Add native interlayer DMI (ext_InterlayerDMI)

[SanthoshSivasubramani]

Add native interlayer DMI (ext_InterlayerDMI)

This adds a native interlayer Dzyaloshinskii–Moriya interaction (chiral
interlayer coupling) as an effective-field term, in the same style as the
ext_RKKY interlayer-exchange term. It is the interlayer analogue of the
intralayer interfacial DMI already in mumax3.

Physics

For two magnetic regions coupled across a (possibly nonmagnetic) spacer, the
interlayer-DMI energy is

E = D * ẑ · (m1 × m2) * A          (areal, D in J/m^2)

whose exact variational-derivative effective fields are

B1 = +(D / (Msat·dz)) · (ẑ × m2)
B2 = −(D / (Msat·dz)) · (ẑ × m1)

i.e. an antisymmetric pair (the sign follows the stacking order). The kernel
follows the ext_RKKY convention 1/Msat (no explicit µ0), and locates the
partner cell by scanning the z-column, so the coupling spans a spacer gap
between the layers rather than only coupling immediately-adjacent cells.

API

ext_InterlayerDMI(region1, region2, D)   // D in J/m^2

May be called multiple times to couple several region pairs. Exposes a
B_idmi vector output. Integrated into SetEffectiveField (self-guards to a
no-op when no pair is defined).

Validation (NVIDIA L4, CUDA 12.3)

Both regression tests pass, matching the analytic field to 6 significant
figures:

test	region 100	region 101
test/idmi.mx3 (adjacent)	(2.22222, 0, 0) ✓	(0, 2.22222, 0) ✓
test/idmi_gap.mx3 (across a spacer)	(2.22222, 0, 0) ✓	(0, 2.22222, 0) ✓

with D = −2e−3 J/m², Msat = 1e6 A/m, dz = 0.9e−9 m → |D/(Msat·dz)| = 2.22222 T. The antisymmetry (region 100 → +x, region 101 → +y) confirms the
chiral form, and the gap test confirms the z-column partner scan.

The CUDA wrapper is generated with cuda2go for the full compute-capability
set (50 52 53 60 61 62 70 72 75 80 86 87 89 90). Code is gofmt-clean.

Files

• cuda/idmi.cu — kernel (addidmi)
• cuda/idmi.go, cuda/idmi_wrapper.go — host wrapper (cuda2go-generated)
• engine/idmi.go — ext_InterlayerDMI API + B_idmi field term
• engine/effectivefield.go — one line: AddInterlayerDMIField(dst)
• test/idmi.mx3, test/idmi_gap.mx3 — regression tests

Follows the same structure as the ext_RKKY PR. Happy to adapt to your
conventions.

[Copilot]

Pull request overview

Adds a native interlayer Dzyaloshinskii–Moriya interaction effective-field term (ext_InterlayerDMI) to the engine, implemented with a CUDA kernel and exposed as a B_idmi output for validation and analysis.

Changes:

• Introduces the ext_InterlayerDMI(region1, region2, D) API and B_idmi vector output in the engine.
• Adds a CUDA kernel + Go host wrapper to compute and accumulate the interlayer-DMI field, including z-column partner scanning across spacer gaps.
• Adds two regression tests covering adjacent layers and coupling across a nonmagnetic spacer.

Reviewed changes

Copilot reviewed 7 out of 7 changed files in this pull request and generated 2 comments.

Show a summary per file

File	Description
test/idmi.mx3	Regression test for adjacent-layer interlayer DMI field magnitude/sign.
test/idmi_gap.mx3	Regression test ensuring partner scan spans a spacer gap correctly.
engine/idmi.go	New engine-side API/storage and field adder wired into B_idmi.
engine/effectivefield.go	Integrates interlayer-DMI contribution into the effective field pipeline.
cuda/idmi.go	Go-side CUDA invocation wrapper for the addidmi kernel.
cuda/idmi.cu	CUDA kernel implementing z-column partner search and field accumulation.
cuda/idmi_wrapper.go	cuda2go-generated wrapper/PTX blobs for the new kernel.

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[SanthoshSivasubramani]

Thanks for the review — pushed 96c184e addressing the comments:

• Interface-only coupling. The areal interlayer-DMI field is now applied only at the interface cell, so it is independent of layer thickness. Added test/idmi_thick.mx3 (2-cell layers) asserting the layer-averaged field halves and E_idmi is thickness-independent.
• Region-id validation. ext_InterlayerDMI now validates both ids via defRegionId.
• Duplicate pairs. Re-calling for the same region pair now overwrites instead of appending.
• Energy. Registered E_idmi / Edens_idmi. The field is the exact variational derivative of the bilinear energy E = D·A·ẑ·(m1×m2), so the standard -1/2 M·B density is exact.

On the O(Nz) z-column scan: kept intentionally so the coupling can span a spacer gap; Nz is small for layered stacks.

Validated on an NVIDIA L4 (CUDA 12.3): all tests pass.