Influence of band structure effects on domain-wall resistance in diluted ferromagnetic semiconductors

Intrinsic domain-wall resistance (DWR) in (Ga,Mn)As is studied theoretically and compared to experimental results. The recently developed model of spin transport in diluted ferromagnetic semiconductors [Van Dorpe et al., Phys. Rev. B 72, 205322 (2005)] is employed. The model combines the disorder-free Landauer-Büttiker formalism with the tight-binding description of the host band structure. The obtained results show how much the spherical $4\times 4$ $\mathit{k}\mathit{p}$ model [Nguyen, Shchelushkin, and Brataas, Phys. Rev. Lett. 97, 136603 (2006)] overestimates DWR in the adiabatic limit, and reveal the dependence of DWR on the magnetization profile and crystallographic orientation of the wall.

Figure 1

(a) The predicted relative domain-wall resistance $R_r$ for (Ga,Mn)As as a function of the DW width parameter ${\lambda }_W$ (in units of the Fermi wavelength ${\lambda }_F=5.7\mathrm{nm}$) for various current directions and domain-wall profiles. (b) $R_r$ for two hole densities $p=1\times {10}^{20}{\mathrm{cm}}^{-3}$ and $p=3.5\times {10}^{20}{\mathrm{cm}}^{-3}$.

Figure 2

The theoretical predictions of intrinsic domain-wall resistance in the absence of the spin-orbit coupling. In the case of DW normal to [100], the relative domain-wall resistance $\left(R_r\right)$ drops exponentially to zero as a function of the DW width parameter normalized by the Fermi wavelength. In the case of DW normal to $\left[\overline{1}10\right]$, the grazing incidence channels cause a slower decay of $R_r$. Spin-orbit interaction is set to zero in this calculation, but all other parameters remain the same as in the calculations leading to a large value of $R_r$ in Fig. 1. The value of ${\lambda }_F$ is the same as in Fig. 1.

Figure 3

Total resistance normalized by the Sharvin resistance, $R_T∕R_S$, calculated within the adiabatic model as a function of the angle between the magnetization and [001] direction for the Bloch and Néel walls. Horizontal lines show $R_T∕R_S$ computed within the full model in the adiabatic limit $({\lambda }_W∕{\lambda }_F=1.4)$ for three types of walls.

Figure 4

Predicted values of the intrinsic domain-wall resistance in the adiabatic limit for various hole concentrations. The data are for the saturation value of spin splitting at a given Mn content $x$.