Microscopic mechanism of spin–orbit-torque switching in exchange-biased PtMn/ferromagnet bilayers: domain-scale reversal, the critical-current discontinuity at exchange-bias onset, and layer-resolved spin–charge conversion

The 2016 demonstration by Fukami, Zhang, DuttaGupta, Kurenkov and Ohno that an antiferromagnet/ferromagnet (AFM/FM) bilayer — antiferromagnetic PtMn with a perpendicular Co/Ni multilayer — both generates a spin–orbit torque (SOT) large enough to switch the FM magnetization and, through the exchange bias it exerts, enables deterministic field-free bipolar switching and memristor-like analogue control, left open three linked microscopic questions that remain only partially answered. This problem asks for a quantitative microscopic account of SOT-induced reversal in exchange-biased PtMn/FM perpendicular stacks: (i) how the stable multi-domain intermediate states and the analogue (memristive) Hall-resistance response arise from the granular exchange-bias landscape — where domains nucleate, why domain-wall propagation is arrested, and what fixes the domain length scale, which the authors' ~10 nm crystalline-grain hypothesis explains only qualitatively; (ii) why the zero-field critical current density $J_C^0$ changes discontinuously at the PtMn thickness (~7 nm) where exchange bias first appears, a behavior that macrospin switching theory cannot produce and for which no quantitative model exists; and (iii) a layer-resolved microscopic characterization of spin–charge conversion in the PtMn (spin Hall angle, spin diffusion length, and the separated Slonczewski-like and field-like torque contributions), whose literature values remain in tension (spin Hall angle ~0.1–0.24; apparent spin diffusion length 0.5 nm versus 2.3 nm). Later work has imaged the pinned, reproducible domain patterns (blocked domains, granular exchange-bias texture) and refined the torque magnitudes, but a predictive theory connecting the measured exchange-bias microstructure to domain dynamics, switching thresholds, and the analogue response is still missing.

Background

A current flowing in a heavy metal with strong spin–orbit coupling generates a transverse spin current, the spin Hall effect; the ratio of the generated transverse spin-current density to the driving charge-current density is the spin Hall angle $\theta_{\text{SH}}$. When such a layer is adjacent to a ferromagnet (FM), the injected spin current exerts spin–orbit torques (SOTs) on the FM magnetization — conventionally decomposed into a Slonczewski-like (damping-like) torque that acts like a field along $\mathbf{M}\times\hat{\mathbf{y}}$ and a field-like torque along $\hat{\mathbf{y}}$, where $\hat{\mathbf{y}}$ is transverse to the current. In nonmagnet/FM (NM/FM) bilayers with perpendicular magnetic anisotropy, SOT can reverse the out-of-plane magnetization, but deterministic bipolar switching normally needs an external in-plane magnetic field collinear with the current to break the reversal symmetry. A macrospin model, in which the magnetization of the whole device rotates coherently, predicts that the critical current density $J_C$ depends smoothly on the saturation magnetization, FM thickness, effective anisotropy field, and effective spin Hall angle.

An antiferromagnet (AFM) offers a second function: exchange bias. When a FM is exchange-coupled to an AFM whose order is set during field cooling or annealing, the FM hysteresis loop shifts by a bias field $H_{\text{bias}}$ — an internal, in-plane symmetry-breaking field that can substitute for the applied field. PtMn (an approximately equiatomic, L1$_0$-ordered — that is, with a layered tetragonal crystal structure — collinear antiferromagnetic metal) is polycrystalline with a fiber texture: the in-plane easy axes of its AFM grains are randomly oriented, and the exchange bias emerges only as a collective average of the grains.

Fukami et al. (Nature Materials 15, 535–541 (2016); preprint arXiv:1507.00888) showed that in PtMn/[Co/Ni] stacks with perpendicular easy axis, the spin Hall effect of the AFM itself produces a SOT large enough for switching, and the exchange bias enables bipolar switching at zero applied field with $J_C^0$ of order $10^{10}$ A m$^{-2}$, comparable to Pt- and Ta-based NM/FM devices; from this they inferred a positive spin Hall angle of order $+0.1$ for PtMn. They measured a combined (Slonczewski-like plus field-like) effective field of $7.8\pm0.5$ mT per $10^{11}$ A m$^{-2}$, and adopted a very short spin diffusion length ($0.5\pm0.1$ nm) from earlier spin-torque measurements on PtMn (Zhang et al., Phys. Rev. Lett. 113, 196602 (2014)) rather than measuring it in their own stacks. Three unexplained features marked the limits of their understanding.

