Putative quantum critical point in the itinerant magnet ZrFe$_4$Si$_2$ with a frustrated quasi-one-dimensional structure

The Fe sublattice in the compound ZrFe$_4$Si$_2$ features geometrical frustration and quasi-one-dimensionality. We therefore investigated the magnetic behavior in ZrFe$_4$Si$_2$ and its evolution upon substituting Ge for Si and under the application of hydrostatic pressure using structural, magnetic, thermodynamic, and electrical-transport probes. Magnetic measurements reveal that ZrFe$_4$Si$_2$ holds paramagnetic Fe moments with an effective moment $\mu_{\rm eff}= 2.18~\mu_{B}$. At low temperatures the compound shows a weak short-range magnetic order below 6 K. Our studies demonstrate that substituting Ge for Si increases the unit-cell volume and stabilizes the short-range order into a long-range spin-density wave type magnetic order. On the other hand, hydrostatic pressure studies using electrical-resistivity measurements on ZrFe$_4$(Si$_{0.88}$Ge$_{0.12}$)$_2$ indicate a continuous suppression of the magnetic ordering upon increasing pressure. Therefore, our combined chemical substitution and hydrostatic pressure studies suggest the existence of a lattice-volume-controlled quantum critical point in ZrFe$_4$Si$_2$.