# Scaled demagnetization models: susceptibility, resonant and relaxation frequency prediction compared to magnetic composite measurements

## TL;DR

This study evaluates various scaled effective medium models for predicting magnetic susceptibility, resonant, and relaxation frequencies in polymer-magnetic composites, demonstrating improved accuracy over classical models across a wide range of susceptibilities.

## Contribution

The paper introduces modifications to BEMT and ScEMT for low volume fractions and compares these models to measurements, showing enhanced predictive capabilities for magnetic properties.

## Key findings

- ScEMT predictions align well with measurements for susceptibility and resonant frequency.
- Modified Schlomann models best predict relaxation frequency across various susceptibilities.
- Classical models like CMA and MGT are less accurate at high susceptibilities.

## Abstract

Maxwell-Garnett Theory (MGT), Bruggeman Effective Medium Theory (BEMT), Coherent Model Approximation (CMA), Scaled Effective Medium Theory (ScEMT) and models of Schlomann (E. Schlomann, Phys. Rev. B, 182, 7, 632 (10 June 1969) and E. Schlomann, Conf. on Mag. and Mag. Materials, AIEE Spec. Publ. T-91, 600 (1956)) are applied to predict magnetic susceptibility, resonant and relaxation frequency in polymer-magnetic particle composites. Particulates had aspect ratios near unity; bulk low frequency susceptibilities ranging from approximately 5 to 4000 and particle volume fractions between 1 and 100%. Previous publications demonstrated that ScEMT improved the prediction of DC susceptibility as compared to classical models. This paper first modifies BEMT and ScEMT for volume fractions below about 10%. A ScEMT based model of composite resonant frequency is presented and compared to MGT, CMA models and measurement. Model and measurement comparisons of resonant frequency are followed by model-measurement comparisons of relaxation frequency. CMA, MGT, models of Schlomann, and volumetric scaled modifications of Schlomann are tested in the relaxation frequency study. The paper emphasizes the broad application of the models and therefore composite data for a wide range of particulate chemistries are presented ScEMT predictions of susceptibility and resonant frequency continue to show reasonable agreement with measurement and represent improvement over the CMA and MGT models. ScEMT modifications to Schlomann show overall best agreement with relaxation frequency measurement. CMA and MGT are most accurate for modest susceptibility (~ < 100) while ScEMT modified Schlomann models are most accurate for large susceptibility.

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Source: https://tomesphere.com/paper/1908.00603