Dimensional crossover in spin-1 Heisenberg antiferromagnets: a quantum Monte Carlo study

TL;DR

This study uses quantum Monte Carlo simulations to explore how the magnetization behavior of spin-1 Heisenberg antiferromagnets changes across different dimensional regimes, revealing the emergence of a Haldane gap and effects of anisotropy.

Contribution

The paper provides large-scale simulation results detailing the dimensional crossover effects on magnetization in spin-1 antiferromagnets, including the appearance of a Haldane gap and anisotropy influences.

Findings

Haldane gap appears in Q1D limit at low magnetic fields.

Magnetization slope increases near saturation, approaching 1D behavior.

Uniaxial anisotropy affects magnetization curves in low-dimensional systems.

Abstract

We present results of large scale simulations of the spin-1 Heisenberg antiferromagnet on a tetragonal lattice. The stochastic series expansion quantum Monte Carlo method is used to calculate equilibrium thermodynamic variables in the presence of an external magnetic field. In particular, the low temperature magnetization curve is investigated in the quasi-one-dimensional (Q1D), quasi-two-dimensional (Q2D), and three-dimensional (3D) limits. Starting from the 3D limit, the Q1D (Q2D) limit is achieved by reducing the in-plane (out-of-plane) spin coupling strength towards zero. In the Q1D limit, a Haldane gap appears in the magnetization curve at low magnetic field. Additionally, near the saturation field the slope of the magnetization curve increases substantially, approaching the infinite-slope behavior of a one-dimensional spin-1 chain. A similar (though less pronounced) effect is seen in the Q2D limit. We also study the effect of uniaxial single-ion anisotropy on the magnetization curve for Q1D and Q2D systems. Our results will be important in understanding the field-induced behavior of a class of low-dimensional Ni-based quantum magnets.