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Synchronization of spin-transfer torque oscillators by spin pumping, inverse spin Hall, and spin Hall effects

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 Added by Mehrdad Elyasi
 Publication date 2015
  fields Physics
and research's language is English




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We have proposed a method to synchronize multiple spin-transfer torque oscillators based on spin pumping, inverse spin Hall, and spin Hall effects. The proposed oscillator system consists of a series of nano-magnets in junction with a normal metal with high spin-orbit coupling, and an accumulative feedback loop. We conduct simulations to demonstrate the effect of modulated charge currents in the normal metal due to spin pumping from each nano-magnet. We show that the interplay between the spin Hall effect and inverse spin Hall effect results in synchronization of the nano-magnets.



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In the normal metal/ferromagnetic insulator bilayer (such as Pt/Y$_{3}$Fe$_{5}$O$_{12}$) and the normal metal/ferromagnetic metal/oxide trilayer (such as Pt/Co/AlO$_{x}$) 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.
The polarization of the spin current pumped by a precessing ferromagnet into an adjacent normal metal has a constant component parallel to the precession axis and a rotating one normal to the magnetization. The former component is now routinely detected in the form of a DC voltage induced by the inverse spin Hall effect (ISHE). Here we compute AC-ISHE voltages much larger than the DC signals for various material combinations and discuss optimal conditions to observe the effect. Including the backflow of spins is essential for distilling parameters such as the spin Hall angle from ISHE-detected spin pumping experiments.
We theoretically examine the spin-transfer torque in the presence of spin-orbit interaction (SOI) at impurities in a ferromagnetic metal on the basis of linear response theory. We obtained, in addition to the usual spin-transfer torque, a new contributioin $sim {bm j}_{rm SH}^{phantom{dagger}} cdot abla {bm n}$ in the first order in SOI, where ${bm j}_{rm SH}^{phantom{dagger}}$ is the spin Hall current driven by an external electric field. This is a reaction to inverse spin Hall effect driven by spin motive force in a ferromagnet.
High spin to charge conversion efficiency is the requirement for the spintronics devices which is governed by spin pumping and inverse spin Hall effect (ISHE). In last one decade, ISHE and spin pumping are heavily investigated in ferromagnet/ heavy metal (HM) heterostructures. Recently antiferromagnetic (AFM) materials are found to be good replacement of HMs because AFMs exhibit terahertz spin dynamics, high spin-orbit coupling, and absence of stray field. In this context we have performed the ISHE in CoFeB/ IrMn heterostructures. Spin pumping study is carried out for $Co_{40}Fe_{40}B_{20} (12 nm)/ Cu (3 nm)/ Ir_{50}Mn_{50} (t nm)/ AlO_{x} (3 nm)$ samples where textit{t} value varies from 0 to 10 nm. Damping of all the samples are higher than the single layer CoFeB which indicates that spin pumping due to IrMn is the underneath mechanism. Further the spin pumping in the samples are confirmed by angle dependent ISHE measurements. We have also disentangled other spin rectifications effects and found that the spin pumping is dominant in all the samples. From the ISHE analysis the real part of spin mixing conductance (textit{$g_{r}^{uparrow downarrow}$}) is found to be 0.704 $pm$ 0.003 $times$ $10^{18}$ $m^{-2}$.
This paper micromagnetically studies the magnetization dynamics driven by the spin-Hall effect in a Platinum/Permalloy bi-layer. For a certain field and current range, the excitation of a uniform mode, characterized by a power with a spatial distribution in the whole ferromagnetic cross section, is observed. We suggest to use the ferromagnet of the bi-layer as basis for the realization of an array of spin-torque oscillators (STOs): the Permalloy ferromagnet will act as shared free layer, whereas the spacers and the polarizers are built on top of it. Following this strategy, the frequency of the uniform mode will be the same for the whole device, creating an intrinsic synchronization. The synchronization of an array of parallely connected STOs will allow to increase the output power, as necessary for technological applications.
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