# Key Contributors to Signal Generation in Frequency Mixing Magnetic Detection (FMMD): An In Silico Study

## TL;DR

This study uses simulations to identify how magnetic nanoparticle properties and external field parameters affect signal generation in frequency mixing magnetic detection.

## Contribution

The study identifies the core size of magnetic nanoparticles as the dominant factor in signal generation for frequency mixing magnetic detection.

## Key findings

- The core size of magnetic nanoparticles (dC>25 nm) strongly influences the nonlinear magnetic response.
- Drive field amplitude shapes the field-dependent response more than anisotropy or hydrodynamic size.
- Narrow size distributions (σ<0.1) help minimize required drive field amplitude for optimal signal generation.

## Abstract

Frequency mixing magnetic detection (FMMD) is a sensitive and selective technique to detect magnetic nanoparticles (MNPs) serving as probes for binding biological targets. Its principle relies on the nonlinear magnetic relaxation dynamics of a particle ensemble interacting with a dual frequency external magnetic field. In order to increase its sensitivity, lower its limit of detection and overall improve its applicability in biosensing, matching combinations of external field parameters and internal particle properties are being sought to advance FMMD. In this study, we systematically probe the aforementioned interaction with coupled Néel–Brownian dynamic relaxation simulations to examine how key MNP properties as well as applied field parameters affect the frequency mixing signal generation. It is found that the core size of MNPs dominates their nonlinear magnetic response, with the strongest contributions from the largest particles. The drive field amplitude dominates the shape of the field-dependent response, whereas effective anisotropy and hydrodynamic size of the particles only weakly influence the signal generation in FMMD. For tailoring the MNP properties and parameters of the setup towards optimal FMMD signal generation, our findings suggest choosing large particles of core sizes dC>25 nm with narrow size distributions (σ<0.1) to minimize the required drive field amplitude. This allows potential improvements of FMMD as a stand-alone application, as well as advances in magnetic particle imaging, hyperthermia and magnetic immunoassays.