  The Fe$_{n}$GeTe$_{2}$ systems are newly discovered two-dimensional
van-der-Waals materials, exhibiting magnetism at room temperature. The
sub-systems belonging to Fe$_{n}$GeTe$_{2}$ class are special because they show
site-dependent magnetic behavior. We focus on the critical evaluation of
magnetic properties and electron correlation effects in Fe$_{n}$GeTe$_{2}$
($n$= 3, 4, 5) (FGT) systems performing first-principles calculations. Three
different ab-initio approaches have been used, viz., i) standard density
functional theory (DFT), ii) incorporating static electron correlation (DFT+U)
and iii) inclusion of dynamic electron correlation effect (DFT+DMFT). Our
results show that DFT+DMFT is the most accurate technique to correctly
reproduce the magnetic interactions and experimentally observed transition
temperatures. The inaccurate values of structural parameters, magnetic moments
and exchange interactions obtained from DFT+U make this method inapplicable for
the FGT family. Correct determination of magnetic properties for this class of
materials is important since they are promising candidates for spin transport
and spintronic applications at room temperature.
