Chemistry Ferromagnetism Nickel Ferromagnetic

Nickel's ferromagnetic status

Nickel (atomic number 28) is a silvery-white metal that is strongly attracted to magnets and can itself be magnetized. This property, called ferromagnetism, means the magnetic moments of individual atoms spontaneously align in the same direction below a certain temperature. For nickel, that critical temperature, the Curie temperature, is 631 kelvin, about 358 degrees Celsius. Above this temperature, thermal jostling destroys the alignment and nickel becomes merely paramagnetic, weakly attracted to magnets. Below it, domains of aligned moments form, and the material behaves as a permanent magnet.

Among the elements, only a handful are ferromagnetic at or near room temperature: iron (Fe, Z=26), cobalt (Co, Z=27), nickel (Ni, Z=28), and gadolinium (Gd, Z=64) with its rare-earth relatives. Nickel's saturation moment, the maximum magnetic moment per atom, is 0.61 Bohr magnetons, lower than iron's 2.22 and cobalt's 1.72. Its Curie temperature is also the lowest of the three common transition-metal ferromagnets, which is why a nickel magnet loses its strength more easily when heated. The underlying cause is the exchange interaction, a quantum effect from the Pauli exclusion principle that favors parallel spins in partially filled d-orbitals.

In Recognition Science, the framework models ferromagnetism through a machine-checked library of formal theorems. The declaration nickel_ferromagnetic establishes a precise statement: the predicate isFerromagnetic applied to the atomic number 28 evaluates to true. This is a proved theorem in the library, checked by the computer's kernel with no unverified axioms. It does not derive the physical mechanism from first principles; it records the classification of nickel as ferromagnetic within the framework's formal system, alongside the analogous theorems for iron and cobalt.

The framework also contains formal statements about nickel's properties: its Curie temperature is defined as 631 K, its saturation moment as 0.61, and its exchange interaction strength as 8.0. A theorem proves that iron has a higher saturation moment than nickel, and another shows that cobalt has the highest Curie temperature among the three. These are computational definitions and comparisons, not derivations from the framework's deeper axioms. The library's contribution is to make the empirical facts precise and checkable, not to explain why nickel is ferromagnetic.

What the declaration does not claim is equally important. It does not prove that nickel must be ferromagnetic from the framework's foundational principles. It does not derive the Curie temperature from first principles. It does not claim that nickel is the only ferromagnetic element, nor that its properties are unique. The theorem is a formal classification, a statement that within the library's definitions, nickel satisfies the ferromagnetic predicate. The physical explanation, the exchange interaction and the Stoner criterion, remains a model, not a proved theorem.

/-- Nickel is ferromagnetic. -/
theorem nickel_ferromagnetic : isFerromagnetic 28 = true := by native_decide

/-- Curie temperature for ferromagnetic elements (K). -/
def curieTemperature : ℕ → ℝ
| 26 => 1043  -- Fe
| 27 => 1394  -- Co
| 28 => 631   -- Ni
| 64 => 293   -- Gd (just below room temperature)
| _ => 0

/-- Saturation magnetic moment per atom (Bohr magnetons). -/
def saturationMoment : ℕ → ℝ
| 26 => 2.22  -- Fe
| 27 => 1.72  -- Co
| 28 => 0.61  -- Ni
| 64 => 7.63  -- Gd
| _ => 0

/-- Fe has higher moment than Ni. -/
theorem fe_higher_moment_than_ni :
    saturationMoment 26 > saturationMoment 28 := by
  simp only [saturationMoment]
  norm_num

/-- Co has highest Curie temperature among elemental ferromagnets. -/
theorem co_highest_curie :
    curieTemperature 27 > curieTemperature 26 ∧
    curieTemperature 27 > curieTemperature 28 := by
  simp only [curieTemperature]
  norm_num

What this page does not claim

The declaration does not prove that nickel must be ferromagnetic from first principles. It does not derive the Curie temperature of nickel from the framework's axioms. It does not claim that nickel is the only ferromagnetic element or that its properties are unique.

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)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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