Universal Method for Separating Spin Pumping from Spin Rectification Voltage of Ferromagnetic Resonance

Abstract

We develop a method for universally resolving the important issue of separating spin pumping (SP) from spin rectification (SR) signals in bilayer spintronics devices. This method is based on the characteristic distinction of SP and SR, as revealed in their different angular and field symmetries. It applies generally for analyzing charge voltages in bilayers induced by the ferromagnetic resonance (FMR), independent of FMR line shape. Hence, it solves the outstanding problem that device specific microwave properties restrict the universal quantification of the spin Hall angle in bilayer devices via FMR experiments. Furthermore, it paves the way for directly measuring the nonlinear evolution of spin current generated by spin pumping. The spin Hall angle in a Py/Pt bilayer is thereby directly measured as 0.021±0.015 up to a large precession cone angle of about 20• . [3][4][5]. Soon after, a consensus was formed that quantitatively, such FMR voltages in FM/NM bilayers involve in general not only the contribution from spin pumping (SP), but also that from spin rectification (SR), where the magnetization dynamics driven by either the microwave field [6] or the spin transfer torque [7] rectifies the microwave current flowing in the FM layer. In 2010, a method based on line shape analysis of the FMR voltage was established for quantitatively separating the two contributions of SP and SR [8]. Although such a line shape analysis is useful and enabled the first quantification of the spin Hall angle via FMR measurement [8], as discussed in a few follow-up studies [9][10][11], it is important to be aware that it only applies on specially designed devices measured under proper configurations which fulfil three conditions: (1) Microwave currents in the non-magnetic metallic layer should be minimized so that contributions from spin transfer torque induced spin rectification can be neglected [7]. (2) The measurement configuration and microwave phase should be such that the spin rectification either makes no contribution to the Lorentzian part † Current affiliation: Colegio de Ciencias e Ingenieria, Universidad San Francisco de Quito, Quito, Ecuador of the electrically detected FMR line shape or can be calibrated [9][10][11]. (3) The cone angle of the magnetization precession should be small so that the FMR line shape is free from nonlinear distortion [12]. These strict conditions limit the broad application of the line shape method for generally analyzing the spin pumping and spin Hall effect in bilayer spintronic devices [13,14]. So far, developing a universal method independent of device-specific microwave properties remains a significant challenge. In particular, there is no applicable method for quantifying the spin pumping effect in the nonlinear regime, where the technologically important question of how efficient a large spin current may be generated by high power microwaves remains open.In this letter, we establish such a universal method based on general symmetry consideration. This method enables the pure spin pumping ...

Current-induced spin torque resonance of a magnetic insulator

“…Oersted fields, however, are affected by the local sample configuration. This may introduce a (dc magnetic field independent) phase offset δ between J c and ρ which can render also the Oersted field induced V SMR largely symmetric [20,28,29]. Therefore, a simple line-shape analysis of the dc voltage detected in magnetic resonance in terms of symmetric and antisymmetric contributions does not allow us to distinguish the individual contributions from spin pumping and spin Hall magnetoresistance rectification or whether the dynamics stem from Oersted fields or the spin transfer torque.…”

“…In magnetic resonance, the high-frequency precession of the magnetization induces a high-frequency oscillation of ρ at the same frequency f MW as J c , which generates a dc rectification voltage [27] (V SMR ). In contrast to the symmetric line shape of V SP , V SMR also depends on the specifics of the phase relation between microwave current and magnetization precession [28], such that both symmetric and antisymmetric resonance line shapes are possible. For spin torque actuated magnetization dynamics the rectification voltage resonance line shape is purely symmetric [21], while for Oersted field induced dynamics it is, in general, at least partially antisymmetric.…”

“…Therefore, the phase offset δ must be determined in order to conclusively establish the role of the spin transfer torque versus the Oersted field. While both V SP and V SMR vanish for magnetic fields in the plane spanned by the film normal and the charge current direction [28], i.e., ϕ = 0 • , for any other value of ϕ their magnitude is differently affected by the polar (out-of-plane) angle θ between the film normal and the magnetization direction [22]. More specifically, the ratio R of the symmetric (S) to antisymmetric (A) contributions to the line shape [20] changes characteristically as a function of θ for a given δ.…”

“…(1) and (2) are as follows: h is the length of the sample, ϕ is the angle between the current and the applied in-plane magnetic field (see Fig. 1) with modulus B ex = μ 0 H ex , δ is the constant phase offset between microwave current and magnetization precession [20,28,29] as discussed above, and the magnetic field B = αω a /γ is the half width of the resonance governed by the Gilbert damping constant α and the excitation angular frequency ω a = 2πf MW . C =ω a / 1 +ω 2 a and C ± = 1 ± 1/ 1 +ω 2 a whereω a = 2ω a /(M s γ μ 0 ) with the gyromagnetic ratio γ .…”

Nanowire spin torque oscillator driven by spin orbit torques

“…Recently, a new type of STO based on current-induced spin orbit (SO) torques in a Permalloy(Py)/platinum(Pt) bilayer was demonstrated [16][17][18] . Spin orbit torques [19][20][21] in this system can arise from the spin Hall effect in Pt [22][23][24][25][26][27][28] and the Rashba effect at the Pt/Py interface [29][30][31][32] .…”