Dear Werner,
Thank you for your Mathcad and .pdf files. I've made sure that using partial derivatives is not appropriate to my problem. The proof is that at some field values the magnetization decreases, whereas it should either increase or stay constant. However, when you used new guess values, the result you showed in the penultimate graph of Magnetization2_Werner file is definitely interesting. This is not what I expected but it is possible from the physics point of view. As I referred to Alan's example in the previous post, from this graph you get the parallel orientation of the magnetic moments in the lowest applied field.
In your example (magnetization3) where you use the same guess values for alpha and phi as Alan, you get the same expected result. Your third example where you use a grid algorithm yields the same result but seems less clear to me as I don't know how it works. But I am going to look into it.
Thank you for your help!
Regards,
Den