Non-planar geometrical effects on the magnetoelectrical signal in a 3D nanomagnetic circuit

Abstract

Bringing nanomagnetism into the third dimension is of growing interest due to many advantages that three-dimensional (3D) structures provide. The introduction of 3D geometrical effects such as curvature and chirality1, as well as the high density and enhanced device connectivity, lead to many opportunities for new physics and applications2,3. When we combine this promising field of 3D nanomagnetism with the well-established field of spintronics, a number of proposals ranging from the ultra-high-density 3D racetrack memory4 to 3D interconnected memristors for neuromorphic computing5 appear. However, before we can fully exploit the promise of 3D spintronics, significant advances in both the integration of 3D nanomagnets into 2D microelectronic circuits，and the understanding of the influence of a 3D geometry on the magnetotransport properties, are required.The implementation of 3D nanomagnetic circuits faces great challenges regarding the fabrication of a 3D nanostructure and its interconnectivity to the electronic components. Until recently, most magnetotransport experiments have concerned cylindrical nanowires, with complex micromanipulations needed to electrically contact them6. In this work, we employ 3D nano-printing capabilities provided by Focused Electron Beam Induced Deposition (FEBID)7, to directly fabricate a high-quality 3D Cobalt nanobridge with well-defined leads on pre-synthesized electrical contacts (Figure 1a). The SEM image shown in Figure 1b demonstrates the successful integration of this complex, high-aspect-ratio 3D nanostructure onto lithographically patterned electrodes. This printed 3D nanomagnetic circuit allows four-probe transport measurements with which we can probe the magnetotransport properties of the 3D nanostructure - and determine the influence of the three-dimensionality on these properties.To fully characterise the magnetotransport (MT) properties of the 3D magnetic nanobridge, we measured MT hysteresis loops for fields applied in different directions in three-dimensions (Figure 2a, b). These magnetotransport measurements, in combination with macrospin and finite element simulations, reveal that the three-dimensional structure of the nanobridge directly affects the magnetotransport in several ways. Firstly, the non-collinear current path in the 3D geometry results in a complex superposition of different MT effects, leading to an unusual angular dependence of well-known effects such as the Anomalous Hall effect. Secondly, we also identify a significant angular-dependence of the magnetoelectric signal due to the magnon magnetoresistance. This strong angular dependence occurs due to the strong influence of the demagnetising field within the non-collinear regions of the 3D geometry, highlighting the importance of magnetostatics in 3D nanostructures8.These new insights into the influence of a 3D geometry on the magnetotransport effects reported in this work provide the basis for the future study of new spintronic effects in 3D magnetic nanostructures, as well as the realization of 3D spintronic technologies. This methodology shown here combining FEBID 3D printing and standard planar lithography can be extended to more complicated geometries and other materials, opening the door to the fundamental study of new phenomena that exploit the interplay between 3D geometry and magnetotransport and may find applications in the future of areas such as magnonics, frustrated magnetic systems, and magnetic neural networks. **