(Color online) Temperature dependence of remnant magnetization in a trilayer sample with respect the  crystallographic direction. The data was collected while warming with the indicated applied fields, after cooling from 200 to 5 K in zero field (a) and 1.5 mT (b). Inset: The structure of the trilayer grown by MBE.
(Color online) Plot of the temperatures at which the alignment changes from antiparallel to parallel vs applied magnetic field. The ZFC and FC data were each fitted to an exponential decay function with the same decay constant. H E was the determined by taking the average of the two curves, shown as the solid blue line. The gray (green) circle marks the value of H E previously determined from a direct hysteresis loop measurement.
(Color online) Fitted PNR data of the trilayer sample plotted as Q-dependent spin asymmetry. Panel (a) corresponds to spin-asymmetry after cooling in zero field to 5 K, collected in an applied field of 0.65 mT; (b) shows 5 K ZFC data after cycling and returning to 0.65 mT; (c) shows spin-asymmetry obtained in 0.18 mT after cooling in zero field to 30 K; and (d) shows spin asymmetry for the ZFC case obtained at 30 K after cycling and returning to 0.18 mT. The magnetic field was applied along the  direction. The solid lines are best fits to the data. The magnetizations corresponding to these best fits are shown in each panel. Dashed lines are fits obtained with the same model, but with the magnetization of the top GaMnAs layer reversed.
(Color online) Free energy of the magnetic layers as a function of the angle of their magnetization [Top layer: gray (red) lines, M t . Bottom layer: black lines, M b ] obtained for the directions of M for both layers shown in the figure. For clarity, a large value of H E is used. (a) H C ≫ H U ; after ZFC, minima of free energy indicate AFM alignment. (H U has the same sign for both layers) (b) H C ≫ H U ; after FC, local free energy minima indicate FM alignment. (H U has the same sign for both layers) (c) For the bottom layer H U > H C and for the top layer H U ∼ 0. For both ZFC and FC, there is AFM alignment at the minimum of the total energy. In the top layer, M is in a multidomain state with the total M t along opposite direction ofM b . (d) Very small H E : H U ≫ H C ; H U has different sign for both layers. In the top layer, M is in multidomain state with the total M t ∼ 0.
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