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

16 pages, 4 figures

References in corpus (28)

• Layer-dependent Ferromagnetism in a van der Waals Crystal down to the Monolayer Limit
• Magnetic 2D materials and heterostructures
• On the origin of magnetic anisotropy in two dimensional CrI${}_3$
• Ab-initio calculations of exchange interactions, spin-wave stiffness constants, and Curie temperatures of Fe, Co, and Ni
• Linear spin wave theory for single-Q incommensurate magnetic structures
• Interplay between Kitaev interaction and single ion anisotropy in ferromagnetic CrI${}_3$ and CrGeTe${}_3$ monolayers
• Topological spin excitations in honeycomb ferromagnet CrI${}_3$
• GPAW: An open Python package for electronic-structure calculations
• Fundamental Spin Interactions Underlying the Magnetic Anisotropy in the Kitaev Ferromagnet CrI${}_3$
• Direct observation of 2D magnons in atomically thin CrI${}_3$
• Many-body Green's function theory of Heisenberg films
• Calculating critical temperatures for ferromagnetic order in two-dimensional materials
• Exchange interaction parameters and adiabatic spin-wave spectra of ferromagnets: A "renormalized magnetic force theorem"
• High throughput computational screening for 2D ferromagnetic materials: the critical role of anisotropy and local correlations
• Magnetic susceptibility, exchange interactions and spin-wave spectra in the local spin density approximation
• Electronic and magnetic properties of the monolayer RuCl${}_3$: A first-principles and Monte Carlo study
• Realistic Spin Model for Multiferroic NiI${}_2$
• Curie Temperature of Emerging Two-Dimensional Magnetic Structures
• Electron-magnon scattering in elementary ferromagnets from first principles: lifetime broadening and band anomalies
• Theory and simulations of critical temperatures in CrI3 and other 2D materials: Easy-axis magnetic order and easy-plane Kosterlitz-Thouless transitions
• Magnetic exchange interactions in monolayer CrI${}_3$ from many-body wavefunction calculations
• Unified Treatment of Magnons and Excitons in Monolayer CrI${}_3$ from Many-Body Perturbation Theory
• Dynamic transverse magnetic susceptibility in the projector augmented-wave method. Application to Fe, Ni, and Co
• Assessing the performance of the Random Phase Approximation for exchange and superexchange coupling constants in magnetic crystalline solids
• Systematic DFT+U and Quantum Monte Carlo benchmark of magnetic two-dimensional (2D) CrX${}_3$ (X = I, Br, Cl, F)
• Magnon-phonon interactions enhance the gap at the Dirac point in the spin-wave spectra of CrI${}_3$ two-dimensional magnets
• First Principles Heisenberg Models of 2D magnetic materials: The Importance of Quantum Corrections to the Exchange Coupling
• Spin waves in alloys at finite temperatures: application for FeCo magnonic crystal

Cited by in corpus (2)

• Predicting the Néel temperatures in general helimagnetic materials: a comparison between mean field theory, random phase approximation, renormalized spin wave theory and classical Monte Carlo simulations
• Thermodynamics of the hyperkagome-lattice $S=1/2$ Heisenberg ferromagnet