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The effect of doping on the electronic structures and magnetic properties of the quaternary Heusler alloys under pressures is investigated. Electronic structure calculations reveal that ZrCoTiSi is a half-metallic ferromagnet with a total magnetic moment of 3.00  μ B , which mostly arises from the 3d electrons of Ti atoms. In order to investigate the doping effects, different proportions of Y, Fe, Sc and Al atoms are substituted for Zr, Co, Ti and Si atoms, respectively. The calculated results on the basis of the density functional theory (DFT) indicate that, except Sc doping for x &gt; 0.50, other substituted alloys can succeed the widely known Slater–Pauling rule (M t  = Z t  − 18) of the ideal half-metallic materials, and preserve their half-metallic properties with full spin polarization. In addition, the behaviors of alloys with different concentrations of x under various pressures are investigated. ZrCoTi[Si(1 − x)Al(x)] and [Zr(1 − x)Y(x)]CoTiSi alloys keep up their half-metallicity by increasing proportions of x doping (0 ≤ x ≤ 1) under higher pressure in the range of 3.01 GPa to 17.61 GPa for Al doping and 3.01 GPa to 14.11 GPa for Y doping. However, in the replacement of Fe for Co in Zr[Co(1−x)Fe(x)]TiSi alloys, the resistance against pressure to conserve half-metallicity decreases from 3.01 GPa to 2.05 GPa. The Sc doping in ZrCo[Ti(1−x)Sc(x)]Si alloys causes loss of half-metallicity for x &gt; 0.50, and endures up to 1.67 GPa external pressure to preserve their half-metallic properties.

Effect of doping and pressure on the electronic and magnetic properties of the quaternary Heusler alloys