Origin of spontaneous magnetization in ferromagnets The observation that ferromagnetic materials consist of domains which exhibit spontaneous magnetization corresponds to which classical hypothesis?

Introduction / Context:
Ferromagnetism arises from exchange interactions causing parallel spin alignment below the Curie temperature. Historically, Pierre Weiss proposed hypotheses to explain ferromagnetic behavior, including the presence of domains that are spontaneously magnetized even without an external field. Recognizing which hypothesis addresses domains is essential for foundational magnetism knowledge.

Given Data / Assumptions:

• Classical (pre-quantum) framework describing ferromagnets.
• Weiss’s ideas: molecular field concept and domain theory.
• Spontaneous magnetization observed experimentally.

Concept / Approach:

Weiss advanced two related ideas. The first hypothesis (molecular or internal field) explains cooperative alignment. The second hypothesis asserts that ferromagnets are divided into many small regions (domains), each spontaneously magnetized to saturation. Macroscopic magnetization is the vector sum over domains; in zero external field, domains are randomly oriented, yielding near-zero net magnetization despite spontaneous magnetization within each domain.

Step-by-Step Reasoning:

Verification / Alternative check:

Standard magnetism texts describe: (1) molecular field hypothesis; (2) domain hypothesis (spontaneous magnetization in domains). Curie–Weiss law instead relates susceptibility and temperature above the Curie point; Boltzmann statistics is a general thermodynamic framework, not a specific ferromagnetic domain postulate.

Why Other Options Are Wrong:

• First hypothesis of Curie: Curie did not propose a domain hypothesis; he studied temperature dependence of magnetization.
• Curie–Weiss law: a susceptibility–temperature relation for paramagnetic region, not domain structure.
• Boltzmann statistics: general theory, not specific to domains.
• First hypothesis of Weiss: deals with molecular field, not the explicit domain picture.

Common Pitfalls:

Confusing Weiss’s two hypotheses or mixing up Curie–Weiss law (paramagnetic regime) with domain theory (ferromagnetic regime below Tc).

Final Answer:

Second hypothesis of Weiss