We present a theory of the scaling behavior of the thermodynamic, transport, and dynamical properties of a three-dimensional metal at an antiferromagnetic (AFM) critical point. We show how the critical spin fluctuations at the AFM wave vector $q=Q$ induce energy fluctuations at small $q$, giving rise to a diverging quasiparticle effective mass over the whole Fermi surface. The coupling of the fermionic and bosonic degrees of freedom leads to a self-consistent relation for the effective mass, which has a strong coupling solution in addition to the well-known weak-coupling spin-density-wave solution. We use the recently introduced concept of critical quasiparticles, employing a scale-dependent effective mass ratio $m^{*}/m$ and quasiparticle weight factor $Z$. We adopt a scale-dependent vertex correction that boosts the coupling of fermions and spin fluctuations. The ensuing spin fluctuation spectrum obeys $\omega /T$ scaling. Our results are in good agreement with experimental data on the heavy-fermion compounds ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ and ${\mathrm{CeCu}}_{6-x}{\mathrm{Au}}_x$ for 3D and 2D spin fluctuations, respectively.

• Received 21 March 2014
• Revised 27 May 2014

DOI:https://doi.org/10.1103/PhysRevB.90.045105