Nearly Antiferromagnetic Fermi Liquids: A Progress Report

I describe recent theoretical and experimental progress in understanding the physical properties of the two dimensional nearly antiferromagnetic Fermi liquids (NAFL's) found in the normal state of the cuprate superconductors. In such NAFL's, the magnetic interaction between planar quasiparticles is strong and peaked at or near the commensurate wave vector, $Q \equiv (\pi,\pi)$. For the optimally doped and underdoped systems, the resulting strong antiferromagnetic correlations produce three distinct magnetic phases in the normal state: mean field above $T_{cr}$, pseudoscaling between $T_{cr}$ and $T_*$, and pseudogap below $T_*$. I present arguments which suggest that the physical origin of the pseudogap found in the quasiparticle spectrum below $T_{cr}$ is the formation of a precursor to a spin-density-wave-state, describe the calculations based on this scenario of the dynamical spin susceptibility, Fermi surface evolution, transport, and Hall effect, and summarize the experimental evidence in its support.