Can anyone provide a step-by-step explanation for the Langevin fitting of an M-H curve? The sample for which I need to calculate the magnetic moment is showing Superparamagnetic behaviour.
In superparamagnetic M(H) = Ms*L(mp,H). Here, Ms is the saturation magnetization of a system of superparamagnetic particles, mp is the average magnetic moment of a particle, and L(mp, H) is the Langevin function: L(mp, H) = coth(mp×H / kT) - 1/(mp×H/kT), k is Boltzmann constant, T is the temperature in [K] at wich M(H) was measured. So you have to fit 2 parameters Ms and mp. The last is the average magnetic moment of a particle. Sometime magnetic moment distribution should be taken in to account.
Thanks for your reply Sergey V Komogortsev . I have got the value for both the parameters from the Langevin fit. I have Fe3+ in my material (confirmed by XPS). But my target is to calculate the spin state of Fe.
Please guide me, how to proceed to this after getting the value of Ms ad mp.
Dear Himan Dev Singh, use the temperature value (that was during mesurement) and your p2 value ( p2=0.4394 T^-1=0.4394E-4 Oe^-1).
p2=mp/kT. For example if T=5K, mp=p2*k*T=0.4394E-4 Oe^-1*1.38E-16 erg/K*5K=3.032E-20erg/G=3.269 mB. Finally the particle moment is 3.269 Bohr magneton. If mp so small, may be it is better to use Brillouin instead of Langevin function. And in your curve one can observe tiny ferromagnetic contribution (small step in low fields). It is worthy to extract it before fitting using Brillouin or Langevin function.
Thanks for the clarification Sergey V Komogortsev , the calculation shown by you above is very clear and convincing but the problem in my case is that the measurement has been done at 300K and accordingly I am getting a magnetic moment of 196 Bohr magneton, which does not make any sense, atleast for Fe3+.