Sodium cobaltate, NaxCoO2, which was originally known as a battery material, has been extensive studied for its other prominent features such as thermoelectricity, superconductivity, and magnetism.2-4 The crystal consists of alternating layers of triangular Co lattice and Na. Varying Na content changes the charge configuration (Co3+, Co4+) in the Co layers. Interestingly, the Na atoms form structural ordering patterns at certain sodium concentrations.5 Due to the subtle interplay of the Na ordering with the charges and spins of the Co ions, a unique and rich phase diagram has been found.6 Recently, the phase diagram has been refined, where only three distinct antiferromagnetic (AF) transitions were found. Structural phase separation was reported in the two regions of 0.76 < x < 0.82 and 0.83 < x < 0.86.7 In particular, the x = 0.82 sample has the most stable AF phase and a well-defined superlattice structure. The local electronic properties and the Co magnetism, in connection with the Na ordering, has been investigated for the concentrations of x = 1/2 (metal-insulator),8 x = 2/3 (Curie-Weiss metal),9 and x = 1 (band insulator).10 To have a complete picture of this atypical magnetic phase diagram, we conduct a nuclear magnetic resonance (NMR) study on the antiferromagnetic phase of a NaxCoO2 single crystal with the particular stable concentration x = 0.825.
We use a high-quality Na0.825CoO2 single crystal, obtained from Prof. F.-C. Chou at National Taiwan University, for our NMR experiments. Na0.825CoO2 has a long-range A-type AF order with the Néel temperature TN = 22 K,4 as shown in Fig. 1 of the magnetic susceptibility.
Figure 1 Magnetic susceptibility of Na0.825CoO2 for magnetic field applied along the crystalline c axis. Antiferromagnetic transition occurs at 22 K. The arrow at ∼ 60 K denotes the deviation from Curie-Weiss behavior.
Standard Hahn-echo pulse sequences were employed throughout our 23Na and 59Co NMR experiments.
Figure 2 shows the temperature-swept spectra for their central (|−1/2 ↔ |+1/2 ) transitions with the magnetic field 88 kG applied parallel to the crystalline c axis. Multiple peaks are observed and these peaks are separated around 60 K. There are total 6 well-resolved peaks of 23Na and 4 peaks of 59Co for the central transition (Fig. 3).
Figure 2 Temperature-swept 23Na and 59Co NMR spectra of Na0.825CoO2 for magnetic field applied along the crystalline c axis.
These sharp peaks suggest that Na vacancies are not randomly distributed in this crystal, but are to form particular pattern, otherwise, the spectra would have been broadened. From the peak numbers, we find that there are 6 and 4 different crystallographic sites for the Na and Co atoms, respectively, which is also confirmed by analyzing their quadrupolar satellite peaks and the spectra with the magnetic field perpendicular to the c axis.
Figure 3 (a) 23Na and (b) 59Co NMR spectra of Na0.825CoO2 for magnetic field applied along the crystalline c axis. There are 6 well-resolved peaks for the central transition (|−1/2 ↔ |+1/2 ) in (a) and 4 peaks in (b).
Vacancies in the Na layers produce two distinguished crystallographic Na sites, called Na1 and Na2.11 Na1 is located directly between the two cobalt atoms from its neighboring Co layers, whereas Na2 is sandwiched by the triangular Co sub-lattices [Fig. 4(a)]. The Co atoms which are right on top and below the Na1 atom are called Co1, and the rest of Co atoms are called Co2, by convention. Depending on the Na contents, the Na vacancy can form different clusters. Several models for the Na ordering patterns in NaxCoO2
have been proposed experimentally and theoretically, but discrepancy exists among the models.5,12-15 For Na0.825CoO2, the tri-vacancy and quadri-vacancy clusters are inferred, according to the vacancy clustering model proposed by Roger et al.13 A di-vacancy cluster model with the superlattice unit cell size
13
a
13a
, however, was suggested based on the x-ray diffraction experiments.3c
7 With these pieces of information, we were motivated to examine all the pro posed vacancy cluster models and to search for the one that could give the 6 Na and 4 Co sites as derived from our NMR experiments. However, we did not find any at all. Since the 3c periodicity of the supercell along the c axis was affirmed,7 we then tried again by keeping the 3c periodicity but with tuning the supercell size a little bit. Eventually, we found that only the Na di-vacancy clusters with the supercell size 12a
12a
[Fig. 4(a)] could give the correct numbers of Na 3c
and Co sites suggested by our NMR. This superlattice is formed by stacking the six 12a
