Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The effect of demagnetization on the susceptibility of single-domain particles and assemblies

Mathias Zambach, Miriam Varón, Mads R. Almind, Matti Knaapila, Ziwei Ouyang, Marco Beleggia, Cathrine Frandsen

Abstract

According to the classical laws of magnetism, the shape of magnetically soft objects limits the effective susceptibility. For example, spherical soft magnets cannot display an effective susceptibility larger than 3. Although this is true for macroscopic multi-domain magnetic materials, we explain why magnetic nanoparticles in a single-domain state do not suffer from this limitation. For single-domain particles, the differences between demagnetization factors along principal axes are relevant and can influence susceptibility but do not limit the susceptibility to an upper value as in the case for multi-domain particles. We experimentally validated this result on spherical nanoparticles with varying diameter (9 to 150 nm) and varying volume fraction (0.1 to 47 vol%). In agreement with our predictions, we measure single-domain particle susceptibilities largely above 3, in fact up to more than 250. Moreover, contrary to an existing model for assemblies of particles, we find that the susceptibility of materials composed of non-interacting single-domain particles in a non-magnetic matrix scales linearly with the volume fraction of particles. This implies that high susceptibilities (>100) are achievable for nanoparticle-based composites and is relevant for the design of magnetically soft materials that are operational at MHz-GHz frequencies with negligible power losses.

The effect of demagnetization on the susceptibility of single-domain particles and assemblies

Abstract

According to the classical laws of magnetism, the shape of magnetically soft objects limits the effective susceptibility. For example, spherical soft magnets cannot display an effective susceptibility larger than 3. Although this is true for macroscopic multi-domain magnetic materials, we explain why magnetic nanoparticles in a single-domain state do not suffer from this limitation. For single-domain particles, the differences between demagnetization factors along principal axes are relevant and can influence susceptibility but do not limit the susceptibility to an upper value as in the case for multi-domain particles. We experimentally validated this result on spherical nanoparticles with varying diameter (9 to 150 nm) and varying volume fraction (0.1 to 47 vol%). In agreement with our predictions, we measure single-domain particle susceptibilities largely above 3, in fact up to more than 250. Moreover, contrary to an existing model for assemblies of particles, we find that the susceptibility of materials composed of non-interacting single-domain particles in a non-magnetic matrix scales linearly with the volume fraction of particles. This implies that high susceptibilities (>100) are achievable for nanoparticle-based composites and is relevant for the design of magnetically soft materials that are operational at MHz-GHz frequencies with negligible power losses.

Paper Structure

This paper contains 3 sections, 17 equations, 2 figures.

Table of Contents

  1. Supplementary Material
  2. Data Availability Statement
  3. References

Figures (2)

  • Figure 1: Initial particle susceptibility and coercive field of fcc Co particles of varying size on Al$_2$O$_3$ support at 200 ° C after full reduction at 900 ° C. The 9 nm particles were measured at room-temperature (RT) and $\chi$ was corrected as 1/$T$ to 200 ° C (indicated by *).
  • Figure 2: Susceptibility of nanocomposites containing randomly oriented 11$\pm$3 nm diameter $\gamma$-Fe$_2$O$_3$ particles as function of particle volume together with theoretic prediction. $\chi_{\textrm{nc,eff}}$ (open circles) is the measured nanocomposite susceptibility and $\chi_{\textrm{nc}}$ (solid squares) is the measured susceptibility corrected for the sample shape as in Eq. \ref{['eq:chi-ns-eff']}. Theoretic prediction based on Eqs. \ref{['eq:ChiRandom']}-\ref{['eq:LinearChi']}, with log-normal size distribution, $M_\textrm{s}=303$ kA/m, and $T=25$ ° C.