Abstract
It is well-established that high spin-orbit coupling (SOC) materials convert a charge current density into a spin current density which can be used to switch a magnet efficiently and there is increasing interest in identifying materials with large spin Hall angle for lower switching current. Using experimentally benchmarked models, we show that composite structures can be designed using existing spin Hall materials such that the effective spin Hall angle is larger by an order of magnitude. The basic idea is to funnel spins from a large area of spin Hall material into a small area of ferromagnet using a normal metal with large spin diffusion length and low resistivity like Cu or Al. We show that this approach is increasingly effective as magnets get smaller. We avoid unwanted charge current shunting by the low resistive NM layer utilizing the newly discovered phenomenon of pure spin conduction in ferromagnetic insulators via magnon diffusion. We provide a spin circuit model for magnon diffusion in FMI that is benchmarked against recent experiments and theory.
Highlights
We argue that this type of problem[22] can be overcome by using an important new discovery namely that of pure spin conduction in ferromagnetic insulators (FMI) like yttrium-iron-granet (YIG) which do not allow charge currents to flow, but allow longitudinal spin currents to flow through magnon generation[23,24,25,26,27,28,29,30]
Based on available experimental data[27,28,29,30] we have developed a spin circuit model for such pure spin conductors (PSC), which we use in conjunction with existing models for giant spin Hall effect (GSHE), normal metal (NM), and FM layers to obtain the result in Fig. 1(c) showing an increase in Js by a factor of ~7, which is less than that in Fig. 1(b), but still quite significant
The interfaces between pure spin conduction (PSC) and adjacent layers are treated by modifying the interface conductance matrix of FMI|NM20,21,44 to incorporate the conductance for spins that are collinear to the magnetization direction[24,32,33]
Summary
Where tg, λg, σg, and θSH are thickness, spin diffusion length, conductivity, and intrinsic spin Hall angle of GSHE. The structure, provides an increase in Js relative to θSHJc′ (green curve in Fig. 1(b)) where Jc′ is the charge current density flowing in the GSHE material and shows decrease in Js relative to θSHJc (red curve in Fig. 1(b)) where Jc is the total charge current density flowing in from the terminals This is because the NM layer needed to funnel the spin current provides a shunt path to the charge current, and there is a large component of the charge current outside the GSHE which does not generate spin currents. Such pure spin conductors are described by a conductance matrix of the following form
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