Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves
We propose a new scheme of modifying spin waves so as to describe the thermodynamic properties of various noncollinear antiferromagnets with particular interest in a comparison between edge- versus corner-sharing triangular-based lattices. The well-known modified spin-wave theory for collinear antif...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | Journal of Physics Communications |
| Online Access: | https://doi.org/10.1088/2399-6528/acd320 |
| _version_ | 1797806017882357760 |
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| author | Shoji Yamamoto Jun Ohara |
| author_facet | Shoji Yamamoto Jun Ohara |
| author_sort | Shoji Yamamoto |
| collection | DOAJ |
| description | We propose a new scheme of modifying spin waves so as to describe the thermodynamic properties of various noncollinear antiferromagnets with particular interest in a comparison between edge- versus corner-sharing triangular-based lattices. The well-known modified spin-wave theory for collinear antiferromagnets diagonalizes a bosonic Hamiltonian subject to the constraint that the total staggered magnetization be zero. Applying this scheme to frustrated noncollinear antiferromagnets ends in a poor thermodynamics, missing the optimal ground state and breaking the local U(1) rotational symmetry. We find such a plausible double-constraint condition for spin spirals as to spontaneously go back to the traditional single-constraint condition at the onset of a collinear Néel-ordered classical ground state. We first diagonalize only the bilinear terms in Holstein-Primakoff boson operators on the order of spin magnitude S and then bring these linear spin waves into interaction in a perturbative rather than variational manner. We demonstrate specific-heat calculations in terms of thus-modified interacting spin waves on various triangular-based lattices. In zero dimension, modified-spin-wave findings in comparison with finite-temperature Lanczos calculations turn out so successful as to reproduce the monomodal and bimodal specific-heat temperature profiles of the triangular-based edge-sharing Platonic and corner-sharing Archimedean polyhedral-lattice antiferromagnets, respectively. In two dimensions, high-temperature series expansions and tensor-network-based renormalization-group calculations are still controversial especially at low temperatures, and under such circumstances, modified spin waves interestingly predict that the specific heat of the kagome-lattice antiferromagnet in the corner-sharing geometry remains having both mid-temperature broad maximum and low-temperature narrow peak in the thermodynamic limit, while the specific heat of the triangular-lattice antiferromagnet in the edge-sharing geometry retains a low-temperature sharp peak followed by a mid-temperature weak anormaly in the thermodynamic limit. By further calculating one-magnon spectral functions in terms of our newly developed double-constraint modified spin-wave theory, we reveal that not only the elaborate modification scheme but also quantum corrections, especially those caused by the O ( S ^0 ) primary self-energies, are key ingredients in the successful description of triangular-based-lattice noncollinear antiferromagnets over the whole temperature range of absolute zero to infinity. |
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| format | Article |
| id | doaj.art-352e55bdaed5474eb2f594dc1ac3a128 |
| institution | Directory Open Access Journal |
| issn | 2399-6528 |
| language | English |
| last_indexed | 2024-03-13T05:59:54Z |
| publishDate | 2023-01-01 |
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| spelling | doaj.art-352e55bdaed5474eb2f594dc1ac3a1282023-06-12T16:59:09ZengIOP PublishingJournal of Physics Communications2399-65282023-01-017606500410.1088/2399-6528/acd320Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin wavesShoji Yamamoto0https://orcid.org/0000-0003-4770-8375Jun Ohara1https://orcid.org/0000-0003-2765-8446Department of Physics, Hokkaido University , Sapporo 060-0810, JapanDepartment of Physics, Hokkaido University , Sapporo 060-0810, JapanWe propose a new scheme of modifying spin waves so as to describe the thermodynamic properties of various noncollinear antiferromagnets with particular interest in a comparison between edge- versus corner-sharing triangular-based lattices. The well-known modified spin-wave theory for collinear antiferromagnets diagonalizes a bosonic Hamiltonian subject to the constraint that the total staggered magnetization be zero. Applying this scheme to frustrated noncollinear antiferromagnets ends in a poor thermodynamics, missing the optimal ground state and breaking the local U(1) rotational symmetry. We find such a plausible double-constraint condition for spin spirals as to spontaneously go back to the traditional single-constraint condition at the onset of a collinear Néel-ordered classical ground state. We first diagonalize only the bilinear terms in Holstein-Primakoff boson operators on the order of spin magnitude S and then bring these linear spin waves into interaction in a perturbative rather than variational manner. We demonstrate specific-heat calculations in terms of thus-modified interacting spin waves on various triangular-based lattices. In zero dimension, modified-spin-wave findings in comparison with finite-temperature Lanczos calculations turn out so successful as to reproduce the monomodal and bimodal specific-heat temperature profiles of the triangular-based edge-sharing Platonic and corner-sharing Archimedean polyhedral-lattice antiferromagnets, respectively. In two dimensions, high-temperature series expansions and tensor-network-based renormalization-group calculations are still controversial especially at low temperatures, and under such circumstances, modified spin waves interestingly predict that the specific heat of the kagome-lattice antiferromagnet in the corner-sharing geometry remains having both mid-temperature broad maximum and low-temperature narrow peak in the thermodynamic limit, while the specific heat of the triangular-lattice antiferromagnet in the edge-sharing geometry retains a low-temperature sharp peak followed by a mid-temperature weak anormaly in the thermodynamic limit. By further calculating one-magnon spectral functions in terms of our newly developed double-constraint modified spin-wave theory, we reveal that not only the elaborate modification scheme but also quantum corrections, especially those caused by the O ( S ^0 ) primary self-energies, are key ingredients in the successful description of triangular-based-lattice noncollinear antiferromagnets over the whole temperature range of absolute zero to infinity.https://doi.org/10.1088/2399-6528/acd320 |
| spellingShingle | Shoji Yamamoto Jun Ohara Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves Journal of Physics Communications |
| title | Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves |
| title_full | Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves |
| title_fullStr | Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves |
| title_full_unstemmed | Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves |
| title_short | Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves |
| title_sort | thermal features of heisenberg antiferromagnets on edge versus corner sharing triangular based lattices a message from spin waves |
| url | https://doi.org/10.1088/2399-6528/acd320 |
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