Spintronic logic lacks a gain element: no device has been shown to sense a weak spin current and deliver a larger, same-sign spin current at room temperature, which prevents spin circuits from cascading with fan-out. Acremann et al. (2008) proposed a concrete route — a single ferromagnet operated as a time-separated, bifurcation-based spin amplifier, in which a control parameter brings the magnetization to an unstable bifurcation point so that a small input spin torque selects the final magnetization state, after which the relaxed magnet polarizes a large unpolarized charge current — and demonstrated only external control of switching hysteresis in a metallic nanopillar. The concept was never quantified: the achievable spin gain gsg_{s}, the minimum input spin polarization for deterministic switching against thermal noise, and a clocked implementation with fan-out greater than one remain undetermined. Later work produced successor concepts (voltage-controlled symmetry breaking, stimulated spin pumping of AC spin currents, geometrical ratchets, antiferromagnetic and plasmonic proposals) and adjacent demonstrations (amplification of spin polarization in semiconductors and magnetic tunnel transistors), but no experimental spin-current gain element for logic; the problem remains open.

Background

Charge-based logic obtains signal restoration and fan-out from the transistor, an element with current gain. Spin-based information processing, in which information is carried by the spin angular momentum of electrons, has lacked such an element: a spin signal injected into a normal metal decays over the spin diffusion length, the characteristic distance over which a non-equilibrium spin polarization relaxes in a nonmagnetic metal (of order a few hundred nanometers in copper at room temperature), and spin-logic proposals dissipate rather than amplify the spin signal at each stage. In the two-current model, a spin-polarized current is described by the spin-up and spin-down electron currents I↑I_{\uparrow} and I↓I_{\downarrow}; the charge current is Ic=I↑+I↓I_{c}=I_{\uparrow}+I_{\downarrow} and the spin current (net rate of angular-momentum flow) is Is=I↑−I↓I_{s}=I_{\uparrow}-I_{\downarrow}. A spin amplifier should sense the sign of an input spin current IsinI_{s}^{\mathrm{in}} and deliver an output spin current IsoutI_{s}^{\mathrm{out}} of the same sign but larger magnitude; its spin gain is gs=∣Isout∣/∣Isin∣g_{s}=|I_{s}^{\mathrm{out}}|/|I_{s}^{\mathrm{in}}|. Before 2008, amplification had been realized only in senses that do not meet this definition: hybrid schemes that detect the spin signal with a ferromagnet, amplify the resulting voltage with conventional charge electronics, and re-inject a spin-polarized current (gain delegated to charge amplifiers); a magnetic tunnel transistor (a three-terminal tunnel-emitter device that spin-filters the transmitted current) that amplified the polarization ratio of a current rather than its spin-current magnitude (Saha et al., 2007); and proposals to tune the Curie temperature of ferromagnetic semiconductors by electric fields, impractical at room temperature. Acremann et al. (2008) proposed to obtain intrinsic gain in a single ferromagnet by time-separating sensing and output generation with a clock-like control parameter. The magnetization of a small thin-film ferromagnetic element with in-plane shape anisotropy — the tendency of a non-circular element to magnetize along its long axis, which creates two stable magnetization directions — has two stable equilibria. If a control perturbation brings the magnetization to a bifurcation point — an unstable symmetric configuration on the separatrix, the boundary between the two basins of attraction — then an arbitrarily small spin-transfer torque (the torque exerted on a magnetization when it absorbs spin angular momentum from a passing spin-polarized current) can select into which equilibrium the magnetization relaxes. Restoring stability afterwards turns the same ferromagnet into a polarizer: driving a large unpolarized charge current through it produces a spin-polarized output current larger than the input. Two control implementations were identified: an ultrafast magnetic-field pulse normal to the film that ballistically precesses the magnetization onto the separatrix (precessional switching), and a simpler static field along the in-plane hard axis (the in-plane direction perpendicular to the long easy axis) that reduces the shape-anisotropy energy barrier. As a laboratory proxy, the authors showed in a metallic current-perpendicular-to-plane nanopillar (a CoFe free layer, the layer whose magnetization switches, separated by a Cu spacer from a fixed reference layer of two antiparallel-coupled ferromagnets, a synthetic antiferromagnet) that hard-axis bias fields reversibly narrow the current-driven magnetoresistance hysteresis loop, demonstrating external control of the free layer's magnetic stability. No input spin signal was injected, so gain, input thresholds, and noise limits were not measured. The subsequent all-spin logic architecture (Behin-Aein et al., 2010), in which nanomagnets communicate through spin currents in a nonmagnetic channel, made the availability of a spin gain element with fan-out greater than one a central standing requirement for spintronic circuits.

Problem Statement

Can the single-ferromagnet, bifurcation-based spin amplifier be quantitatively characterized, and its room-temperature realization established by analysis and by device and clocking design, without requiring a new experiment? The three parts below are jointly required, and each is independently assessable: (1) what spin gain gs=∣Isout∣/∣Isin∣g_{s}=|I_{s}^{\mathrm{out}}|/|I_{s}^{\mathrm{in}}| is achievable in the proposed metallic multilayer implementation, as a function of the ferromagnet's polarization and the applied unpolarized charge current, and whether it can exceed one; (2) what is the minimum input spin current IsinI_{s}^{\mathrm{in}} (equivalently the minimum input spin polarization at a stated injection charge current) required to bias the bifurcation deterministically against thermal noise — that is, what are the switching error probabilities as functions of the input spin current and temperature; (3) whether a control and clocking protocol (for example, the ultrafast precessional field pulses, or the timed dc hard-axis bias cycles, described in the source concept) can implement, in one device, the sensing phase in which the sign of a small input spin current selects the final magnetization state and the output phase in which the relaxed magnet polarizes a larger output current. A physical laboratory demonstration is out of scope for this task: resolution requires a quantitative characterization of the achievable gain and switching statistics together with a control and clocking design whose room-temperature feasibility is argued from the source device parameters.

References

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