  Single-molecule spin transport represents the lower limit of miniaturization
of spintronic devices. These experiments, although extremely challenging, are
key to understand the magneto-electronic properties of a molecule in a
junction. In this context, theoretical screening of new magnetic molecules
provides invaluable knowledge before carrying out sophisticated experiments.
Herein, we investigate the transport properties of three equatorially
low-coordinated erbium single ion magnets with $C_{3v}$ symmetry:
Er[N(SiMe$_3$)$_2$]$_3$ (1), Er(btmsm)$_3$ (2) and Er(dbpc)$_3$ (3), where
btmsm = bis(trimethylsilyl)methyl and dbpc = 2,6-di-tert-butyl-p-cresolate. Our
ligand field analysis, based on previous spectroscopic data, confirms a ground
state mainly characterized by $M_J$ =$\pm$15/2 in all three of them. The
relaxation of their molecular structures when placed between two Au (111)
electrodes leads to an even more symmetric $\sim D_{3h}$ environment, which
ensures that these molecules would retain their single-molecule magnet behavior
in the device setup. Hence, we simulate spin dependent transport using the DFT
optimized structures on the basis of the non-equilibrium Green's function
formalism, which, in 1 and 2, suggests a remarkable molecular spin filtering
under the effect of an external magnetic field.
