Fig. 1. (Color online) Magnetoresistance of (Ga,Mn)As/GaAs multilayers measured with magnetic field applied near the [110] direction at T = 30 K. Although the AMR typical for (Ga,Mn)As layers dominates the MR observed in most of the samples, giant magnetorsistance (GMR)-like effect is clearly seen in samples B3 and B4, indicating the presence of AFM IEC in those specimens. The arrows indicate the direction of field scan. (Adapted from Ref. [20])

Fig. 2. (Color online) Magnetoreistance observed in six (Ga,Mn)As/GaAs multilayers with different structural parameters. Samples C1, D1, and E2 show only anisotropic magnetoresistance (AMR), characteristic of FM IEC between the (Ga,Mn)As layers; Samples C3, D2, and E3 show a GMR-like behavior, indicating the presence of AFM IEC in these samples similar to that seen in the [(Ga,Mn)As/GaAs:Be]₁₀ multilayer discussed in detail in the Fig. 1.

Fig. 3. (Color online) Summary plot of IEC type for the various (Ga,Mn)As multilayers depending on carrier concentrations and spacer layer thicknesses. Black open squares and red open circles show FM IEC and AFM IEC, respectively. (Adapted from Ref. [16])

Fig. 4. (Color online) The process of magnetization reversal in the [(Ga,Mn)As/GaAs:Be]10 multilayer system. (a) MR is measured at 35 K as the field is cycled between −100 and 100 Oe. The down- and up-scans, shown by solid (blue) and open (red) circles, respectively, have a completely symmetrical behavior. Two types of fully AFM spin configurations between the (Ga,Mn)As layers, AFM1 and AFM2, can be realized at zero field, as shown schematically by the vertical arrows. Each field scan (down or up) contains a four-step restoring process and a five- step saturation process, with resistance plateaus marked as R1–R4 and S1–S4. (b) The number of pairs with AFM alignment between adjacent (Ga,Mn)As layers in the multilayer is obtained by minimizing the IEC energy given by Eq. (1) during the down-scan of the field. The field is scaled in terms of the NN IEC strength J₁. The reversal process determined from calculation using Eq. (1) clearly shows a four-step restoring and a five-step saturation process, similar to that observed in the MR experiment shown in the upper panel. The crossing of the calculated energies for the R3, R4 and FM1 states is shown in the inset. The spin configuration corresponding to each plateau in the field scan is indicated schematically by vertical arrows. (Adapted from Ref. [40])

Fig. 5. (Color online) Magnetic field dependence of MR and IEC energy during (a) up-scan and (b) down-scan of applied field for samples used in this study. The experimentally measured MR at 23 K and calculated IEC energy for possible spin configurations are plotted in left and right columns of each figure, respectively. (Adapted from Ref. [43])

Fig. 6. (Color online) Minor MR hysteresis loops obtained during the “restoring” process for our three samples. The minor loops are plotted with red open circles on top of main loops shown by black lines. The magnetization alignments involved in the minor loop of each sample are schematically shown by arrows at corresponding values of MR. The solid vertical lines indicate minor loop shifts HMLS from zero field. (Adapted from Ref. [43])

Table 1. Description of parameters and structures for the sample series from A to E. (Adapted from Ref. [16])

Table 2. Calculated IEC field H_IEC and experimentally observed minor loop shifts H_MLS. (Adapted from Ref. [43])