Defining the magnetic configuration of the artificial spin system by FIB fabrication

Focused ion beam (FIB) is a popular technique for patterning material layers and designing a variety of geometries. When a magnetic layer is patterned, the final magnetic state of the layer depends not only on the shape of the fabricated structures but also on the FIB fabrication history. This provides an opportunity to define the desired magnetic state of the structure during the FIB fabrication process. We demonstrate this principle numerically and experimentally by FIB fabrication of the artificial spin system with a ferrotoroidal order of magnetic moments. Namely, we process the Permalloy square in the magnetic vortex state using FIB. The square is cut along straight horizontal, vertical, and diagonal lines into an array of identical isosceles right triangles in single-domain states representing artificial spins. Groups of four neighboring triangles form small square unit cells. To develop the ferrotoroidal magnetic state, we show that by choosing a specific recursive order of cut lines during the FIB processing, the magnetic moments of triangles in each unit cell circulate in the same direction. After n iterations of this process, the original square with a vortex state can be divided into 2n×2n smaller squares with toroidal magnetic order.