PHYSICAL REVIEW APPLIED 12, 034022 (2019) Field-Free Switching of Perpendicular Magnetization Through Spin Hall and Anomalous Hall Effects in Ferromagnet–Heavy-Metal–Ferromagnet Structures Chi Sun , * Jiefang Deng, S. M. Rafi-Ul-Islam, Gengchiau Liang, Hyunsoo Yang, and Mansoor B. A. Jalil † Department of Electrical and Computer Engineering, National University of Singapore, 117576 Singapore (Received 27 March 2019; revised manuscript received 24 June 2019; published 12 September 2019) Spin-orbit coupling (SOC) in nonmagnetic heavy metals (HMs) gives rise to the spin Hall effect (SHE), which is widely used to switch perpendicularly magnetized structures with an assistive magnetic field. In a similar manner, the anomalous Hall effect (AHE) arising from bulk SOC in ferromagnets (FMs) can also induce spin polarization. We theoretically show how both SHE and AHE can be used to realize field-free switching of perpendicular magnetization in FM1(fixed)/HM/FM2(free) trilayer structures. We calculate the resulting spin torque due to SHE (in the HM) and/or AHE (in the fixed FM1) analytically and numerically, and perform macrospin switching simulation without an assistive magnetic field. While it is understandable that AHE can achieve field-free switching due to the out-of-plane polarization it generates, rather surprisingly, field-free switching of perpendicular magnetization can also occur in the sole presence of SHE when the fixed FM1 has an out-of-plane magnetization. In addition, the AHE and SHE can be combined constructively for magnetization switching by having spin Hall and anomalous Hall angles of opposite signs. DOI: 10.1103/PhysRevApplied.12.034022 I. INTRODUCTION Spin-orbit coupling (SOC) plays essential roles in manipulating spin polarization and generating spin-orbit torques (SOTs) [1–5], which is conventionally provided by a nonmagnetic heavy metal (HM) [6–8]. In a HM with strong SOC, charge flowing in the electric field direction (e.g., x direction) generates spin flowing toward the inter- face normal (z direction) due to the bulk spin Hall effect (SHE). This SHE-generated spin current is in-plane polar- ized (i.e., spin along the y direction) and injected into an adjacent ferromagnet (FM), creating SOTs to switch the magnetization. However, when using SOTs with in-plane spin polarization to achieve deterministic magnetization switching in structures with perpendicular magnetization anisotropy (PMA), an external assistive magnetic field is required to break the symmetry in the system [6,9–12]. Considerable efforts have been devoted to eliminating this external field to avoid scalability issues in practical appli- cations, for example, wedged structural engineering [13], exchange bias or interlayer exchange-coupling-based tech- niques [14–16], geometrical domain-wall pinning [17], out-of-plane spin polarization [18,19], and so on. It has been theoretically proposed that the anomalous Hall effect (AHE) due to SOC in the FM can be used * e0021580@u.nus.edu † elembaj@nus.edu.sg to create spin torques in a similar manner as the SHE [20]. In the FM layer, the spin current excited by the bulk AHE has spins pointing along the local magnetiza- tion direction (i.e., m), and flowing in the m × E direction with E = E ˆ x, where E is the electric field accompanied by the applied electric current (I 0 = I 0 ˆ x). The anoma- lous spin torque generated by a FM due to the AHE has been experimentally observed by means of spin-torque ferromagnetic resonance (ST-FMR) measurement on a FM(fixed)/Cu/FM(free) structure [21,22]. Compared to the conventional SHE within HMs whose spin polarization is confined along the in-plane direction, AHE in the FM gives greater control over the spin polarization because it is determined by the magnetization direction [20,23], which can be changed. Therefore, by having an out-of- plane magnetization component in the fixed FM layer, one can achieve an out-of-plane spin polarization and thereby break the symmetry in the structure and realize field-free perpendicular magnetization switching. Since both SHE and AHE can be used as spin polar- ization sources, we propose a FM1(fixed)/HM/FM2(free) trilayer structure (Fig. 1) where switching of the free (FM2) layer is induced by SHE (in HM) and/or AHE (in FM1). Here, the fixed layer FM1 is chosen to be made of FM material with a large anomalous Hall angle, for example, Fe-Mn-Pt, while the PMA free layer FM2 is made of conventional FM material exhibiting PMA, which usually has negligible AHE. The magnetizations of FM1 2331-7019/19/12(3)/034022(12) 034022-1 © 2019 American Physical Society