Phenomenological trends for heavy Fermi liquids and narrow-band metals

A phenomenological correlation is presented for the magnetic susceptibility ${\chi }^{\mathrm{*}}$ and the electronic heat-capacity coefficient ${\gamma }^{\mathrm{*}}$ of a large number of narrow-band and heavy-fermion metals. A novel method of plotting ${\chi }^{\mathrm{*}}$/${\gamma }^{\mathrm{*}}$ vs ${\gamma }^{\mathrm{*}}$ reveals quantitative boundaries for distinct regions of superconducting, magnetically ordered, and paramagnetic ground states. It is suggested that magnetic interactions are a primary limitation for the $T_c$ of ‘‘conventional’’ superconductors, whereas a more delicate interplay exists between magnetic order, paramagnetism, and superconductivity above a threshold value of ${\gamma }^{\mathrm{*}}$ which defines the onset of magnetic order.