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Interplay of Spin and Spatial Anisotropy in Low-Dimensional Quantum Magnets with Spin 1/2. CRYSTALS 2018. [DOI: 10.3390/cryst9010006] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates between the spin liquid and the ordered collinear Néel state with the partially reduced order parameter. The diversity of additional exchange interactions offers variety of quantum models derived from the aforementioned paradigms. Besides the spatial anisotropy of the exchange coupling, controlling the lattice dimensionality and ground-state properties, the spin anisotropy (intrinsic or induced by the magnetic field) represents another important effect disturbing a rotational symmetry of the spin system. The S = 1/2 easy-axis and easy-plane XXZ models on the square lattice even for extremely weak spin anisotropies undergo Heisenberg-Ising and Heisenberg-XY crossovers, respectively, acting as precursors to the onset of the finite-temperature phase transitions within the two-dimensional Ising universality class (for the easy axis anisotropy) and a topological Berezinskii–Kosterlitz–Thouless phase transition (for the easy-plane anisotropy). Experimental realizations of the S = 1/2 two-dimensional XXZ models in bulk quantum magnets appeared only recently. Partial solutions of the problems associated with their experimental identifications are discussed and some possibilities of future investigations in quantum magnets on the square and rectangular lattice are outlined.
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Sarkar S, Chaudhury R, Paul SK. The connection between vortex-like topological excitations and conventional excitations in quantum ferromagnetic spin systems on two-dimensional lattice and their stability. INTERNATIONAL JOURNAL OF MODERN PHYSICS B 2015; 29:1550209. [DOI: 10.1142/s0217979215502094] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/19/2023]
Abstract
In this paper, we present a scheme for the construction of quantum states of vortex-like topological excitations corresponding to spin-1/2 strongly XY-anisotropic nearest neighbor Heisenberg ferromagnet on two-dimensional lattice. The procedure involving Pauli spin basis states is carried out corresponding to both infinite dilute limit and finite density limit of vortex/anti-vortex. It is found that the corresponding quantum mechanical states representing charge 1 quantum vortices/anti-vortices can be expressed as linear combinations of single magnon states, composite multi-magnon states and the ground state. Detailed calculations show that these states are quantum mechanically stable states of the Hamiltonian only when the system size exceeds certain threshold value. Our analysis indicates that the interactions between different magnon modes can very well generate these topological excitations. Possible applications of our calculations to real magnetic systems are also discussed. Magnetic measurements probing spin dynamics may be undertaken to verify the existence of the threshold size for the stability of vortices.
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Affiliation(s)
- Subhajit Sarkar
- S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700098, India
| | - Ranjan Chaudhury
- S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700098, India
| | - Samir K. Paul
- S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700098, India
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Wysin GM. Magnetic vortex mass in two-dimensional easy-plane magnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:15156-15162. [PMID: 9985576 DOI: 10.1103/physrevb.54.15156] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Pereira AR. Vibrational mode of solitons in two-dimensional easy-plane antiferromagnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:11918-11920. [PMID: 9985030 DOI: 10.1103/physrevb.54.11918] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Pereira AR, Coelho FO, Pires AS. Normal modes of vortices in easy-plane antiferromagnets: Exact results and Born approximation. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:6084-6087. [PMID: 9986613 DOI: 10.1103/physrevb.54.6084] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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