Magnetic Ordering and Spin Waves in ${\mathrm{Na}}_{0.82}{\mathrm{CoO}}_2$

${\mathrm{Na}}_x{\mathrm{CoO}}_2$, the parent compound of the recently synthesized superconductor ${\mathrm{Na}}_x{\mathrm{CoO}}_2:y{\mathrm{H}}_2\mathrm{O}$, exhibits bulk antiferromagnetic order below $\sim 20\mathrm{K}$ for $0.75\le x\le 0.9$. We have performed neutron scattering experiments in which we observed Bragg reflections corresponding to $A$-type antiferromagnetic order in a ${\mathrm{Na}}_{0.82}{\mathrm{CoO}}_2$ single crystal and characterized the corresponding spin-wave dispersions. The spin waves exhibit a strongly energy-dependent linewidth. The in-plane and out-of-plane exchange constants resulting from a fit to a nearest-neighbor Heisenberg model are similar in magnitude, which is unexpected in view of the layered crystal structure of ${\mathrm{Na}}_x{\mathrm{CoO}}_2$. Possible implications of these observations are discussed.

Figure 1

Normalized SF intensity (equal to the SF intensity divided by the NSF intensity, viz., the inverse of the flipping ratio as it is usually defined; see text) at $\mathbf{Q}=(101)$ and (100), as a function of temperature. The data were taken with the neutron polarization $\mathbf{P}\parallel \mathbf{Q}$, with $k_i=2.662{\AA }^{-1}$. The lines are a guide for the eye. Inset: the $A$-type AF structure, shown with Co $\mathrm{\text{spins}}\parallel c$.

Figure 2

Scans at constant-energy transfer $\hslash \omega$ taken along the $(hh0)$ direction through (001) (for $\hslash \omega \le 5\mathrm{meV}$) or (003), at 1.6 K. The fits are to double Lorentzians. The red bar indicates an estimate of the FWHM of the instrumental resolution for the scan at $\hslash \omega =5\mathrm{meV}$. For clarity, the data have been offset vertically for the scans with $\hslash \omega <15\mathrm{meV}$ (the corresponding vertical-axis zeros are indicated at right) and the 15 meV data have been scaled by a factor of 2. Inset: constant-energy scans along $(hh0)$ through (001) at energy transfer of 5 meV, at 1.6 and 100 K. The fits are to double Gaussians. The axis units are the same as in the main panel.

Figure 3

Constant-$\mathbf{Q}$ scans taken at different values of $(0,0,3-l)$, with $T=1.6\mathrm{K}$ and $k_f=2.662{\AA }^{-1}$. The curves are the results of convolutions of the full spin-wave dispersion (see Fig. 4) with the instrumental resolution ellipsoid; the blue bar indicates an estimate of the FWHM of the instrumental resolution for the scan with $l=0.25$.

Figure 4

(a) Spin-wave dispersion along $(hh0)$; the peak positions are from Fig. 2. (b) Dispersion along $(00l)$, with peak positions from Fig. 3. All data were taken at 1.6 K. The dispersion curves are the result of a fit to the model described in the text.