  Since the discovery of pressure-induced superconductivity in the two-leg
ladder system BaFe$_2X_3$ ($X$=S, Se), with the 3$d$ iron electronic density $n
= 6$, the quasi-one-dimensional iron-based ladders have attracted considerable
attention. Here, we use Density Functional Theory (DFT) to predict that the
novel $n = 6$ iron ladder BaFe$_2$Te$_3$ could be stable with a similar crystal
structure as BaFe$_2$Se$_3$. Our results also indicate that BaFe$_2$Te$_3$ will
display the complex 2$\times$2 Block-type magnetic order. Due to the magnetic
striction effects of this Block order, BaFe$_2$Te$_3$ should be a magnetic
noncollinear ferrielectric system with a net polarization $0.31$ $\mu$C/cm$^2$.
Compared with the S- or Se-based iron ladders, the electrons of the Te-based
ladders are more localized, implying that the degree of electronic correlation
is enhanced for the Te case which may induce additional interesting properties.
The physical and structural similarity with BaFe$_2$Se$_3$ also suggests that
BaFe$_2$Te$_3$ could become superconducting under high pressure.
