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We report measurements on Ti$_4$MnBi$_2$, where a crystal structure involvinglinear chains of Mn ions suggests one-dimensional magnetic character. Theelectrical resistivity is metallic, consistent with the results of electronicstructure calculations that find a robust Fermi surface albeit with moderateelectronic correlations. Curie-Weiss fit to the magnetic susceptibility findsthat the Mn moments are in the low-spin $S = 1/2$ configuration. Neutrondiffraction measurements detect weak antiferromagnetic order within the Mnchains, with further evidence for the small staggered moment coming from theentropy associated with the ordering peak in the specific heat as well as fromthe results of spin-polarized electronic structure calculations. Theantiferromagnetic 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 thatforms the Mn moment or to the one-dimensional character of Ti$_4$MnBi$_2$,nearly overcome magnetic order.

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