Spin-transfer torque¶

Physical problem¶

This page is the public physical and authoring contract for the interaction. It separates authored semantics, planner resolution, executable backend lanes, and scientific qualification.

Governing equations¶

Slonczewski CPP/MTJ torque¶

For spin-polarization direction \(\hat{\mathbf p}\),

The canonical model uses a signed normal current density, an oriented stack normal, target \(M_s\), and either a free-layer thickness or an explicitly resolved interface realization. The angular efficiency is a named formula version based on polarization and asymmetry parameters. Current sign, stack-normal orientation, and fixed-layer polarization must remain independent authored quantities.

Zhang–Li CIP torque¶

For conventional current density \(\mathbf J_c\),

and

The exact sign is tied to conventional current, positive elementary charge \(e\), and the Fullmag LLG convention. Documentation must not switch to electron-flow language mid-equation.

Symbols and SI units¶

Capability matrix¶

The exact result depends on formula version (legacy versus canonical), target kind, current source, and realization.

Python API and stage-first example¶

# %% Study, execution lane, and magnetic body
import fullmag as fm

nm = 1.0e-9
study = fm.study("slonczewski_reference")
study.engine("fdm")
study.device("cpu", precision="double")
study.mode("strict")
study.objects.mesh.defaults(cell_size=(2 * nm, 2 * nm, 2 * nm))
body = study.geometry(fm.Box(40 * nm, 20 * nm, 4 * nm), name="film")
body.Ms = 8.0e5
body.Aex = 13.0e-12
body.alpha = 0.02
body.m = fm.texture.uniform(1.0, 0.0, 0.0)

stt = fm.SlonczewskiSTT(
    current_density=(0.0, 0.0, 5.0e10),
    spin_polarization=(0.0, 0.0, 1.0),
    degree=0.4,
    lambda_asymmetry=1.0,
    epsilon_prime=0.0,
    free_layer_thickness_m=4 * nm,
)
study.spin_torque(stt)
study.stages.add_run(stage_id="drive", until=1.0e-12)

The previous public API example used non-existent parameters (polarization, efficiency, direction_fixed, interface_inPlane), passed a scalar where a three-vector was required, and declared no stage. The actual compatibility constructors are documented by the parameter tables below.

At the audited revision, these cells prove constructor and lowering semantics only. Do not claim a complete executable stage unless the selected study facade, planner, target, formula version, and current-source route are all registered and accepted. A normal stage shell without an attached torque is not an STT example.

Constructor parameters¶

ProblemIR and provenance¶

The IR must preserve:

• kind and formula_version;

• legacy versus canonical semantics;

• signed current source and its identity;

• target and stack/interface orientation;

• thickness/interface realization;

• all polarization/asymmetry parameters.

Canonical export must not erase a legacy formula version or silently upgrade it.

Validation requirements¶

Python validation should reject non-finite vectors/scalars, zero polarization direction, invalid degree/asymmetry domains, conflicting current sources, incomplete canonical identity, invalid target, and missing realization. Planner validation additionally owns mesh derivatives, target materialization, source availability, backend/device support, and current-field cardinality.

Required numerical validation¶

• zero-current and zero-polarization limits;

• odd current scaling and exact sign reversal;

• \(\mathbf m\parallel\hat{\mathbf p}\) zero damping-like torque;

• finite-difference/analytic single-cell torque oracles;

• Zhang–Li translation of a one-dimensional wall;

• μMAG Standard Problem 5 with fully declared convention;

• source-bound versus prescribed-current equivalence;

• CPU/GPU trajectories with matched timestep, precision, and formula version;

• proof that Gilbert conversion is applied exactly once.

Limitations and extensions¶

The local Slonczewski model does not solve tunnelling, spin accumulation, backflow, heating, or bias-dependent polarization. Zhang–Li is a diffusive adiabatic/non-adiabatic local model. Solved drift–diffusion torque is documented separately and must not be replaced by fitted local coefficients.

Scientific bibliography¶

1. J. C. Slonczewski, Journal of Magnetism and Magnetic Materials 159, L1–L7 (1996), DOI: 10.1016/0304-8853(96)00062-5.

2. S. Zhang and Z. Li, Physical Review Letters 93, 127204 (2004), DOI: 10.1103/PhysRevLett.93.127204.

3. NIST μMAG Standard Problem 5.

Control Room crosswalk¶

This is a navigation page; the selected interaction or foundation is configured by its linked Python API and object/stage editor. The category itself has no standalone control. frontend support is not implemented applies to physical parameters without a matching control. See {doc}/frontend/capability-register; do not infer UI support from backend or Python availability.

Python/API crosswalk¶

The linked Python API page is authoritative for exact functions, arguments, units, and failure semantics. If this page is a foundation or category overview, runnable Python is ot applicable here and must be taken from the terminal API page.

Bibliography and source scope¶

Use the scientific bibliography and source-code index on the linked terminal page. This block adds no new equation or unverified implementation claim.

Round-trip and failure semantics¶

Requested intent preserves the authored model, coefficients, orientations, targets, and execution request. Resolved execution records the selected solver, device, precision, discretization, and capability decision. Validation errors reject malformed or contradictory data before runtime. Unsupported combinations fail closed and are not silently omitted or converted to another interaction.

Assumptions and validity¶

The authored model is valid only within the continuum, discretization, boundary, and capability limits stated on this page.

Implementation mapping¶

Python owns authoring and serialization, ProblemIR owns canonical intent, planners own legality and realization selection, and backend kernels own numerical evaluation.

Source-code index¶