Spin correlations and cobalt charge states: Phase diagram of sodium cobaltates

Using ${}^{23}\text{N}\text{a}$ NMR measurements on sodium cobaltates at intermediate dopings $\left(0.44\le x\le 0.62\right)$, we establish the qualitative change in behavior of the local magnetic susceptibility at $x^{\ast }=0.63–0.65$, from a low-$x$ Pauli-like regime to the high-$x$ Curie-Weiss regime. For $0.5\le x\le 0.62$, the presence of a maximum $T^{\ast }$ in the temperature dependence of the susceptibility shows the existence of an $x$-dependent energy scale. $T_1$ relaxation measurements establish the predominantly antiferromagnetic character of spin correlations for $x<x^{\ast }$. This contradicts the commonly assumed uncorrelated Pauli behavior in this $x$ range and is at odds with the observed ferromagnetic correlations for $x>x^{\ast }$. It is suggested that at a given $x$ the ferromagnetic correlations might dominate the antiferromagnetic ones above $T^{\ast }$. From ${}^{59}\text{C}\text{o}$ NMR data, it is shown that moving toward higher $x$ away from $x=0.5$ results in the progressive appearance of nonmagnetic ${\text{Co}}^{3+}$ sites, breaking the homogeneity of Co states encountered for $x\le 0.5$. The main features of the NMR-detected ${}^{59}\text{C}\text{o}$ quadrupolar effects, together with indications from the powder x-ray diffraction data, lead us to sketch a possible structural origin for the ${\text{Co}}^{3+}$ sites. In light of this ensemble of experimental observations, a phase diagram taking into account the systematic presence of correlations and their $x$ dependence is proposed.

Figure 1

(Color online) X-ray powder-diffraction diagram for the studied hexagonal phases. $hkl$ indices are indicated for the Bragg peaks corresponding to the mean structure, while stars designate satellites linked to the modulation of the Na layers. The unit cell of the $x=0.5$ phase is shown in the inset. Cobalts are marked as green squares, sodiums as blue circles (a full/dashed line indicates the ion is above/below the cobalts). The bottom labels refer to the Na1 and Na2 bands in the upper plane, with Na1 ions being directly above cobalts and Na2 ions being above a triangle of cobalts.

Figure 2

Relation between the $c$ lattice parameter and the magnitude of the modulation wave vector $q\left(r^{\ast }\right)$. The top axis yields $x$ through the relation $x=1-q\left(r^{\ast }\right)$. The solid line is a linear fit of the full data set.

Figure 3

(Color online) Temperature dependence of the macroscopic magnetic susceptibility, as measured with field cooling and an applied field of 10 kG, save for $x=1$ (1 kG) and $x=0.58/0.62$ (50 kG). The inset shows on an expanded scale the progressive evolution at intermediate dopings ($x=1$ has been omitted for low-$T$ clarity). Singularities due to intrinsic ordering $\left(x=0.5\right)$ and spurious phases are better seen here. The $x=0.5$, $x=0.67$, and $x=1$ data are from (or similar to those of) previous publications (Refs. 5, 19, 31).

Figure 4

(Color online) Temperature dependence of the sodium NMR shift, including data from (or similar to those of) previous publications for $x=0.35$ and $x=0.67$ (Ref. 31), $x=0.5$ O (Ref. 19), and $x=1$ (Ref. 5). The down-pointing arrows indicate the maxima for $x=0.5–0.62$ [for $x=0.5$, data at high $T$ has only been taken on the rhombohedral (R) structure sample]. The corresponding temperatures $T^{\ast }$ are used for rescaling the data, as shown in the inset.

Figure 5

(Upper panel) Na ionic diffusion as seen from the Na NMR central line: typical temperature dependence of the linewidth, here for the $x=0.55$ main Na site along the $c$ direction, with the dotted line indicating the intrinsic linewidth. (Lower panel) Doping dependence of the corresponding $T_{\text{diff}}$ diffusion temperature.

Figure 6

(Color online) Temperature dependence of the sodium $T_1^{-1}$ relaxation rate for $x=0.58$, along the $c$ direction. Drawn as a black line is a fit (see text) which is the sum of the sodium diffusion contribution (“diff.”) and the metallic contribution (“metal.”), both drawn as red lines. The inset shows the negligible contribution of ionic diffusion at low temperature.

Figure 7

(Color online) Temperature dependence of the sodium $T_1^{-1}$ relaxation rate for all studied dopings, along the $c$ direction and at low temperature, with dotted lines crossing the origin as visual guides for the metallic contribution to relaxation.

Figure 8

(Color online) Doping dependence of the low temperature $\left(T\le 100\text{K}\right)$ Korringa ratio $R$ for Na nuclei. The filled squares are from this study; open circles have been extracted from Alloul et al. (Ref. 14). The lower region (blue) corresponds to our calculation of the $R$ value expected for noncorrelated or ferromagnetically correlated metals (see text), while the upper region (orange) corresponds to nonferromagnetically correlated metals.

Figure 9

(Color online) Cobalt NMR spectra at various dopings with the applied field $H$ along the $c$ axis (left panel) and along the $ab$ plane (right panel). The filled squares and circles indicate quadrupolar satellites from the A and B sites of the $x=0.5$ phase, while open circles correspond to the extra Co sites appearing for $x\ge 0.55$. As the $x=0.5$ spectrum has been taken in different experimental conditions, its central line has been brought into coincidence with the others $\left({\nu }_0=59.3\text{MHz}\right)$ by shifting the spectrum, in order to allow for comparison of the quadrupolar splittings. For $H$ in the $ab$ plane, this has been done so that the spectra coincide at $K=2\%$, the shift of the newly detected Co sites (see text). Vertical shifts (0.1 along $c$, arbitrary along $ab$) have been applied for clarity.

Figure 10

(Color online) Proposed structure for $x>0.5$, through introduction of stripes of Na2 sites in the $x=0.5$ structure whose unit cell is recalled on the left (bottom labels refer to Na1 and Na2 bands in the upper plane). The limited segregation of three bands of Na2 sites establishes in the middle of the stripe a band of Co sites with fully occupied first-neighbor Na2 sites as in ${\text{Na}}_1{\text{CoO}}_2$. It is proposed that the structure evolves merely by reduction in the distance between such triple bands with increasing Na concentration.

Figure 11

(Color online) Proposed phase diagram for the Na cobaltates. In the top panel we report the temperature $T^{\ast }$ for which ${\chi }_{\text{spin}}$ is maximal (the dotted line is a visual guide), as well as the nature of spin correlations in the two distinct Na concentration ranges. The known superconducting and magnetically long-range ordered phases are also indicated. In the bottom panel, the concentration of ${\text{Co}}^{3+}$ as determined by NMR is plotted versus $x$, the Co charge being homogeneous up to $x=0.5$ and undergoing disproportionation above [the $x=1$ point and the open circles are from previous studies of our group (Refs. 5, 14); see also Julien et al.(Ref. 48) for a similar result for $x=0.75$]. The dotted lines are visual guides, the high slope $\left(y=2x-1\right)$ corresponding to the simple substitution of $3.5+$ sites by $3+$ sites, while the low slope $\left(y=x-0.5\right)$ corresponds to $3+$ sites appearing in the middle of Na2 stripes.