T1 spin-lattice relaxation times, deviation from exponential relationship

For longitudinal relaxation, one would think that the magnetic moment obeys this simple relationship


$$M\_z = M\_0\left[1 - 2\exp\left(\frac{-t}{T\_1}\right)\right].$$ 


However there is always a point of inflection when magnetisation is zero. Does anyone knows why?


edit: I deleted the image and added some from my own experiment for mineral oil.


In this scenario, the sample is placed under a large longitudinal z-magnetic field. To measure T1, a 180 degree pulse is applied to flip Mz, then a 90 degree pulse after time t. Mo is the equilibrium longitudinal magnetic moment.


I don't think this is due to the mixture of compounds, because it is observed in all samples I tried e.g glycerine, Fe(NO3)3.


[![enter image description here](https://i.stack.imgur.com/C1YSi.png)](https://i.stack.imgur.com/C1YSi.png)


[![enter image description here](https://i.stack.imgur.com/1ANYU.png)](https://i.stack.imgur.com/1ANYU.png)


