Frustrated two dimensional quantum magnets

TL;DR

This paper reviews the effects of exchange frustration and quantum fluctuations in two-dimensional quantum magnets, analyzing various phases and properties through numerical and analytical methods, with relevance to experimental materials.

Contribution

It provides a comprehensive overview of the phase diagram and physical properties of frustrated 2D quantum magnets using the $J_1$-$J_2$ model, combining numerical and analytical approaches.

Findings

Identification of various magnetic and nonmagnetic quantum phases.

Analysis of ground state properties like magnetization and structure factor.

Finite temperature properties such as susceptibility and specific heat.

Abstract

We overview physical effects of exchange frustration and quantum spin fluctuations in (quasi-) two dimensional (2D) quantum magnets ($S=1/2$) with square, rectangular and triangular structure. Our discussion is based on the $J_1$-$J_2$ type frustrated exchange model and its generalizations. These models are closely related and allow to tune between different phases, magnetically ordered as well as more exotic nonmagnetic quantum phases by changing only one or two control parameters. We survey ground state properties like magnetization, saturation fields, ordered moment and structure factor in the full phase diagram as obtained from numerical exact diagonalization computations and analytical linear spin wave theory. We also review finite temperature properties like susceptibility, specific heat and magnetocaloric effect using the finite temperature Lanczos method. This method is powerful to determine the exchange parameters and g-factors from experimental results. We focus mostly on the observable physical frustration effects in magnetic phases where plenty of quasi-2D material examples exist to identify the influence of quantum fluctuations on magnetism.