A modified theoretical model on tunnelling giant magnetoresistance of granular films

Abstract

Based on the model of Inoue, a modified phenomenological theory is presented to study the tunnelling magnetoresistance (TMR) of granular films under high applied field (larger than 1 T). In this Letter the size distribution of granules in granular films was described by the log-normal function. According to Cullity et al.'s classification we take D 1 ( T ) as the critical size distinguished superparamagnetic granules from single domain ferromagnetic granules and D 2 ( T ) as the critical size distinguished the single domain from the multi-domain. In addition, we introduce, respectively, two phenomenological parameters: k 1 describing the effect of matrix characteristic in granular films on the spin polarization of ferromagnetic granules and k 2 characterizing the weight of single domain granules relative to superparamagnetic granules with TMR. The calculated results, including TMR vs. applied magnetic field, measuring temperature or the size of granule, are in agreement with the experiments when the single domain ferromagnetic granules play a key role ( k 2 > 1 ) in TMR for granular films, which indicates that our modified model is reasonable.