Ultra-small moment incommensurate spin density wave order masking a ferromagnetic quantum critical point in NbFe$_2$

In the metallic magnet Nb$_{1-y}$Fe$_{2+y}$, the low temperature threshold of ferromagnetism can be investigated by varying the Fe excess $y$ within a narrow homogeneity range. We use elastic neutron scattering to track the evolution of magnetic order from Fe-rich, ferromagnetic Nb$_{0.981}$Fe$_{2.019}$ to approximately stoichiometric NbFe$_2$, in which we can, for the first time, characterise a long-wavelength spin density wave state burying a ferromagnetic quantum critical point. The associated ordering wavevector $\mathbf{q}_{\rm SDW}=$(0,0,$l_{\rm SDW}$) is found to depend significantly on $y$ and $T$, staying finite but decreasing as the ferromagnetic state is approached. The phase diagram follows a two order-parameter Landau theory, for which all the coefficients can now be determined. Our findings suggest that the emergence of SDW order cannot be attributed to band structure effects alone. They indicate a common microscopic origin of both types of magnetic order and provide strong constraints on related theoretical scenarios based on, e.g., quantum order by disorder.