Thermal noise power properties of magnetic nanoparticles: theory and experiment

Abstract

Magnetic nanoparticles are powerful tools in biomedical applications, where they are employed in both diagnosis and therapy. A prerequisite for the efficiency of these applications are precisely characterized particles. To this end, several magnetic measurement techniques are established. They all have in common that they measure the magnetic response of the particles exposed to an externally applied magnetic field, which may change the aggregation state of the particles [1].To overcome this limitation, the method of Thermal Noise Magnetometry (TNM) has been developed tocharacterize magnetic nanoparticle ensembles without the use of an external magnetic excitation [2]. Amplitude variations in the net magnetic moment of the sample are measured, which are caused by thermal fluctuations in the system. Rather than measuring the dissipation or impedance in the system as a result of the application of the external field, the thermal fluctuations are studied in the absence of the external excitation. The dissipation-fluctuation theorem describes the accordance between the conventional dissipation characterization techniques such as Magnetorelaxometry (MRX) or AC-Susceptibility (ACS) measurements [4, 5], and the fluctuation-based TNM technique.The total switching rate of the magnetic moments depends on volume, anisotropy, aggregation of the particles and the viscosity and temperature of the suspension. TNM measurements have been proven to be feasible, and complementary to other characterization techniques due to its diminutive impact on the sample [2, 5].In this contribution we present a numerical framework which we use to mirror our TNM measurements, in order to further establish this characterization method. First, we numerically investigate and explain the dependence of the stochastic TNM signal on basic parameters such as the number of particles and their volume. The linear dependence on the number of particles is experimentally verified.Next, we designed a sample holder geometry by solving an optimization problem, maximizing the noise power in our setup (see Fig. 1). Its performance is compared to that of a cylindrical sample holder, typically used for MRX measurements. This was done by measuring the noise power as a function of the sample distance from the detector (i.e. the depth profile of the experimental setup), both computationally and experimentally (Fig. 2). We obtained an increase in noise signal by a factor of 3.5 for the optimized sample holder, while the volume of the sample decreased by more than half. The superior signal amplitude of our optimized sample holder and the match between computed and measured depth profile demonstrate the accuracy and importance of our TNM simulations. The theoretical framework allows us to study aspects of TNM which are hard to accomplish experimentally, making it possible to visualize them and gain insight in the experiment. Our results therefore contribute to the further establishment of TNM as a magnetic nanoparticle characterization method. **