  The phase stabilities and ordering tendencies in the quaternary full-Heusler
alloys NiCoMnAl and NiCoMnGa have been investigated by in-situ neutron
diffraction, calorimetry and magnetization measurements. NiCoMnGa was found to
adopt the L2$_1$ structure, with distinct Mn and Ga sublattices but a common
Ni-Co sublattice. A second-order phase transition to the B2 phase with disorder
also between Mn and Ga was observed at 1160 K. In contrast, in NiCoMnAl slow
cooling or low-temperature annealing treatments are required to induce
incipient L2$_1$ ordering, otherwise the system displays only B2 order. Linked
to this L2$_1$ ordering, a drastic increase in the magnetic transition
temperature was observed in NiCoMnAl, while annealing affected the magnetic
behavior of NiCoMnGa only weakly due to the low degree of quenched-in disorder.
First principles calculations were employed to study the thermodynamics as well
as order-dependent electronic properties of both compounds. It was found that a
near half-metallic pseudo-gap emerges in the minority spin channel only for the
completely ordered Y structure, which however is energetically unstable
compared to the predicted ground state of a tetragonal structure with
alternating layers of Ni and Co. The experimental inaccessibility of the
totally ordered structures is explained by kinetic limitations due to the low
ordering energies.
