# Strontium Ferromolybdate-Based Magnetic Tunnel Junctions
## 3 Results and Discussion
### Attainable Tunnel Magnetoresistance  
A spin-polarization value of \(P\) = 0.85 was deduced by means of the Julliere model for an SFMO/STO/Co junction at 4 K, where the SFMO possesses an antisite disorder parameter \(ASD\) = 0.15 [2]. The \(P\) values obtained for SFMO single crystals were 0.67 \(\pm\) 0.03, 0.66 \(\pm\) 0.02, and 0.59 \(\pm\) 0.05 at \(T\) = 1.2 K for \(ASD\) amounting to 0.11, 0.15, and 0.16, respectively [83]. The spin-polarization values were found to be independent of temperature, which was anticipated in the considered temperature range from 1.2-3.76 K, well below the Curie temperature of SFMO. Taking into account data in [83], Equation (15) was approximated choosing \(P_{0}\) = 0.9. Here, Equation (16) yields a zero-temperature TMR of about 430%. The parameter \(\alpha\) determined using the data for (Ba\({}_{0.8}\)Sr\({}_{0.2}\))\({}_{2}\)FeMoO\({}_{6}\) given in [84]  
Figure 4: Thickness dependence of the saturation magnetization \(M_{\rm s}\) of SFMO thin films measured in a magnetic field of 400 mT at 10 K [76] in comparison with the DL model (Equation (11)). Additionally, an outlook is given for high-quality SFMO thin films possessing a saturation magnetization of 3.75 μ\(\mu\)B/f.u.  
amounts to \(1.31\times 10^{-4}\) K\({}^{-3/2}\), which is one order of magnitude larger than the values for Co, permalloy [41], NiFe [85], and FeNiB\({}_{0.5}\)[42, 43], and about three times the value for La\({}_{2/3}\)Sr\({}_{1/3}\)MnO\({}_{3}\), but on the order of the values obtained for La\({}_{2/3}\)Sr\({}_{1/3}\)MnO\({}_{3}\) grown on various barrier materials (SrTiO\({}_{3}\), TiO\({}_{2}\), LaAlO\({}_{3}\)). It amounts to about one-third of the value for the La\({}_{2/3}\)Sr\({}_{1/3}\)MnO\({}_{3}\) free surface [64]. Inserting the obtained \(\alpha\) value of SFMO into Equation (15), we find \(P(298\) K) = 0.293 and, correspondingly, using Equation (16), \(TMR(298\) K) = 19%. For an SFMO(150 nm)/STO(2 nm)/SFMO(50 nm) MTJ device, an experimental value of TMR(298 K) \(\approx\) 7% was reported in [6], corresponding to spin polarization of 18%. As for conventional tunnel junctions, the presence of defect states in the barrier reduces the MR [86]. Unpaired electrons will increase the spin-flip rate so that MR could vanish with increasing defect concentration. On the other hand, the discrepancy between experimental observation and direct spin-dependent tunneling theory can be overcome by additionally taking into account the spin-independent tunneling. One such tunneling mechanism is hopping through chains of \(N\) localized states resulting in additional conductivity that is temperature-independent for \(N=1\) and exhibits power laws \(T^{4/3}\) and \(T^{5/2}\) for \(N=2\) and \(N=3\), respectively [87]. This adds a correction to \(R_{AP}\), yielding for \(N=2\) a TMR of [44]  
\[TMR=\frac{2P_{0}^{2}(1-\alpha T^{3/2})^{2}-\beta_{SI}(T)}{1-P_{0}^{2}(1- \alpha T^{3/2})^{2}+\beta_{SI}(T)}, \tag{20}\]  
where \(\beta_{SI}(T)\) is a coefficient, both temperature- and barrier-dependent, attributed to second-order inelastic tunneling that displays a conductivity contribution of \(\sigma\propto T^{4/3}\). The room-temperature TMR of SFMO matches the experimental data described above [6] for \(\beta_{SI}(298\) K) \(\approx\) 0.1.