Interplay between mesoscopic phase separation and bulk magnetism in the layered Na x CoO 2

Specific heat of layered ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}$ ($x=0.65$, 0.70, and 0.75) oxides has been measured in the temperature range of 3\char21{}360 K and magnetic fields of 0 and 9 T. The analysis of data, assuming the combined effect of interlayer superexchange and the phase separation into mesoscopic magnetic domains with localized spins embedded in a matrix with an itinerant electronic character, suggests that the dominant contribution to the specific heat in the region of short-range ordering is mediated by quasi-two-dimensional antiferromagnetic clusters, perpendicular to the ${\mathrm{CoO}}_{2}$ layers.