Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets
Abstract
We present that residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-Z2-flux variables in Kitaev models, the freezing of one set of degrees of freedom and the establishment of local constraints are marked by a plateau in entropy as a function of temperature. Yet, with the exception of the rare-earth pyrochlore family of spin-ice materials, evidence for such plateaus is rarely seen in real materials, raising questions about their robustness. Following recent experimental findings of the absence of such plateaus in the triangular-lattice Ising antiferromagnet (TIAF) TmMgGaO4 by Li et al., we explore in detail the existence and rounding of entropy plateaus in TIAF. We use a transfer-matrix method to numerically calculate the properties of the system at different temperatures and magnetic fields, with further neighbor interactions and disorder. In conclusion, we find that temperature windows of entropy plateaus exist only when second-neighbor interactions are no more than a couple of percent of the nearest-neighbor ones, and they are also easily destroyed by disorder in the nearest-neighbor exchange variable, thereby explaining the challenge in observing such effects.
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; National Science Foundation (NSF)
- OSTI Identifier:
- 1597042
- Alternate Identifier(s):
- OSTI ID: 1558173
- Grant/Contract Number:
- SC0014671; FG02-04ER46111; 1855111
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 6; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Entropy; Frustrated magnetism; Phase transitions; 2-dimensional systems; Antiferromagnets; Transfer matrix calculations
Citation Formats
Bradley, Owen, Feng, Chunhan, Scalettar, Richard T., and Singh, Rajiv R. P. Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.100.064414.
Bradley, Owen, Feng, Chunhan, Scalettar, Richard T., & Singh, Rajiv R. P. Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets. United States. https://doi.org/10.1103/PhysRevB.100.064414
Bradley, Owen, Feng, Chunhan, Scalettar, Richard T., and Singh, Rajiv R. P. Tue .
"Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets". United States. https://doi.org/10.1103/PhysRevB.100.064414. https://www.osti.gov/servlets/purl/1597042.
@article{osti_1597042,
title = {Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets},
author = {Bradley, Owen and Feng, Chunhan and Scalettar, Richard T. and Singh, Rajiv R. P.},
abstractNote = {We present that residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-Z2-flux variables in Kitaev models, the freezing of one set of degrees of freedom and the establishment of local constraints are marked by a plateau in entropy as a function of temperature. Yet, with the exception of the rare-earth pyrochlore family of spin-ice materials, evidence for such plateaus is rarely seen in real materials, raising questions about their robustness. Following recent experimental findings of the absence of such plateaus in the triangular-lattice Ising antiferromagnet (TIAF) TmMgGaO4 by Li et al., we explore in detail the existence and rounding of entropy plateaus in TIAF. We use a transfer-matrix method to numerically calculate the properties of the system at different temperatures and magnetic fields, with further neighbor interactions and disorder. In conclusion, we find that temperature windows of entropy plateaus exist only when second-neighbor interactions are no more than a couple of percent of the nearest-neighbor ones, and they are also easily destroyed by disorder in the nearest-neighbor exchange variable, thereby explaining the challenge in observing such effects.},
doi = {10.1103/PhysRevB.100.064414},
journal = {Physical Review B},
number = 6,
volume = 100,
place = {United States},
year = {2019},
month = {8}
}
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Works referenced in this record:
Antiferromagnetism. The Triangular Ising Net
journal, July 1950
- Wannier, G. H.
- Physical Review, Vol. 79, Issue 2
Spin Ice, Fractionalization, and Topological Order
journal, March 2012
- Castelnovo, C.; Moessner, R.; Sondhi, S. L.
- Annual Review of Condensed Matter Physics, Vol. 3, Issue 1
Phase diagram of a nearest neighbor triangular antiferromagnet in an external field
journal, August 1973
- Metcalf, B. D.
- Physics Letters A, Vol. 45, Issue 1
Phase transition of a triangular lattice Ising antiferromagnet
journal, September 2010
- Katsumata, K.; Katori, H. Aruga; Kimura, S.
