Electrodynamics in Iron and Steel

TL;DR

This paper investigates the complex electrodynamics of iron and steel, revealing new dispersion curves and phenomena like Bose-Einstein-like condensation in spin waves, challenging classical models and enhancing understanding of ferromagnetic materials.

Contribution

It introduces novel dispersion curves for spin waves in iron and steel, demonstrating phenomena like Bose-Einstein-like condensation driven by weak electromagnetic fields.

Findings

Discovery of an extremely small effective mass for spin waves

Identification of a dispersion curve related to bound states

Observation of magneto-elastic coupling in long wavelength modes

Abstract

In order to calculate the reflected EM fields at low amplitudes in iron and steel, more must be understood about the nature of long wavelength excitations in these metals. A bulk piece of iron is a very complex material with microstructure, a split band structure, magnetic domains and crystallographic textures that affect domain orientation. Probing iron and other bulk ferromagnetic materials with weak reflected and transmitted inductive low frequency fields is an easy operation to perform but the responses are difficult to interpret because of the complexity and variety of the structures affected by the fields. First starting with a simple single coil induction measurement and classical EM calculation to show the error is grossly under estimating the measured response. Extending this experiment to measuring the transmission of the induced fields allows the extraction of three dispersion curves which define these internal fields. One dispersion curve yielded an exceedingly small effective mass of 1.8 10^{-39}kg (1.3 10^{-9} m_e) for those spin waves. There is a second distinct dispersion curve more representative of the density function of a zero momentum bound state rather than a propagating wave. The third dispersion curve describes a magneto-elastic coupling to a very long wave length propagating mode. These experiments taken together display the characteristics of a high temperature Bose-Einstein like condensation that can be initiated by pumping two different states. A weak time dependent field drives the formation of coupled J=0 spin wave pairs with the reduced effective mass reflecting the increased size of the coherent state. These field can dominate induction measurements well past the Curie temperature.