  We report the synthesis of the entire $Ln$AuAl$_4$Ge$_2$ ($Ln$ = Y, Pr, Nd,
Sm, Gd, Tb, Dy, Ho, Er, and Tm) series and focus on the magnetic properties of
GdAuAl$_4$Ge$_2$ and TbAuAl$_4$Ge$_2$. Temperature and magnetic field dependent
magnetization, heat capacity, and electrical resistivity measurements reveal
that both compounds exhibit several magnetically ordered states at low
temperatures, with evidence for magnetic fluctuations extending into the
paramagnetic temperature region. For magnetic fields applied in the $ab$-plane
there are several ordered state regions that are associated with metamagnetic
phase transitions, consistent with there being multiple nearly degenerate
ground states. Despite Gd being an isotropic $S$-state ion and Tb having an
anisotropic $J$-state, there are similarities in the phase diagrams for the two
compounds, suggesting that factors such as the symmetry of the crystalline
lattice, which features well separated triangular planes of lanthanide ions, or
the Ruderman-Kittel-Kasuya-Yosida interaction as defined by the Fermi surface
topography control the magnetism. We also point out similarities to other
centrosymmetric compounds that host skyrmion lattices such as Gd$_2$PdSi$_3$,
and propose that the $Ln$AuAl$_4$Ge$_2$ family of compounds are of interest as
reservoirs for complex magnetism and electronic behaviors such as the
topological Hall effect.
