A microscopic model of Ca : YIG minimal system in the form of a pair of the tetrahedral (d) iron -oxygen clusters, separated by the octahedral (a) cluster, coupled in series to the electrodes, is employed in an interpretation of the experimentally observed intriguing behaviour of anisotropic magnetoresistance (MR). Two possible origins of the anisotropy of MR are viewed. The extrinsic one results from orbital contributions to magnetic moments of the central clusters and reveals itself in the external magnetic field. The intrinsic one is caused by different spin polarisation of the left and the right d clusters with respect to the middle a cluster. The effect is connected with a presence of a compensating hole at one of the tetrahedral clusters.
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