- Physical Review B, Vol. 82, Issue 10
The Structure and Entropy of Ice and of Other Crystals with Some Randomness of Atomic Arrangement
journal, December 1935
- Pauling, Linus
- Journal of the American Chemical Society, Vol. 57, Issue 12
Models and materials for generalized Kitaev magnetism
journal, November 2017
- Winter, Stephen M.; Tsirlin, Alexander A.; Daghofer, Maria
- Journal of Physics: Condensed Matter, Vol. 29, Issue 49
Spin- Kitaev model: Classical ground states, order from disorder, and exact correlation functions
journal, September 2008
- Baskaran, G.; Sen, Diptiman; Shankar, R.
- Physical Review B, Vol. 78, Issue 11
Why Spin Ice Obeys the Ice Rules
journal, November 2005
- Isakov, S. V.; Moessner, R.; Sondhi, S. L.
- Physical Review Letters, Vol. 95, Issue 21
Thermal Transport in the Kitaev Model
journal, September 2017
- Nasu, Joji; Yoshitake, Junki; Motome, Yukitoshi
- Physical Review Letters, Vol. 119, Issue 12
The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties
journal, July 1998
- Jüttner, G.; Klümper, A.; Suzuki, J.
- Nuclear Physics B, Vol. 522, Issue 3
Phenomenological scaling approach to the triangular Ising antiferromagnet
journal, April 1981
- Kinzel, W.; Schick, M.
- Physical Review B, Vol. 23, Issue 7
Competing phases of the Hubbard model on a triangular lattice: Insights from the entropy
journal, April 2014
- Li, Gang; Antipov, Andrey E.; Rubtsov, Alexey N.
- Physical Review B, Vol. 89, Issue 16
Short-range magnetic interactions in the spin-ice compound
journal, July 2001
- Cornelius, A. L.; Gardner, J. S.
- Physical Review B, Vol. 64, Issue 6
Thermodynamic Properties of the One-Dimensional Half-Filled-Band Hubbard Model
journal, March 1972
- Shiba, H.; Pincus, P. A.
- Physical Review B, Vol. 5, Issue 5
Vindication of as a Model Exchange Quantum Spin Ice
journal, August 2012
- Applegate, R.; Hayre, N. R.; Singh, R. R. P.
- Physical Review Letters, Vol. 109, Issue 9
Nonmonotonic Zero-Point Entropy in Diluted Spin Ice
journal, September 2007
- Ke, X.; Freitas, R. S.; Ueland, B. G.
- Physical Review Letters, Vol. 99, Issue 13
Monte Carlo simulations on a triangular Ising antiferromagnet with nearest and next-nearest interactions
journal, May 2005
- Rastelli, E.; Regina, S.; Tassi, A.
- Physical Review B, Vol. 71, Issue 17
Thermodynamic properties of Yb Ti O pyrochlore as a function of temperature and magnetic field: Validation of a quantum spin ice exchange Hamiltonian
journal, May 2013
- Hayre, N. R.; Ross, K. A.; Applegate, R.
- Physical Review B, Vol. 87, Issue 18
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
journal, December 2012
- Sorella, Sandro; Otsuka, Yuichi; Yunoki, Seiji
- Scientific Reports, Vol. 2, Issue 1
Long-Range Order at Low Temperatures in Dipolar Spin Ice
journal, July 2001
- Melko, Roger G.; den Hertog, Byron C.; Gingras, Michel J. P.
- Physical Review Letters, Vol. 87, Issue 6
Physical properties of the half-filled Hubbard model in infinite dimensions
journal, September 1993
- Georges, Antoine; Krauth, Werner
- Physical Review B, Vol. 48, Issue 10
Anyons in an exactly solved model and beyond
journal, January 2006
- Kitaev, Alexei
- Annals of Physics, Vol. 321, Issue 1
Kitaev-Heisenberg Hamiltonian for high-spin Mott insulators
journal, January 2018
- Sano, Ryoya; Kato, Yasuyuki; Motome, Yukitoshi
- Physical Review B, Vol. 97, Issue 1
Nonequilibrium random-field Ising model on a diluted triangular lattice
journal, January 2015
- Kurbah, Lobisor; Thongjaomayum, Diana; Shukla, Prabodh
- Physical Review E, Vol. 91, Issue 1
Magnetic pyrochlore oxides
journal, January 2010
- Gardner, Jason S.; Gingras, Michel J. P.; Greedan, John E.
