Quantum Anisotropic Antiferromagnetic Heisenberg Model for Description of Magnetic Properties at Low Temperatures from KTb(WO₄)₂

Abstract

Low-dimensional magnetic materials have attracted the attention of several researchers in recent decades, mainly because of the exotic magnetic properties and superconductivity of some of these materials. One of these materials is KTb(WO$_4$)$_2$, generally considered a prototype of the 2D Ising model. However, KTb(WO$_4$)$_2$ has some peculiarities in its magnetization behaviour under a magnetic field low-temperature regime. This peculiarity especially concerns the nonlinear dependence of magnetization to an applied magnetic field which is a behaviour that cannot be described using a pure two-dimensional Ising model. KTb(WO$_4$)$_2$ undergoes a metamagnetic phase transition at low temperatures, and we believe that such behaviour may be related to quantum effects and high magnetic anisotropy. Therefore, KTb(WO$_4$)$_2$ cannot be a perfect prototype for the 2D Ising model. In this work, we present a proposal to use the anisotropic quantum Heisenberg model to describe the magnetic properties of the KTb(WO$_4$)$_2$ quasi-doublet. Our main objective is to describe nonlinear magnetic properties at the low-temperature regime (T < 0.5 K). To achieve our objective, we simulate the magnetic properties of the material considering the anisotropy parameter $\Delta$ values via quantum Monte Carlo (QMC) and compare the results to published experimental data. For comparison, we plot diagrams of magnetization versus field and susceptibility as a T function of temperature. Our results show close agreement with the experimental data, especially at low temperatures and for intermediate values of the magnetic anisotropy parameter.