EuO and EuS Materials are used in study. As per Weiss mean field approximation (MFA), below certain critical temperature(Tc) ferromagnetic materials have spontaneous magnetization — i.e., a sizable macroscopic magnetic moment even in the absence of an external magnetic field. The effective field acting on a magnet in a ferromagnetic medium is H+gM(T), term gM(T) is called self-consistent molecular field.
Magnetization M is given by,
Langevin function describes the average alignment of magnetic moments with an applied magnetic field at a given temperature.
x=uB/kT
For very large T, x becomes small and Langevin function becomes
For H = 0 and T slightly below TC , The equation becomes
Brillouin function is a quantum mechanical function that describes the magnetization of a system of spins in response to an applied magnetic field at a given temperature.
The study shows that M(T) exhibits anomalous scaling near Tc, with a scaling index β≈1/3, consistent with experimental data for EuO and EuS.
This result differs from the classical MFA prediction of β=1/2
The Weiss-Heisenberg MFA value of the Curie Temperature Tc wh ≈ 86.6K in EuO was observed.(about 20 % larger than its experimental value Tc exp≈ 69.8 K). spin-wave included MFA equations match with experimental data across all temperature ranges.
Source: https://arxiv.org/abs/2412.10124
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