First, in exchange-biased devices the Hall resistance $R_{\text{H}}$ (the out-of-plane readout of the net perpendicular magnetization) could be tuned continuously by the current-pulse amplitude — memristor-like analogue behavior useful for neuromorphic computing — implying stable intermediate multi-domain states. Magneto-optical Kerr microscopy with 1 μm resolution saw no domain pattern, so the domain period is below 1 μm, far smaller than the 1–10 μm expected from the Kaplan–Gehring model (the standard thin-film domain-period theory balancing domain-wall energy against magnetostatic energy). The authors stated that a thorough understanding of the multi-domain formation mechanism required further investigation, and offered only a qualitative hypothesis: reversal proceeds in units of crystalline grains (~10 nm), with domain walls unable to cross grain boundaries because neighboring AFM grains have different in-plane easy axes.

Second, $J_C^0$ changes discontinuously at $t_{\text{PtMn}}=7.0$ nm, exactly the thickness above which exchange bias appears, while the macrospin-model inputs (saturation magnetization, anisotropy field, and — given the short spin diffusion length — the effective spin Hall angle) are essentially independent of $t_{\text{PtMn}}$; the macrospin picture therefore fails, pointing instead to domain-level physics (nucleation versus domain-wall propagation) controlled by the exchange-bias microstructure.

Third, the spin Hall angle was only inferred from switching-threshold benchmarks, not measured independently in the layer-resolved manner available for NM/FM systems, and the damping-like and field-like contributions were reported only combined.

Later literature, reviewed below, has imaged the reversal directly and refined the torque numbers, establishing that the ferromagnetic domains are multi-grain rather than single ~10 nm grains, that reversal proceeds by domain-wall displacement from 'blocked' ferromagnetic regions (domains that never switch, up to ~24% of the area), and that the exchange-bias field is spatially granular with AFM domains below ~100 nm. What remains missing is the quantitative, predictive link from the measured exchange-bias and anisotropy distributions to the observed domain patterns, analogue response, and switching thresholds.

Problem Statement

Establish the microscopic mechanism of spin–orbit-torque-induced magnetization reversal in exchange-biased antiferromagnet/ferromagnet bilayers based on antiferromagnetic PtMn and a perpendicular ferromagnet (the Co/Ni multilayer system of Fukami et al., Nature Materials 15, 535 (2016)) — a quantitative, predictive account linking the PtMn exchange-bias microstructure to the observed switching behavior:

1. Domain-scale reversal and the memristive response. Determine experimentally and theoretically how the stable multi-domain intermediate states and the analogue (memristor-like) current-controlled Hall-resistance response arise: where reversed domains nucleate, why domain-wall propagation is arrested between regions with different exchange-bias directions, what fixes the observed sub-micrometer domain length scale (inconsistent with the Kaplan–Gehring thin-film domain-period expectation), and what the microscopic origin is of the 'blocked' ferromagnetic regions identified by later imaging; each of these four sub-questions is individually required. The experimental determination rests on quantitative re-analysis of the already-published imaging and transport data on these stacks rather than on new measurements. The source paper's ~10 nm crystalline-grain picture is a hypothesis requiring proof or correction; the account is to reproduce the measured domain patterns and the analogue $R_{\text{H}}(I)$ response from the measured grain-scale exchange-bias and anisotropy distributions.

2. Critical-current discontinuity at exchange-bias onset. Provide a quantitative explanation of the discontinuous change of the zero-field critical current density $J_C^0$ at the PtMn thickness ($t_{\text{PtMn}}\approx 7$ nm) where exchange bias first appears — a feature that macrospin switching theory, which predicts a smooth dependence on saturation magnetization, ferromagnet thickness, anisotropy field, and effective spin Hall angle, cannot produce. The explanation should specify how exchange-bias-induced grain-to-grain variations, pinning landscapes, and domain-wall energetics quantitatively alter the switching threshold, and should be predictive for stack and device design (including how thresholds scale when the exchange bias is engineered or partially switched by the current itself).

3. Layer-resolved spin–charge conversion. Characterize microscopically the spin–charge conversion in the PtMn/FM stacks: the spin Hall angle and its sign, the spin diffusion length in these stacks (reconciling the tension between the $0.5\pm0.1$ nm value adopted from earlier PtMn measurements and the ~2.3 nm apparent value reported with interface engineering), the layer-resolved generation of spin (and orbital) currents, and the separated Slonczewski-like and field-like torque contributions acting on the ferromagnet. Each listed quantity is required in its own right and must be determined for these stacks rather than inferred from other systems; this characterization is what underwrites a first-principles prediction of the item-2 switching thresholds.

References

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