Reliable Estimation of TaB Spin Hall Angle by Incorporating the Interfacial Transparency and Isolating Inverse Spin Hall Effect in ST-FMR Analysis

The requirement of low power consumption, high speed, high endurance for emerging next generation universal memory, a three terminal (separate read/write terminals) spin-orbit-torque (SOT) based non-volatile memory (SOT-MRAM) devices have been gaining much interests than two-terminal spin-transfer-torque MRAM (STT-MRAM) due to its improved magnetization switching, exploiting the spin Hall effect (SHE) mechanism [1–6]. The free layer of SOT-MRAM devices, consists of heavy metal (HM)/ferromagnet metal (FM) bilayer structure, essentially rely on two factors, first the magnitude of SOT from HM which is proportional to spin Hall angle (SHA), and the second is the effective damping constant $( \alpha _{\mathrm{eff}})$ of FM in FM/HM bilayer structure. Since the switching current in SOT-MRAM using in-plane magnetization of magnetic tunnel junction (i-MTJ) is inversely proportional to HM’s SHA and directly proportional to FM’s $\alpha_{\mathrm{eff}}$, we need to search for HM materials with high SHA and at the same time with low $\alpha _{\mathrm{eff}}$ of FM for HM/FM bilayer structure combination. Previously, we have shown the excellent magnetization switching behavior of SOT-MRAM using Ta
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B
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(HM), and evaluated its SHA by spin Hall magnetoresistance (SMR) measurement [7]. However, analysis of SHA based on SMR assume a simple drift-diffusion model and as for estimation of the effective damping constant, SMR cannot be applied. In this study, the spin-transfer ferromagnetic resonance (ST-FMR) method was used to evaluate both SHA of Ta
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(HM) and $\alpha _{\mathrm{eff}}$ of Co
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Fe
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(FM) for Ta
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($t$ nm)/Co
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Fe
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B
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(4 nm) bilayer structure. The ST-FMR mixed-signal can be fitted by the combination of symmetrical and asymmetrical components by $\mathrm {V_{Total}} = \mathrm {V_{Sym}} + \mathrm {V_{Asym}}$, where $\mathrm {V_{Total}}$ is total mixed signal, $\mathrm {V_{Sym}}$ is total symmetrical signal due to spin current, and $\mathrm {V_{Asym}}$ is total asymmetrical component due to charge current. The ST-FMR signal, its fitting and extracted each individual components are shown in Fig. 1 (a). The SHA evaluation is not straightforward, since other parameters/mechanisms, which are taking place simultaneously, have to be taken into account. At ferromagnetic resonance two phenomenons are taking place concurrently, the SHE from HM to FM and spin pumping (SP) from FM to HM. The SP induced spin current is converted back to charge current in HM through the inverse spin Hall effect (ISHE) which is reflected in symmetrical ST-FMR voltage signal and can be represented by $\mathrm {V_{Sym}} = \mathrm {V_{ST-FMR}} + \mathrm {V_{ISHE}}$. In order to remove the SP influence or considering contribution only from SHE i.e. $\mathrm {V_{ST-FMR}}$, the ratio of $\mathrm {V_{ST-FMR}}$ to $\mathrm {V_{Sym}}$ defined by η, is crucial and can be expressed as $\eta = \mathrm{V_{ST-FMR}}/ \mathrm{V_{Sym}} = \mathrm{V_{ST-FMR}}/ (\mathrm{V_{ST-FMR}}+ \mathrm{V_{ISHE}})$. This ratio η is very important, since both SHE and ISHE have the same angle dependence (due to similar mechanism), it is very difficult to isolate them, as suggested by other groups too [8, 9]. In addition, the influence of transparency $T$ at Ta
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/Co
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Fe
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interface has to be taken into account for reliable SHA estimation [9, 10]. The transparency, which controls the spin trasnmittance at interface, is related to spin mixing conductance at the HM/FM interface. The spin mixing conductance was calculated from the enhancement of damping constant $( \Delta \alpha )$ of FM due to spin pumping from its intrinsic value $( \alpha _{0})$. The real value of SHA can be calculated by incorporating interface transparency $T$ and isolating the ISHE $( \mathrm{V_{ISHE}})$ contribution from $\mathrm{V_{Sym}}$, that is η. These contributions are incorporated by mathematically multiplying $T$ and η to conventional SHA $\Theta _{\mathrm{SH(r)}} = \eta T \Theta _{\mathrm{SH(m)}}$, where $\Theta _{\mathrm{SH(r)}}$ is the real value of SHA while $\Theta _{\mathrm{SH(m)}}$ is the observed value of SHA estimated by typical approach. In the observed SHA value, neither SHE contributions were separated nor was interface transparency considered, which leads to the overestimation of SHA. The values η, $T$ and $\eta T$ are shown as a function of Ta
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layer thickness in Fig. 1 (b). As it is clear that the ratio η decreases systematically with Ta
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layer thickness, however the interface transparency $T$ increases steeply and then saturates at around 2.5 nm. Their product $\eta T$ shows initial enhancement and after peak, a systematic decrease is observed. It is obvious that at lower Ta
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thickness, interface transparency controls whereas at higher thickness the $V_{ST-FMR}$ contribution dominates. In the Fig. 1 (c), each individual symmetrical components are shown, which is required for reliable SHA estimation. The dependency of $\Theta _{\mathrm{SH(r)}}$ on Ta
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layer thickness is illustrated in Fig. 1(d). By considering only SHE contribution and interface transparency we are able to evaluate the real value of SHA. This SHA value is nearly consistent with the derived SHA from separately fabricated SMR devices [7]. In conclusion, we have successfully estimated the SHA (-0.18) of Ta
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B
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by isolating SHE contribution from total ST-FMR signal combined with transparency at Co
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Fe
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Ta
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interface. Additionally, we were able to achieve desired low damping constant $( \alpha _{\mathrm{eff}}) \approx 0.008$ for Co
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Fe
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/Ta
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bilayer which is also crucial factor for realizing low switching current for future SOT-MRAM applications.