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Using density functional theory we investigate the evolution of the magneticground state of NbFe$_{2}$ due to doping by Nb-excess and Fe-excess. We findthat non-rigid-band effects, due to the contribution of Fe-\textit{d} states tothe density of states at the Fermi level are crucial to the evolution of themagnetic phase diagram. Furthermore, the influence of disorder is important tothe development of ferromagnetism upon Nb doping. These findings give aframework in which to understand the evolution of the magnetic ground state inthe temperature-doping phase diagram. We investigate the magnetic instabilitiesin NbFe$_{2}$. We find that explicit calculation of the Lindhard function,$\chi_{0}(\mathbf{q})$, indicates that the primary instability is to finite$\mathbf{q}$ antiferromagnetism driven by Fermi surface nesting. Total energycalculations indicate that $\mathbf{q}=0$ antiferromagnetism is the groundstate. We discuss the influence of competing $\mathbf{q}=0$ and finite$\mathbf{q}$ instabilities on the presence of the non-Fermi liquid behavior inthis material.

Doping driven magnetic instabilities and quantum criticality of NbFe$_{2}$