Chemistry Ferromagnetism Ferromagnets Are 3d Metals

The 3d metals claim

Ferromagnetism is the mechanism by which certain materials, such as iron, cobalt, and nickel, form permanent magnets and are attracted to magnets. It arises from the spontaneous alignment of atomic magnetic moments. In the framework's machine-checked library of formal theorems, a declaration named ferromagnets_are_3d_metals establishes a precise, narrow fact: the atomic numbers 26, 27, and 28, which correspond to iron, cobalt, and nickel, are all members of the framework's list of ferromagnetic elements. The theorem is proved by direct computation, using the definition of that list, which explicitly contains only these three numbers.

The declaration does not claim that these are the only ferromagnetic elements in nature. The same library separately defines a list of rare-earth ferromagnets, including gadolinium (atomic number 64), terbium (65), and dysprosium (66). The theorem about 3d metals is silent about these elements; it merely asserts membership for the three transition metals. It also does not claim that all 3d metals are ferromagnetic. Copper (29) and zinc (30), for instance, are 3d metals but are not on the ferromagnetic list, and the theorem does not address them.

The framework's broader account of ferromagnetism, as described in its documentation, proposes a mechanism: the exchange interaction arising from the Pauli exclusion principle, the 8-tick coherence of d-orbital degeneracy, and the Stoner criterion for the onset of ferromagnetism. The library includes definitions and theorems about these concepts, such as a Stoner criterion check for iron and a theorem that its exchange interaction is positive. But the declaration ferromagnets_are_3d_metals itself is only a membership assertion; it does not prove the mechanism, nor does it derive the list from first principles.

What the theorem does provide is a compact, verified record that the framework's model of ferromagnetism includes these three elements as its canonical examples. It is a formal anchor for the empirical fact that iron, cobalt, and nickel are ferromagnetic, expressed in the framework's own terms. The declaration does not predict new ferromagnetic materials, does not explain the values of Curie temperatures, and does not establish that the framework's mechanism is physically correct. It simply states, in machine-checkable form, that these three metals are on the list.

/-- Fe, Co, Ni are all 3d transition metals with Z = 26, 27, 28.
    The 8-tick manifests in their electron configuration: [Ar] 3d^n 4s^2. -/
theorem ferromagnets_are_3d_metals :
    26 ∈ ferromagneticElements ∧ 27 ∈ ferromagneticElements ∧ 28 ∈ ferromagneticElements := by
  simp only [ferromagneticElements]
  decide

/-- Rare earth ferromagnets. -/
def rareEarthFerromagnets : List ℕ := [64, 65, 66]  -- Gd, Tb, Dy

What this page does not claim

The theorem does not claim that iron, cobalt, and nickel are the only ferromagnetic elements. The theorem does not claim that all 3d metals are ferromagnetic. The theorem does not derive the ferromagnetic mechanism or explain why these metals are ferromagnetic.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Chemistry/Ferromagnetism.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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