Weak coupling SDW ground state with strong Fermi surface gapping in Na$_{x}$CoO$_{2}$ , x $\approx $ 0.8

In Na$_{x}$CoO$_{2}$ the electrons move on a triangular lattice and in the Na-rich composition range (x $\ge $ 0.75) form a SDW ground state below T$_{c}\approx $ 22.5 K with a small ordered moment. We have studied this Fermi surface instability with heat capacity, magnetic and transport measurements on a series of samples with various nominal Na content. The SDW phase is characterized by a jump $\Delta $C at T$_{c }$ and an associated reduction of the electronic density of states. This removal of DOS has been deduced from the high-temperature value of the Sommerfeld $\gamma $ and the extrapolation from below 1K to T $\to $ 0. Interestingly, the ratio $\Delta $C/($\delta \gamma $.T$_{c })\approx $1.5 is close to the BCS weak coupling value. Even more surprising is the observation that up to $\approx $ 80{\%} of the DOS is removed in this Fermi surface instability. In addition to the gapped electronic excitation spectrum a broad hump in the specific heat is measured above $\approx $5K, consistent with excitations of the gapped spin wave spectrum in the SDW ordered state. Crystal structure analysis reveals for the SDW an orthorhombic symmetry and thus a slight distortion of the triangular lattice. Similarities and differences to the CDW-like state, which forms at x=0.5 also in a distorted triangular lattice, will be discussed.