<p>In this work, we report
on a systematic first-principles study of the structural, electronic,
vibrational and thermodynamic properties of the cubic Fe<sub>2</sub>NiAl and
tetragonally distorted Co<sub>2</sub>NiAl full Heusler compounds. We
discuss systematically the competition between the inverse Heusler structure
and a T<i><sup>p</sup></i>-type layered atomic ordering formed by the
alternating planes of (Fe,Co) and Ni atoms in terms of the electronic and
vibrational density of states.</p>
<p>Such an arrangement is
predicted to be the ground state of Fe<sub>2</sub>NiAl. For Co<sub>2</sub>NiAl,
layered ordering has slightly higher energy in comparison with the inverse one,
however, we show that it might be stabilized at
rather low temperatures.</p>
<p> </p>
<p>Due to the broken
symmetry, layered T<i><sup>p</sup></i>-Fe<sub>2</sub>NiAl possesses a large MAE
of the same order as tetrataenite FeNi - even in a phase with cubic
lattice parameters, which makes a T<i><sup>p</sup></i>-type layered order an
interesting feature for rare-earth free permanent magnets in Heusler-type
compounds.</p>