Inter-region couplings¶

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¶

For opposing surfaces,

With this sign convention, positive \(J_1\) favors parallel alignment. The sign and magnitude of \(J_2\) control whether collinear or canted configurations are favored and must be interpreted from the full polynomial.

For adjacent material regions, the default exchange link is

An explicit mode uses authored \(A_{ab}\); a disabled mode sets the link to zero. This cell-link operator is not the same as a surface energy.

Symbols and SI units¶

Capability matrix¶

Front matter must therefore be partial, not implemented.

Python API and stage-first example¶

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

nm = 1.0e-9
study = fm.study("region_exchange_reference")
study.engine("fdm")
study.device("cuda", 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)

left = body.add_region("left", fm.Box(20 * nm, 20 * nm, 4 * nm).translate((-10 * nm, 0.0, 0.0)))
right = body.add_region("right", fm.Box(20 * nm, 20 * nm, 4 * nm).translate((10 * nm, 0.0, 0.0)))
study.couplings.exchange(source=left, target=right, mode="explicit", inter_exchange=13.0e-12)
study.stages.add_relax(stage_id="relax", algorithm="llg_overdamped", dt=5.0e-13, max_steps=500, tolT=1.0e-6)

The two region shapes are explicitly displaced; overlapping identical boxes must not be presented as a left/right partition.

ProblemIR¶

{
  "coupling_id": "exchange:bilayer_left:bilayer_right",
  "kind": "exchange",
  "source": {"kind": "region", "object": "bilayer", "region_id": "bilayer:left"},
  "target": {"kind": "region", "object": "bilayer", "region_id": "bilayer:right"},
  "enabled": true,
  "parameters": {
    "kind": "exchange",
    "mode": "explicit",
    "inter_exchange": 1.3e-11
  },
  "capability_policy": "require_runtime"
}

Validation boundary and source-map correction¶

Python owns endpoint kind, selector names, mode/policy enums, and scalar consistency. Planner owns resolved region IDs, material coefficients, backend capability, and link materialization. coupling_id should be validated in __post_init__, not delayed until to_ir().

The current source map has an empty public constructor/parameter inventory despite a substantial public table. Regenerate it from the actual CouplingRegistry API and current audited revision.

Required numerical validation¶

• parallel/antiparallel/canted energy ordering for \(J_1,J_2\);

• derivative of surface energy versus torque/field;

• disabled-link exact decoupling;

• harmonic versus explicit region-link coefficients;

• interface and surface-area convergence;

• endpoint orientation and face-pair symmetry;

• strict rejection on all unsupported lanes;

• future CPU reference before GPU-only surface coupling is promoted.

Limitations and roadmap¶

RKKY and interlayer exchange are presently representable, not executable. Future FEM support must define trace spaces, face pairing, quadrature, normal orientation, energy reduction, and mesh convergence. Curved contacts and spacer-mediated transport need separate typed geometry/physics contracts.

Scientific bibliography¶

1. P. Grünberg et al., Physical Review Letters 57, 2442 (1986).

2. S. S. P. Parkin, N. More, and K. P. Roche, Physical Review Letters 64, 2304 (1990).

3. NIST reference material on interlayer exchange coupling benchmarks.

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¶