Velocity of domain wall motion induced by current in a ferromagnetic semiconductor (Ga,Mn)As structure

1. Background

We have investigated current-induced domain wall (DW) motion in (Ga,Mn)As with magnetic easy axis perpendicular to the plane. Current-induced DW motion in (Ga,Mn)As structures [1] has been demonstrated by the application of current pulse of the order of magnitude 10⁵ A/cm^2, which is 2-3 orders lower than that is required for DW propagation in ferromagnetic metal (NiFe) [2,3]. In this study [4], we have measured the dependence of DW velocity on current density and have investigated mechanisms for current-induced DW motion by quantitative comparison between obtained results and theories.

2. Device fabrication and measurement sequence

The sample was grown by molecular beam epitaxy. Figure 1(a) shows schematic drawing of sample structure. Magnetic easy axis of (Ga,Mn)As layer is perpendicular to the plane due to tensile strain introduced from InAlAs buffer layers and its ferromagnetic transition temperature (TC) is about 115 K. First, the sample was processed into 5 µm wide channel, then the surface of half part of the channel was etched by 10 nm (Figure 1 (b)). After that, Au/Cr electrodes were defined on the channel as shown in Figure 1 (b). Since etching of (Ga,Mn)As surface leads to difference of coercive force (HC) between etched and nonetched region [1], we can prepare a DW at the
boundary by external magnetic field.

The measurement sequence was as follows. First, DW was prepared at the boundary between etched and nonetched region by external magnetic field or current pulse. Magneto-optical polar Kerr effect (MOKE) image of this initial domain configuration was taken as a reference image. Then, current pulse was applied to the channel shutting off the light from the device. After that, MOKE image was taken. Finally, in order to improve the contrast of the images, we had differential image before and after the application of the current pulse. In the differential image, the region where contrast is different from other indicates the region swept by DW.

Figure 1. Schematic drawing of sample structure (a) and device (b) for DW velocity measurement.

3. Results (1)

Figure 2(a) shows the dependence of MOKE images on pulse width (wp) at j = 8.0 x 10⁵ A/cm² and ambient temperature Tn = 100 K. White region is the region, where magnetization direction is reversed from the direction pointing into the plane to out of the plane by the DW motion. DW moves in the opposite direction of current pulse as the previous work [1] and the area swept by DW increases with wp. We defined effective DW displacement (deff) as the area swept by DW divided by channel width. Figure 2(b) shows the dependence of deff on wp obtained from Figure 2(a). deff depends almost linearly on wp. In order to study the terminal DW velocity, we defined effective DW velocity veff as the linear slope at deff > 15 µm. Since device temperature increases by Joule heating, correction of device temperature is necessary. We corrected device temperature by comparing temperature dependence of device resistance measured with low dc current (j = 5x10³ A/cm²) with current density dependence of device resistance during the application of current pulse.

Figure 2. (a) The dependence of MOKE images on pulse width (wp) at Tn = 100 K and j = 8.0x10⁵ A/cm². (b) The dependence of effective displacement (deff) on wp obtained from (a). The broken line shows the linear fitting at deff > 15 µm.

4. Results (2)

Figure 3 (linear plot) and the inset (semi logarithmic plot) of Figure 4 show the dependence of veff on j at corrected temperatures. There exists a critical current density (jc). Above jc ( j > ∼3x10^5 A/cm^2 ), veff increases almost linearly with j. At j < ∼3x10^5 A/cm^2, slow DW motion is still seen and veff dramatically increases with j (Figure 3, 4).

Tatara and Kohno has proposed intrinsic pinning theory [5], which is one of the theories for the dependence of DW velocity (v) on current density (j) in spin transfer mechanism. According to the theory, there exists jc related to anisotropy energy and DW dose not move below jc. Above jc, DW is moved by transfer of spin angular momentum from carrier to localized magnetic spin. From the quantitative comparison between experimental results and the theory, it is found that DW motion in high current density regime (j > ∼3x10⁵ A/cm²) is explained well by intrinsic pining theory. In the low current density regime, as shown in Figure 4, veff obeys over many decades an empirical scaling law, ln(veff) = a(T) - b(T) j^-ν, where ν ∼ 1/2, a(T) ∼ (TC－T), b(T) ∝ (TC－T)². We obtained this scailing law from the dependence of DW creep velocity on magnetic field [6] by assuming that effects of current on DW are equivalent to those of magnetic field. This indicates that DW creep is induced by current in the low current density regime.

Figure 3. The dependence of veff on j at corrected temperatures in linear plot.

Figure 4. The dependence of veff on (TC - T)² j^-1/2 at corrected temperatures. The inset shows the dependence of veff on j at corrected temperatures in semi logarithmic plot.

5. Summary

In this study, we measured the dependence of DW velocity on current density in (Ga,Mn)As with magnetic easy axis perpendicular to the plane. From the quantitative comparison between experimental results and theories, it is found that DW motion in high current density regime (j > ∼3x10⁵ A/cm²) is explained well by spin transfer mechanism (intrinsic pining theory). In the low current density regime, veff obeys an empirical scaling law, which indicating that current-induced creep dominates the DW motion in this regime.

References
[1] M. Yamanouchi, D. Chiba, F. Matsukura, and H. Ohno, Nature 428, 539 (2004). [2] A. Yamaguchi et al., Phys. Rev. Lett. 92, 077205 (2004). Erratum 96, 179904 (2006). [3] N. Vernier el al., Europhys. Lett. 65, 526 (2004). [4] M. Yamanouchi, D. Chiba, F. Matsukura, T. Dietl, and H. Ohno, Phys. Rev. Lett. 96, 096601 (2006). [5] G. Tatara and H. Kohno, Phys. Rev. Lett. 92, 086601 (2004). [6] S. Lemerle et al., Phys. Rev. Lett. 80, 849 (1998).

References

[1] M. Yamanouchi, D. Chiba, F. Matsukura, and H. Ohno, Nature 428, 539 (2004).
[2] A. Yamaguchi et al., Phys. Rev. Lett. 92, 077205 (2004). Erratum 96, 179904 (2006).
[3] N. Vernier el al., Europhys. Lett. 65, 526 (2004).
[4] M. Yamanouchi, D. Chiba, F. Matsukura, T. Dietl, and H. Ohno, Phys. Rev. Lett. 96, 096601 (2006).
[5] G. Tatara and H. Kohno, Phys. Rev. Lett. 92, 086601 (2004).
[6] S. Lemerle et al., Phys. Rev. Lett. 80, 849 (1998).