Shape of temperature dependence of spontaneous magnetization of various ferromagnets

TL;DR

This study analyzed the temperature dependence of spontaneous magnetization in about forty ferromagnets, fitting data with superellipse equations to understand the shape and coupling effects.

Contribution

It introduces a method using superellipse fits to characterize magnetization curves and explores the relationship between squareness and Curie temperature across various materials.

Findings

Good fit of superellipse equations with experimental data for most materials.

Squareness parameter varies from 1.4 to 3.0, reflecting coupling strength.

In metallic alloys, squareness generally increases with Curie temperature.

Abstract

The shape of temperature dependence of spontaneous magnetization was analyzed on about forty ferromagnetic materials. The shape squareness was determined from the magnetization curves fits by the superellipse equation (Lame curve). The agreement of Lame curve fits with experimental data was good for most materials. The squareness parameter (the power coefficient in the superellipse equation), which reflects coupling strength between the nuclei vibrations and magnetic moments of electrons, was in the range from 1.4 to 3.0. The largest squareness showed iron, the smallest - antiferromagnetic materials and the Ni55Cu45 alloy. The squareness parameter was studied as a function of the Curie temperature, Tc. For metallic alloys the general tendency was observed - squareness increases with the Curie temperature increase. The only exception was cobalt that showed the same magnetization curve in the reduced coordinates as nickel despite of two times higher TC. Addition to iron or nickel either ferromagnetic or nonferromagnetic metals leads to the decrease of the squareness. No influence of the thermal expansion coefficient on the magnetization curve was observed - the zero-expansion invar have a standard shape following the Lame curve.