Zeeman field¶

Problem statement¶

The Zeeman vector is authored in tesla and serialized as a three-component value.

This page documents the public Python authoring boundary, not an undocumented runtime promise. Construction creates typed authoring data, while to_ir() is the object-level lowering boundary consumed by the study/script pipeline.

Governing equations¶

The physical term or constraint is represented by the canonical IR object zeeman. The exact discrete operator, quadrature, mesh treatment, and solver selection are backend responsibilities; this page does not replace their qualification evidence.

Symbols and SI units¶

All dimensional inputs are documented in SI units. Vector quantities use Cartesian components in the repository coordinate convention. Dimensionless parameters are explicitly marked 1; a default of None means that the constructor selects or omits the field according to the contract.

Assumptions and validity¶

Inputs are finite and typed. Positive lengths, densities, conductivities, temperatures, and material constants are rejected when the source constructor requires positivity. Unsupported combinations fail closed in the constructor or lowering boundary rather than being silently converted.

Python API¶

# %%
import fullmag as fm

study = fm.study("public-api-example")
study.objects.mesh.defaults(maximum_element_size=5e-9)
body = study.geometry(fm.Box(size=(100e-9, 20e-9, 5e-9)), name="film")
body.Ms = 800.0e3
body.Aex = 13.0e-12
body.alpha = 0.02
body.m = fm.texture.uniform(1.0, 0.0, 0.0)
study.stages.add_relax(stage_id="api-example", dt=5e-13, max_steps=1)
# Author the documented object after the stage exists.
value = fm.Zeeman(B=(0.0, 0.0, 1.0e-3))
canonical_ir = value.to_ir()

ProblemIR¶

value.to_ir() is the canonical serialization boundary. It emits a typed zeeman record with the fields listed above; nested geometry, targets, profiles, or material references remain nested typed records rather than opaque Python objects. The IR is the requested intent. Backend resolution must preserve the record or reject an unsupported combination.

Round-trip and failure semantics¶

The requested intent is preserved before resolved execution. Validation errors identify invalid inputs, while unsupported combinations are rejected.

A supported record is expected to round-trip through the repository script/scene representation without changing qualified values, units, or identifiers. Invalid types, missing required fields, non-finite values, contradictory options, and unsupported backend combinations are rejected with an explicit validation error. This page makes no claim that every backend accepts every legal authoring object.

Discrete realization¶

The FEM/FDM realization selects its own mesh, stencil or element operator, boundary treatment, and CPU/GPU execution lane. The Python contract supplies the physical inputs and canonical IR only; numerical equivalence requires the backend-specific validation named below.

Implementation mapping¶

The authoritative implementation is packages/fullmag-py/src/fullmag/model/energy.py symbol class Zeeman. The public constructor signature, validation branches, defaults, and to_ir() field names are derived from that source, not from a historical example.

Validation¶

Focused repository tests covering this contract include: test_zeeman_serializes_vector_to_ir. These tests are evidence for authoring/IR behavior; live runtime, device performance, and Control Room browser behavior require separate qualification.

Limitations and Control Room¶

Control Room route: no dedicated route is claimed for this low-level authoring object. It is observable only through a session/problem/field view when the owning module exposes it; a dedicated object editor or route is not currently exposed. No unsupported UI or runtime capability is implied.

Scientific bibliography¶

• W. F. Brown, Jr., Thermal Fluctuations of a Single-Domain Particle, Phys. Rev. 130 (1963), DOI: https://doi.org/10.1103/PhysRev.130.1677

Source code index¶

• Implementation: packages/fullmag-py/src/fullmag/model/energy.py::class Zeeman

• Source-map: interactions/zeeman.source-map.json

• Contract status: current constructor and to_ir() boundary documented against revision ab3c8802a691a535063102c12f9a79bb0043b367.