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

Abstract

The critical temperature for magnetic order comprises a crucial property of any magnetic material and ranges from a few Kelvin in certain antiferromagnets to 1400 K in ferromagnetic Co. However, the prediction of critical temperatures based on, for example, a spin wave dispersion is in general non-trivial. For ferromagnets and simple collinear antiferromagnets, estimates may be obtained from the Heisenberg model using either renormalized spin wave theory or the Green's function random phase approximation (RPA), but a systematic assessment of the accuracy of such approaches seems to be lacking in the literature. In this work, we propose generalizations of both renormalized spin wave theory and RPA to calculate the critical temperatures of single-$Q$ helimagnetic ground states, which include ferromagnets and antiferromagnets as special cases. We compare the methods to classical Monte Carlo simulations and Mean field theory, using experimental exchange parameters for a wide range of materials; MnO and NiO (single site Néel ground states), MnF${}_2$ (altermagnet), Cr${}_2$O${}_3$ and Fe${}_2$O${}_3$ (two site Néel states) and Ba${}_3$NbFe${}_3$Si${}_2$O${}_{14}$ (incommensurate helimagnet). In all cases, we observe that predictions from RPA are in excellent agreement with experimental values and RPA thus constitutes a rather reliable all-purpose method for calculating critical temperatures.

arXiv comment17 pages, 8 figures. Clarified RPA-HP relation

References in corpus (10)

• Linear spin wave theory for single-Q incommensurate magnetic structures
• Magnetic octupoles as the order parameter for unconventional antiferromagnetism
• Unified Molecular Field Theory for Collinear and Noncollinear Heisenberg Antiferromagnets
• Role of Dzyaloshinskii-Moriya interaction for magnetism in transition-metal chains at Pt step-edges
• Parity Broken Chiral Spin Dynamics in Ba${}_3$NbFe${}_3$Si${}_2$O${}_{14}$
• Assessing the performance of the Random Phase Approximation for exchange and superexchange coupling constants in magnetic crystalline solids
• Antiferromagnetism in two-dimensional materials: progress and computational challenges
• Plane wave implementation of the magnetic force theorem for magnetic exchange constants: Application to bulk Fe, Co and Ni
• A deep investigation of NiO and MnO through the first principle calculations and Monte Carlo simulations
• Beyond the random phase approximation for calculating Curie temperatures in ferromagnets: application to Fe, Ni, Co and monolayer CrI3

Cited by in corpus (1)

• Incommensuration in odd-parity antiferromagnets