Determination of intrinsic switching field distributions in perpendicular recording media: numerical study of the $\Delta H(M, \Delta M)$ method

TL;DR

This study numerically evaluates the $ riangle H(M, riangle M)$ method for determining intrinsic switching field distributions in magnetic media, highlighting its accuracy for weak interactions and failure under strong inter-granular coupling.

Contribution

It demonstrates the conditions under which the $ riangle H(M, riangle M)$ method accurately estimates switching fields and identifies its limitations when interactions are strong.

Findings

Accurate for small ferromagnetic interactions ($J/\sigma$).

Fails when exchange interactions are comparable to intrinsic field distribution width.

Failure correlates with deviations from data set redundancy.

Abstract

We present a numerical study of the $\Delta H(M,\Delta M)$ method and its ability to accurately determine intrinsic switching field distributions in interacting granular magnetic materials such as perpendicular recording media. In particular, we study how this methodology fails for large ferromagnetic inter-granular interactions, at which point the associated strongly correlated magnetization reversal cannot be properly represented by the mean-field approximation, upon which the $\Delta H(M,\Delta M)$ method is based. In this study, we use a 2-dimensional array of symmetric hysterons that have an intrinsic switching field distribution of standard deviation $\sigma$ and ferromagnetic nearest-neighbor interactions $J$. We find the $\Delta H(M,\Delta M)$ method to be very accurate for small $J/\sigma$ values, while substantial errors develop once the effective exchange field becomes comparable with $\sigma$, corroborating earlier results from micromagnetic simulations. We furthermore demonstrate that this failure is correlated with deviations from data set redundancy, which is a key property of the mean-field approximation. Thus, the $\Delta H(M,\Delta M)$ method fails in a well defined and quantifiable manner that can be easily assessed from the data sets alone.