Subnanosecond spin-transfer switching: Comparing the benefits of free-layer or pinned-layer biasing

T. Devolder, C. Chappert, and K. Ito

Phys. Rev. B 75, 224430 – Published 27 June 2007

Abstract

We analyze the statistical distribution of switching durations in spin-transfer switching induced by current steps and discuss biasing strategies to enhance the reproducibility of switching durations in spin valves. We use a macrospin approximation to describe a thin nanomagnet having easy-plane shape anisotropy and uniaxial magnetocrystalline anisotropy. We model the effect of finite temperature as a Boltzmann distribution of initial magnetization states (adiabatic limit). We compare three model spin valves: a spin valve with a free layer whose easy axis is parallel to the pinned-layer magnetization (standard geometry), a pinned layer with magnetization tilted with respect to the free-layer easy axis (pinned-layer biasing), and a free layer whose magnetization is pulled away from the easy axis by a hard-axis bias (free-layer biasing). In the conventional geometry, the switching durations follow a broad regular distribution, with an extended long tail comprising very long switching events. For the two biasing strategies, the switching durations follow a multiply stepped distribution, reflecting the precessional nature of the switching and the statistical number of precession cycles needed for reversal. We derive analytical criteria to avoid switching events lasting much longer than the average switching duration in order to achieve the highest reproducibilities. Depending on the current amplitude and the biasing strength, the width of the switching time distribution can be substantially reduced, the best reproducibility being achieved for free-layer biasing at overdrive current of a few times unity. An even smaller distribution of switching time is expected if the field is applied abruptly and synchronously with the current, following a so-called dynamic free-layer biasing configuration.

Received 13 February 2007

DOI:https://doi.org/10.1103/PhysRevB.75.224430

Authors & Affiliations

T. Devolder¹, C. Chappert¹, and K. Ito²

¹Institut d’Electronique Fondamentale, CNRS UMR 8622, Bâtiment 220, Université Paris-Sud, 91405 Orsay, France
²Hitachi Cambridge Laboratory, Hitachi Europe, Ltd., Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom

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Vol. 75, Iss. 22 — 1 June 2007

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Images

Figure 1
(Color online) Sketch of the biasing configurations. (A) Standard configuration with no applied field and free-layer magnetization $M$ along its anisotropy axis $(x)$ , chosen parallel to the pinned-layer spin polarization $Π$ . (B) Pinned-layer biasing configuration. (C) Free-layer biasing configuration, where a biasing field (either exchange field or external field) is applied along $(y)$ the direction of the hard axis of the free layer.Reuse & Permissions
Figure 2
(Color online) (A) Switching duration versus initial magnetization state in the standard configuration for $J_{a p p l i e d} = - 3 \times 10^{11} A ∕ m^{2}$ . The gray level is scaled to white for $400 ps$ or less switching duration and to black for $2 ns$ or more switching duration. Considering thermal fluctuations, most initial states will be inside the core of the thermal distribution that is sketched as the green ellipse superimposed on the switching duration map. (B) Probability of being already switched at a given variable time after the onset of the pulsed current. Calculation is done for the standard configuration when the applied current is $J_{a p p l i e d} = - 3 \times 10^{11} A ∕ m^{2}$ at $T = 300 K$ .Reuse & Permissions
Figure 3
Switching durations versus initial magnetization state in the pinned-layer biasing configuration [panels (A)–(D)] and in the free-layer biasing configuration [panels (E)–(H)]. The applied current increases from left panels to right panels. The gray level is scaled to white for $400 ps$ [panels (A), (B), (E), and (F)], for $300 ps$ [panels (C) and (G)], and for $150 ps$ [panels (D) and (H)]. The gray level is scaled to black for $2 ns$ [panels (A) and (B)], for $1.2 ns$ [panels (B) and (F)], for $800 ps$ [panels (C) and (G)], and for $600 ps$ [panels (D) and (H)]. The center of each panel corresponds to the equilibrium position of the magnetization.Reuse & Permissions
Figure 4
(Color online) Projections along $m_{z}$ [panel (A)] and along $m_{y}$ [panel (B)] of the distance between the spiral center $m_{SC}$ and the equilibrium magnetization position $m_{EQ}$ for the two biasing configurations versus the applied current density. The shaded areas have widths that are twice the standard deviation $Δ m_{TH}$ of the initial magnetization away from equilibrium position.Reuse & Permissions
Figure 5
(Color online) Statistical distributions of the switching duration versus applied current for the pinned-layer biasing configuration with $p_{y} = 0.2$ [panel (A)] or with $p_{y} = 0.4$ [panel (B)] and for the free-layer biasing configuration with $h_{y} ∕ h_{k} = 0.2$ [panel (C)] or with $h_{y} ∕ h_{k} = 0.4$ [panel (D)]. The calculations are done at $T = 300 K$ .Reuse & Permissions
Figure 6
(Color online) Comparison of the statistical distribution of the switching duration in the standard configuration, free-layer biasing configuration, and pinned-layer biasing configuration at $T = 300 K$ for $J_{a p p l i e d} = - 6 \times 10^{11} A ∕ m^{2}$ [panel (A)] and for $J_{a p p l i e d} = - 8 \times 10^{11} A ∕ m^{2}$ [panel (B)].Reuse & Permissions

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