Beyond the random phase approximation for calculating Curie temperatures in ferromagnets: application to Fe, Ni, Co and monolayer CrI3
arxiv(2024)
摘要
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.
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