## 3 Magnetic Characterization Instruments
### Fluxgate Magnetometers  
An extremely popular measuring instrument is the fluxgate magnetometer. This device measures the time domain changes of the magnetic flux and therefore provides measurements of the time domain magnetic field in the three axes [26]. One of its major advantages is that are highly sensitive devices, with low noise levels (1 pT to 1 nT/\(\sqrt{\text{Hz}}\) at 1 Hz) in comparison to Hall sensors and magnetoresistors [121]. According to [47], usually the fluxgate magnetometers that exist on the market present white-noise values in the range of a few pT/Hz\({}^{1/2}\), while the lowest value of an already existing fluxgate magnetometer is 350 fT/Hz\({}^{1/2}\) at 1 kHz. In addition, these devices can work at room temperature, while their structure is simple, without moving parts [121]. Moreover, they present high precision, are affordable, and can find application in the investigation of magnetic fields between 20 pT and 100 uT [20; 26; 42]. However, they are limited by their bandwidth in the lower kHz range [47]. As far as their dimensions are concerned, the size of the sensor varies from 1 mm, when the fluxgate is integrated, to 7 cm for the magnetometer with great precision [121]. Fluxgate magnetometers appear in a great range of applications. The signal in a fluxgate magnetometer has a proportional relationship with the density of the magnetic flux, contrary to the SQUID magnetometer where the signal is proportional to the average magnetic flux. Another important difference between a thin film SQUID and a fluxgate  
Figure 4: The hybrid magnetometer with vibrating and rotating sample [58]. magnetometer is that the first is a vector magnetometer, while the second is a 3D device, whose sensitivity changes according to the factor of demagnetization on the shape of the magnetometer [47]. Fluxgate magnetometers, especially those with a differential arrangement, are compact and robust devices and sensitive low-noise sensors [15,19]. Compared to SQUIDs, there is no need for cryogenic cooling, and this method does not use extremely sensitive sensors so there is no need for magnetic shielding. Moreover, it can record the magnetic signal when an external field is also present as well as the signal behavior after canceling of the magnetic field because it measures the absolute value of the magnetic field and not only the changes of the magnetic field. Finally, it does not present susceptibility to magnetic disturbances [8,20,32,42,47,98]. To achieve measurements of the whole magnetization-relaxation cycle, these devices have the sensitive axes of the two magnetometers with perpendicular orientation, concerning the magnetic field, and thus exclusively the stray field from the nanoparticles is detected [20]. Moreover, using SQUID for magnetorelxometry measurements, one can take data only in a specific period, after the deactivation of the external field, called dead time, and it lasts from several ms up to some hundred ms. Contrary to SQUIDs, using a fluxgate magnetometer, it is possible to know the signal before its deactivation, which allows obtaining knowledge about all nanoparticles' magnetic moment [8]. In comparison to the SQUIDs, the fluxgate magnetometers present lower resolution [42]. In addition, the core of the fluxgate magnetometer is made of ferromagnetic material; consequently, the phenomenon of saturation and, for this reason, the magnetometer can affect the magnetic behavior of the nanoparticles [47]. However, the finding in [20] indicates that the magneto-relaxation of the ferromagnetic (in our case catalytic) nanoparticles is indeed influenced neither by the ferromagnetic core of the fluxgate sensors nor by the field of the feedback coils and that data from both systems (SQUIDs vs. FLUXGATE MAGNETeters.) can directly be compared. Two common measurement ways, through the fluxgate magnetometers, are by using the single fluxgate arrangement and using the differential fluxgate arrangement, as Figure 5 depicts.