Non Fermi Liquid behavior in the under-screened Kondo model

Using the Schwinger boson spin representation, we reveal a new aspect to the physics of a partially screened magnetic moment in a metal, as described by the spin $S$ Kondo model. We show that the residual ferromagnetic interaction between a partially screened spin and the electron sea destabilizes the Landau Fermi liquid, forming a singular Fermi liquid with a $1/ (T \ln ^{4} (T_{K}/T))$divergenceinthelowtemperaturespecificheatcoefficient$C_{V}/T$\mathrm{.}Amagneticfield$B$ tunes this system back into Landau Fermi liquid with a Fermi temperature proportional to $B{\ln }^2(T_K\mathrm{/}B)$. We discuss a possible link with field-tuned quantum criticality in heavy electron materials.