Avoiding the zero-coercivity anomaly in first order reversal curves: FORC+

P B Visscher

doi:10.1063/1.5080101

Abstract

In conventional FORC (First Order Reversal Curve) analysis of a magnetic system, reversible and low-coercivity irreversible materials are treated as being qualitatively different: the FORC distribution shows low-coercivity materials but completely hides reversible (zero-coercivity) ones. This distinction is artificial – as the coercivity approaches zero, the physical properties of an irreversible material change smoothly into those of a reversible material. We have developed a method (called FORC+, implemented in free software at http://MagVis.org) for displaying the reversible properties of a system (a reversible switching-field distribution, R-SFD) together with the irreversible ones (the usual FORC distribution), so that there is no sudden discontinuity in the display when the coercivity becomes zero. We will define a “FORC+ dataset” to include the usual FORC distribution, the R-SFD, the saturation magnetization, and what we will call the “lost hysteron distribution” (LHD) such that no information is lost – the original FORC curves can be exactly recovered from the FORC+ dataset. We also give an example of the application of FORC+ to real data – it uses a novel complementary-color display that minimizes the need for smoothing. In systems which switch suddenly (thus having sharp structures in the FORC distribution) direct display of un-smoothed raw data allows visualization of sharp structures that would be washed out in a conventional smoothed FORC display.

Highlights

The FORC method1–4 for the characterization of magnetic systems has come into wide use in the past 15 years or so
The fundamental result behind the FORC idea is that this Preisach distribution can be obtained by measuring “first order reversal curves” – that is, by saturating the sample in the positive direction, decreasing the field to a reversal field HR, reversing dH/dt from negative to positive and measuring the magnetization m(H, HR) as the field increases again past each value H
The FORC distribution is repeated on the lower right, but rotated by 45○ so the coercivity axis is vertical. This is done so the reversible switching-field distribution (R-SFD) can be plotted upward as a bar graph, starting from scitation.org/journal/adv the Hc = 0 zero-coercivity line. This ensures a smooth transition as the coercivity of each hysteron decreases (Fig. 1(b), (c)) – it moves upward in the FORC distribution, and when each hysteron reaches Hc = 0 it reappears at the same field value in the upper right display (R-SFD)

Summary

INTRODUCTION

The FORC method for the characterization of magnetic systems has come into wide use in the past 15 years or so. This particular distribution has no negative density, but negative density is displayed in the complementary color (0, 0.5, 1). Scitation.org/journal/adv the Hc = 0 zero-coercivity line This ensures a smooth transition as the coercivity of each hysteron decreases (Fig. 1(b), (c)) – it moves upward in the FORC distribution, and when each hysteron reaches Hc = 0 it reappears at the same field value in the upper right display (R-SFD). There has been previous work on including reversible effects in the FORC formalism, some of which was aimed at incorporating the reversible material into the FORC distribution as a singular delta function, and some of which involved a separate plot of the reversible part, but none of these ensured that exactly the same scale was used for the reversible and irreversible displays

Invertibility

EXAMPLE

CONCLUSIONS