Structural, electronic, magnetic, and elastic properties of quaternary ZrTM(TM = V, Cr, Mn)TiSi Heusler alloys: first-principles study

First-principles calculations were used to explore the electronic,magnetic and elastic properties of ZrTM(TM = V, Cr, Mn)TiSi Heusler alloys. A detailed discussion is presented regarding the half-metallic and magnetic properties at their equilibrium lattice constants. The results showed that for all compounds ZrTM(TM = V, Cr, Mn)TiSi, the type Y1 is energetically more stable at the equilibrium volume. These compounds' band structures and density of states were examined, and the reason behind half-metallicity was explored. ZrVTiSi and ZrCrTiSi have a total magnetic moment of $1\,\mu_B$ and $0\,\mu_B$ per formula unit respectively, and it obeys the Slater–Pauling rule: $\mu_T=18-Z_T$ ($\mu_T$ is the total magnetic moment per unit cell and $Z_T$ is the valence concentration). The computed elastic constants C$_{11}$, C$_{12}$, and C$_{44}$ are all positive and follow the Born criteria, which confirmed that these Heusler compounds are mechanically stable.