In-plane and out-of-plane planar Hall effect

The planar Hall effect (PHE) has attracted significant attention due to its low thermal drift and high signal-to-noise ratio, which provide distinct advantages in characterizing the intrinsic properties of materials and in the applications of spintronic devices. Previous studies focused on only one measurement mode: rotating the magnetic field in the in-plane direction. This implies that the use of PHE to study the properties of a sample has significant limitations, that is, it can only be used to analyze the in-plane properties of a sample. Here, we define PHE, which was previously measured by rotating the magnetic field in a plane, as in-plane PHE and introduce the concept of out-of-plane PHE and its corresponding test method. Subsequently, we investigated the in-plane and out-of-plane PHE of Sb2Te3 as a case study, confirming the soundness and reliability of the in-plane and out-of-plane PHE concepts proposed in this paper, along with the corresponding testing methods. Out-of-plane PHE was proposed to address the limitations of using PHE to explore relevant properties in materials. For example, it is now possible to explore the anisotropic transport properties of materials in the in-plane and out-of-plane directions using PHE. Furthermore, we propose a design idea for a PHE-based four-state logic cell that combines in-plane and out-of-plane PHE. Overall, our study introduces the concept of out-of-plane PHE and its corresponding testing method, thereby solving a problem in current PHE research, paving the way for better understanding of PHE, and opening additional opportunities for PHE applications.