Minimal Model of Spin-Transfer Torque and Spin Pumping Caused by the Spin Hall Effect

Abstract

In the normal metal/ferromagnetic insulator bilayer (such as Pt/Y3Fe5O12) and the normal metal/ferromagnetic metal/oxide trilayer (such as Pt/Co/AlOx) where spin injection and ejection are achieved by the spin Hall effect in the normal metal, we propose a minimal model based on quantum tunneling of spins to explain the spin-transfer torque and spin pumping caused by the spin Hall effect. The ratio of their damping-like to field-like component depends on the tunneling wave function that is strongly influenced by generic material properties such as interface s − d coupling, insulating gap, and layer thickness, yet the spin relaxation plays a minor role. The quantified result renders our minimal model an inexpensive tool for searching for appropriate materials. [6,7]. Unlike in metallic heterostructures, the usual way of spin injection by using a spin-polarized charge current in the currentperpendicular-to-plane (CPP) geometry is difficult in NM/FMI because the insulating FMI impedes the charge current. Instead, the spin injection in this system is done by using the spin Hall effect (SHE) in the NM, which in the current-in-plane (CIP) geometry injects a pure spin current into the FMI to cause STT. In the reciprocal process, SHE converts the pure spin current generated from spin pumping into electric signals. Despite pointing at promising applications in magnetic memory devices, the microscopic mechanism concerning how the pure spin current tunnels into an insulator to cause STT and spin pumping remains unclear, especially if spin relaxation plays a crucial role as in metallic heterostructures [1].

Edelstein and inverse Edelstein effects caused by the pristine surface states of topological insulators

“…Let us consider that the TI occupies the z < 0 half-space, and the FMM film of finite thickness 0 ≤ z ≤ F . The principle is to solve the Bloch equation of the conduction electron spin in the FMM [40,41]…”

Current-induced switching of proximity-induced ferromagnetic surface states in a topological insulator

“…1b). Since the efficient spin transfer to the FMI layer requires strong couplings with wellordered interfaces between the TI surface state and the magnetic moments in the FMI layer 26,27 , the CGT/TI heterostructures may be of great advantage for highly efficient switching. Through the optimization of the CGT thickness for the switching ratio and efficiency, the magnetization of the CGT layer can be almost fully switched by the in-plane current injection on the TI layer as low as 2-4 A cm −1 in the CGT thickness range of 3-5 nm (corresponding to four to seven CGT monolayers).…”

Theory of in-plane current induced spin torque in metal/ferromagnet bilayers

“…This is a very peculiar feature of the CIP configuration with SHE induced out-of-plane spin injection, in contrast to the CPP configuration where angular momentum conservation is satisfied exactly at the interface [2]. This feature is not included in our previous treatments [27,43,44]. Comparing Eqs.…”

“…The thickness of NM and FMM are labeled by lN and lF M , respectively, and the interfac is located at x = 0. voltage causes spin injection. We define the out-of-plane direction to bex and the direction of charge current to bê y [1,27,43,44], as shown in Fig. 1, in contrast to the experimental convention of coordinates which are denoted by (x ′ , y ′ , z ′ ).…”