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Journal of Physics Conference Series

Magnetization properties, super-stable points, and cycles of antiferromagnetic spin-1 diamond chains with nodal-nodal interactions

Gayane A. Amatuni, Č. Burdík, Hasmik Poghosyan, L. Ananikyan, N.S. Ananikian

Published Dec 1, 2023• 0 citations
Publisher

Abstract

Abstract This study is devoted to the discovery of super-stable points and cycles in antiferromagnetic Ising and Ising-Heisenberg models with spin 1 on diamond chains with nodal-nodal interactions. These phenomena are important for understanding the complex behavior of magnetic systems. We specifically investigate their connection with magnetization plateaus, which serve as critical indicators of the model’s characteristics. Employing the recurrence relations technique, we derive multidimensional rational mappings that give insights about the statistical properties of the models. Carefully examining the stability properties of these mappings, in particular, by analyzing the maximum Lyapunov exponent, we have revealed the complex relationship between the magnetization plateau and dynamic properties. Throughout our extensive research, we have comprehensively studied the existence and behavior of super-stable points and cycles for various parameter configurations in spin-1 models on the diamond chains. By highlighting the basic properties of dynamics and stability, our research advances a fundamental understanding of complex magnetic systems and their fascinating properties.

DOI
10.1088/1742-6596/2667/1/012062

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Abstract This study is devoted to the discovery of super-stable points and cycles in antiferromagnetic Ising and Ising-Heisenberg models with spin 1 on diamond chains with nodal-nodal interactions. These phenomena are important for understanding the complex behavior of magnetic systems. We specifically investigate their connection with magnetization plateaus, which serve as critical indicators of the model’s characteristics. Employing the recurrence relations technique, we derive multidimensional rational mappings that give insights about the statistical properties of the models. Carefully examining the stability properties of these mappings, in particular, by analyzing the maximum Lyapunov exponent, we have revealed the complex relationship between the magnetization plateau and dynamic properties. Throughout our extensive research, we have comprehensively studied the existence and behavior of super-stable points and cycles for various parameter configurations in spin-1 models on the diamond chains. By highlighting the basic properties of dynamics and stability, our research advances a fundamental understanding of complex magnetic systems and their fascinating properties.
Abstract We study spin-1 antiferromagnetic Ising–Heisenberg models on diamond chains with biquadratic nodal–nodal interactions, focusing on the emergence of superstable points and cycles. Using recurrence relations to derive multidimensional rational mappings, we analyze their stability via the maximum Lyapunov exponent. This reveals a clear link between dynamical features and magnetization plateaus. Our results highlight how super-stable behavior reflects key aspects of the system’s magnetic and dynamic properties across various parameter regimes.
The geometrically magnetic frustrations and quantum thermal entanglement of antiferromagnetic metal-containing compounds are considered on a diamond chain. We researched the magnetic and thermal properties of the symmetric Hubbard dimers with delocalized interstitial spins and the quantum entanglement states. It is presented magnetization plateaus and negativity in spin-1 Ising-Heisenberg model using transfer matrix technique. Applying the dynamic system approach we study the magnetic curves, Lyapunov exponents and superstable point in the two-dimensional mapping for the partition function of spin-1 classical and Ising-Heisenberg models at T → 0 on a diamond chain.
The low-dimensional quantum spin systems have been extensively studied in the past three decades due to the novel ground states and rich magnetic behaviors,especially the quantum spin chain with diamond topology structure. Motivated by recent experimental success in Cu3(CO3)2(OH)2 compound,which is regarded as a model material of spin-1/2 diamond chain,researchers have paid a lot of attention to various variants of diamond spin chains.In this paper,we mainly examine the magnetic properties of an antisymmetric spin-1/2 Ising-Heisenberg diamond chain with the secondneighbor interaction between nodal spins.By using exact diagonalization and transfer-matrix methods,the ground-state phase diagram,magnetization behavior and macroscopic thermodynamics are exactly solved for the particular case that all magnetic bonds yield antiferromagnetic couplings,which usually shows the most interesting magnetic features closely related to a striking interplay between geometric frustration and quantum fluctuations.To clearly illustrate the effect of second-neighbor interaction item,we consider a highly frustrated situation that all Ising-Heisenberg bonds and Heisenberg bonds possess the same interaction strength.The calculation results indicate that the second-neighbor interaction item will enrich ground states and magnetization plateaus.A classical ferrimagnetic phase FRI1 corresponding to a novel two-thirds of intermediate plateau with translationally broken symmetry is introduced,manifesting itself as up-up-up-down-up-up spin configuration at a ground-state.In addition,there are other four distinct ground states which can be identified from the phase diagram,i.e.,one saturated paramagnetic phase SP,one classical ferrimagnetic phase FRI2,one quantum ferrimagnetic phase QFI and the unique quantum antiferromagnetic phase QAF.The classical phase FRI2 and quantum phase QFI both generate one-third of magnetization plateau.It is worth mentioning that all the values of these magnetization plateaus satisfy the Oshikawa-Yamanaka-Affleck condition.Besides,the results also have shown a rich variety of temperature dependence of total magnetization and specific heat.The magnetization displays the remarkable thermal-induced changes as the external field is sufficiently close to critical value where two or more than two different ground states coexist.At the critical field relevant to a coexistence of two different states,the total magnetization displays a monotonic decrease trend.The thermal dependence of zero-field specific heat displays relative complex variations for different second-neighbor interactions between nodal spins.At first,the specific heat presents only a single rounded Schottky-type maximum.Using the second-neighbor interaction,another sharp peak arises at low-temperature and is superimposed on this round maximum,and the specific heat exhibits a double-peak structure. On further strengthening,the low-temperature one keeps its height shifting towards high temperature,while the hightemperature round peak suffers great enhancement and moves in an opposite direction.Finally,the low temperature peak entirely merges with the Schottky-type peak at a certain value of second-neighbor interaction,and above this value, the specific curve recovers its single peak structure.The observed double-peak specific heat curves mainly originate from thermal excitations between the ground-state spin configuration QAF and the ones close enough in energy to the ground state.
The work is devoted to the theoretical study of the energy spectrum and magnetic properties of the modified antiferromagnetic spin (1/2, s) diamond chain. This is a frustrated mixed spin system with the unit cells formed by two spin ½ and one spin s>1/2. On the base of extended Lieb theorem we proved the possibility of the appearance of quantum phase transitions mediated by ratio of coupling parameters at arbitrary nonzero value of the spin s for the above model. The results of our exact diagonalization study for some finite chain clusters with s=1 supports this conclusion. We also studied analytically and numerically magnetic properties of Heisenberg –Ising diamond mixed spin chain. The exact energy spectrum of this model is found in analytical form at arbitrary values of model parameters. On the base of this spectrum we studied the field dependence of two-particle correlators for neighbor Ising spins. It was found that at special relation between coupling parameters there is a critical value of external magnetic field for which the above correlator takes zero value (the absence of the correlation between Ising spins). For infinite spin chain model we studied field dependence of specific magnetization by means of classical transfer- matrix method and found intermediate plateau in the low-temperature magnetization profile. According to our calculations, the size of this plateau depends strongly on the relations between coupling parameters of the model. We hope this feature of our model gives new possibilities for the design of new magnetic chemo-sensors.
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.