Energetics and electronic structure of native point defects in antiferromagnetic CrN

We present a detailed analysis of the role of native point defects in the antiferromagnetic (AFM) phases of bulk chromium nitride (CrN). We perform first-principles calculations by using the local spin-density approximation, including local interaction effects $\left(\text{LSDA}+U\right)$, to study the two lowest energy AFM models expected to describe the low-temperature phase of the material. We study the formation energies, lattice deformations, and electronic and magnetic structure introduced by native point defects. We find that, as expected, nitrogen vacancies are the most likely defect present in the material at low temperatures. Nitrogen vacancies present different charged states in the cubic AFM model, exhibiting two transition energies, which could be measured by thermometry experiments and could help identify the AFM structure in a sample. These vacancies also result in partial spin polarization of the induced impurity band, which would have interesting consequences in experiments. Other point defects have also signature electronic and magnetic structure that could be identified in scanning probe experiments.

Figure 1

Unit cells of CrN for (a) cubic ${\text{AFM}}_{\left[010\right]}^1$, and (b) orthorhombic ${\text{AFM}}_{\left[110\right]}^2$ structures. Silver spheres and red spheres indicate alternating magnetic moment direction on Cr sites. Smaller blue spheres are N atoms. Black arrows indicate different lattice directions.

Figure 2

Formation energies for the different $V_{\text{N}}$ nitrogen vacancy different charged states in the ${\text{AFM}}_{\left[010\right]}^1$ model structure. $E_F=0$ is set at the edge of the valence band. Over the $E_F$ range in the figure, there are two transition energies at ${\varepsilon }_{-1,0}=-0.147\mathrm{eV}$ and ${\varepsilon }_{0,1}=0.46\mathrm{eV}$. Vertical lines at $E_{\mathrm{gap}}^{\text{LDA}+U}$ and $E_{\mathrm{gap}}^{\mathrm{TB}-\mathrm{mBJLDA}}$ (see Ref. [9]) indicate the corresponding estimates of the energy gap in this phase.

Figure 3

Partial density of states in the ${\text{AFM}}_{\left[010\right]}^1$ structure for the nearest-neighbor atoms $\text{[Cr}(\uparrow ),\text{Cr}(\downarrow )$, and N] surrounding each specific point defect, for up (positive) and down (negative) spin projections. Individual $d$ orbitals of the Cr and $p$ orbitals of N are shown with different colors. The vertical line at zero energy represents the Fermi level.

Figure 4

Partial density of states for the ${\text{AFM}}_{\left[110\right]}^2$ structure for nearest-neighbor atoms surrounding each specific point defect. Spin-up (spin-down) projections are shown as positive (negative) values. Individual Cr $d$ orbitals and N $p$ orbitals shown with different colors. Vertical line at zero energy represents the Fermi level.

Figure 5

Charge density near chromium and nitrogen vacancies for the ${\text{AFM}}_{\left[010\right]}^1$ and ${\text{AFM}}_{\left[110\right]}^2$ models. Red and green represent charge deficiency and excess, respectively. Blue spheres represent N atoms; gray represent Cr. The isosurface value was taken as 0.075 electron/${\mathrm{Bohr}}^3$.

Figure 6

Two-dimensional map of the spin polarization on (001) plane, for point defects in the ${\text{AFM}}_{\left[010\right]}^1$ structure. Red and blue amplitudes represent extremal spin projections (up and down, respectively), as per color bars. Notice the very different scale in the case of $V_{\text{N}}$. $x,y$, and spin projections are given in atomic units. Images in the background represent the atom positions obtained after full structure relaxations. Blue and gray spheres represent N and Cr atoms, respectively.

Figure 7

Two-dimensional spin polarization map on (001) plane for point defects in the ${\text{AFM}}_{\left[110\right]}^2$ model. Red and blue represent extremal spin projections (up and down respectively), as per color bars. Notice different scale for $V_{\text{N}}$. $x,y$, and spin projections given in atomic units. Images in the background show atom positions of fully relaxed structure. Blue (gray) spheres represent N (Cr) atoms, respectively.