Central role of domain wall depinning for perpendicular magnetization switching driven by spin torque from the spin Hall effect

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Central role of domain wall depinning for perpendicular magnetization switching driven by spin torque from the spin Hall effect

O. J. Lee, L. Q. Liu, C. F. Pai, Y. Li, H. W. Tseng, P. G. Gowtham, J. P. Park, D. C. Ralph, and R. A. Buhrman

Phys. Rev. B 89, 024418 – Published 28 January 2014

Abstract

We study deterministic magnetic reversal of a perpendicularly magnetized Co layer in a Co/MgO/Ta nanosquare driven by spin Hall torque from an in-plane current flowing in an underlying Pt layer. The rate-limiting step of the switching process is domain wall (DW) depinning by spin Hall torque via a thermally assisted mechanism that eventually produces full reversal by domain expansion. An in-plane applied magnetic field collinear with the current is required, with the necessary field scale set by the need to overcome DW chirality imposed by the Dzyaloshinskii-Moriya interaction. Once Joule heating is taken into account the switching current density is quantitatively consistent with a spin Hall angle $θ_{S H} \approx 0.07$ for 4 nm of Pt.

Received 17 November 2013

DOI:https://doi.org/10.1103/PhysRevB.89.024418

Authors & Affiliations

O. J. Lee¹, L. Q. Liu¹, C. F. Pai¹, Y. Li¹, H. W. Tseng¹, P. G. Gowtham¹, J. P. Park¹, D. C. Ralph^1,2, and R. A. Buhrman¹

¹Cornell University, Ithaca, New York 14853, USA
²Kavli Institute at Cornell University, Ithaca, New York 14853, USA

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Vol. 89, Iss. 2 — 1 January 2014

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Figure 1
(a) Schematic of the cross-bar device structure for Hall effect measurements. A Co/MgO/Ta nanosquare is patterned at the center of a Pt cross bar. (b) Measured average switching field $〈 | H_{p} | 〉$ (for an out-of-plane field) for a 300 nm × 300 nm Co nanosquare as a function of the measurement time ( $t_{m}$ ) at room temperature. Inset: Example of a hysteresis loop, $r_{H} = d V_{H} / d I$ as a function of $H_{z}$ at $I_{dc}$ = 0. (c) Measured switching field $H_{p} (θ)$ , normalized by $H_{p}$ (θ = 0°), as a function of a tilt angle (θ) from the easy axis. The solid line shows the predicted behavior for reversal via domain wall depinning. The dotted line shows the ideal Stoner-Wohlfarth prediction for a single domain nanomagnet. (d) Schematic of reversed domain having a domain wall with a fixed chirality (left-handed) due to the Dzyaloshinskii-Moriya interaction. (Red dots=down moments, blue dots=up.) The direction of the out-of-plane component of the equivalent spin Hall field, $H_{S H, z}$ on the domain wall magnetization is indicated schematically for the right and left regions of the wall where $\hat{m} = \pm {\hat{m}}_{x}$ , respectively.
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Figure 2
(a),(b) Examples of hysteresis curves for magnetic switching, from differential Hall measurements, for an out-of-plane external applied field $H_{z}$ = ± 200 Oe. (c) Switching phase diagram of the ⊥Co showing the average switching current as a function of $H_{z}$ . (d),(e) Examples of the current-induced deterministic switching of the ⊥Co under an in-plane external $H_{x}$ = ± 300 Oe collinear with the current. (f) Switching phase diagram of the ⊥Co showing the average switching current as a function of $H_{x}$ .
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Figure 3
(a) The estimated Curie temperature ( $T_{c}$ ) of the ⊥Co ≈ 583 ± 23 K was determined by fitting to $Δ R_{H} [T (J)] = R_{H 0}^{} {1 - {[T (J) / T_{c}]}^{α}}^{β}$ where $R_{H} (I) = Δ V_{H} (I) / 2 I$ is the maximum Hall resistance (for $| m_{z} | \approx 1$ ) at a given value of $I$ for large $H_{z} = \pm 1.5$ kOe. (The fit parameters are $R_{H 0}$ ≈ 0.96 Ω, α ≈ 0.59, and β ≈ 0.69.) We assume that $R_{H} [T (I)]$ is linearly proportional to $M_{s} (T)$ . (b) Deterministic current-driven switching is absent in the ⊥Co nanosquare for $H_{x} = 50$ Oe. There is no magnetic reversal unless the heating is sufficient to destroy the PMA, then upon cooling the PMA is restored with seemingly random orientation $m_{z}$ = ± 1. (c) Left: Schematic of a domain wall structure in which the chirality favored by the DMI [Fig. 1] is eliminated by a large external field $H_{x}$ . Magnetic reversal occurs when $m_{x} > 0$ throughout the majority of the domain wall so that the equivalent out-of-plane field from SHE is strong enough to drive expansion of a domain in all lateral directions. The direction of the out-of-plane component of the equivalent spin Hall field, $H_{S H, z}$ on the domain wall magnetization is indicated schematically for the left, right, top, and bottom regions of the domain wall where $\hat{m} = {\hat{m}}_{x}$ in all cases due to the strong $H_{x}$ . Right top: A cross-sectional schematic of the device structure where an electrical current density $J_{x}$ in the Pt generates a transverse spin current $J_{s}$ that exerts an effective spin Hall field via spin-transfer torque on the spatially varying magnetization of the Co. Right bottom: Polar representation of the spin Hall–generated equivalent field, small light (red) arrows, as the function of the Co magnetization direction, large dark (blue) arrows.
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Figure 4
Estimate for the current-induced spin Hall equivalent field per unit current density ( $H_{S H, z} / J$ ) considering the effects of heating on the magnetic system. (a) Estimated effects of Joule heating: η( $J$ ) is the normalized reduction in $H_{p, 0}^{z}$ , ξ( $J$ ) is normalized reduction in $M_{s}$ , and χ( $J$ ) is the normalized reduction in $E_{p}$ . (b) Values of $H_{S H, z} /$ $J$ obtained from analysis of the switching phase diagram [Fig. 2].
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