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 NaxCoO2. This material was conjectured to undergo a Lifshitz-type topological transition at x=xc=0.62, in which a new electron Fermi pocket emerges at the Γ point, in addition to the existing hole pocket with large kF. The data show that near x=xc, the temperature dependence of C(T)/T at low T gets stronger as x approaches xc from below and then reverses the trend and changes sign at x≥xc. We argue that this behavior can be quantitatively explained within the spin-fluctuation theory. We show that magnetic fluctuations are enhanced near xc at momenta around kF, and their dynamics changes between x≤xc and x>xc, 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.