## 4 Results  
Figure 1 shows the maximum of the magnetically induced birefringence recorded at equilibrium conditions (long times) at a magnetic induction of 1.5 T as a function of the PA molar ratio (X). It can  
be seen that only a restricted region of composition i.e., in the range \(0.3<\) X \(<0.5\) a significant effect is present. It must be noted that the composition at which the birefringence shows its maximum is different to that at which the viscosity has its maximum. The birefringence taking place at X = 0.33 has been then measured as a function of time and as a function of magnetic field strength. This has been reported in Figure 2a. It can be noticed that the saturation value of induced birefringence, as well as the time necessary to reach the saturation condition, depend on the magnetic field induction. Additionally, the trend of induced birefringence has been tailored after the field has been switched off, as schematically shown in Figure 2b, which shows the behavior after steeply switching the field at 1 T on and off. Interestingly, when the field is switched on and off, the system response takes different times, and this happens for all the magnetic field explored. It was found that this phenomenon is reversible, independently of the history of the sample. In order to quantify these observations, we described the time dependence of induced birefringence by a stretched exponential function:  
\[\left(\frac{\Delta n}{\lambda}\right)=\left(\frac{\Delta n}{\lambda}\right)_{ MAX}\cdot\left(1-e^{-(\frac{t}{\tau})^{\beta}}\right)\text{for field ON} \tag{2}\]  
Figure 1: Normalized induced birefringence as a function of composition. The inset shows the viscosity as a function of propylamine molar ratio (X), with data taken from Reference [12]. Figure 2: (**a**) Time dependences of the induced birefringence recorded for a binary mixture Dibutyl Phosphate (DBP) / Propylamine (PA) at X = 0.33 for the different intensity of magnetic field applied. Black symbols show experimental data, red lines are fit with Equation (2). (**b**) Time dependences of the induced birefringence recorded for a binary mixture DBP/PA with X = 0.33 as the magnetic field of induction B = 1.T was turned on and off again. \[\left(\frac{\Delta n}{\lambda}\right)=\left(\frac{\Delta n}{\lambda}\right)_{MAX}e^{ -\left(\frac{t}{\tau}\right)^{\beta}}\text{ for field OFF} \tag{3}\]  
where \((\Delta n/\lambda)_{MAX}\) is the amplitude of induced birefringence normalized to wavelength of probing light \(\lambda\), \(\tau\) is the characteristic equilibration/relaxation time and \(\beta\) describes stretching of the relaxation time distribution. Stretched exponential functions have been chosen since simple exponential functions did not give adequate description of the experimental data. The fitting was satisfactory, as can be seen by comparing the red lines (fitting curves) and the experimental points (black open circles) in Figure 2a. The fitting parameters, i.e., the time constant \(\tau\), the stretching of the relaxation time distribution \(\beta\) and the amplitude of induced birefringence normalized to wavelength \((\Delta n/\lambda)_{MAX}\), have been derived and reported in Figure 3 as a function of magnetic induction, both for switching the magnetic field on (full symbols) and off (open symbols). As can be seen from Figure 3a, after the liquid mixture is exposed to the external magnetic field, the time needed to reach the stationary birefringence conditions decreases with increasing the magnetic induction value. On the other hand, the return to the equilibrium (after the magnetic field has been turned off) is almost independent of the magnetic field value. In other words, return to equilibrium takes the same amount of time (within the limit of accuracy) independently of the history of the sample. As can be seen from Figure 3b, similarly to the characteristic relaxation times, their distributions also depend on whether the magnetic field was turned on or tuned off.