Analytic modeling of dipolar field requirements for robust coupling in a non-identical biaxial two-magnet system

Magnetic bodies interact with each other through magnetic dipolar fields that depend on the instantaneous magnetization vectors of the coupled magnetic bodies in a system. Previous studies have shown that reliable, deterministic coupling can be achieved in identical two-magnet systems and is a function of the longitudinal and perpendicular components of the dipolar field. In this work, we extend previous work significantly by developing analytic models that map the regions of dipolar field driven magnetization reversal of a non-identical two-magnet system. Models are obtained for mono-domain magnetic bodies with biaxial magnetic anisotropy. The analytic models presented map the necessary requirements for a deterministically coupled two-magnet system. In these deterministic, stable reversals, the two-magnet system stabilizes in an anti-parallel configuration along the natural free-axis of the system, regardless of thermal effects. However, non-deterministic reversals can also occur in certain non-identical systems. These pseudo-reversals occur because only one of the nanomagnets meets the critical field requirements. In this case, the system reversal is a result of thermal drift and therefore complex function system parameters and observation time. We also note that multi-magnet systems may find steady-state orientations away from the free-axis if the perpendicular components of the dipolar field are too large. We present models which accurately map the field magnitudes which result in these meta-stable reversals. Lastly, models to interpret the impact of dipolar coupling on the critical current requirement for spin-transfer-torque driven magnetization switching are also presented in this manuscript. This work greatly expands our understanding of the complex-field interaction in multi-magnet systems and is crucial when evaluating complex magnetic devices.