- Reviews of Modern Physics, Vol. 82, Issue 1
Colloquium : Theory of intertwined orders in high temperature superconductors
journal, May 2015
- Fradkin, Eduardo; Kivelson, Steven A.; Tranquada, John M.
- Reviews of Modern Physics, Vol. 87, Issue 2
Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings
journal, September 2010
- Chandra, Samarth; Ramola, Kabir; Dhar, Deepak
- Physical Review E, Vol. 82, Issue 3
Finite-temperature properties of strongly correlated fermions in the honeycomb lattice
journal, September 2013
- Tang, Baoming; Paiva, Thereza; Khatami, Ehsan
- Physical Review B, Vol. 88, Issue 12
Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets
journal, April 2000
- den Hertog, Byron C.; Gingras, Michel J. P.
- Physical Review Letters, Vol. 84, Issue 15
Degeneracy of antiferromagnetic Ising lattices at critical magnetic field and zero temperature
journal, September 1978
- Metcalf, B. D.; Yang, C. P.
- Physical Review B, Vol. 18, Issue 5
Ground-state and Thermodynamic Properties of an S = 1 Kitaev Model
journal, June 2018
- Koga, Akihisa; Tomishige, Hiroyuki; Nasu, Joji
- Journal of the Physical Society of Japan, Vol. 87, Issue 6
Dynamic Phase Transition of the Globally-Coupled Kinetic Ising Model in the Low-Frequency Region
journal, February 2008
- Kim, Beom Jun; Hong, Hyunsuk
- Journal of the Korean Physical Society, Vol. 52, Issue 2
Characteristic Crossing Points in Specific Heat Curves of Correlated Systems
journal, February 1997
- Vollhardt, D.
- Physical Review Letters, Vol. 78, Issue 7
Ground state spin orderings of the triangular Ising model with the nearest and next nearest neighbor interaction
journal, January 1974
- Metcalf, B. D.
- Physics Letters A, Vol. 46, Issue 5
Zero-point entropy in ‘spin ice’
journal, May 1999
- Ramirez, A. P.; Hayashi, A.; Cava, R. J.
- Nature, Vol. 399, Issue 6734
Generic Spin Model for the Honeycomb Iridates beyond the Kitaev Limit
journal, February 2014
- Rau, Jeffrey G.; Lee, Eric Kin-Ho; Kee, Hae-Young
- Physical Review Letters, Vol. 112, Issue 7
Thermodynamics of the three-dimensional Hubbard model: Implications for cooling cold atomic gases in optical lattices
journal, February 2011
- De Leo, Lorenzo; Bernier, Jean-Sébastien; Kollath, Corinna
- Physical Review A, Vol. 83, Issue 2
Relevance of the Heisenberg-Kitaev Model for the Honeycomb Lattice Iridates
journal, March 2012
- Singh, Yogesh; Manni, S.; Reuther, J.
- Physical Review Letters, Vol. 108, Issue 12
Signatures of spin and charge energy scales in the local moment and specific heat of the half-filled two-dimensional Hubbard model
journal, March 2001
- Paiva, Thereza; Scalettar, R. T.; Huscroft, Carey
- Physical Review B, Vol. 63, Issue 12
Majorana fermions in the Kitaev quantum spin system α-RuCl3
journal, September 2017
- Do, Seung-Hwan; Park, Sang-Youn; Yoshitake, Junki
- Nature Physics, Vol. 13, Issue 11
Phase diagram of a diluted triangular lattice Ising antiferromagnet in a field
journal, September 2010
- Žukovič, M.; Borovský, M.; Bobák, A.
- Physics Letters A, Vol. 374, Issue 41
Specific heat of the half-filled Hubbard chain: A Feynman path-integral Monte Carlo investigation
journal, June 1996
- Schulte, Joachim; Böhm, Michael C.
- Physical Review B, Vol. 53, Issue 23
Antiferromagnetism. The Triangular Ising Net
journal, June 1973
- Wannier, G. H.
- Physical Review B, Vol. 7, Issue 11
Monte Carlo study of a compressible Ising antiferromagnet on a triangular lattice
journal, May 1996
- Gu, Lei; Chakraborty, Bulbul; Garrido, P. L.
