Domain Walls in the $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ Diluted Magnetic Semiconductor

We report experimental and theoretical studies of magnetic domain walls in an in-plane magnetized $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ dilute moment ferromagnetic semiconductor. Our high-resolution electron holography technique provides direct images of domain wall magnetization profiles. The experiments are interpreted based on microscopic calculations of the micromagnetic parameters and Landau-Lifshitz-Gilbert simulations. We find that the competition of uniaxial and biaxial magnetocrystalline anisotropies in the film is directly reflected in orientation dependent wall widths, ranging from approximately 40 to 120 nm. The domain walls are of the Néel type and evolve from near-90° walls at low temperatures to large angle $[1\overline{1}0]$-oriented walls and small angle [110]-oriented walls at higher temperatures.

Figure 1

Lorentz micrographs (left-hand column) and phase images amplified by a factor of 4 (right-hand column) acquired at (a) 30.5 K, (b) 25.4 K, and (c) 9.8 K. Three different types of DWs are observed, marked by white arrows: (i) a wall parallel to $[1\overline{1}0]$ that is near-180° type at high temperature and near-90° type at low temperature, (ii) a pair of DWs that is near-180° head-on type at high temperature and near-90° type at low temperature, and (iii) a near-90° type wall parallel to [110] that appeared at low temperature. The local $\mathbf{B}$ directions are denoted by black arrows.

Figure 2

Magnitude ($|\mathbf{B}|$) and direction ($\theta$) of $\mathbf{B}$ as a function of temperature ($T$). Only results with subtraction of paramagnetic phase images for thickness variation correction and further linear wedge correction are displayed.

Figure 3

Phase image amplified by a factor of 4, acquired at 8 K (a) and 22 K (b). $x$-differentiated (c) and $y$-differentiated (d) images of (a). The DW positions are indicated by white arrows. Projected profile of the phase gradient across the $[1\overline{1}0]$ ($x$)-oriented DW (e) and [110] ($y$)-oriented DW (f) along lines indicated by white rectangles.

Figure 4

(a) Microscopic calculations of $K_u/K_c$ for the whole range of doping parameters considered; inset shows the effective barrier energies for the two walls and the specified hole and local moment densities. (b) LLG simulations for the low-temperature micromagnetic parameters of the studied $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$. Magnetization orientations in the individual domains are highlighted by arrows.