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 = x(c) = 0.62, in which a new electron Fermi pocket emerges at the Gamma 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 log T. This behavior extends to progressively lower T as x increases towards a magnetic instability at x approximate to 0.75.