Domain-Wall Resistance in Ferromagnetic (Ga,Mn)As

A series of microstructures designed to pin domain walls (DWs) in (Ga,Mn)As with perpendicular magnetic anisotropy has been employed to determine extrinsic and intrinsic contributions to DW resistance. The former is explained quantitatively as resulting from a polarity change in the Hall electric field at DW. The latter is 1 order of magnitude greater than a term brought about by anisotropic magnetoresistance and is shown to be consistent with disorder-induced mistracking of the carrier spins subject to spatially varying magnetization.

Figure 1

(a) Optical micrograph of Hall bar and schematic cross-sectional view of structure under white line in the micrograph. Current $I=40\mu \mathrm{A}$) direction is $[\overline{1}10]$. (b) Temperature dependence of sheet resistance $R_s$ and (c) coercivity ${\mu }_0{H}_{\mathrm{c}}$ of nonetched and etched regions. Magnetic hysteresis loops measured by anomalous Hall effect at 5 K and three MOKE images at 55–65 K are displayed as insets to (c), where black (white) stripes in the channel correspond to negative (positive) values of $M$.

Figure 2

(a) Magnetoresistance $\Delta R_s$ for various directions of the magnetic field at 55 K. (b) Definition of relation between crystal orientation and angles $\theta$ and $\varphi$ of the applied magnetic field. (c) Hysteresis cycle of $R_s(H)$. (d) Dependence $\Delta R_s(\theta )$ at 0.5 T.

Figure 3

Optical micrographs of (a) unpatterned (device A) and (b) patterned (device B) layers for the domain-wall resistance measurements. (c) Schematic cross-sectional view under the white line of (b).

Figure 4

Magnetoresistance of device A (a) and device B (b) at 45 K (current $I=30\mu \mathrm{A}$). Insets show MOKE images in various magnetic fields disclosing relation between number of domain walls and resistance.

Figure 5

(a) Magnetoresistance of devices C1–C4 (current $I=10,20,40,60\mu \mathrm{A}$, respectively) with different channel width $w$. Solid lines have slopes expected from Fig. 2c for complete antiparallel orientation of domains, and their extrapolation to $H=0$ gives DWR. (b) DWR vs $w^{-1}$, which provides extrinsic and intrinsic contributions per one DW ($R^{\mathrm{ext}}$ and $R^{\mathrm{int}}{A}_d$), shown by open circles in (c) and (d), respectively. Open triangles in (c) show computed $R^{\mathrm{ext}}$. Open triangles and inverse triangles in (d) are theoretical calculated assuming that the conductance polarization is equal or 1.2 times greater that thermodynamic polarization, respectively.