within the
to 40 K (= 0.8T ) to a typical power law behavior,
CO existingtheoreticalframeworks[10,25,26]areconsistent
∆νc ∼ ∆B ∼ (T −T )β′, we found the critical ex-
Q hf CO with our experimental finding of charge ordering on
′
ponent β =0.3±0.1. Interestingly,this value is compa- Co(1) sites. Clearly,moretheoreticalworksarerequired.
rable to the critical exponent β = 0.28±0.02 observed
for the sub-lattice magnetization, M(T)∼(T −T )β at
N
T = 86 K for the antiferromagnetic N´eel transition of Acknowledgment
N
Co(2) sites [9]. We thank P.A. Lee for helpful communications and
To conclude, we have presented unequivocal zero-field encouragement. TI acknowledges support from NSERC
NMR evidence that static differentiation of charge den- and CIFAR. FCC acknowledges support from NSC-
sitiesdevelopsbelowT ∼51K inthe onedimensional Taiwan under contract number NSC-95-2112-M-002.
CO
chain structure of Co(1) sites. In contrast, Co(2) sites
[1] K. Takada, H. Sakurai, E. Takayama-Muromachi, (2006).
F. Izumi, R. Dilanian, and T. Sasaki, Nature 422, 53 [10] S.ZhouandZ.Wang,Phys.Rev.Lett.98,226402(2007).
(2003). [11] B. Pedrini, J. L. Gavilano, S. Weyeneth, J. Hinderer,
[2] T. Fujimoto, G. Q. Zheng, Y. Kitaoka, R. L. Meng, M. Weller, H. R. Ott, S. M. Kazakov, and J. Karpinski,
J. Cmaidalka, and C. W. Chu, Phys. Rev. Lett. 92, Phys. Rev.B 72, 214407 (2005).
047004 (2004). [12] J. Bobroff, G. Lang, H. Alloul, N. Blanchard, and
[3] K. Ishida, Y. Ihara, Y. Maeno, C. Michioka, M. Kato, G. Collin, Phys. Rev.Lett. 96, 107201 (2006).
K. Yoshimura, K. Takada, T. Sasaki, H. Sakurai, and [13] F. L.Ning, unpublished.
E. Takayama-Muromachi, J. Phys. Soc. Jpn. 72, 3041 [14] H.W.Zandbergen,M.Foo,Q.Xu,V.Kumar,andR.J.
(2003). Cava, Phys.Rev.B 70, 024101 (2004).
[4] S.P.Bayrakci,I.Mirebeau,P.Bourges,Y.Sidis,M.En- [15] Q. Huang, M. L. Foo, R. A. Pascal, J. W. Lynn, B. H.
derle, J. Mesot, D. P. Chen, C. T. Lin, and B. Keimer, Toby,T.He,H.W.Zandbergen,andR.J.Cava,J.Phys.
Phys.Rev.Lett. 94, 157205 (2005). Condens. Matter 16, 5803 (2004).
[5] M.L.Foo,Y.Y.Wang,S.Watauchi,H.W.Zandbergen, [16] P. H. Zhang, R. B. C. ad M. L.C˜ohen, and S. G. Louie,
T. He, R. J. Cava, and N. P. Ong, Phys. Rev. Lett. 92, Phys. Rev.B 71, 153102 (2005).
247001 (2004). [17] M. Roger, D. J. P. Morris, D. A. Tennant, M. J.
[6] J. M. Tranquada, B. J. Sternlieb, J. D. Axe, Y. Naka- Gutmann, J. P. Goff, J. U. Hoffman, R. Feyerherm,
mura, and S.Uchida, Nature375, 561 (1995). E. Dudzik, D. Prahakaran, A. T. Boothroyd, et al., Na-
[7] A.J. Millis and J. Orenstein, Science 288, 468 (2000). ture 445, 631 (2007).
[8] L. Balicas, M. Abdel-Jawad, N. E. Hussey, F. C. Chou, [18] F. C. Chou, M.-W. Chu, G. Shu, F. T. Huang, W. W.
and P. A.Lee, Phys.Rev.Lett. 94, 236402 (2005). Pai, H. S. Sheu, T. Imai, F. L. Ning, and P. A. Lee,
[9] G.Gasparovic,R.A.Ott,J.H.Cho,F.C.Chou,Y.Chu, arXiv:0709.0085.
J. W. Lynn, and Y. S. Lee, Phys. Rev. Lett. 96, 046403 [19] F.L.Ning,T.Imai,B.W.Statt,andF.C.Chou,Phys.
4
Rev.Lett. 93, 237201 (2004).