12a
Na di-vacancy layers along the c axis as illustrated in Fig. 4(b), where the Na vacancy layers are offset each other by a lattice vector. Six different Na sites and four Co sites are identified as shown in Fig. 4(c), where the numbers next to the site labels denote the occupancies of these sites in a unit supercell. For this superstructure, the Na content is x = 0.833(= 10/12) which is very close to our nominal content x = 0.825. To further examine this superlattice model, we can compare the relative NMR peak intensity with the site occupancy for these different Na and Co sites. Note that a square of frequency correction and the spin-spin relax ation (T2) effect are needed to be considered in order to obtain the true spectrum intensity.9 We found that all the 6 Na sites have a very similar T2 relaxation time at 30 K, so that the Na peak intensities in Fig. 3(a) reflect the true site occupancies by chance. We found that the 4th and 6th peaks have a roughly half intensity compared to that for the rest 4 peaks. This is in consistent with the relative site occupancies of Na as shown in Fig. 4(c). However, we are unable to assign the peaks to which Na site, because of equal occupancy 0.2 for the 4 sites (Na2a, Na2b, Na2c, Na2d) and 0.1 for the rest 2 sites. As for the Co sites, we found that the T2 effect is significant in correcting the intensities in Fig. 3(b), where the peak at a higher frequency has a faster relaxation rate 1/T2 as seen in Na2/3CoO2.9 The corrected relative intensity ratio that we obtained for the peaks 1 to 4 is 1 : 0.7 : 1 :2.3. We consider this ratio is compatible with the occupancy ratio 1:1:1:3 in Fig. 4(c), and the 4th peak could be assigned to the Co2b site. The poor accuracy of the intensity comparison could be due to the experimental error, where the NMR pulse parameters were optimized only for the 1st Co peak and the same pulse parameters were used for obtaining the rest peaks.
Figure 4 The superlattice model derived from our NMR data. (a) A Na di-vacancy layer with the supercell size 12
a
12a
. (b) The superlattice formed by stacking the 6 Na di-vacancy layers which are offset each other by one lattice vector. The supercell size is 3c along the c axis. (c) The 6 different Na sites and 4 Co sites, extracted from (b).Figure 5 shows the 23Na NMR spectrum for magnetic field B⊥c and B∥c. The quadrupolar satellites for
B⊥c are barely seen and are scattered on both sides of the central peaks, unlike those for B∥c. The NMR
resonance frequency for the transition |m ↔ |m − 1 is determined by the equation,
/ 2
1
Q
1/ 2 3cos 2 1 sin2 cos 2 / 2
f K B f m ,
where γ is nuclear gyromagnetic ratio, K is the frequency shift, B is the applied magnetic field, fQ is the nuclear quadrupolar frequency, and θ and ϕ are the polar and azimuthal angles of the magnetic field relative to the principle axes of the electric field gradient.16 η is an asymmetry parameter that characterizes the axial symmetry of the electric field gradients. η = 0 is for the nuclear site to have a uniaxial symmetry. According to Fig. 4(c), all the Na sites do not posses uniaxial symmetry so that η ≠ 0 and their quadrupolar satellite peak position depends on ϕ, when magnetic field perpendicular to the c axis. For spectrum in this field direction, we notice that all the Na2a sites in a unit supercell do not have the same ϕ, due to their EFG principle axes oriented differently with respect to the magnetic field in the three-dimensional stacking of the Na layers, as illustrated in Fig. 5. Four different ϕs are found for the Na2a sites, as well as for the Na2b, Na2c, and Na2d sites, but only one ϕ is found for the Na1 and Na2e sites. Each ϕ gives a set of the quadrupolar satellite peaks.
Therefore, there would be 18 (= 4 × 4 + 2) sets of the quadrupolar peaks that are scattered on both sides of the central peaks. According to this superstructure model, the simulated spectrum is shown in Fig. 5(a), which qualitatively captures the feature of the experimental curve. Overall, we have tried numerous superstructures, and this proposed superlattice model is the only structure that we could found to best describe our NMR data and to give the correct Na content x for our sample.
Figure 5 23Na NMR spectra of Na0.825CoO2 for magnetic field applied (a) perpendicular (b) parallel to the crystalline c axis. The red curve in (a) is a simulated spectrum. The top two Na layers in Fig. 4(b) are illustrated here to show that the azimuthal angle ϕ of the magnetic field relative to the electric field gradient principle axes of the 4 Na2a (cyan) sites are different.
