Classification for the universal scaling of N\'eel temperature and staggered magnetization density of three-dimensional dimerized spin-1/2 antiferromagnets

TL;DR

This study uses quantum Monte Carlo simulations to explore the universal scaling relations between Nél temperature and staggered magnetization in 3D dimerized antiferromagnets, clarifying microscopic effects and experimental discrepancies.

Contribution

It reveals that the universal scaling relations depend on the strength of antiferromagnetic couplings, providing a new categorization based on microscopic interactions.

Findings

Universal scaling relations depend on the amount of stronger couplings.

Numerical evidence supports the categorization of scaling behavior.

Discussion of relevance to TlCuCl$_3$ experiments.

Abstract

Inspired by the recently theoretical development relevant to the experimental data of TlCuCl$_3$, particularly those associated with the universal scaling between the N\'eel temperature $T_N$ and the staggered magnetization density $M_s$, we carry a detailed investigation of 3-dimensional (3D) dimerized quantum antiferromagnets using the first principles quantum Monte Carlo calculations. The motivation behind our study is to better understand the microscopic effects on these scaling relations of $T_N$ and $M_s$, hence to shed some light on some of the observed inconsistency between the theoretical and the experimental results. Remarkably, for the considered 3D dimerized models, we find that the established universal scaling relations can indeed be categorized by the amount of stronger antiferromagnetic couplings connected to a lattice site. Convincing numerical evidence is provided to support this conjecture. The relevance of the outcomes presented here to the experiments of TlCuCl$_3$ is briefly discussed as well.