Collapse of Ferrimagnetism in Two-Dimensional Heisenberg Antiferromagnet due to Frustration

Abstract

We study ferrimagnetism in the ground state of the antiferromagnetic Heisenberg model on the spatially anisotropic kagome lattice, in which ferrimagnetism of the conventional Lieb-Mattis type appears in the region of weak frustration whereas the ground state is nonmagnetic in the isotropic case. Numerical diagonalizations of small finite-size clusters are carried out to examine the spontaneous magnetization. We find that the spontaneous magnetization changes continuously in the intermediate region between conventional ferrimagnetism and the nonmagnetic phase. Local magnetization of the intermediate state shows strong dependence on the site position, which suggests non-Lieb-Mattis ferrimagnetism.KEYWORDS: antiferromagnetic Heisenberg spin model, ferrimagnetism, frustration, numerical-diagonalization method, Lanczos methodFerrimagnetism has been studied extensively as an important phenomenon that has both ferromagnetic nature and antiferromagnetic nature at the same time. One of the fundamental keys to understanding ferrimagnetism is the Marshall-Lieb-Mattis (MLM) theorem.1,2) This theorem clarifies some of the magnetic properties in the ground state of a system when the system has a bipartite lattice structure and when a spin on one sublattice interacts antiferromagnetically with a spin on the other sublattice. Under the condition that the sum of the spin amplitudes of spins in each sublattice is different between the two sublattices, one finds that the ground state of such a system exhibits ferrimagnetism. In this ferrimagnetic ground state, spontaneous magnetization is realized and its magnitude is a simple fraction of the saturated magnetization. We hereafter call ferrimagnetism of this type the Lieb-Mattis (LM) type.Some studies in recent years, on the other hand, reported cases when the magnitude of the spontaneous magnetization of the ferrimagnetism is not a simple fraction of the saturated magnetization.3-9) The ferrimagnetic ground state of this type is a nontrivial quantum state whose behavior is difficult to explain well only within the classical picture. Ferrimagnetism of this type was first predicted in ref. 10 using the quantum rotor model. The mechanism of this ferrimagnetism has not been understood sufficiently up to now. Hereafter, we call this case the non-Lieb-Mattis (NLM) type. Note that in the cases when NLM ferrimagnetism is present, the structure of the lattices is limited to being one-dimensional. Recall that the above conditions of the MLM theorem do not include the spatial dimension of the system; the MLM theorem holds irrespective of the spatial dimensionality. We are then faced with a question: can NLM ferrimagnetism be realized when the spatial dimension is more than one?The purpose of this letter is to answer the above question concerning the existence of NLM ferrimagnetism in higher dimensions. In this letter, we consider a case when we introduce a frustrating interaction into a two-dimensional lattice whose interactions satisfy the conditions of the MLM theorem. When the frustrating...

Frustration and Dzyaloshinsky-Moriya anisotropy in the kagome francisitesCu3Bi(SeO3)2ORousochatzakis1, Richter2, Zinke3 et al. 2015Phys. Rev. B534682View full textAdd to dashboardCite

“…This kind of ferrimagnetism is often called Lieb-Mattis ferrimagnetism [54][55][56][57][58] . Francisites exhibit a frustration-induced unconventional (non-Lieb-Mattis) ferrimagnetism, where the GS is noncollinear and the net magnetization is not a simple fraction of the saturated magnetization 43,56 . The first main result of the present study is that this magnetism cannot be captured by isotropic Heisenberg interactions alone in the case of the kagome francisites.…”

Spin-Flop Phenomenon of Two-Dimensional Frustrated Antiferromagnets without Anisotropy in Spin Space

“…The relationship between the two cases will be clarified in future studies. Near the undistorted point J B = J A , another ferromagnetic phase of the non-Lieb-Mattis type is known to be realized 22,23 owing to a distortion of a different type. Further investigations from various viewpoints are required to understand much better the physics of the undistorted point J B = J A .…”

Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet

“…When the kagome lattice is spatially anisotropic, a non-Lieb-Mattis-type ferrimagnetic ground state of the S = 1/2 system exists near the isotropic point. 63,64 It should be examined in future what happens to these nontrivial phenomena when S ≥ 1. Further study on general spin-S systems would greatly contribute to our understanding of the frustration effect in quantum spin systems.…”