Anisotropy of the Hopping Integrals of Calcium Doped Yttrium Iron Garnet

Abstract

The main objective of this paper is to indicate a possible origin of strong magnetic anisotropy of the electric resistance in calcium-doped yttrium-iron garnets (Ca : YIG). Recent measurements of the electric resistance of the as-grown Ca : YIG samples show strong anisotropy connected with differ- ent orientations of the applied magnetic field with respect to the electric current. The relative change in the resistance can be either positive for the orientations of the field perpendicular to the current, or negative for the parallel orientation of the magnetic field. The mere change of the orienta- tion gives rise to an about 10% change in the saturated resistance [1], In order to interpret these interesting results we propose a simple microscopic model in which the occurrence of this phenomenon is attributed to the orbital contribution to the magnetic moment of compensating holes being charge carriers in the system. It has been assumed that a possible microscopic mechanism of the hopping electric conductivity in doped YIG can be explained within the framework of the electronic cluster model based on the three-band Hubbard Hamiltonian [2, 3]. The Hubbard Hamiltonian takes the following form: $$ \hat (H) = \hat (H)_{3d} + \hat (H)_{2p} + \hat (H)_{p-d} $$ (1)