Accurate modeling of transfer curves is a fundamental requirement for the sophisticated design of Tunneling Magnetoresistance (TMR) sensors, which have emerged as leading candidates for weak magnetic field detection due to their superior sensitivity and wideband response. To eliminate hysteresis and achieve high linearity, TMR sensors frequently utilize magnetic tunnel junctions (MTJs) with high-aspect-ratio elliptical geometries. This design strategy leverages strong longitudinal shape anisotropy to stabilize the magnetization state; however, it inevitably introduces a significant spatial non-uniformity in the internal bias field. This non-uniformity is primarily driven by complex edge demagnetizing effects and magnetostatic coupling between the ferromagnet layers, which are often oversimplified in standard analytical models.
While our previous anisotropic magnetoresistance model based on a uniform effective field hypothesis has proven effective for standard devices, it exhibits significant physical distortion when applied to high-aspect-ratio MTJs, resulting in inaccurate predictions in non-ideal conditions. To overcome these limitations, this paper proposes an enhanced method that incorporates the non-uniform distribution of the internal bias field. The proposed methodology centers on a deterministic discrete bias field distribution. The free layer is discretized into multiple regions represented by three distinct groups of hysterons. Each group is subjected to a unique internal bias field consisting of a static invariant component and a spatially-dependent variable component, thereby capturing the field gradient from the device center to its boundaries. Furthermore, the macroscopic resistance is derived by synthesizing the parallel tunneling conductance of these local regions. A parasitic, tunnel-independent resistance is integrated into the model to represent the non-magnetic contributions from electrodes and leads in the junctions array, ensuring a rigorous match with experimental conditions.
Experimental verification conducted on 4 µm×16 µm elliptical MTJs demonstrates that the traditional uniform model produces anomalous resistance peak at an external field angle of 120° and broad plateaus at 140°. These discrepancies are fundamentally caused by the abrupt coherent rotation of the entire free layer, which triggered by the synchronized competition between external and uniform internal fields. In contrast, the proposed non-uniform model effectively captures the non-coherent characteristics of the magnetization reversal process. By accounting for spatial non-uniformity, the model accurately predicts the asynchronous reversal across different regions of the free layer. This leads to a phase cancellation effect that suppresses the non-physical resistance peak and reproduces the smooth transfer characteristics observed in high-sensitivity working regions of MTJs. Additionally, the model provides a unique physical insight into the slight increase in modeling error observed near the equivalent hard axis (approximately 110°), where the system physically approaches an ideal single-domain state. In conclusion, this research establishes a powerful theoretical bridge between microscopic magnetic dynamics and macroscopic sensor outputs, providing a precise theoretical tool for the optimization and performance prediction of high-sensitivity TMR sensors.