# Absence of Weak Localization Effects in Strontium Ferromolybdate
## 2 Methods  
First, we estimate the coefficient (\(A^{\prime}\)) in Equation (15). Taking \(l_{\sigma}\) \(<\) 0.46 nm at room temperature [35] and \(b\) = 20 nm [25], the ratio of the coefficients \(A^{\prime}/B^{\prime}\) are in the order of \(10^{-2}\). Because for arguments larger than one, the natural logarithm function is smaller than the root function, the logarithmic term can be neglected. A further indication of small \(A^{\prime}\) coefficients arises from the depth of the conductance minimum, i.e., the difference between \(\rho(0)\) and \(\rho(T_{min})\), which changes with increasing magnetic flux [27]. Values larger than 35 m\(\Omega\cdot\)cm in the absence of a magnetic field and down to 2.4 m\(\Omega\cdot\)cm at 7 T [36] yield coefficients of \(A^{\prime}=10^{-2}\cdot\rho(0)-\rho(T_{min})\)) [28; 37]. In La\({}_{0.7}\)Sr\({}_{0.3}\)MnO\({}_{3}\) ultrathin films (3.5 to 40 nm) deposited by molecular beam epitaxy [25], the agreement of fits of conductivity data to Equation (15) with only the \(A^{\prime}\)ln\(T\) term (\(B^{\prime}\) = 0) was much worse than in the case with only the \(B^{\prime}T^{1/2}\) term (\(A^{\prime}\)= 0). Therefore, in the following, we neglect the term \(A^{\prime}\)ln\(T\). This corresponds to the common practice of describing similar materials, such as La\({}_{0.7-x}\)Y\({}_{x}\)Sr\({}_{0.3}\)MnO\({}_{3}\) (0 \(\leq\) x \(\leq\) 0.2) ceramics with 1 mm thickness prepared by conventional solid-state reaction [29], La\({}_{0.7}\)A\({}_{0.3}\)MnO\({}_{3}\) (A = Ca, Sr, Ba) ceramics prepared by conventional solid-state reaction [30] and SrRuO\({}_{3}\) thin films with a thickness of 6 to 8 nm deposited by pulsed laser deposition onto (100)SrTiO\({}_{3}\) substrates [24]. The coefficient \(B^{\prime}\) is given by [23]:  
\[Bt=0.0309\cdot\frac{e^{2}}{\hbar}\cdot\sqrt{\frac{k}{\hbar D}}=\frac{2.72149 \cdot\Omega^{-1}\mathrm{K}^{-1/2}\mathrm{s}^{-1/2}}{\sqrt{D[\mathrm{m}^{2}/ \mathrm{s}]}}. \tag{16}\]  
where \(\hbar\) = \(h/2\pi\) is the Planck constant expressed in J s radian\({}^{-1}\). For a mean free path (\(l_{e}\)) of 0.46 nm at room temperature [35] and a carrier relaxation time (\(\tau\)) of 1.6 \(\times\) 10\({}^{-14}\) s [38], the carrier diffusion constant is 1.32 \(\times\) 10\({}^{-5}\) m\({}^{2}\) s\({}^{-1}\), yielding a coefficient of \(B^{\prime}\)\(\approx\) 748 \(\Omega^{-1}\) m\({}^{-1}\) K\({}^{-1/2}\), in satisfactory agreement with values of \(B^{\prime}\)\(\approx\) 360 \(\dots\) 500 \(\Omega^{-1}\) m\({}^{-1}\) K\({}^{-1/2}\) in (Ni\({}_{0.5}\)Zr\({}_{0.5}\))\({}_{1-x}\)Al\({}_{x}\) metallic glasses [39] and with a universal value of \(B^{\prime}\)\(\approx\) 600 \(\Omega^{-1}\) m\({}^{-1}\) K\({}^{-1/2}\) of amorphous and disordered metals [40]. The coefficient \(C_{n}\) is calculated as follows. We start with Drude conductivity:  
\[\rho_{D}=\frac{\hbar k_{F}}{n_{e}e^{2}l_{e}}, \tag{17}\]  
where \(n_{e}\) is the electron density, and \(e\) is the electron charge. Taking \(n_{e}\) = 1.1 \(\times\) 10\({}^{28}\) m\({}^{-3}\)[41], we obtain \(\hbar k_{F}\) = 4.8 \(\times\) 10\({}^{-25}\) Jsm\({}^{-1}\) and  
\[\rho_{D}=\frac{1.87\cdot 10^{-15}\Omega\mathrm{m}}{l_{e}[\mathrm{m}]}, \tag{18}\]  
We assume electron mean free paths of \(l_{e}\) = 0.46 nm and 1.11 nm at room temperature and 4 K, respectively, calculated according to the ordinary Hall coefficient [35]. This yields \(\rho_{\mathrm{D}}\) = 4.07 u\(\Omega\)m at room temperature and \(\rho_{\mathrm{D}}\) = 1.68 u\(\Omega\)m at 4 K, in satisfactory agreement with experimental data on single-crystal SFMO reported in [42]. Now, we assume that in a ferromagnetic state below room temperature, magnetic scattering controls electrical transport in SFMO at low temperatures [35].