Packing 360∘ domain walls of identical circulation on planar ferromagnetic nanowires with notches using circular magnetic fields

360∘ domain walls (DWs) have generated substantial interest with the recognition that their minimal stray field creates only short range interactions, leading to a potentially higher packing density for data storage devices compared to 180∘ DWs. The topology of neighboring 360∘ DWs with identical circulation allows a higher packing density than that of 360∘ DWs of opposite circulation. Our simulations demonstrate the process by which we can pack 360∘ DWs of identical circulation on a long wire with 100 nm width (in y) and 4 nm thickness (in z), studying different size and shape notches to pin the DWs. The process to generate these walls follows a series of circular fields with non-uniform magnetic field strength that decreases as 1/r as if created by an infinitely long wire passing current into or out of the page and centered just above the notches. We are able to pin two 360∘ DWs of the same circulation on adjacent 16 nm (x) by 32 nm (y) rectangular notches 100 nm apart and on adjacent triangular notches of the same area that are 100 nm apart. The location and strength required of the series of fields is different for the different notches. Such stable high density packing of 360∘ DWs in simulations is unprecedented and suggests the potential for high density information storage.