Surface images [(a) and (c)] and distribution of structural domains [(b) and (d)] obtained by EBSD analysis. The MnAs layers were prepared using SPE on GaAs(111)B, sample 1, and GaAs(113)A, sample 2, substrates for the left- and right-hand-side columns, respectively. The scan area is large. The direction of the substrates is set in the horizontal direction. Major domain boundaries are depicted in the top part of (a) and (c). In (b), the axis of the -plane is tilted from the vertical direction by −60°, 0°, and 60° in the blue (dark gray), orange (medium gray), and yellow (light gray) areas, respectively. In (d), the axis of the -plane is tilted by ±42.7° away from the vertical direction for the two colored areas. Identification of Kikuchi pattern failed in the white area. The insets in (a) and (c) show SEM images viewed actually in the direction of the surface normal. The insets in (b) and (d) show AFM images. The scale of the images in the main panels and insets is identical.
Distribution of domain size, i.e., the probability density vs domain size , obtained by numerical simulations. The filled and open symbols correspond to, respectively, square and hexagonal lattices consisting of cells. Periodic boundary conditions were assumed. The degree of freedom of the “crystal orientation” in each cell is 2, 3, and 4 for the circles (red), triangles (green), and squares (blue), respectively. The lines show fits to a form given in Eq. (1). The values of the fit parameters are plotted in Fig. 3.
Values of parameters , (a), and , (b), used in the fits shown in Fig. 2. A -vs- graph is shown in the inset of (b). The average domain size and a ratio are plotted in (c). The filled and open symbols correspond to the square and hexagonal lattices, respectively. The solid lines show a linear dependence with the -intercept 1.5 and 2.
Probability of the size of structural domains being larger than . The filled and open circles correspond to samples 1 and 2, respectively. The solid curves are fits assuming a probability density in the form of Eq. (1). The power-law exponent was set to be . The cut-off parameter is 4 and for samples 1 and 2, respectively. The dotted line shows the slope corresponding to .
Scanning electron micrographs of sample 3. Only the thick islands (the type-A islands indicated with “A”) are practically seen in (a). The thin films (the type-B islands indicated with “B”) are visible in (b), which was taken using the in-lens detector of SEM, in the area surrounding the type-A islands.
XRD curve ( scan) of sample 3. The three- and four-index notations of the reflection peaks refer to GaAs and MnAs, respectively.
Scanning electron micrograph, (a), and distribution of structural domains [(b) and (c)] obtained by EBSD analysis of sample 3, which is a MnAs layer grown at on GaAs(111)B. The scan area is large. The direction of the substrate is shown by an arrow in (a). In (b), the areas shown by yellow, orange, green, blue, and brown (from light gray to dark gray) correspond to -, -, -, -, and (0001)-orientations, respectively. The tolerance for deviation from the nominal surface orientations was set to be 10°. Only the Kikuchi pattern of the GaAs substrate was detected in the black area. The white area corresponds to other orientations and fit errors. The axis orientation within the surface plane for the components is displayed in (c). The inclination of the axis from the direction of the substrate is −60°, 0°, and 60° in the yellow (light gray), orange (medium gray), and brown (dark gray) areas, respectively. In the white area, the -axis orientation is either perpendicular to the plane or unknown.
Intensity of XRD in the vicinity of the (0002)- and -reflection peaks in sample 3.
Magnetization curves of sample 3 at a temperature of . An in-plane external magnetic field was applied in the and directions of the substrate for the solid and dotted curves, respectively. The right inset shows the hysteresis loops with expanded scales. The temperature dependence of magnetization is shown in the left inset. An in-plane external magnetic field of 10 kOe was applied. The diamagnetic contribution of the GaAs substrate has been subtracted.
Temperature dependence of resistance in sample 3. Voltage probes with a separation of were attached to single thick (type-A) islands for the solid curves. The distance between the voltage probes was for the dotted curve.
Distribution of domain size [the probability density vs domain size ] in quasi-one-dimensional square lattices. The number of square cells in the transverse direction of the chains is , 2, and 4 for the triangles, circles, and squares, respectively. The degree of freedom is 2 in (a) and (b) and 3 in (c) and (d).
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