doFORC tool for calculating first-order reversal curve diagrams of noisy scattered data

Abstract

First-order reversal curves (FORC) diagram method is one of the most successful characterization techniques used to characterize complex hysteretic phenomena not only in magnetism, but also in other areas of science like in ferroelectricity, geology, archeology, light-induced and pressure hysteresis in spin-transition materials, etc. Because the definition of the FORC diagram involves a second-order derivative, the main problem in their numerical calculation is that the derivative of a function for which only discrete noise-contaminated data values are available magnifies the noise that is inevitably present in measurements. In this paper we present doFORC tool for calculating FORC diagrams of noise scattered data. It can provide both a smooth approximation of the measured magnetization and all its partial derivatives. doFORC is a free, portable application working on various operating systems, with an easy to use graphical interface, with four regression methods implemented to obtain a smooth approximation of the data which may then be differentiated to obtain approximations for derivatives. In order to perform the diagnostics and goodness of fit doFORC computes residuals to characterize the difference between observed and predicted values, generalized cross-validation to measure the predictive performance, two information criteria to quantify the information that is lost by using an approximate model, and three degrees of freedom to compare different amounts of smoothing being performed by different smoothing methods. Based on these doFORC can perform automatic smoothing parameter selection.

Beyond the qualitative description of complex magnetic nanoparticle arrays using FORC measurement

“…To overcome these shortcomings, one solution is to take only one derivative from the FORC data to calculate the switching field distributions [36][37][38][39]. In this approach, the switching field distributions are functions of both H and H r fields leading to 2D heat-maps that inherently share the complex data interpretation and analysis of the FORC method [40][41][42]. To further suppress these limitations, we propose to decompose the irreversible and reversible switching fields (ISF and RSF, respectively) and only investigate the ISF distributions at the H=H r and H=0, figure 1(a).…”

“…Any moment measurement, standard or fast, such as MOKE-FORC [25,45] and AC FORC methods [37,46,47], can be used to measure these 5 points. In addition, complex data processing and smoothing are not required [27,[40][41][42]48].…”

Facile decoding of quantitative signatures from magnetic nanowire arrays

“…This makes ISFD even more ideal for real-time diagnosis and quality control. Specifically, these signatures do not require massive data processing as required by the conventional FORC analysis [43][44][45][46] . For example, conventional FORC analysis typically requires 20-100 curves with 20-100 points each (= 400 to 10,000 points).…”

“…First, FORC usually requires very long measurement times, which is not efficient for biomedical applications or industrial quality control [40][41][42] . Second, smoothing is required for data processing and can induce spurious features [43][44][45][46] . Third, taking two derivatives amplifies noise that can conceal the real features.…”

A Guideline for Effectively Synthesizing and Characterizing Magnetic Nanoparticles for Advancing Nanobiotechnology: A Review

“…In another example, Zamani Kouhpanji reported on the application of the FORC technique for demultiplexing the magnetic nanowires embedded inside the biological species [143]. Regardless of the complex data processing of the FORC [147][148][149], this technique is significantly slower than the other magnetic characterization techniques because it requires scanning the whole area of the hysteresis loop to a detailed analysis [107,108,129]. In this direction, several works have been done to enhance the measurements by introducing modifications to the standard protocol of the FORC technique.…”