Structure and magnetic properties of MnN, CrN, and VN under volume expansion

Using a first principles density functional method, we studied how the structure and the magnetic properties of the early transition metal nitrides MnN, CrN, and VN change with expansion and compression of volume. We found that the zinc blende (ZB) state is lower in energy for MnN than the experimentally observed slightly tetragonally distorted $\theta$ phase, which suggests that the latter is stabilized by N vacancies. Under small volume compression the rock salt (RS) structure becomes lower in energy than the ZB one. While at its theoretical equilibrium lattice constant MnN is found to have ferromagnetic (FM) order, it becomes antiferromagnetic $\mathrm{AFM}\text{−}{\left[001\right]}_1$ ordered for larger lattice constants in agreement with experiment. The ZB phase is nonmagnetic for its minimum energy lattice constant and below but develops first AFM[001] order and then $\mathrm{AFM}{\left[111\right]}_1$ order for larger lattice constants. For CrN and VN, the global energy minimum corresponds to the RS structure. Under a certain volume expansion, both NiAs and ZB structures can become metastable. CrN exhibits antiferromagnetic order in the NiAs structure $\left({\left[0001\right]}_1\right)$ and the RS phase $\left({\left[110\right]}_1\right)$ and ferromagnetic order in the ZB structure. Under lattice expansion the RS structure magnetic configuration changes from ${\left[110\right]}_1$ to ${\left[110\right]}_2$, the experimentally observed structure at equilibrium when an orthorhombic distortion is taken into account, and finally to FM at even larger lattice constant. VN has nonzero magnetic moment at a volume around or larger than the equilibrium volume. However, its magnetic interactions among the neighboring moments are very weak as the energy differences between the FM and the AFM ordering are very small. The ferromagnetic states of all three nitrides in the ZB structure become half-metallic under large volume expansion. The partial densities of states (PDOS) for each sublattice in the AFM states show similar structure to the PDOS in the FM state. The effects of the volume expansion on the electronic structure of ZB and RS structure are discussed in detail.

Figure 1

(Color online) Total energy vs lattice constant for MnN (top), CrN (middle), and VN (bottom) in ZB, WZ, NaCl, and NiAs structures and for AFM (filled symbols) and FM (open symbols) ordering. The lattice constants are for cubic structure.

Figure 2

(Color online) Energies of different AFM ordering for MnN and CrN in NaCl structure under different lattice constants. The energies are relative to the energy of the FM state.

Figure 3

(Color online) The stable and metastable structures and the magnetic ordering for different lattice constants.

Figure 4

(Color online) The PDOS for MnN in both RS and ZB structures and with lattice constants of $4.3$ and $4.9\mathrm{\AA }$, respectively. Solid lines Mn $d$; dashed lines N $p$.

Figure 5

(Color online) The DOS for CrN in both RS and ZB structures and with lattice constants of $4.3$ and $4.9\mathrm{\AA }$, respectively.

Figure 6

(Color online) The DOS for MnN and CrN in AFM state and in RS structure and with lattice constants of $4.3$ and $4.9\mathrm{\AA }$, respectively.

Figure 7

Band structure of MnN in the FM state in both ZB (top) and RS (bottom) structures at the same lattice constant of $4.3\mathrm{\AA }$.