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Sahoo S, Dey D, Saha SK, Kumar M. Haldane and dimer phases in a frustrated spin chain: an exact groundstate and associated topological phase transition. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:335601. [PMID: 32244238 DOI: 10.1088/1361-648x/ab8663] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/01/2020] [Accepted: 04/03/2020] [Indexed: 06/11/2023]
Abstract
A Heisenberg spin-schain with alternating ferromagnetic (FM) (-J1F<0) and antiferromagnetic (J1A>0) nearest-neighbor (NN) interactions, exhibits the dimer and spin-2sHaldane phases in the limitsJ1F/J1A→0andJ1F/J1A→∞respectively. These two phases are understood to be topologically equivalent. Induction of the frustration through the next NN FM interaction (-J2F<0) produces a very rich quantum phase diagram. With frustration, the whole phase diagram is divided into a FM and a nonmagnetic (NM) phase. Fors= 1/2, the full NM phase is seen to be of Haldane-dimer type, but fors> 1/2, a spiral phase comes between the FM and the Haldane-dimer phases. The study of a suitably defined string-order parameter and spin-gap at the phase boundary indicates that the Haldane-dimer and spiral phases have different topological characters. We also find that, along theJ2F=12J1Fline in the NM phase, an NN dimer state is theexactgroundstate, providedJ1A>JC=κJ1Fwhereκ⩽s+hfor applied magnetic fieldh. Without magnetic field, the position ofJCis on the FM-NM phase boundary whens= 1/2, but fors> 1/2, the location ofJCis on the phase separation line between the Haldane-dimer and spiral phases.
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Affiliation(s)
- Shaon Sahoo
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
- Department of Physics, Indian Institute of Technology Tirupati, Tirupati 517506, India
| | - Dayasindhu Dey
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
| | - Sudip Kumar Saha
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
| | - Manoranjan Kumar
- S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700106, India
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Sahoo S, Durga Prasad Goli VML, Sen D, Ramasesha S. Studies on a frustrated Heisenberg spin chain with alternating ferromagnetic and antiferromagnetic exchanges. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:276002. [PMID: 24935169 DOI: 10.1088/0953-8984/26/27/276002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(F)(1)) and antiferromagnetic (J(A)(1)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(F)(2)). In this model frustration is present due to the non-zero J(F)(2). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(F)(2)and large J(F)(1)/J(A)(1). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(F)(1), the phase diagram in the space of J(A)(1)-J(F)(2) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
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Affiliation(s)
- Shaon Sahoo
- Solid State & Structural Chemistry Unit, Indian Institute of Science, Bangalore 560 012, India
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Mazurenko VV, Valentyuk MV, Stern R, Tsirlin AA. Nonfrustrated interlayer order and its relevance to the Bose-Einstein condensation of magnons in BaCuSi2O6. PHYSICAL REVIEW LETTERS 2014; 112:107202. [PMID: 24679324 DOI: 10.1103/physrevlett.112.107202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2013] [Indexed: 06/03/2023]
Abstract
Han purple (BaCuSi2O6) is not only an ancient pigment, but also a valuable model material for studying Bose-Einstein condensation of magnons in high magnetic fields. Using precise low-temperature structural data and extensive density-functional calculations, we elucidate magnetic couplings in this compound. The resulting magnetic model comprises two types of nonequivalent spin dimers, in excellent agreement with the Cu63,65 nuclear magnetic resonance data. We further argue that leading interdimer couplings connect the upper site of one dimer to the bottom site of the contiguous dimer, and not the upper-to-upper and bottom-to-bottom sites, as assumed previously. This finding is verified by inelastic neutron scattering data and implies the lack of frustration between the layers of spin dimers in BaCuSi2O6, thus challenging existing theories of the two-dimensional-like Bose-Einstein condensation of magnons in this compound.
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Affiliation(s)
- Vladimir V Mazurenko
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, 620002 Ekaterinburg, Russia
| | - Maria V Valentyuk
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, 620002 Ekaterinburg, Russia and Institute of Theoretical Physics, University of Hamburg, Jungiusstraße 9, 20355 Hamburg, Germany
| | - Raivo Stern
- National Institute of Chemical Physics and Biophysics, 12618 Tallinn, Estonia
| | - Alexander A Tsirlin
- National Institute of Chemical Physics and Biophysics, 12618 Tallinn, Estonia
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Landee CP, Turnbull MM. Recent Developments in Low-Dimensional Copper(II) Molecular Magnets. Eur J Inorg Chem 2013. [DOI: 10.1002/ejic.201300133] [Citation(s) in RCA: 62] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Naseri MS, Japaridze GI, Mahdavifar S, Shayesteh SF. Magnetic properties of the spin S = 1/2 Heisenberg chain with hexamer modulation of exchange. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:116002. [PMID: 22353943 DOI: 10.1088/0953-8984/24/11/116002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.
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Affiliation(s)
- M Shahri Naseri
- Department of Physics, University of Guilan, 41335-1914 Rasht, Iran
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Mahdavifar S, Abouie J. Effects of a space modulation on the behavior of a 1D alternating Heisenberg spin-1/2 model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2011; 23:246002. [PMID: 21613724 DOI: 10.1088/0953-8984/23/24/246002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
The effects of a magnetic field (h) and a space modulation (δ) on the magnetic properties of a one-dimensional antiferromagnetic-ferromagnetic Heisenberg spin-1/2 model have been studied by means of numerical exact diagonalization of finite size systems, the nonlinear σ model, and a bosonization approach. The space modulation is considered on the antiferromagnetic couplings. At δ = 0, the model is mapped to a gapless Lüttinger liquid phase by increasing the magnetic field. However, the space modulation induces a new gap in the spectrum of the system and the system experiences different quantum phases which are separated by four critical fields. By opening the new gap, a magnetization plateau appears at ½M(sat). The effects of the space modulation are reflected in the emergence of a plateau in other physical functions such as the F-dimer and the bond-dimer order parameters, and the pair-wise entanglement.
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Yang TH, Knowles ES, Pajerowski DM, Xia JS, Yin L, Gao S, Meisel MW, Zheng LM. Metal Monophosphonates M{(2-C5H4NO)CH2PO3}(H2O)2 (M = Co, Ni, Mn, Cd): Synthesis, Structure, and Magnetism. Inorg Chem 2010; 49:8474-80. [DOI: 10.1021/ic101033n] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ting-Hai Yang
- State Key Laboratory of Coordination Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, People's Republic of China
| | - Elisabeth S. Knowles
- Department of Physics and the National High Magnetic Field Laboratory, University of Florida, Gainesville, Florida 32611-8440
| | - Daniel M. Pajerowski
- Department of Physics and the National High Magnetic Field Laboratory, University of Florida, Gainesville, Florida 32611-8440
| | - Jian-Sheng Xia
- Department of Physics and the National High Magnetic Field Laboratory, University of Florida, Gainesville, Florida 32611-8440
| | - Liang Yin
- Department of Physics and the National High Magnetic Field Laboratory, University of Florida, Gainesville, Florida 32611-8440
| | - Song Gao
- Beijing National Laboratory for Molecular Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
| | - Mark W. Meisel
- Department of Physics and the National High Magnetic Field Laboratory, University of Florida, Gainesville, Florida 32611-8440
| | - Li-Min Zheng
- State Key Laboratory of Coordination Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, People's Republic of China
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