1. Anti-Damping Torque Engineering in Trilayer Spin-Hall System
Gaurav Gupta, Mansoor Bin Abdul Jalil, and Gengchiau Liang
Department of Electrical and Computer Engineering, National University of Singapore, Singapore
Tel: (65) , Fax: (65) , {a , elembaj,
Abstract
Objective: Control and Improve the Anti-Damping Torque in Spin-Hall System
A trilayer system with perpendicularly magnetized metallic (FMM) free-layer, heavy metal (HM) with strong spin-hall effect and ferromagnetic insulating (FMI) substrate has been proposed to significantly enhance the anti-damping torque acting on FMM. Its magnitude can be engineered by configuring the magnetization of the FMI. The analytical solution has been developed for four stable magnetization states (non-magnetic and magnetization along three Cartesian axis) of FMI to comprehensively appraise the anti-damping torque on FMM and the Gain factor. It is shown that the proposed system has much larger gain and torque compared to a bilayer system (or with non-magnetic substrate). The performance improvement may be extremely large for system with a thin HM. Device optimization is shown to be non-trivial and various constraints have been explained. These results would enable design of more efficient spin-orbit torque memories and logic with faster switching at yet lower current.
Introduction
FMI controls the reflected spin-current at the FMI-HM interface to regulate the spin-injection through FMM-HM interface and torque on FMM layer.
Fig. 1: Heavy metal (HM) with strong spin-hall effect (SHE) is sandwiched between ferromagnetic metal (FMM) and ferromagnetic insulator (FMI) substrate with magnetization vectors mM and mI respectively. Electron current (Jc) along x-axis generates spin current (Js) along z-axis to switch FMM magnetization.
Boundary Condition: Js is zero at z = b and c surfaces, Js and spin accumulation (S) is continuous at z = 0 and a surfaces.
Fig. 2: Gain factor or Spin Hall Efficiency as a function of HM thickness for bi-layer (FMM-HM) system. The maximum is obtained at tH = λsf.
Key Equations
Drift-Diffusion & Torque
Spin Accumulation (mI = [0 my 0])
Anti-damping torque Ty acting on region-B is,
Field-like torque Tx acting on region-B is,
Spin Accumulation (mI = [mx 0 0])
Spin Accumulation (mI = [0 0 mz])
Results
Observe :
Large change in Ty and Gain for small HM thickness.
Ty and Gain scale with Diffusion Coefficient.
Large change in Tx and Gain for small HM thickness. But, Tx contribution is much smaller in SHE system w.r.t. Ty.
Fig. 5: Effect of Diffusion coefficient of ferromagnetic materials w.r.t DHM (set to one) on the percentage change in anti-damping torque Ty (a, c) and Gain (b, d), over a range of HM thickness (tH) and FMI magnetization mI. Insets for (a, c) show the zoom-in for smaller range of tH.
Fig. 3: Spin-Density (a-e) and Spin-Current (f-j) distribution in a trilayer system for different mI (stated over each column) for perpendicularly magnetized mM = [0 0 1]. Thickness parameters are c = 3 nm, a = 1 nm, b = 2.5 nm.
Fig. 4: Effect of HM thickness on anti-damping torque Ty (a), percentage change in Ty normalized with respect to (w.r.t.) non-magnetic trivial substrate (b) and Gain (c) for different mI of FMI stated over the figure. Dashed lime-green line is for 1-sech(tH/λHsf) behaviour of bilayer system and dark blue is a numerical solution for trilayer system with trivial substrate for reference. The insets show the zoom-in of region in dashed box.
Fig. 6: Effect of HM thickness and mI on (a) field-like torque Tx normalized w.r.t non-magnetic trivial substrate (b) percentage change in Tx with respect to non-magnetic substrate (c) Gain factor and (d) Torque ratio between anti-damping and field-like component. Insets show the zoom-in of the main figure.
Conclusion
Acknowledgements
We have examined the anti-damping torque and gain factor in trilayer spin-hall system with ferromagnetic insulating substrate whose magnetization mI controls the spin-current through heavy metal, to affect the spin-distribution across the system which subsequently affects the switching torque acting on the ferromagnetic metal (free-layer). Extremely large performance improvement has been observed, especially for systems with thin HM. The addition of FMI provides an additional handle on gain factor and for optimizing device design for peak performance. The significant enhancement in torque and gain factor may enable design of more efficient spin-orbit torque memories and logic with faster switching at yet lower current and power.
The work at the NUS was supported by MOE under Grant No. R and MOE2013-T , and NRF Grant No. NRF-CRP and NRFCRP
2015 International Conference on Solid State Devices and Materials (SSDM)