Title: Field-free switching of perpendicular magnetization by cooperation of planar Hall and orbital Hall effects

Abstract: Spin-orbit torques (SOTs) generated through the conventional spin Hall effect and/or Rashba-Edelstein effect are promising for manipulating magnetization. However, this approach typically exhibits non-deterministic and inefficient behaviour when it comes to switching perpendicular ferromagnets. This limitation posed a challenge for write-in operations in high-density magnetic memory devices. Here, we determine an effective solution to overcome this challenge by simultaneously leveraging both a planar Hall effect (PHE) and an orbital Hall effect (OHE). Using a representative Co/PtGd/Mo trilayer SOT device, we demonstrate that the PHE of Co is enhanced by the interfacial coupling of Co/PtGd, giving rise to a finite out-of-plane damping-like torque within the Co layer. Simultaneously, the OHE in Mo layer induces a strong out-of-plane orbital current, significantly amplifying the in-plane damping-like torque through orbital-to-spin conversion. While either the PHE or OHE alone proves insufficient for reversing the perpendicular magnetization of Co, their collaborative action enables high-efficiency field-free deterministic switching. Our work provides a straightforward strategy to realize high-speed and low-power spintronics.