Out-of-plane angle resolved second harmonic Hall analysis in perpendicular magnetic anisotropy systems

TL;DR

The paper tackles the challenge of quantifying spin–orbit torque efficiencies in PMA HM/FM bilayers by introducing an out-of-plane polar-angle resolved SHH method to extract damping-like and field-like terms ($\xi_{DL}$ and $\xi_{FL}$) from low-frequency magnetization dynamics. Using Pt/Co and Ta/CoFeB PMA stacks, it finds $\xi_{DL}=0.12$, $\xi_{FL}=-0.05$ for Pt/Co, and $\xi_{DL}=-0.16$ with an anomalous $m_z^2$-dependent $\xi_{FL}$ in Ta/CoFeB, which requires a modified effective field $h_{FL}$ parameterized by $a=-0.66$. AHE-based STFMR measurements yield $\xi_{DL}=0.12$ and $\xi_{FL}=-0.04$, corroborating the SHH results. The work also demonstrates an equivalence between SHH and dc voltage in this regime and provides a framework for PMA SOT characterization with cross-validation between SHH and STFMR, revealing a noteworthy FL torque anomaly in Ta/CoFeB with potential implications for device design. $\xi_{DL}$ and $\xi_{FL}$ are central to predicting switching efficiency and energy consumption in spintronic memories and logic.

Abstract

Spin orbit torques (SOT) are used to manipulate magnetization of ferromagnets in heavy metal / ferromagnetic bilayers and thus are technologically relevant from magnetization switching perspective. This necessitates development of methods which give an insight into SOT behaviour and enable SOT efficiency estimation. In this article, we demonstrate an experimental approach of out-of-plane (OOP) angle resolved Second Harmonic Hall (SHH) measurement, in Pt/Co and Ta/CoFeB perpendicular magnetic anisotropy (PMA) systems, for damping-like and field-like SOT efficiency estimation. This method reveals a unique anomalous field-like torque dependent on magnetization direction in Ta/CoFeB system. The damping-like and field-like SOT efficiencies are extracted by solving LLGS equation in the low frequency limit of magnetic susceptibility. Along with SHH measurements, we also experimentally demonstrate anomalous Hall effect (AHE) based spin-torque ferromagnetic resonance (STFMR) technique for SOT efficiency quantification in PMA systems.

Figures (6)

• Figure 1: (a) Schematic of the Pt/Co PMA stack Hall bar along with the reference frame (b) AHE hysteresis loop of the Pt/Co PMA stack (c)(d) Longitudinal and transverse resistance plots respectively of Pt/Co PMA stack at an in-plane external field of 10 kOe.
• Figure 2: Out-of-plane angle sweep harmonic Hall measurements of Pt/Co PMA stack at 4mA current (symbols represent experimental data and solid lines represent fit to the data). (a) Schematic of OOP rotation of external magnetic field direction in xz plane for longitudinal case (b)-(c) First and second harmonic Hall voltages for longitudinal case at 20 kOe (d) Schematic of OOP rotation in yz plane for transverse case (e)-(f) First and second harmonic Hall voltages for transverse case at 10 kOe
• Figure 3: (a) AHE hysteresis loop of the Ta/CoFeB PMA stack (b) $R_{xy}$ vs $\phi_H$ plot showing contributions from PHE/SMR and AHE
• Figure 4: SHH plots of PMA Ta/CoFeB system acquired at 0.6mA current by OOP angle sweep (a)-(b) $V_{2w}$ for longitudinal and transverse scans respectively for 8, 10 and 12 kOe externally applied magnetic fields. (c) SHH plot at 8000 Oe in longitudinal case (d) SHH plot at 8000 Oe in transverse case
• Figure 5: OOP angle sweep $V_{2\omega}$ and $V_{dc}$ signals of Pt/Co PMA stack at 10 kOe externally applied magnetic field for (a) longitudinal case (b) transverse case