Correlations and incipient antiferromagnetic order within the linear Mn chains of metallic Ti$_4$MnBi$_2$

We report measurements on Ti$_4$MnBi$_2$, where a crystal structure involving linear chains of Mn ions suggests one-dimensional magnetic character. The electrical resistivity is metallic, consistent with the results of electronic structure calculations that find a robust Fermi surface albeit with moderate electronic correlations. Curie-Weiss fit to the magnetic susceptibility finds that the Mn moments are in the low-spin $S = 1/2$ configuration. Neutron diffraction measurements detect weak antiferromagnetic order within the Mn chains, with further evidence for the small staggered moment coming from the entropy associated with the ordering peak in the specific heat as well as from the results of spin-polarized electronic structure calculations. The antiferromagnetic moments are apparently associated with the $d_{x^{2}-y^{2}}$ and $d_{xy}$ orbitals of Mn while the remaining Mn orbitals are delocalized. Strong quantum fluctuations, possibly related to an electronic instability that forms the Mn moment or to the one-dimensional character of Ti$_4$MnBi$_2$, nearly overcome magnetic order.