Thickness dependent Curie temperature and power-law behavior of layering transitions in ferromagnetic classical and quantum thin films described by Ising, XY and Heisenberg models

TL;DR

This study investigates how the Curie temperature in ferromagnetic thin films varies with thickness, revealing that the shift exponent depends on surface exchange strength and shows no significant difference between classical and quantum models.

Contribution

It provides a detailed analysis of the thickness dependence of Curie temperature and the shift exponent in classical and quantum thin films using effective field theory.

Findings

Curie temperature decreases with film thickness.

Shift exponent depends on surface exchange coupling.

No significant difference between classical and quantum exponents.

Abstract

Ferromagnetic-paramagnetic phase transitions in classical and quantum thin films have been studied up to 50 mono-layers using effective field theory with two-site cluster approximation. Variation of the Curie temperature as a function of film thickness has been examined. The relative shift of the Curie temperature from the corresponding bulk value has been investigated in terms of the shift exponent $\lambda$. We have found that shift exponent $\lambda$ clearly depends on the strength of the ferromagnetic exchange coupling of the surface. Moreover, we have not observed any significant difference between classical and quantum exponents for a particular model.