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The field dependence of the magnetic moment of an piece of film of Fe, thick, deposited on the surface of GaAs. The field is along the in-plane  direction. The black curve with circles is part of a major hysteresis loop. The blue curve with squares is a minor loop started just beyond the coercive field of the major loop. This clearly crosses over the major loop. This is an indication of regions of increased magnetic anisotropy with the pinning direction depending on past history of the applied fields. Note that the magnetization does not saturate as expected for a field along the hard axis for uniaxial anisotropy.
Calculated magnetization curves (solid lines and dashed for instability) compared with the results of Fig. 1 for cubic plus uniaxial anisotropy with the easy axis along the  direction so that the in-plane  direction is an intermediately hard direction. The solid line to the left is for the cubic anisotropy of Fe. It applies only if the magnetic field were first applied along the  direction, for once the instability field is reached, the magnetization saturates in the  direction and stays saturated until the field is increased in the negative direction to a value greater than the instability field. The resulting hysteresis loops would be fully square loops. If sufficient uniaxial anisotropy is added, while reducing the contribution of the cubic anisotropy to keep the initial slope as it was without the uniaxial anisotropy, the hysteresis can be suppressed as shown in the middle curve (dark green). If there is only uniaxial anisotropy the magnetization process is linear to saturation as shown at the right.
Comparison of the magnetization loops for the field in the  and  directions for Fe electrodeposited on the GaAs surface. Note that the coercive field is the same for both directions, indicating that the same domain wall motions are contributing to the reversal processes. Note that the  curve does saturate below 1 kG and there is a rounding of the magnetization curve in the  axis, which could possibly be the result of a distribution of preferred axes, but which here will be attributed to the inhomogeneous magnetization process from regions of uniaxial anisotropy along each of the three  axes.
Modeling the hysteresis using local regions of uniaxial anisotropy with the cubic anisotropy of iron acting everywhere. The instability curve for uniform rotation with the cubic anisotropy of iron (a) is repeated from Fig. 2, but here it uses the actual cubic anisotropy of Fe rather than treating the anisotropy as a fitting parameter as was done in Fig. 2. The blue curve (b) with hysteresis is for a smaller value for the local uniaxial anisotropy than the red curve (c) without hysteresis. Surprisingly, the addition of the local anisotropy increases the magnetization in low fields. The red curve (c) is in fair agreement with the minor loop of Fig. 1, which is shown here with black diamonds. The modeling is for a periodic distribution of regions of uniaxial anisotropy. A more realistic model would have variations in the spacing of these regions, but such a calculation is prohibitive for the available computing resources.
Contours of constant magnetization as the configuration passes over the barrier of the  hard axis in the plane of the film to which the magnetization is confined by the effects of the demagnetizing field that arises if the magnetization tries to leave that plane. The contours of and bound the region that has yet to surmount the  barrier on decreasing field from saturation.
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