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Russian Journal of Physical Chemistry B

Magnetic Properties of a Spin Delta-Chain

V. Ya. Krivnov, Д. В. Дмитриев, Nikolay S. Erikhman

Published Nov 1, 2019• 3 citations
Publisher

Abstract

Abstract A quantum spin model of a delta-chain with ferro- and antiferromagnetic exchange interactions has been analyzed. Special attention has been paid to the analysis of magnetic properties at the critical point that separates the ferro- and ferrimagnetic phases of the ground state. The ground state is macroscopically degenerate in this case, and the entropy at zero temperature is finite. The gap in the excitation spectrum is exponentially small, and the spectrum itself has a multiscale structure that determined the low-temperature thermodynamics. The results obtained are used to analyze the magnetic properties of recently synthesized molecules with a record-breaking spin value of the ground state.

DOI
10.1134/s1990793119060228

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Abstract A quantum spin model of a delta-chain with ferro- and antiferromagnetic exchange interactions has been analyzed. Special attention has been paid to the analysis of magnetic properties at the critical point that separates the ferro- and ferrimagnetic phases of the ground state. The ground state is macroscopically degenerate in this case, and the entropy at zero temperature is finite. The gap in the excitation spectrum is exponentially small, and the spectrum itself has a multiscale structure that determined the low-temperature thermodynamics. The results obtained are used to analyze the magnetic properties of recently synthesized molecules with a record-breaking spin value of the ground state.
We investigate the spin-1/2 Heisenberg model on the delta chain (sawtooth chain) with ferromagnetic nearest-neighbor and antiferromagnetic next-neighbor interactions. For a special ratio between these interactions there is a class of exact ground states formed by localized magnons and the ground state is macroscopically degenerate. The degree of this degeneration is found analytically. It is shown that the residual entropy per spin is s0=12ln2{s}_{0}=\frac{1}{2}ln\phantom{\rule{0.16em}{0ex}}2s0​=21​ln2. An important feature of this model is a sharp decrease of the gaps for excited states with an increase of the number of magnons. These excitations give an essential contribution to the low-temperature thermodynamics. The corresponding thermodynamic quantities are calculated using full exact diagonalization of finite chains up to N=22N=22N=22. The behavior of the considered model is compared with that of the delta chain with both antiferromagnetic interactions.
Background. Low-dimensional quantum magnets based on geometrically frustrated lattices are of considerable interest last time. As a typical example of such systems is the delta-chain which is a linear chain of triangles with spins on vertices. The delta-chain with AF exchange interactions is well studied and has a number of unusual properties. However, the same model with competing ferro (F)-and antiferromagnetic (AF) interactions is less studied. The purpose of this work is the study of the anisotropic F-AF delta-chain on the critical line separating different ground state phases, the calculation of the ground state degeneracy, residual entropy etc. Materials and methods. The study of this model is both analytically and numerically. It is proposed a method of construction of exact ground state wave functions and accounting of the number of ground ststes states in each spin sector. The analytical results are confirmed by numerical calculations of finite chains. Results. It is shown that the ground state manifold of the F-AF delta-chain on the critical line consists of localized magnons. Together with isolated magnons there are bound magnon complexes which give dominated contribution in ground state manifold in the thermodynamic limit. Conclusions. Spin systems with macroscopically degenerated ground state and with residual entropy demonstrate significant magnetocaloric effect. Taking into account great progress in a synthesis of frustrated magnets, it can be expected that real compounds of the FAF delta-chain type with parameters close to critical ones will be obtained and these compounds will be used for the construction of effective magnetocooling devices.
Abstract A quantum spin model of a delta chain with exchange interactions of ferro- (F) and antiferromagnetic (AF) types is studied. The model properties significantly depend on the frustration parameter α (the ratio of the constants of AF and F interactions). When α < 1/2, the ground state is ferromagnetic, and at α = 1/2, a quantum phase transition occurs to another phase. Based on the numerical calculations and analysis of the model at large values of α it is concluded that the ground state at α > 1/2 is magnetically ordered and the total spin of the ground state is half the maximum possible spin. Comparison of the properties of the ground state of the classical and quantum models shows that the considered model is an example of a system in which quantum effects are responsible for the appearance of order from disorder.
We study the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions in an external magnetic field which generalizes the field-free case studied previously. This model plays an important role for the recently synthesized compound Fe10Gd10{\mathrm{Fe}}_{10}{\mathrm{Gd}}_{10}Fe10​Gd10​, which is nearly quantum critical, as well as for the new kagome fluoride Cs2LiTi3F12{\mathrm{Cs}}_{2}{\mathrm{LiTi}}_{3}{\mathrm{F}}_{12}Cs2​LiTi3​F12​. The classical version of the model is solved exactly and explicit analytical results for the low-temperature thermodynamics are obtained. The sss-spin quantum model is studied using exact diagonalization and finite-temperature Lanczos techniques. Particular attention is focused on the magnetization and the susceptibility. The magnetization of the classical model in the ferromagnetic part of the phase diagram defines the universal scaling function which is valid for the quantum model. The dependence of the susceptibility on the spin quantum number sss at the critical point between the ferro- and ferrimagnetic phases is studied and the relation to Fe10Gd10{\mathrm{Fe}}_{10}{\mathrm{Gd}}_{10}Fe10​Gd10​ is discussed.
We consider analytically and numerically an anisotropic spin-[Formula: see text] delta-chain (sawtooth chain) in which exchange interactions between apical and basal spins are ferromagnetic and those between basal spins are antiferromagnetic. In the limit of strong anisotropy of exchange interactions this model can be considered as the Ising delta chain with macroscopic degenerate ground state perturbed by transverse quantum fluctuations. These perturbations lift the ground state degeneracy and the model reduces to the basal XXZ spin chain in the magnetic field induced by static apical spins. We show that the ground state of such a model is ferrimagnetic. The excitations of the model are formed by ferrimagnetic domains separated by domain walls with a finite energy. At low temperatures the system is effectively divided into two independent subsystems, the apical subsystem described by the Ising spin-[Formula: see text] chain and the basal subsystem described by the XXZ chain with infinite zz interactions.
Frustrated spin-12model consisting of a linear chain of triangles with ferro (F)- and antiferromagnetic interactions connected by ferromagnetic interactions (triangles chain) is studied. The ground state phase diagram depending on the interaction ratios consists of ferromagnetic, two ferrimagnetic and singlet phases. The magnetic properties in these phases are analyzed both analytically and numerically. We show that in some regions of the singlet phase the magnetization curves have magnetization plateau and magnetization jumps. We study the thermodynamics and its relation to the specific structure of the excitation spectrum of the triangle chain.