The Langevin formula for describing the magnetization curve of a magnetic liquid

It has been shown that, at the initial stage of the magnetization curve, the magnetic susceptibility of magnetic liquid determined as $\chi=M\mu_{0}/B$ ($M$ is the magnetization, $B$ is the magnetic induction in a sample) obeys the Curie law, and the magnetic susceptibility determined as $\chi=M/H$ ($H$ is the magnetic field intensity in a sample) obeys the Curie–Weiss law. Since the Curie law is a particular case of the Langevin dependence, it is assumed that an experimental magnetization curve is described by the Langevin formula with a Langevin parameter $\xi=PB/kT$, where $P$ is the magnetic moment of a particle and $T$ is the temperature. Experimental verification has shown that, at parameter $\xi$, the mean relative deviation between the values of $M$ measured and calculated by the Langevin formula is 5%. This deviation can be accounted for by the influence of dispersion of the magnetic moments of nanoparticles.