Magnetic fluctuations and specific heat in NaxCoO2 near a Lifshitz transition

We analyze the temperature and doping dependence of the specific heat C(T) in Na x CoO 2 . This material was conjectured to undergo a Lifshitz-type topological transition at x=x c =0.62 , in which a new electron Fermi pocket emerges at the Γ point, in addition to the existing hole pocket with large k F . The data show that near x=x c , the temperature dependence of C(T)/T at low T gets stronger as x approaches x c from below and then reverses the trend and changes sign at x≥x c . We argue that this behavior can be quantitatively explained within the spin-fluctuation theory. We show that magnetic fluctuations are enhanced near x c at momenta around k F , and their dynamics changes between x≤x c and x>x c , when the new pocket forms. We demonstrate that this explains the temperature dependence of C(T)/T . We show that at larger x (x>0.65 ) the system enters a magnetic quantum critical regime where C(T)/T roughly scales as logT . This behavior extends to progressively lower T as x increases towards a magnetic instability at x≈0.75 .