Coupling Reliability Models of Two-Magnet Systems for Slow-Reversal Cases
This paper follows previous works which investigated the strength of dipolar coupling in two-magnet systems. While these works focused on qualitative analysis, this manuscript elucidates reversal through dipolar coupling culminating in analytical expressions for reversal reliability in two-magnet systems. The dipolar field generated by a mono-domain magnetic body can be represented by a tensor containing both longitudinal and perpendicular field components; this field changes orientation and magnitude based on the magnetization of neighboring nanomagnets. While the dipolar field does reduce to its longitudinal component at short time-scales, for slow magnetization reversals, the simple longitudinal field representation greatly underestimates the scope of parameters that ensure reliable coupling. For the first time, analytical models which map the geometric and material parameters required for reliable coupling in two-magnet systems are developed. It is shown that in biaxial nanomagnets, the xˆ and yˆ components of the dipolar field contribute to the coupling while all three dimensions contribute to the coupling between a pair of uniaxial magnets. Additionally, the ratio of the longitudinal and perpendicular components of the dipolar field is also very important. If the perpendicular components in the dipolar tensor are too large, the nanomagnet pair may come to rest in an undesirable meta-stable state away from the free axis. The analytical models formulated in this manuscript map the minimum and maximum parameters for reliable coupling. Using these models, it is shown that there is a very small range of material parameters which can facilitate reliable coupling between PMA nanomagnets; hence, in-plane nanomagnets are more suitable for coupled systems.