Theoretical study of the structural stability, electronic, and magnetic properties of MBi (⁠$M=V$⁠, Cr, and Mn) compounds

We present theoretical studies of the structural stability, electronic, and magnetic properties of MBi (⁠$M=V$⁠, Cr, Mn) compounds using the full-potential linear augmented plane wave method. To find the most stable structure for each compound, total energy calculations of several phases are considered, and magnetic and antiferromagnetic states for each compound are taken into consideration. Our calculation indicates that the antiferromagnetic NiAs structure is the stable state for VBi and CrBi, whereas MnBi is stable in the ferromagnetic hexagonal NiAs structure. Our results for the magnetic stability, the stable structure, and the structural parameters are in perfect agreement with theoretical calculation and experimental values. The calculated total magnetic moment for MnBi of $3.55μB$ agrees with the measured moment of $3.60μB$⁠. For the zinc-blende phase, our calculations predict that VBi, CrBi, and MnBi are half-metallic ferromagnet with a magnetic moment 2, 3, and $4μB$⁠, respectively. The magnetism comes essentially from the $d$ orbitals of V, Cr, and Mn atoms, while the half metallic character is the fingerprint of the $p(Bi)-d(M)$ interaction. The exchange interaction increases, while the crystal field splitting decreases from V to Mn with the increases of the filling of the $d$ bands of the transition metals M atoms, as a consequence: (i) For the spin-up channel, the antibonding state $Γ12$ is pushed close to $Ef$ for VBi, while in CrBi and MnBi, this state is below the Fermi level for CrBi and MnBi, respectively. (ii) The $t2g(Γ15)$ bands of both majority and minority spins are filled while the $eg(Γ12)$ bands of minority spin are empty. (iii) The exchange splitting $Δeg$ is roughly equal to $A$ $M$⁠, where $M$ is the magnetic moment. We found A $∼0.93μB/eV$⁠, $0.99μB/eV$⁠, and $1μB/eV$ for VBi, CrBi, and MnBi, respectively, this is close to the value of the exchange integral $I$ of transition metals which have a value about $0.9μB/eV$⁠. We also studied the effect of spin-orbit coupling on the half-metallicity of these compounds. We found a relative small reduction in polarization, ranging from above $P=97,27%$ for CrBi, $P=85.49%$ for CrBi to $P=81.88%$⁠, for MnBi.