- Physical Review B, Vol. 53, Issue 18
Incipient and well-developed entropy plateaus in spin- Kitaev models
journal, December 2018
- Oitmaa, J.; Koga, A.; Singh, R. R. P.
- Physical Review B, Vol. 98, Issue 21
Anisotropic magnetic properties of the triangular plane lattice material TmMgGaO 4
journal, September 2018
- Cevallos, F. Alex; Stolze, Karoline; Kong, Tai
- Materials Research Bulletin, Vol. 105
Nearly universal crossing point of the specific heat curves of Hubbard models
journal, April 1999
- Chandra, N.; Kollar, M.; Vollhardt, D.
- Physical Review B, Vol. 59, Issue 16
Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
journal, January 2009
- Jackeli, G.; Khaliullin, G.
- Physical Review Letters, Vol. 102, Issue 1
Magnetic monopoles in spin ice
journal, January 2008
- Castelnovo, C.; Moessner, R.; Sondhi, S. L.
- Nature, Vol. 451, Issue 7174
Thermal fractionalization of quantum spins in a Kitaev model: Temperature-linear specific heat and coherent transport of Majorana fermions
journal, September 2015
- Nasu, Joji; Udagawa, Masafumi; Motome, Yukitoshi
- Physical Review B, Vol. 92, Issue 11
Long-Range Order at Low Temperatures in Dipolar Spin Ice
text, January 2001
- Gingras, Michel J. P.; Melko, Roger G.; Den Hertog, Byron C.
- The American Physical Society
Magnetic Monopoles in Spin Ice
journal, January 2008
- Castelnovo, C.; Moessner, R.; Sondhi, S. L.
- Topologica, Vol. 1, Issue 1
Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
text, January 2008
- Baskaran, G.; Sen, Diptiman; Shankar, R.
- arXiv
Spin Ice, Fractionalization and Topological Order
text, January 2011
- Castelnovo, C.; Moessner, R.; Sondhi, S. L.
- arXiv
Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
text, January 2012
- Sorella, Sandro; Otsuka, Yuichi; Yunoki, Seiji
- arXiv
Thermodynamic properties of the Yb2Ti2O7 pyrochlore as a function of temperature and magnetic field: validation of a quantum spin ice exchange Hamiltonian
text, January 2012
- Hayre, N. R.; Ross, K. A.; Applegate, R.
- arXiv
Generic spin model for the honeycomb iridates beyond the Kitaev limit
text, January 2013
- Rau, Jeffrey G.; Lee, Eric Kin-Ho; Kee, Hae-Young
- arXiv
Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
text, January 2015
- Nasu, Joji; Udagawa, Masafumi; Motome, Yukitoshi
- arXiv
Models and Materials for Generalized Kitaev Magnetism
text, January 2017
- Winter, Stephen M.; Tsirlin, Alexander A.; Daghofer, Maria
- arXiv
Anisotropic magnetic properties of the triangular plane lattice material TmMgGaO4
text, January 2017
- Cevallos, F. Alex; Stolze, Karoline; Kong, Tai
- arXiv
Ground-state and thermodynamic properties of an $S=1$ Kitaev model
text, January 2018
- Koga, Akihisa; Tomishige, Hiroyuki; Nasu, Joji
- arXiv
Incipient and well-developed entropy plateaus in spin-S Kitaev models
text, January 2018
- Oitmaa, J.; Koga, A.; Singh, R. R. P.
- arXiv
Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets
text, January 2000
- Hertog, Byron C. den; Gingras, Michel J. P.
- arXiv
Short-range Magnetic interactions in the Spin-Ice compound Ho$_{2}$Ti$_{2}$O$_{7}$
text, January 2001
- Cornelius, A. L.; Gardner, J. S.
- arXiv
Why spin ice obeys the ice rules
text, January 2005
- Isakov, S. V.; Moessner, R.; Sondhi, S. L.
- arXiv
The Hubbard chain at finite temperatures: ab initio calculations of Tomonaga-Luttinger liquid properties
text, January 1997
- Juttner, G.; Klumper, A.; Suzuki, J.
- arXiv