Reliable magnetic domain wall propagation in cross structures for advanced multi-turn sensor devices

We develop and analyze an advanced concept for domain wall based sensing of rotations. Moving domain walls in n closed loops with n-1 intersecting convolutions by rotating fields, we can sense n rotations. By combining loops with coprime numbers of rotations, we create a sensor system allowing for the total counting of millions of turns of a rotating applied magnetic field. We analyze the operation of the sensor and identify the intersecting cross structures as the critical component for reliable operation. In particular depending on the orientation of the applied field angle with the magnetization in the branches of the cross, a domain wall is found to propagate in an unwanted direction yielding failures and counting errors in the device. To overcome this limiting factor, we introduce a specially designed syphon structure to achieve the controlled pinning of the domain wall before the cross and depinning and propagation only for a selected range of applied field angles. By adjusting the syphon and the cross geometry, we find that the optimized combination of both structures prevents failures in the full sensor structure yielding robust operation. Our modeling results show that the optimized element geometry allows for the realization of the sensor with cross-shaped intersections and operation that is tolerant to inaccuracies of the fabrication.