## 3 Results and Discussion
\[F(t)=F_{\rm A}(t)=\exp\left(-\left|D_{\rm A}t\right|-i\delta_{\rm d}D_{\rm A}\,t\right) \tag{3}\]  
At the intermediate area, \(F(t)\) is described by more complicated relations represented in Reference [9]. These relations were applied to calculate the resonance absorption line \(g(\omega)\) presented in Figure 4 as the Fourier transform of \(F(t)\). General analysis of the resonance line is fulfilled in terms of monopole and Anderson widths. We use the aspect ratio \(N_{\rm el}=\left(\frac{n_{l}^{3}}{N_{n}}\right)^{1/2}\) to measure the aggregate elongation. Here \(N_{n}\) is the total number of particles in the aggregate of a length \(l\), \(n_{l}=l/d\), and \(d\) is nanoparticle's diameter. The aspect ratio can be calculated from the equation  
\[\varphi\kappa N_{\rm el}^{2}=\frac{81\sqrt{3}}{50\pi^{2}}\left(\frac{D_{\rm A }}{D_{\rm m}}\right)^{3} \tag{4}\]  
where \(\varphi\) is a volume fraction of magnetic particles in the sample and \(\kappa\) is the fraction of aggregated particles. Fitting the theoretical spectrum to the experimental one was carried out by variation of the parameters of \(F(t)\). It was assumed that only a part of nanoparticles was aggregated (\(\kappa\leq 1\)) and therefore  
\[F_{\rm tot}(t)=F(t,D_{\rm m},D_{\rm A})\cdot\exp\left(-\left|D_{\rm A1}t \right|-iD_{\rm A1}\delta_{\rm d}t\right) \tag{5}\]  
where \(D_{\rm A1}=(1-\kappa)D_{\rm A}^{\rm\ 0}\) and \(D_{\rm A1}\delta_{\rm d}\) are the Anderson line width and fluctuation shift produced by isolated (nonaggregated) nanoparticles, and \(D_{\rm A}^{\rm\ 0}\) is defined by Equation (1). Note that \(D_{\rm A}^{\rm\ 0}=D_{\rm A}\) if all particles are aggregated, and \(D_{\rm A}^{\rm\ 0}=D_{\rm A1}\) if there are no aggregated particles in the system. For the calculation of FID \(F(t,D_{\rm m},D_{\rm A})\) only aggregated particles are taken into account. Figure 4 shows that the theoretical spectrum obtained in this framework has satisfactory agreement with the experimental spectrum of the sensor in magnetoanisotropic gel (\(M_{\rm G}=0.64(7)\) G) in both the shape of line and its position in the field. For the experimental spectrum under study (Figure 4), the line width parameters \(D_{\rm A}\) and \(D_{\rm m}\) are equal to \(2.01(5)\) and \(2.05(6)\) G, respectively. The Anderson line width in the absence of aggregates \(D_{\rm A}^{\rm\ 0}=3.22(35)\) G. The fraction of aggregated particles \(\kappa=62(6)\%\) was calculated as the ratio of \(D_{\rm A}\) and \(D_{\rm A}^{\rm\ 0}\). The aspect ratio of the aggregates in the analyzed sample \(N_{\rm el}=12.6(1.3)\) was obtained from Equation (4). These values can be compared with the results for the magnetic liquid, where both the fraction of the aggregated particles and the average aggregate's length are larger than in the gel. They reach 100% and 60(6), respectively [10]. The latter value is greater than the average aggregate's length in the gel by a factor of about five. The first reason for the difference consists in the fact that the aggregate formation in the magnetic hydrosol was realized at approximately a two times higher magnetic field than in the gel. The second reason results from the prevention of aggregate development by the gel formation process. The difference in the aspect ratio and fraction of aggregated particles for magnetic liquid and gel obtained here are expected because the efficiency of aggregation in magnetic liquid is higher than in magnetic gel.