## 2 Materials and Methods
### Magnetic Measurements and Data Quantifying
The measured dependences Re\(M_{2}\)(\(H\), \(T\)) and Im\(M_{2}\)(\(H\), \(T\)) were processed using the formalism of the numerical solution for the kinetic FP equation for the stochastic magnetization dynamics of superparamagnetic (SPM) particles with arbitrary directions of anisotropy axes [25],  
\[2\tau_{N}\frac{\partial W}{\partial t}=-\frac{1}{\sin\vartheta}\left[\frac{ \partial}{\partial\vartheta}(\widetilde{J}_{\vartheta}\sin\vartheta)+\frac{ \partial}{\partial\varphi}\widetilde{J}_{\varphi}\right]\,, \tag{1}\]  
with  
\[\widetilde{J}_{\vartheta}=-\left[\beta\left(\frac{\partial\mathcal{H}}{ \partial\vartheta}-\frac{1}{\alpha\sin\vartheta}\frac{\partial\mathcal{H}}{ \partial\varphi}\right)W+\frac{\partial W}{\partial\vartheta}\right]\,, \tag{2}\]  
\[\widetilde{J}_{\varphi}=-\left[\beta\left(\frac{1}{\alpha}\frac{\partial \mathcal{H}}{\partial\vartheta}+\frac{1}{\sin\vartheta}\frac{\partial \mathcal{H}}{\partial\varphi}\right)W+\frac{1}{\sin\vartheta}\frac{\partial W }{\partial\varphi}\right]\,. \tag{3}\]  
Here, \(W\)(\(t\)) is the nonequilibrium probability-density function for directions of the particle magnetic moment \(\mathbf{m}\) with the damping constant \(\alpha\) and the time scale \(\tau_{N}\) being the Neel free-diffusion (zero-potential) relaxation time proportional to \(\alpha^{-1}\) and \(\beta=1/k_{\mathrm{B}}T\). The magnetic potential \(\mathcal{H}\) consists of the _uniaxial_ anisotropy energy and the energy of the magnetic moment in the total magnetic field \(\mathbf{H}=\mathbf{H}_{0}+\mathbf{h}\):  
\[\mathcal{H}=-\frac{E_{\alpha}}{m^{2}}(\mathbf{m}\mathbf{n})^{2}-\mathbf{m} \mathbf{H}\,\]  
where \(\mathbf{n}\) is the anisotropy axis direction. The direction of \(\mathbf{m}\) defined by the spherical angles \(\vartheta\) and \(\varphi\) thermally fluctuates in the field \(\mathbf{H}\) (Figure 1). The function \(W\)(\(t\)) is expanded in the series on spherical harmonics  
\[W(t,\vartheta,\varphi)=\sum_{lm}c_{lm}(t)\Upsilon_{lm}(\vartheta,\varphi)\, \tag{4}\]  
Figure 1: Magnetic field geometry. and in the Fourier series reducing Equation (1) to a set of linear equations which, in turn, is expressed as a continuous-fraction matrix equation  
\[\mathbf{S}_{n}=-\left[\mathbf{Q}_{n}+\mathbf{Q}_{n}^{+}\mathbf{S}_{n+1}\mathbf{Q }_{n+1}\right]^{-1}\,, \tag{5}\]  
with the matrices \(\mathbf{Q}_{n}\), \(\mathbf{Q}_{n}{}^{+}\) and \(\mathbf{Q}_{n+1}\) (n = 1, 2,...) composed of the spherical harmonics indices, the direction cosines \(\gamma_{i}\) and \(\gamma^{\prime}{}_{i}\) of the magnetic fields relative to the anisotropy axis \(\mathbf{n}\) (Figure 1), as well as of the parameters entering Equations (1)-(3) and the magnetic potential \(\mathcal{H}\). The normalized \(k\)th Fourier harmonic of the magnetic moment in the field direction is  
\[m_{k}(\omega)=\sqrt{\frac{4\pi}{3}}\left[\gamma_{3}c_{10}^{k}(\omega)+\frac{( \gamma_{1}+i\gamma_{2})c_{1-1}^{k}(\omega)-(\gamma_{1}-i\gamma_{2})c_{11}^{k} (\omega)}{\sqrt{2}}\right]\,, \tag{6}\]  
where \(c_{ij}^{k}(\omega)\) are the Fourier transforms of \(c_{lm}(t)\) in Equation (4). The quantities \(c_{ij}^{k}(\omega)\) are the elements of the column vector \(\mathbf{S}_{1}\), the solution of Equation (5). The complex fit function for the \(M_{2}\) response is obtained by the convolution of \(m_{k}(\omega)\) for \(k\) = 2 with the distribution over the values of magnetic moments \(f_{M}\):  
\[M_{2}(H_{0})=\widetilde{M}\int f_{M}m_{2}(\omega,h,H_{0})dM\,, \tag{7}\]  
where \(\widetilde{M}\) is the total saturation magnetization of the sample. The function \(f_{M}\) corresponds to the distribution over the particle volumes when all the particles are magnetically homogeneous with the same, size-independent magnetization. In most cases, the log-normal distribution is valid. Computation of the fit function (7) at each experimental point requires multiple solving of Equation (5). The solution accuracy is determined by the retained terms in the spherical harmonics and Fourier expansions.