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Spin delta-chain with competing exchange interactions

V. Ya. Krivnov, Dmitriy V. Dmitriev

Published Jan 1, 2024• 0 citations

Abstract

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.

DOI: 10.21685/2072-3040-2024-4-11

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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 consider a spin-[Formula: see text] kagome-like chain with competing ferro- and antiferromagnetic anisotropic exchange interactions. The ground state phase diagram of this model consists of the ferromagnetic and ferrimagnetic phases. We study the ground state and the low-temperature properties on the phase boundary between these phases. The ground state on this phase boundary is macroscopically degenerate and consists of localized magnon states. We calculate the ground state degeneracy and corresponding residual entropy. The spontaneous magnetization has a jump on the phase boundary confirming the first-order type of the phase transition. In the limit of a strong anisotropy, the spectrum of the low-energy excitations has multi-scale structure governing the peculiar features of the specific heat behavior.

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

{s}_{0}=\frac{1}{2}ln\phantom{\rule{0.16em}{0ex}}2

. 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=22

. The behavior of the considered model is compared with that of the delta chain with both antiferromagnetic interactions.

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 consider analytically and numerically an anisotropic $\text{spin}\ensuremath{-}\frac{1}{2}$ delta chain (sawtooth chain) with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interactions. For certain values of the interactions a lowest one-particle band becomes flat and there is a class of localized-magnon eigenstates which form a ground state with a macroscopic degeneracy. In this case the model depends on a single parameter which can be chosen as the anisotropy of the exchange interactions. When this parameter changes from zero to infinity the model interpolates between the one-dimensional isotropic ferromagnet and the frustrated Ising model on the delta chain. It is shown that the low-temperature thermodynamic properties in these limiting cases are governed by the specific structure of the excitation spectrum. In particular, the specific heat has one or infinite number of low-temperature maxima for the small or the large anisotropy parameter, correspondingly. Qualitative features of such behavior survive when the interaction parameters deviate from the relations providing the local magnon ground state.

We consider a class of anisotropic spin-12models with competing ferro- and antiferromagnetic interactions on two-dimensional Tasaki and kagome lattices consisting of corner sharing triangles. For certain values of the interactions the ground state is macroscopically degenerated in zero magnetic field. In this case the ground state manifold consists of isolated magnons as well as the bound magnon complexes. The ground state degeneracy is estimated using a special form of exact wave function which admits arrow configuration representation on two-dimensional lattice. The comparison of this estimate with the result for some special exactly solved models shows that the used approach determines the number of the ground states with exponential accuracy. It is shown that the main contribution to the ground state degeneracy and the residual entropy is given by the bound magnon complexes.