  In this paper we use the Nuclear Magnetic Resonance (NMR) to write eletronic
states of a ferromagnetic system into a high-temperature paramagnetic nuclear
spins. Through the control of phase and duration of radiofrequency pulses we
set the NMR density matrix populations, and apply the technique of quantum
state tomography to experimentally obtain the matrix elements of the system,
from which we calculate the temperature dependence of magnetization for
different magnetic fields. The effects of the variation of temperature and
magnetic field over the populations can be mapped in the angles of spins
rotations, carried out by the RF pulses. The experimental results are compared
to the Brillouin functions of ferromagnetic ordered systems in the mean field
approximation for two cases: the mean field is given by (i) $B=B_0+\lambda M$
and (ii) $B=B_0+\lambda M + \lambda^\prime M^3$, where $B_0$ is the external
magnetic field, and $\lambda, \lambda^\prime$ are mean field parameters. The
first case exhibits second order transition, whereas the second case has first
order transition with temperature hysteresis. The NMR simulations are in good
agreement with the magnetic predictions.
