Overview: Study of magnetization temperature in ferromagnetic crystals


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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