“…Exchange interactions occurring across some of the APBs must be antiferromagnetic (AF), and experimental evidence suggests that these AF-APBs dominate the magnetic and magnetotransport properties of Fe 3 O 4 thin films. 20,32,34 It was shown that if the spins on neighboring ions are not parallel but, instead, form an angle ϕ nn , the transfer integral is reduced tot = t o cos ϕ nn /2. 32 Therefore, the transfer of the conduction electrons between ions with antiparallel spins at an AF-coupled APB is blocked and, according to the model, the conductivity reduces to zero.…”