[20] M.Yokoi,T.Moyoshi,Y.Kobayashi,M.Soda,Y.Yasui, Fig.2. 59CoNMRlinesatCo(1)sites(blue)andCo(2)
M. Sato, and K. Kakurai, J. Phys. Soc. Jpn. 74, 3046 sites (orange) at 110 K (paramagnetic state, B = 0),
hf
(2005).
60 K (N´eel ordered state), 30 K and 4.2 K (charge
[21] G. J. Shu, A. Prodi, S. Y. Chu, Y. S. Lee, H. S. Sheu,
ordered state). Vertical lines represent theoretical fit
and F. C. Chou, arXiv:0708.0280.
of resonance frequencies f for Co(1) (black), Co(1a)
[22] F.C.Chou,J.H.Cho,P.A.Lee,E.T.Abel,K.Matan, m
and Y. S.Lee, Phys. Rev.Lett. 92, 157004 (2004). (dark blue), Co(1b) (light blue), and Co(2) (orange).
[23] T. P. Das and E. L. Hahn, Solid State Physics, Supple- Peak(s) near 6 MHz (green) are not associated with
ment 1, 1 (1958). Co(1) or Co(2) sites (see main text).
[24] T. Imai, C. P. Slichter, K. Yoshimura, and K. Kosuge,
Phys.Rev.Lett. 70, 1002 (1993). Fig.3. f (m = 0,1,2 and 3) for Co(1) (black)
m
[25] H. Watanabe and M. Ogata, J. Phys. Soc. Jpn. 75, above T , and Co(1a) (dark blue) and Co(1b) (light
CO
063702 (2006).
blue) below T . Vertical arrows roughly represent the
CO
[26] T. P. Choy, D. Galanakis, and P. Philips, Phys. Rev. B magnitude of νc for Co(1a) and Co(1b) sites.
75, 073103 (2007). Q
Fig.4. (a) Temperature dependence of νc(Na) at
Q
Na(1) and Na(2) sites. The distribution of νc(Na)
Q
is about the size of the symbols. (b) Temperature
Fig.1. Ordered magnetic moments on Co(1) sites
dependence of νc, and (c) hyperfine field B in Co(1)
pointeitherup(•)ordown(×),whilemomentsonCo(2) Q hf
sites. Color convention is the same as in Fig.2 and
sites point within the plane (arrows) [20]. Co(1) sites
Fig.3. (d) ∆νc : the splitting ofνc betweenCo(1b)and
have either in-plane antiferromagnetic order (left panel) Q Q
or in-plane ferromagnetic order (right panel). In the Co(1a) sites deduced from Fig.4b (left axis, diamond).
latter case, Co(1) sites in the adjacent CoO2 layers have ∆Bhf : the splitting of Bhf between Co(1a)and Co(1b)
opposite spin orientation. Dark blue and light blue on deduced from Fig.4c (right axis, filled circles). Solid
Co(1a) and Co(1b) sites, respectively, represent possible curve shows a best fit to ∆νQc ∼ ∆Bhf ∼ (T −TCO)β′
′
charge ordering patterns to be determined in this work. with acriticalexponentβ =0.3. The dashedline shows
Red dashed lines represent the unit cell in each possible T ∼51 K.
CO
configuration.
a
c
b
Co(1a) Co(1b) Co(2)
m= 110 K
±2±1 ±2 ±3 ±3
(NQR)
60 K
30 K
4.2 K
m= 0 1 2 3 -3 -2 -1 0 1 23
5 10 15 20 25
Frequency [MHz]
16
+3
14
+2
12
]
z
H
M
[ +1

F 10
m=0
8 T T
CO N
6
0 20 40 60 80 100
T [K]
ν
a Na(2) c
1.4 Q
(
N
a
)
[
1.3 M
Na(1) H
z
]
2.95 b Co(1b)
]
z
H
M
∆νc
[
Q
Q
c 2.75
ν
Co(1a)
c
] 0.73
a
Co(1a)
l
s
∆Β
e
T hf
[
f
h
B 0.63 Co(1b)
0.05
d
0.16
0.04
0.12
]
z 0.03 ∆
H B
M h
f
[ 0.08 [T
Q e
0.02
c s
ν
l
∆ a
]
∆νc
0.04 Q
0.01
∆Β
hf
0 0
0 10 20 30 40 50 60
T [K]