{"title":"Fe2Cu2 聚合物支链中的量子磁性:从精确求解的 Ising-Heisenberg 模型中获得的启示","authors":"Dávid Sivý, Katarína Karl’ová, Jozef Strečka","doi":"10.3389/fphy.2024.1408429","DOIUrl":null,"url":null,"abstract":"The spin-1/2 Ising-Heisenberg branched chain, inspired by the magnetic structure of three isostructural polymeric coordination compounds [(Tp)<jats:sub>2</jats:sub>Fe<jats:sub>2</jats:sub>(CN)<jats:sub>6</jats:sub>X (bdmap)Cu<jats:sub>2</jats:sub>(H<jats:sub>2</jats:sub>O)] ⋅ H<jats:sub>2</jats:sub>O to be further denoted as Fe<jats:sub>2</jats:sub>Cu<jats:sub>2</jats:sub> (Tp = tris(pyrazolyl)hydroborate, bdmapH = 1,3-bis(dimethylamino)-2-propanol, HX = acetic acid, propionic acid or trifluoroacetic acid), is rigorously studied using the transfer-matrix method. The overall ground-state phase diagram reveals three distinct phases: a quantum antiferromagnetic phase, a quantum ferrimagnetic phase and a classical ferromagnetic phase. In the zero-temperature magnetization curve, two quantum ground states are manifested as intermediate plateaus at zero and half of the saturation magnetization, while the magnetization reaches its saturated value within the classical ferromagnetic phase. The bipartite entanglement between nearest-neighbor Heisenberg spins is more pronounced in the quantum ferrimagnetic phase compared to the quantum antiferromagnetic phase due to a fully polarized nature of the Ising spins. A reasonable agreement between theoretical predictions for the spin-1/2 Ising-Heisenberg branched chain and experimental data measured for a temperature dependence of the magnetic susceptibility and a low-temperature magnetization curve suggests strong antiferromagnetic coupling between nearest-neighbor Cu<jats:sup>2+</jats:sup>-Cu<jats:sup>2+</jats:sup> magnetic ions and moderately strong ferromagnetic coupling between nearest-neighbor Cu<jats:sup>2+</jats:sup>-Fe<jats:sup>3+</jats:sup> magnetic ions in the polymeric compounds Fe<jats:sub>2</jats:sub>Cu<jats:sub>2</jats:sub>. A thermal entanglement between nearest-neighbor Cu<jats:sup>2+</jats:sup>-Cu<jats:sup>2+</jats:sup> magnetic ions persists up to a relatively high threshold temperature <jats:italic>T</jats:italic> ≈ 224 K and undergoes a transient magnetic-field-driven strengthening.","PeriodicalId":12507,"journal":{"name":"Frontiers in Physics","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantum magnetism in Fe2Cu2 polymeric branched chains: insights from exactly solved Ising-Heisenberg model\",\"authors\":\"Dávid Sivý, Katarína Karl’ová, Jozef Strečka\",\"doi\":\"10.3389/fphy.2024.1408429\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The spin-1/2 Ising-Heisenberg branched chain, inspired by the magnetic structure of three isostructural polymeric coordination compounds [(Tp)<jats:sub>2</jats:sub>Fe<jats:sub>2</jats:sub>(CN)<jats:sub>6</jats:sub>X (bdmap)Cu<jats:sub>2</jats:sub>(H<jats:sub>2</jats:sub>O)] ⋅ H<jats:sub>2</jats:sub>O to be further denoted as Fe<jats:sub>2</jats:sub>Cu<jats:sub>2</jats:sub> (Tp = tris(pyrazolyl)hydroborate, bdmapH = 1,3-bis(dimethylamino)-2-propanol, HX = acetic acid, propionic acid or trifluoroacetic acid), is rigorously studied using the transfer-matrix method. The overall ground-state phase diagram reveals three distinct phases: a quantum antiferromagnetic phase, a quantum ferrimagnetic phase and a classical ferromagnetic phase. In the zero-temperature magnetization curve, two quantum ground states are manifested as intermediate plateaus at zero and half of the saturation magnetization, while the magnetization reaches its saturated value within the classical ferromagnetic phase. The bipartite entanglement between nearest-neighbor Heisenberg spins is more pronounced in the quantum ferrimagnetic phase compared to the quantum antiferromagnetic phase due to a fully polarized nature of the Ising spins. A reasonable agreement between theoretical predictions for the spin-1/2 Ising-Heisenberg branched chain and experimental data measured for a temperature dependence of the magnetic susceptibility and a low-temperature magnetization curve suggests strong antiferromagnetic coupling between nearest-neighbor Cu<jats:sup>2+</jats:sup>-Cu<jats:sup>2+</jats:sup> magnetic ions and moderately strong ferromagnetic coupling between nearest-neighbor Cu<jats:sup>2+</jats:sup>-Fe<jats:sup>3+</jats:sup> magnetic ions in the polymeric compounds Fe<jats:sub>2</jats:sub>Cu<jats:sub>2</jats:sub>. A thermal entanglement between nearest-neighbor Cu<jats:sup>2+</jats:sup>-Cu<jats:sup>2+</jats:sup> magnetic ions persists up to a relatively high threshold temperature <jats:italic>T</jats:italic> ≈ 224 K and undergoes a transient magnetic-field-driven strengthening.\",\"PeriodicalId\":12507,\"journal\":{\"name\":\"Frontiers in Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-06-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Frontiers in Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.3389/fphy.2024.1408429\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Frontiers in Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3389/fphy.2024.1408429","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Quantum magnetism in Fe2Cu2 polymeric branched chains: insights from exactly solved Ising-Heisenberg model
The spin-1/2 Ising-Heisenberg branched chain, inspired by the magnetic structure of three isostructural polymeric coordination compounds [(Tp)2Fe2(CN)6X (bdmap)Cu2(H2O)] ⋅ H2O to be further denoted as Fe2Cu2 (Tp = tris(pyrazolyl)hydroborate, bdmapH = 1,3-bis(dimethylamino)-2-propanol, HX = acetic acid, propionic acid or trifluoroacetic acid), is rigorously studied using the transfer-matrix method. The overall ground-state phase diagram reveals three distinct phases: a quantum antiferromagnetic phase, a quantum ferrimagnetic phase and a classical ferromagnetic phase. In the zero-temperature magnetization curve, two quantum ground states are manifested as intermediate plateaus at zero and half of the saturation magnetization, while the magnetization reaches its saturated value within the classical ferromagnetic phase. The bipartite entanglement between nearest-neighbor Heisenberg spins is more pronounced in the quantum ferrimagnetic phase compared to the quantum antiferromagnetic phase due to a fully polarized nature of the Ising spins. A reasonable agreement between theoretical predictions for the spin-1/2 Ising-Heisenberg branched chain and experimental data measured for a temperature dependence of the magnetic susceptibility and a low-temperature magnetization curve suggests strong antiferromagnetic coupling between nearest-neighbor Cu2+-Cu2+ magnetic ions and moderately strong ferromagnetic coupling between nearest-neighbor Cu2+-Fe3+ magnetic ions in the polymeric compounds Fe2Cu2. A thermal entanglement between nearest-neighbor Cu2+-Cu2+ magnetic ions persists up to a relatively high threshold temperature T ≈ 224 K and undergoes a transient magnetic-field-driven strengthening.
期刊介绍:
Frontiers in Physics publishes rigorously peer-reviewed research across the entire field, from experimental, to computational and theoretical physics. This multidisciplinary open-access journal is at the forefront of disseminating and communicating scientific knowledge and impactful discoveries to researchers, academics, engineers and the public worldwide.