By using the first-principles method, the electronic structures and magnetism of equiatomic quaternary Heusler alloys FeRhCrSi and FePdCrSi were calculated. The results show that both FeRhCrSi and FePdCrSi compounds are ferrimagnets. Both compounds are half-metals and their half-metallicity can be maintained in a wide range of variation of the lattice constant under hydrostatic strain and c/a ratio range under tetragonal distortion, implying that they have low sensitivity to external interference. Furthermore, the total magnetic moments are integers, which are typical characteristics of half-metals. The calculated negative formation energy and cohesive energy indicate that these two alloys have good chemical stability. Furthermore, the value of the elastic constants and the various moduli indicate the mechanical stability of these two alloys. Thus, FeRhCrSi and FePdCrSi are likely to be synthesized in the experiment.

The electronic structures and magnetic properties of FeRuCrP and FeRhCrP quaternary Heusler compounds with LiMgPbSb-type structures have been investigated via first-principles calculations. The calculational results show that both FeRuCrP and FeRhCrP compounds present perfect half-metallic properties: Showing large half-metallic band gaps of 0.39 eV and 0.38 eV, respectively. The total magnetic moments of FeRuCrP and FeRhCrP are 3 μB and 4 μB per formula unit, respectively. The magnetism of them mainly comes from the 3d electrons of Cr atoms and follows the Slater-Paulig behavior of Heusler compounds: M_t = Z_t − 24. Furthermore, the half-metallic properties of FeRuCrP and FeRhCrP compounds can be kept in a quite large range of lattice constants (about 5.44–5.82 Å and 5.26–5.86 Å, respectively) and are quite robust against tetragonal deformation (c/a ratio in the range of 0.94–1.1 and 0.97–1.1, respectively). Moreover, the large negative cohesion energy and formation energy of FeRuCrP and FeRhCrP compounds indicate that they can be synthesized experimentally.