## 5 Discussion  
### Data  
The very first comment must focus on the composition dependence of the induced birefringence (Figure 1). An influence of binary mixture composition on the dependence of induced birefringence composition is expected. It was shown before [20], that already in weakly interacting liquid mixtures, measured birefringence slightly deviates from simplest additive behavior (maximum deviation in \(\Delta n/\lambda\) at 1.5 T is about \(-4\times 10^{-4}\) m\({}^{-1}\) for equimolar composition). This can be rationalized by formation of statistical binary molecular pairs. In this respect, the induced birefringence observed for currently studied amphiphile mixture behaves much differently. Instead of smooth composition dependence of \(\Delta n/\lambda\), a distinct increase in a relatively small composition range is observed. More importantly, the magnitude of the birefringence in this range reaches the value of 0.1 m\({}^{-1}\), being about three orders of magnitude higher than for simple mixtures. As the effect is observed in mixture of molecules characterized with small optical anisotropy, this proves that the effect does not come from orientation of individual molecules. In this limited composition range, molecules have to be organized in supra-molecular structures. The negative sign of induced birefringence indicates that the direction of the highest magnetic polarizability is perpendicular with the direction of the highest electric polarizability. The fact that induced birefringence takes place only in a restricted interval of composition suggests a specific DBP/PA ratio at which the effect is maximized. The strongest effect takes place around X = 0.33, which means that the DBP-to-PA ratio is 2:1. It must be noted that this composition is different to that at which the viscosity has its maximum (see inset of Figure 1, with the viscosity data taken from Reference [12]). This observation is important, since it suggests that the birefringence and viscosity increase are related to different phenomena. Whereas viscosity increase is due to the generation of charged species as a result of the DBP-to-PA proton migration and formation of ionic liquid (see Scheme 2), the birefringence must be ascribed to something else. At X = 0.33, in fact, (i) the system can be described as DBP-PA ionic liquids dissolved in the excess of DBP [12]. It can be argued that at this composition, the excess DBP, which is, however, capable of forming H-bonds, can establish strong and directional H-bonds with the charged species of protonated PA and deprotonated DBP. This would further increase the local anisotropy helping the building up of bigger aggregates (see later). A comparison with the magnetically induced birefringence shown by dibutylphosphate/bis (2-ethylhexyl) amine [18], i.e., where the amine molecular architecture is bigger having two branched alkyl tails (instead of a single and short one as in the case of PA), can be useful. In that mixture, the magnitude of the induced birefringence is even higher (\(|\Delta n/\lambda|>0.8\)) and occurs at a different composition (amine molar ratio of 0.7). This means that the alkyl chain size/length can play a pivotal role in determining this effect, highlighting the complexity of the scenario of all the interactions involved in the magnetically-induced intermolecular assembly in surfactant-based liquid mixtures. Another interesting observation regards the time evolution of the system after the field is switched on (see Figure 3a): the process is very slow (hours), strikingly slower than expected from typical molecular rotational diffusion. This is itself worth of note, since the response to a magnetic field is typically fast even in solutions of big molecules such as peptides [26].