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arXiv:1911.03081 · Physical review. B./Physical review. B

Exact magnetic properties for classical delta-chains with ferromagnetic and antiferromagnetic interactions in applied magnetic field

Д. В. Дмитриев, V. Ya. Krivnov, Jürgen Schnack, Johannes Richter

Published Feb 19, 2020• 13 citations
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Abstract

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 ${\mathrm{Fe}}_{10}{\mathrm{Gd}}_{10}$, which is nearly quantum critical, as well as for the new kagome fluoride ${\mathrm{Cs}}_{2}{\mathrm{LiTi}}_{3}{\mathrm{F}}_{12}$. The classical version of the model is solved exactly and explicit analytical results for the low-temperature thermodynamics are obtained. The $s$-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 $s$ at the critical point between the ferro- and ferrimagnetic phases is studied and the relation to ${\mathrm{Fe}}_{10}{\mathrm{Gd}}_{10}$ is discussed.

DOI
10.1103/physrevb.101.054427

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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.
Low-temperature magnetization curves of the classical frustrated ferromagnetic chain in the external magnetic field near the transition point between the ferromagnetic and the helical phases is studied. It is shown that the calculation of the partition function in the scaling limit reduces to the solution of the Schr\"odinger equation of the special form for the quantum particle. It is proposed that the magnetization of the classical model in the ferromagnetic part of the phase diagram including the transition point defines the universal scaling function which is valid for the quantum model as well. Explicit analytical formulas for the magnetization are given in the limiting cases of low and high magnetic fields. The influence of the easy-axis anisotropy on the magnetic properties of the model is studied. It is shown that even small anisotropy essentially changes the behavior of the susceptibility in the vicinity of the transition point.
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 We study the delta-chain with spin-1 on basal sites and spin- 1 2 on apical sites. The Heisenberg interaction between neighbor basal spins is antiferromagnetic (AF) and the interaction between basal and apical spins is ferromagnetic (F). We show that the magnetization curve of this model is the same as that of the spin- 1 2 kagome-like chain with competing Heisenberg interactions. The ground state phase diagram of the latter as a function of the ratio between the AF and F interaction, α, consists of the ferromagnetic, ferrimagnetic and singlet phases. We study the magnetic properties in each ground state phase and analyze the magnetization curves. We show that there are magnetization plateaus and jumps in definite regions of value α. We compare the magnetic properties of considered models with those of the spin- 1 2 delta chain.
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.
We investigate the ground state properties, magnetization, and low-temperature thermodynamics of the ferromagnetic-antiferromagnetic spin-sss model on diamond-decorated lattices with ideal diamond units, incorporating bilinear Heisenberg and higher-order exchange interactions between diagonal spins-σσσ. Local conservation of the composite spin on each diamond diagonal enables exact analysis. For the pure Heisenberg case, the system undergoes a series of 2σ2σ2σ transitions between monomer-dimer (MD), ferrimagnetic (Ferri) and ferromagnetic (F) phases with different optimal composite spin values as the coupling ratio varies. In the presence of higher-order interactions, a multicritical point exists where the states with all possible values of composite spin are degenerate, leading to maximal ground state degeneracy. The case s=σ=1s=σ=1s=σ=1 with bilinear and biquadratic interactions is studied in detail. Its phase diagram comprises three phases - F, Ferri and MD, which meet at a triple point. On the phase boundaries, the ground state becomes macroscopically degenerate. For the diamond chain, we calculate the ground state degeneracy exactly; for higher dimensions, the problem maps onto a bond percolation framework, solved numerically. The residual entropy per spin reaches up to 60%60\%60% of the maximal value, peaking at the triple point. Low-temperature magnetization curves in external magnetic fields exhibit plateaus and jumps. The excitation spectrum is gapped in the MD phase, gapless in the F phase, and resembles that of the Lieb-Mattis ferrimagnet in the Ferri phase. The high residual entropy suggests potential applications in ultra-low-temperature cooling and quantum thermal machines.