Direct Link between Low-Temperature Magnetism and High-Temperature Sodium Order in ${\mathrm{Na}}_x{\mathrm{CoO}}_2$

We prove the direct link between low-temperature ($T$) magnetism and high-$T$ ${\mathrm{Na}}^{+}$ ordering in ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ using the example of a so far unreported magnetic transition at 8 K which involves a weak ferromagnetic moment. The 8 K feature is characterized in detail and its dependence on a diffusive ${\mathrm{Na}}^{+}$ rearrangement around 200 K is demonstrated. Applying muons as local probes this process is shown to result in a reversible phase separation into distinct magnetic phases that can be controlled by specific cooling protocols. Thus the impact of ordered ${\mathrm{Na}}^{+}$ Coulomb potential on the ${\mathrm{CoO}}_2$ physics is evidenced opening new ways to experimentally revisit the ${\mathrm{Na}}_x{\mathrm{CoO}}_2$ phase diagram.

Figure 1

Presence of the 8 K magnetic phase in the “slowly cooled” state, and absence of it in the “fast cooled” state of the same ${\mathrm{Na}}_{0.85}{\mathrm{CoO}}_2$ crystal as seen in specific heat (a) and magnetization [b, measured in field cooled (fc) and zero-field cooled (zfc) mode for $H=1\mathrm{kOe}$ and $H\parallel ab$]. (c) The shift of transition temperatures in a magnetic field (data from $C_p$ measurements). (d) Remanent magnetization extracted from $M(H)$ loops up to $H=\pm 4\mathrm{kOe}$ for $H\parallel ab$ and $H\parallel c$.

Figure 2

(a) Magnetically ordered volume fraction as determined from transverse-field $\mu \mathrm{SR}$ data on ${\mathrm{Na}}_{0.85}{\mathrm{CoO}}_2$ (right-hand scale: asymmetry of 0.676 MHz Gaussian contribution imposed by external field). (b) Fourier spectra of asymmetry histograms for zero-field measurements give the spectral distribution of muon frequencies. slowly cooled: red; fast cooled: blue. Solid lines are a guide to the eye.

Figure 3

Magnetic signature of the Na rearrangement near 200 K in a ${\mathrm{Na}}_{0.8}{\mathrm{CoO}}_2$ crystal. (a) Normalized magnetization as a function of time while sample is kept at $T_Q$ before subsequent cooldown to monitor the size of the 8 K transition. (b) Direct correspondence between the degree of Na rearrangement around 200 K and the FM moment developing at 8 K (measured as the increase in $M/H$). (c) Inverse time constant of diffusion fit to $M(t)$ [broken lines in (a)] versus quenching temperature $T_Q$.

Figure 4

Lattice distortion caused by Na rearrangement. Thermal expansion anomalies in a ${\mathrm{Na}}_{0.85}{\mathrm{CoO}}_2$ crystal due to the Na rearrangement near 200 K (a) and Na ordering transition at 285 K (b), $ab$-plane data multiplied by 2.85.