## 2 Magnetic Characterization Techniques
### Magnetic Susceptibility  
A widespread method for nanoparticle characterization is the measurement of the AC susceptibility (ACS) as a function of frequency [30; 31; 32]. In an AC susceptibility measurement, the MNP sample is exposed to a sinusoidal magnetic field of constant amplitude, and the frequency is swept [8]. The first measurement setup based on this technology was introduced in 1925 by Hartshorn and contained a mutual inductance bridge [33]. Then, a variety of AC susceptometers using this technology appeared. This method can provide rapid magnetic characterization of magnetic nanoparticles [34]. The AC magnetometers can detect the magnetic responses using the Neel and Brown relaxation parameters. To have the most accurate measurement, there is a vital need for the sensors to be very sensitive and also have a high range of excitation frequency. This will provide knowledge about all magnetic relaxations that exist in the nanoparticle system [34; 35; 36]. This way, it is possible to determine the magnetic properties of the nanoparticles. The fields in which AC susceptometry has applications are many: magnetic detection, magnetic hyperthermia, the dynamic magnetic characterization of magnetic nanoparticles, and studies of particle stability [35]. Every AC magnetometer consists of two parts. The first part is the detection system, while the second part is the excitation system. One very common device that is used for sensor purposes is the induction coil because it is characterized by a simple structure and high sensitivity. As far as the excitation system is concerned, solenoid or Helmholtz coils, with conduction or superconduction coils, are utilized [36]. The use of alternating magnetic fields for magnetic characterization presents advantages over the use of direct current measurements because it can provide knowledge about the magnetization dynamic that measurement with direct current cannot [33]. Although the susceptometers that exist in the market present high precision in low frequencies, it is difficult to maintain an invariable excitation field, as well as to measure the induced voltage for higher frequencies. For these reasons, the use of susceptometers is limited for high frequencies [33].  
The most important studies that use AC magnetometers for nanoparticle characterization are summarized below. Consequently, in [33], a mutual inductance AC susceptometer used for cobalt ferrite (CoFe\({}_{2}\)O\({}_{4}\)) nanoparticle characterization is proposed. This device has a constant excitation field with a value greater than 4.25 Oe and has the capability to operate between 10 kHz and 1 MHz. In [34], an induction AC magnetometer, for determining the profile of magnetic nanoparticles in bio-sensing applications, is presented. This device contains inductive coils, which offer a simple structure, economically efficient operation, as well as high frequency and dynamic range, compared to other magnetic sensors like SQUIDs, optically pumped magnetometers, or fluxgate magnetometers. One of the drawbacks of this device is the increased thermal noise that presents, but the phenomenon can be treated with methods like cooling with liquid nitrogen or optimizing the coil geometry, etc. In [35], a sensitive AC susceptometer is presented, which can operate in high frequencies from 25 kHz to 10 MHz. The sensors will be used for nanoparticle characterization purposes in a magnetic hyperthermia application. In [36], an AC magnetometer, which utilizes a resonant excitation coil with automatic frequency switching, is proposed for defining the characteristics of the nanoparticles.