Competing magnetic phases in Li-Fe-Ge kagome systems

Competing interlayer magnetic interactions in kagome magnets can lead to diverse magnetic phases, which enable promising topological or quantum material properties. Here, the electronic structure and magnetic properties are studied using first-principles calculations for the $\mathrm{Li}{\mathrm{Fe}}_{6}\mathrm{G}{\mathrm{e}}_{6}, \mathrm{Li}{\mathrm{Fe}}_{6}\mathrm{G}{\mathrm{e}}_{4}$, and $\mathrm{Li}{\mathrm{Fe}}_{6}\mathrm{G}{\mathrm{e}}_{5}$ compounds sharing the kagome $\mathrm{F}{\mathrm{e}}_{3}\mathrm{Ge}$ layer motif but with different interlayer arrangements. For $\mathrm{Li}{\mathrm{Fe}}_{6}\mathrm{G}{\mathrm{e}}_{4}$ and $\mathrm{Li}{\mathrm{Fe}}_{6}\mathrm{G}{\mathrm{e}}_{5}$, the predicted magnetic ground states are collinear antiferromagnetic (AFM) states involving a mix of ferromagnetic (FM) and AFM interlayer orientations. In contrast, for $\mathrm{Li}{\mathrm{Fe}}_{6}\mathrm{G}{\mathrm{e}}_{6}$, an incommensurate cycloidal spin spiral ground state is stabilized, although its energy is close to a collinear A-type AFM state. The analysis of magnetic RKKY exchange coupling confirms the results of calculations. The values of atomic magnetic moments are in good agreement with existing experimental estimations. Our experiments on $\mathrm{Li}{\mathrm{Fe}}_{6}\mathrm{G}{\mathrm{e}}_{6}$ single crystals reveals AFM ordering at \ensuremath{\sim}540 K and transition to another magnetic phase with a small FM component, possibly with spin canting, below \ensuremath{\sim}270 K.