Three-dimensional micromagnetic domain structure of MnAs films on GaAs(001): Experimental imaging and simulations

The micromagnetic domain structure of MnAs films on GaAs(001) has been systematically investigated by micromagnetic imaging and simulations. The magnetic force microscopy (MFM) contrast resulting from the stray field of the simulated three-dimensional domain patterns was calculated and found to be in excellent agreement with MFM experiments. By combining three-dimensional stray-field imaging by MFM with surface sensitive probing and micromagnetic simulations, we were able to derive a consistent picture of the micromagnetic structure of MnAs. For example, the origin of the comblike contrast observed through MFM was identified as a metastable domain configuration exhibiting a cross-tie wall.

Figure 1

$5\times 5\mu {\mathrm{m}}^2$ image of the surface magnetization of a $120\text{−}\mathrm{nm}$-thick MnAs film obtained by XMCD-PEEM. The ferromagnetic $\alpha \text{−}\mathrm{Mn}\mathrm{As}$ stripes (dark and bright) are separated by nonferromagnetic $\beta \text{−}\mathrm{Mn}\mathrm{As}$ stripes (gray, i.e., no magnetic contrast). The standard domain types are indicated in the image and illustrated below. Reprinted from Ref. 23, Fig. 2 $(28°\mathrm{C})$. Copyright Springer-Verlag 2006. With kind permission of Springer Science and Business Media.

Figure 2

(a) $5\times 5\mu {\mathrm{m}}^2$ image of the stray field of a $180\text{−}\mathrm{nm}$-thick MnAs film obtained by MFM at $18°\mathrm{C}$. Besides the standard domain types (rectangular markers), comblike structures are found (circular markers) that are labeled C(I) and C(II) referring to their connection to type (I) and (II) domains, respectively. (b) Sketch illustrating the contrast mechanism in MFM. Bright contrast corresponds to an attractive interaction between tip and sample and dark contrast to a repulsive interaction.

Figure 3

Sketch of (a) the $\alpha \text{−}\beta$-stripe structure of a MnAs film on GaAs(001) and (b) the simulated surface magnetization. (c) Isosurface plot (for ten constant $M_y$ values) of the three-dimensional magnetization distribution. (d) Cross-sectional magnetization patterns are shown at the positions indicated in (c). The arrows indicate the magnetization in the basal plane. Their grayscale corresponds to the $M_y$ component, and the underlying image to the $M_z$ component of the magnetization. The stripe geometry corresponds to a sample temperature of $28°\mathrm{C}$.

Figure 4

Magnetization distribution for the relaxed, extended standard domain types (I), (II), and (III). The grayscale represents the value of the in-plane magnetization component $M_y$. The surface contrast corresponds to the magnetization distribution observed in XMCD-PEEM images. The stripe width is observed at a sample temperature of $28°\mathrm{C}$.

Figure 5

Magnetization pattern of the comblike domain structure. The isosurfaces of the normalized magnetization $(M_y=M_x=\pm 0.707)$ illustrate transitions from in-plane to out-of-plane oriented magnetization vectors. At selected positions, cross-sectional cuts are shown below in (a) and (b). The underlying grayscale corresponds to the out-of-plane component $M_z$, whereas the gray value of the arrows represents the in-plane component $M_y$. The stripe width corresponds to a sample temperature of $18°\mathrm{C}$.

Figure 6

Illustration of the tip magnetization used for the MFM simulations. The scale represents the relative magnitude of the normalized magnetization component $M_z$.

Figure 7

MFM simulations of the standard domain types (I)–(III), shown in (a)–(c), respectively. The grayscale corresponds to the magnetic interaction force gradient in mN/m. The black bars correspond to $200\mathrm{nm}$. The MFM contrast originating from the comblike domain structure is shown in (d). The dotted lines indicate the edges of the ferromagnetic stripe. The respective insets show the corresponding calculated XMCD-PEEM contrast.

Figure 8

Comparison of the simulated and measured MFM response (line scans) across ferromagnetic stripes showing (a) a type (I) domain, (b) a type (II) domain, and (c) a type (III) domain. The simulated MFM response is given in mN/m and the measured MFM response in arbitrary units (arb. units).

Figure 9

Comparison of the simulated and measured MFM response (line scans) across a comblike domain structure [type (CII)]. The solid symbols represent a cut through an arm of the comb structure [cut (a)], and the open symbols a cut in between two arms [cut (b)], as indicated in Fig. 5.