# Multiparametric robust sensing via readout of characteristic magnetization loops

## TL;DR

This paper introduces a new method for robust multiparametric sensing using magnetization loops, enabling accurate and simultaneous measurement of temperature and magnetic field.

## Contribution

The novel approach uses Fourier components of nonlinear responses to achieve gain and delay invariant sensing.

## Key findings

- Characteristic shape parameters from harmonics enable independence from external factors.
- A magneto-optical method was demonstrated for parallel detection of temperature and magnetic field.
- Lookup-table and random forest regressor achieved accurate parameter extraction.

## Abstract

Simultaneous measurements of multiple physical quantities under variable conditions are essential from fundamental research to application. However, multiparametric sensors often need intricate calibration procedures which can be compromised by changing environmental conditions. Here, we present a robust sensing concept based on the Fourier components of a nonlinear response of an excitation. By extracting amplitude ratios and phase differences between different harmonics, a set of characteristic shape parameters are extracted ensuring independence from external factors such as amplifier gain or instrumental delays. This principle is demonstrated using magneto-optical readout of magnetization loops in a perpendicular bismuth-substituted yttrium iron garnet indicator film. Two-dimensional parameter maps spanning both temperature and magnetic field are measured, providing a sensor-specific fingerprint for parallel detection. Using lookup-table interpolation and a random forest regressor, robust and accurate simultaneous extraction of temperature and magnetic field is demonstrated. The presented magneto-optical method offers a universal, gain and delay invariant framework for multiparametric sensing in nonlinear materials.

The online version contains supplementary material available at 10.1038/s41598-026-42763-x.