Cobalt atoms situated in such a superstructure could produce non-trivial electron correlation and collective magnetic behavior. We notice that the magnetic susceptibility curve in Fig. 1 deviates from the Curie-Weiss behavior at ∼ 60 K before entering the AFM phase. This is often attributed to the onset of short-range magnetic correlation or ordering. However, we found that the 23Na and 59Co NMR spectra do not have apparent line broadening, as anticipated for any short-range magnetic ordering at 60 K, until the temperature is close to 30 K, before the AFM transition at 22 K. The crystal field effect is ruled out here because the splitting between the lower-lying t2g and higher-lying eg bands is ∼ 2.5 eV, much higher than this temperature range.17 Since the NMR frequency shift is a measure of the local magnetic susceptibility, we then compare the frequency shifts of all the Na and Co peaks with the bulk susceptibility as shown in Fig. 6 (a) and (b). Interestingly, the local susceptibility deviates from the bulk susceptibility, usually called shift anomaly,18 at the same temperature where the Curie-Weiss behavior breaks down. This indicates that an additional local susceptibility component might arise due to the coherence of the delocalized Co 3d electrons, as seen in the Kondo lattices.18 According to Ref. 18, the bulk susceptibility may be modeled as
T 1 f T
d
T f T
0 T , where the χd and χ0 are the susceptibilities of the localized and the coherent d electrons, respectively. The ratio of these two components is a function of temperature characterized by f(T). The frequency shift is given by, K(T) = Adχd + A0χ0, where Ad and A0 are the nuclear hyperfine coupling constants. The shift anomaly is then obtained if it is written as an explicit function of the
bulk susceptibility. Since there are several Na and Co sites, we could further express the shift of the j-th Na (or Co) site in terms of the shift of the i-th Na (or Co) site, such as, Kj = (Ad,j/Ad,i)Ki + [A0,j − (Ad,j/Ad,i)A0,i]χ0. Figures 6(c) and (d) are the plots of the Na and Co shifts with respect to the Na#1 and Co#1 shifts, respectively. The linear relation between the individual shifts is interrupted at ∼ 60 K and then is restored around 30 K. This suggests that χ0 emerges at 60 K and then saturates, and all the Na and Co sites see χ0. If the shift anomaly is caused by the short-range ordering, the breakdown of the linear relation in Figs. 6(c) and (d) should persist into the long-range order regime.
Figure 6 (a) and (b) are the comparisons of 23Na and 59Co NMR frequency shifts, respectively, with the bulk magnetic susceptibility. The curve labels denote the peak indices as assigned in Fig. 3. Figures (c) and (d) are plots of the 23Na and 59Co shifts versus the Na#1 and Co#1 shifts, respectively.
Na0.825CoO2 has an A-type AFM order. When applying magnetic field, it can undergo a metamagnetic transition, where the AFM state is spin-flopped into a ferromagnetic (FM) state.6 Our NMR spectra were taken at 88 kG, which happens to make the sample to be in a state near the metamagnetic phase boundary.
According to Fig. 2, the sample first enters a FM state at 22 K, and returns to an AFM phase at 3.9 K. At 4.2 K, we accidentally observed that the 23Na spectrum shows time dependence after the sample was warmed up from 2.7 K to 4.2 K. It took about 120 min. for the sample to recover from the AFM to FM state. This slow spin dynamic indicates that spin glass might occur near the metamagnetic boundary. According to Ref. 19, the interlayer AFM exchange coupling is not too different from the intralayer FM exchange coupling, so that a little non-uniform magnetic field in the sample could cause a mixture of the two phases. The spin frustration, due to the competing AFM and FM interactions, then could occur for the Co spins in a triangular lattice as illustrated in Fig. 7(b). In principle, the conditions required for a spin glass, such as lattice disorder and spin frustration, are fulfilled in Na0.825CoO2. It would be interesting to further investigate this magnetic field-induced glassy behavior to see if it has similar properties as ordinary spin glasses.
Figure 7 (a) Time-dependent 23Na NMR spectra of Na0.825CoO2 at 88 kG and 4.2 K, near the AFM and FM phase boundary. (b) The magnetic structures of the AFM and FM phases in Na0.825CoO2. The Co spins in the triangular lattice are frustrated near the AFM-FM phase boundary (see text).
In summary, we refine the 3-dimensional superstructure in a Na0.825CoO2 single crystal by NMR experiments. We found that additional susceptibility component emerging at ∼ 60 K, due to the onset of electron coherence. A magnetic field-induced glassy behavior is observed near a FM-AFM metamagnetic phase boundary. With Our superlattice model, theorists may be able to solve the localized and itinerant issues of the Co 3d electrons that produce the metallic antiferromagnetism in Na0.825CoO2. The manuscript for this work will be submitted to Phys. Rev. Lett. soon.