A theory of ferromagnetism by Ettore Majorana

TL;DR

This paper explores an early, lesser-known theory of ferromagnetism by Ettore Majorana from the 1930s, which offers a different mathematical approach and makes unique predictions about the conditions for ferromagnetism.

Contribution

It introduces a novel theoretical framework for ferromagnetism developed by Majorana, distinct from Heisenberg's approach, including specific predictions about neighbor interactions.

Findings

Successfully describes main features of ferromagnetism

Predicts the number of nearest neighbors needed for ferromagnetism

Provides applications to linear and triangular chains

Abstract

We present and analyze in detail an unknown theory of ferromagnetism developed by Ettore Majorana as early as the beginnings of 1930s, substantially different in the methods employed from the well-known Heisenberg theory of 1928 (and from later formulations by Bloch and others). Similarly to this, however, it describes successfully the main features of ferromagnetism, although the key equation for the spontaneous mean magnetization and the expression for the Curie temperature are different from those deduced in the Heisenberg theory (and in the original phenomenological Weiss theory). The theory presented here contains also a peculiar prediction for the number of nearest neighbors required to realize ferromagnetism, which avoids the corresponding arbitrary assumption made by Heisenberg on the basis of known (at that time) experimental observations. Some applications of the theory (linear chain, triangular chain, etc.) are, as well, considered.