Temperature-dependent resistivity and anomalous Hall effect in NiMnSb from first principles

We present implementation of the alloy analogy model within fully relativistic density-functional theory with the coherent potential approximation for a treatment of nonzero temperatures. We calculate contributions of phonons and magnetic and chemical disorder to the temperature-dependent resistivity, anomalous Hall conductivity (AHC), and spin-resolved conductivity in ferromagnetic half-Heusler NiMnSb. Our electrical transport calculations with combined scattering effects agree well with experimental literature for Ni-rich NiMnSb with 1–2% Ni impurities on Mn sublattice. The calculated AHC is dominated by the Fermi surface term in the Kubo-Bastin formula. Moreover, the AHC as a function of longitudinal conductivity consists of two linear parts in the Ni-rich alloy, while it is nonmonotonic for Mn impurities. We obtain the spin polarization of the electrical current $P>90\%$ at room temperature and we show that $P$ may be tuned by chemical composition. The presented results demonstrate the applicability of an efficient first-principles scheme to calculate temperature dependence of linear transport coefficients in multisublattice bulk magnetic alloys.

Figure 1

Total averaged magnetic moment (per formula unit) of Ni- and Mn-rich NiMnSb and spin magnetic moments of individual atoms for zero temperature. The Ni/Mn-impurity data set presents the local magnetic moments of Ni and Mn atoms placed on the crystallographic position of the second atom.

Figure 2

Temperature and alloying disorder dependence of the half-metallicity in NiMnSb. Atomic concentrations are used as weights of the local DOS and data for impurities (Mn and Ni). (a) The 10% Mn-rich NiMnSb preserves the half-metallic character for all of the considered atomic displacements. Mn-impurity virtual bound state forms in the majority spin-channel. (b) Stoichiometric NiMnSb exhibits the half-metallic band gap also at room temperature. Inset (c) shows that magnetic disorder (tilted magnetic moments with $\theta =0.1\pi$) has almost no influence on DOS, especially in the minority channel. (d) The 10% Ni-rich NiMnSb is no longer half metal and the states around $E_F$ are almost independent on temperature.

Figure 3

Total DOS at the Fermi level (solid lines) as well as the local DOS for Ni impurities (dashed lines) are increasing with higher substitution of Mn atoms by Ni. The spin-up states (red lines, squares) are dominant for less than 10% of Ni impurities, after 12% the spin-down states (blue lines, circles) prevail. The total DOS (sum of the spin channels, not shown here) increases monotonically.

Figure 4

(a) The isotropic resistivity and (b) anomalous Hall effect (${\rho }_{xy}$) of Ni- and Mn- rich NiMnSb monotonously increase with increasing temperature. Experimental results [24, 39, 55] agree with our theoretical data obtained for the Ni-rich case with low concentration of impurities. (c) The model of finite-relaxation time (stoichiometric NiMnSb) for an unknown disorder qualitatively agrees with calculated data at nonzero temperature.

Figure 5

Negative sign of the calculated ($T=0$) total AHC ${\sigma }_{xy}$ (black solid line) was observed only for ${\mathrm{Ni}}_{0.98}{\mathrm{Mn}}_{1.02}\mathrm{Sb}$, which is caused by a small contribution of the intrinsic term (red dashed line with squares) but dominant vertex corrections (blue dashed line with circles).

Figure 6

Total resistivity (a) for zero and finite (540 K) temperature is monotonic in the Mn-rich region but it has a maximum in the Ni-rich case at 10% and 8% of Ni impurities for $T=0$ and 540 K, respectively. Zero-temperature AHC plotted as a function of the total conductivity has (b) two piecewise linear parts for the Ni-rich NiMnSb, one having a negative slope (fitted from 1, 2, 4, 6, 8, and 10% of Ni) and the second with a positive slope (10, 12, 14, 16, 18, and 20% of Ni). The parts are distinguishable when the resistivity for the same data is plotted (c). The same dependence in the Mn-rich region (d) exhibits a linear (2, 4, and 6% of Mn impurities) and a nonmonotonic (8, 10, 12, 14, 16, 18, and 20% of Mn) behavior; a ratio of resistivities (e) shows a smooth transition between both parts.

Figure 7

The spin-polarization of the electrical current for the in-plane direction is almost unity for the Mn-rich NiMnSb (small total conductivity) and it is predicted to be larger than 90% also in the Ni-rich system at room temperature.

Figure 8

${\sigma }_{\mu \nu }^{\left(1\right)}$ (left axes, red lines with triangles) and ${\sigma }_{\mu \nu }^{\left(2\right)}$ (right axes, blue lines with squares) contribution to the anomalous Hall effect in NiMnSb: (a) Total conductivity, (b) its coherent part, and (c) the vertex contribution to ${\sigma }_{xy}^{\left(1\right)}$.

Figure 9

Bloch spectral functions displayed for the Fermi level and $k_z=0$ for the majority spin (a), (b), and (c) and the minority one (d), (e), and (f); (a) and (d) for ${\mathrm{Ni}}_{1.06}{\mathrm{Mn}}_{0.94}\mathrm{Sb}$, (b) and (e) for ${\mathrm{Ni}}_{1.10}{\mathrm{Mn}}_{0.90}\mathrm{Sb}$, and (c) and (f) for ${\mathrm{Ni}}_{1.14}{\mathrm{Mn}}_{0.86}\mathrm{Sb}$.

Figure 10

Bloch spectral functions of (a) ${\mathrm{Ni}}_{1.06}{\mathrm{Mn}}_{0.94}\mathrm{Sb}$, (b) ${\mathrm{Ni}}_{1.10}{\mathrm{Mn}}_{0.90}\mathrm{Sb}$, and (c) ${\mathrm{Ni}}_{1.14}{\mathrm{Mn}}_{0.86}\mathrm{Sb}$ for spin-up (upper panels) and spin-down (lower panels) channels.

Figure 11

The spin-resolved in-plane (perpendicular to the magnetization) coherent conductivity for the majority channel (a) differs by several orders of magnitude for the Mn- and Ni-rich cases. On the other hand, the conductivity for the minority channel (b) is almost independent of the temperature, except for extreme displacements in the Mn-rich case. Both the spin-flip term (c) and vertex part of the conductivity (d) are larger for the Ni-rich system than in the Mn-rich region.