Beyond the random phase approximation for calculating Curie temperatures in ferromagnets: application to Fe, Ni, Co and monolayer CrI3

TL;DR

This paper compares different theoretical methods for calculating Curie temperatures in ferromagnets, showing that a combined RPA and Callen decoupling approach yields the most accurate results, especially for low-dimensional systems like monolayer CrI3.

Contribution

It introduces a combined RPA and Callen decoupling scheme that improves the accuracy of Curie temperature predictions in both 3D and 2D ferromagnetic systems.

Findings

Callen decoupling is most accurate for classical 3D systems.

RPA combined with Callen decoupling best matches experimental data for Fe, Ni, Co.

The new approach correctly predicts the absence of magnetic order in S=1/2 monolayer CrI3.

Abstract

The magnetic properties of solids are typically analyzed in terms of Heisenberg models where the electronic structure is approximated by interacting localized spins. However, even in such models the evaluation of thermodynamic properties constitutes a major challenge and is usually handled by a mean field decoupling scheme. The random phase approximation (RPA) comprises a common approach and is often applied to evaluate critical temperatures although it is well known that the method is only accurate well below the critical temperature. In the present work we compare the performance of the RPA with a different decoupling scheme proposed by Callen as well as the mean field decoupling of interacting Holstein-Primakoff (HP) magnons. We consider three-dimensional (3D) as well as two-dimensional (2D) model systems where the Curie temperature is governed by anisotropy. In 3D, the Callen method is the most accurate in the classical limit, and we show that the Callen decoupling produces the best agreement with experiments for bcc Fe, fcc Ni and fcc Co with exchange interactions obtained from first principles. In contrast, for low spin systems where a quantum mechanical treatment in pertinent, the HP and RPA methods appear are superior to the Callen decoupling. In 2D systems with magnetic order driven by single-ion anisotropy, it is shown that HP fails rather dramatically and both RPA and Callen approaches severely overestimates Curie temperatures. The most accurate approach is then constructed by combining RPA with the Callen decoupling of single-ion anisotropy, which yields the correct lack of order for S=1/2. We exemplify this by the case of monolayer CrI3 using exchange constant extracted from experiments.