Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds

Abstract

An exactly solvable model of the sawtooth chain with Ising and Heisenberg bonds and with coupling to lattice distortion for Heisenberg bonds is considered in the magnetic field. Using the direct transfer-matrix formalism an exact description of the thermodynamic functions is obtained. The ground state phase diagrams for all regions of parameters values containing phases corresponding to the magnetization plateaus at M = 0, 1/4 and 1/2 have been obtained. Exact formulas for bond distortions for various ground states are presented. A mechanism of magnetization plateau stabilization with doubling of unit cell is reported. This mechanism is related with the inequivalence of right and left interaction bonds for certain lattice sites.

Correlation functions in one-dimensional spin lattices with Ising and Heisenberg bonds

“…As the technique, despite its clearness and simplicity, leads to rather cumbersome expressions, we will present explicit calculations for the simplest models which have been investigated earlier in a context of magnetic and thermodynamic properties 1-26 . One can distinguish at least two classes of HIC: the models where each block has a left-right symmetry with respect to the interaction with σ spins [1][2][3][4][5][6][7][8][9]11,14 , which implies that the term describing the interaction between block spins and their left and right σ-neighbors has the form K (σ j + σ j+1 ) a S z j,a , which is completely symmetric with respect to the permutation of the operators S z j,a , and the models which are non symmetric with respect to left and right σ-spins on each block 10,13,19 . It is worth mentioning, that the experimentally obtained single chain magnet compound with Ising and Heisenberg bonds, which is an existing example of HIC, belongs to the second type 32,34 .…”

Antiferromagnetism and the emergence of frustration in the sawtooth lattice chalcogenide olivines Mn2SiS4−xSex ( xNhalil1, Baral2, Khamala3 et al. 2019Phys. Rev. B101160View full textAdd to dashboardCite

“…The saw-tooth antiferromagnetic chain has a frustrated topology of corner-sharing triangles of spins where the ground state of the spin-half saw-tooth chain is understood exactly [1][2][3] . Variety of ground states are predicted for the saw-tooth lattice depending on the ratio of the exchange interaction strengths between the base-base and the base-vertex pairs [4][5][6][7][8] . The saw-tooth systems attain importance in connection with the zero energy flat-band modes similar to the case of Kagome lattices 9,10 and are valuable as potential materials for magnonics 11 .…”

Quantum decoration transformation for spin models

“…The decoration transformation can also be applied to classical-quantum spin models, such as Ising-Heisenberg models. Several quasi-one-dimensional models have been investigated, similar to that diamond-like chain [12,13,14,15,16,17,18,19,20] and references therein, as well as two-dimensional lattice spin models [21,22,23,24,25,26,27,28,29]. Furthermore, it can be applied even for three-dimensional decorated systems [30], this approach can also be applied combining with Monte Carlo simulation for 3D systems [31,32].…”