Quantum critical fluctuations in the itinerant antiferromagnet Nb$_{12}$O$_{29}$

Monoclinic Nb$_{12}$O$_{29}$ is a metallic antiferromagnet with T$_{N} \approx $12 K. [1] We have studied critical behaviors near T$_{N}$ by measuring the resistivity ($\rho )$, specific heat (C$_{p})$, and thermoelectric power (S). As T$_{N}$ is approached from T$_{N}^{+}$, critical behaviors used in ferromagnetic metals, d$\rho $/dT = (a$^{+}$/$\alpha )\vert $t$\vert ^{-\alpha }$+ b$^{+ }$+ c$^{+}$t and C$_{p }$= (A$^{+}$/$\alpha )\vert $t$\vert ^{-\alpha }$+ B$^{+}$ + C$^{+}$t provide the best description for d$\rho $/dT and C$_{p}$, respectively. We found an identical $\alpha \quad \approx $ 0.2(2) in both d$\rho $/dT and C$_{p}$, as predicted by Fisher and Langer in a ferromagnetic metal. [2] These observations indicate strong critical scattering of conduction electrons by short-range spin fluctuations near T$_{N}$. In addition, the S is strongly enhanced at low temperatures. The temperature dependence of S above T$_{N}$ follows closely the formula S/T $\propto \quad -$lnT, which suggests that quantum critical fluctuations [3] plays a role in enhancing the thermoelectric power on top of the classic critical fluctuations. \\[0pt] [1] R. J. Cava, \textit{et al}., Phys. Rev. B \textbf{44}, 6973 (1991).\\[0pt] [2] M. E. Fisher and J. S. Langer, Phys. Rev. Lett. \textbf{20}, 665 (1968).\\[0pt] [3] I. Paul and G. Kotliar, Phys. Rev. B \textbf{64}, 184414 (2001).