The Heisenberg antiferromagnet on the square-kagomé lattice

Richter Richter,Schulenburg Schulenburg,Tomczak Tomczak,Schmalfuß Schmalfuß

doi:10.5488/cmp.12.3.507

Abstract

e lattice. This magnetic system belongs to the class of highly frustrated spin systems with an innite non-trivial degeneracy of the classical ground state as it is also known for the Heisenberg antiferromagnet on the kagom · and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet with a nite spin gap and with a large number of non-magnetic excitations within this gap. We also discuss the magnetization versus eld curve that shows a plateaux as well as a macroscopic magnetization jump to saturation due to independent localized magnon states. These localized states are highly degenerate and lead to interesting features in the low-temperature thermodynamics at high magnetic elds such as an additional low-temperature peak in the specic heat and an enhanced magnetocaloric effect.

Highlights

The magnetic properties of low-dimensional antiferromagnetic quantum spin systems have been a subject of many theoretical studies in recent years [1,2]
A lot of activities in this area were focused on frustrated spin-half Heisenberg antiferromagnets like the J1–J2 antiferromagnet on the square lattice and on three-dimensional cubic lattices [29,30,31,32,33], the Heisenberg antiferromagnet (HAFM) on the star lattice [12,11,34] and last but not least the HAFM on the kagome lattice
As a result of the interplay between quantum fluctuations and strong frustration for the kagome lattice, the ground state is most likely magnetically disordered with a spin gap to the triplet excitations and an exceptional density of low-lying singlets below c J

Summary

Introduction

The magnetic properties of low-dimensional antiferromagnetic quantum spin systems have been a subject of many theoretical studies in recent years [1,2]. There is most likely no magnetic ground state order for the quantum spinhalf HAFM on both lattices, the nature of both quantum ground states as well as the low-lying spectrum are basically different It was argued [12] that the origin for this difference lies in the existence of nonequivalent nearest-neighbor (NN) bonds in the star lattice whereas all NN bonds in the kagome lattice are equivalent. The HAFM on the square-kagome lattice is strongly frustrated and exhibits an infinite non-trivial degeneracy of the classical ground state, see section 3. The classical ground state of the HAFM on the star lattice exhibits an infinite non-trivial degeneracy Due to these similarities we can expect that the HAFM on the square-kagome lattice is another candidate for a quantum paramagnetic ground state. The question arises, whether the quantum ground state displays similar properties as that for the kagome lattice or as that for the star lattice or for none of them

The model

Semi-classical ground state

The quantum ground state and low-lying excitations at zero field

Magnetization process

Low-temperature thermodynamics

Summary and conclusions