Energetics and magnetic impact of $3d$-metal doping of the half-metallic ferromagnet NiMnSb

We have performed a theoretical study of the effect of doping the half-Heusler alloy NiMnSb with the magnetic $3d$ metals Cr, Mn, Fe, Co, and Ni, with respect to both energetics and magnetic properties. Starting from the formation energies, we discuss the possibility of placing the dopant on different crystallographic positions in the alloy. We calculate total and local magnetic moments, effective exchange interactions, and density of states and also outline strategies to tune the magnetic properties of the alloy. Doping of NiMnSb with Cr as well as substituting some Ni with extra Mn have the largest impact on magnetic interactions in the system while preserving its half-metallic property. Therefore, we suggest the possibility that these dopants increase the thermal stability of half-metallicity in NiMnSb, with implications for its possible usage in spintronics applications.

Figure 1

(Color online) Formation energies of $3d$-metal defects in NiMnSb. Defects on the Mn sublattice are shown by black circles, defects on the Ni sublattice are shown by red squares, and interstitial defects are shown by green diamonds. The cost to form Mn and Ni vacancies are shown by large blue circles.

Figure 2

(Color online) The local moments of the dopants on different crystallographic positions. Note that the Ni and Mn moments of the host are included for comparison (open red bars).

Figure 3

(Color online) The site projected DOS of the dopant (thin black line) in the substitutional positions at the Ni sublattice for a 5% doping level of (a) Cr, (b) Mn, (c) Fe, and (d) Co. The site projected DOS of the Ni site in pure NiMnSb is shown with a thick red line for comparison.

Figure 4

(Color online) The site projected DOS of the dopant (thin black line) in the substitutional positions at the Mn sublattice for a 5% doping level of (a) Cr, (b) Fe, (c) Co, and (d) Ni. The site projected DOS of the Mn site in pure NiMnSb is shown with a thick red line for comparison.

Figure 5

(Color online) The site projected DOS of the dopant (thin black line) in the interstitial position for a 5% doping level of (a) ${\text{Cr}}_{\text{I}}$, (b) ${\text{Mn}}_{\text{I}}$, and (c) ${\text{Fe}}_{\text{I}}$. The site projected DOS of the interstitial site in pure NiMnSb is shown with a thick red line for comparison.

Figure 6

(Color online) The site projected DOS of the dopant (thin black line) in the interstitial position for 5% doping level of (a) ${\text{Co}}_{\text{I}}$ and (b) ${\text{Ni}}_{\text{I}}$. The site projected DOS of the interstitial site in pure NiMnSb is shown with a thick red line for comparison.

Figure 7

Calculated pair magnetic exchange parameters $J_{ij}$ corresponding to Mn-Mn and Ni-Mn interactions in pure NiMnSb as a function of the distance between the moments (in units of the lattice spacing, a). Inset: On-site magnetic exchange parameters $J_0$ for Ni and Mn in pure NiMnSb.

Figure 8

On-site magnetic exchange parameter $J_0$ for (a) Ni, (b) $X_{\text{Ni}}$ dopant, and (c) Mn moments in a $\left({\text{Ni}}_{0.95}{X}_{0.05}\right)\text{MnSb}$ alloy for different $3d$-metal dopants at the Ni sublattice. Note the different scales on the $y$ axes and the correspondence between $X_{\text{Ni}}=\text{Ni}$ and the ideal NiMnSb host.

Figure 9

On-site magnetic exchange parameter $J_0$ for (a) Ni, (b) $X_{\text{Mn}}$ dopant, and (c) Mn moments in a $\text{Ni}\left({\text{Mn}}_{0.95}{X}_{0.05}\right)\text{Sb}$ alloy for different $3d$-metal dopants at the Mn sublattice. Note the different scales on the $y$ axes and the correspondence between $X_{\text{Mn}}=\text{Mn}$ and the ideal NiMnSb host.

Figure 10

On-site magnetic exchange parameter $J_0$ for (a) Ni, (b) $X_{\text{I}}$ dopant, and (c) Mn moments in an interstitially doped $\text{Ni}{X}_{0.05}\text{MnSb}$ alloy for different $3d$-metal dopants. Note the different scales on the $y$ axes and the values for pure NiMnSb that are presented for comparison.

Figure 11

(Color online) Magnetic pair exchange parameters $J_{ij}$ between the moments of the $X_{\text{Ni}}$ dopants and their Mn nearest neighbors. The coupling is extremely strong in the ${\text{Cr}}_{\text{Ni}}$ and ${\text{Mn}}_{\text{Ni}}$ cases.

Figure 12

(Color online) Magnetic pair exchange parameters $J_{ij}$ between the moments of the $X_{\text{Mn}}$ dopants, between the dopant and the Mn of the host, and between the dopant and the Ni of the host. The values in pure NiMnSb is shown for comparison.

Figure 13

(Color online) Magnetic pair exchange parameters $J_{ij}$ between the moment of the $X_{\text{I}}$ dopant and its Mn nearest neighbors as well as the $X_{\text{I}}\text{−}{X}_{\text{I}}$ interaction. The dopant moment is strongly coupled to the Mn nearest neighbors in the ${\text{Cr}}_{\text{i}}$ and ${\text{Co}}_{\text{I}}$ cases and almost uncoupled in the case with Mn, Fe, and Ni doping.

Figure 14

(Color online) The effect of 5% $X_{\text{Ni}}$ doping on the magnetic pair exchange parameters of the host.

Figure 15

(Color online) The effect of 5% $X_{\text{Mn}}$ doping on the magnetic pair exchange parameters of the host.

Figure 16

(Color online) The effect of 5% ${\text{Cr}}_{\text{I}}$, ${\text{Mn}}_{\text{I}}$, and ${\text{Fe}}_{\text{I}}$ dopings on the magnetic pair exchange parameters of the host.

Figure 17

(Color online) The effect of 5% ${\text{Co}}_{\text{I}}$ and ${\text{Ni}}_{\text{I}}$ dopings on the magnetic pair exchange parameters of the host.