Antiferromagnetism, structural instability and frustration in intermetallic AFe$_4$X$_2$ systems

Magnetic systems with reduced dimensionality or frustration attract strong interest because these features lead to an increase of quantum fluctuations and often result in unusual properties. Here, we present a detailed study of the magnetic, thermodynamic, and structural properties of the intermetallic $A$Fe$_4$X$_2$ compounds ($A$=Sc,Y,Lu,Zr; X=Si,Ge) crystallizing in the ZrFe$_4$Si$_2$ structure type. Our results evidence that these compounds cover the whole regime from frustrated AFM order up to an AFM quantum critical point. Susceptibility $\chi$(T), specific heat, resistivity, and T-dependent XRD measurements were performed on polycrystalline samples. In all compounds we observed a Curie-Weiss behavior in $\chi$(T) at high T indicating a paramagnetic moment of about 3$\mu_B$/Fe. Magnetic and structural transitions as previously reported for YFe$_4$Ge$_2$ occur in all compounds with trivalent $A$. However, transition temperatures, nature of the transition as well as the relation between structural and magnetic transitions change significantly with the A element. Low $T_N$'s and large $\theta_{CW}/T_N$ ratios confirm the relevance of frustration. The results are analyzed and discussed with respect to electronic, structural and magnetic instabilities applying DFT calculations.