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J. Semicond. > 2021, Volume 42?>?Issue 12?> 120401

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Berezinskii-Kosterlitz-Thouless phase transition in a 2D-XY ferromagnetic monolayer

Jiesu Wang

+ Author Affiliations

 Corresponding author: Jiesu Wang, wangjs@baqis.ac.cn

DOI: 10.1088/1674-4926/42/12/120401

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[1]
Hohenberg P C. Existence of long-range order in one and two dimensions. Phys Rev, 1967, 158, 383 doi: 10.1103/PhysRev.158.383
[2]
Mermin N D, Wagner H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys Rev Lett, 1966, 17, 1133 doi: 10.1103/PhysRevLett.17.1133
[3]
Berezinskiǐ V. Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. Quantum systems. Sov Phys JETP, 1972, 34, 610
[4]
Kosterlitz J M, Thouless D J. Ordering, metastability and phase transitions in two-dimensional systems. J Phys C, 1973, 6, 1181 doi: 10.1088/0022-3719/6/7/010
[5]
Kosterlitz J M. The critical properties of the two-dimensional xy model. J Phys C, 1974, 7, 1046 doi: 10.1088/0022-3719/7/6/005
[6]
Chaikin P M, Lubensky T C. Principles of condensed matter physics. Cambridge, UK: Cambridge University Press, 2020
[7]
Pires T, Sergio A. Theoretical tools for spin models in magnetic systems. IOP ebooks. Bristol, UK: IOP Publishing, 2021
[8]
Bedoya-Pinto A, Ji J R, Pandeya A K, et al. Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer. Science, 2021, 374, 616 doi: 10.1126/science.abd5146
[9]
Huang B, Clark G, Navarro-Moratalla E, et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature, 2017, 546, 270 doi: 10.1038/nature22391
[10]
Ghazaryan D, Greenaway M T, Wang Z, et al. Magnon-assisted tunneling in van der Waals heterostructures based on CrBr3. Nat Electron, 2018, 1, 344 doi: 10.1038/s41928-018-0087-z
[11]
Gong C, Li L, Li Z L, et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature, 2017, 546, 265 doi: 10.1038/nature22060
[12]
Deng Y J, Yu Y J, Song Y C, et al. Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2. Nature, 2018, 563, 94 doi: 10.1038/s41586-018-0626-9
[13]
Bonilla M, Kolekar S, Ma Y J, et al. Strong room-temperature ferromagnetism in VSe2 monolayers on van der Waals substrates. Nat Nanotechnol, 2018, 13, 289 doi: 10.1038/s41565-018-0063-9
[14]
Webster L, Yan J A. Strain-tunable magnetic anisotropy in monolayer CrCl3, CrBr3, and CrI3. Phys Rev B, 2018, 98, 144411 doi: 10.1103/PhysRevB.98.144411
[15]
St?hr J, Siegman H C. Magnetism: From fundamentals to nanoscale dynamics. Berlin, Germany: Springer, 2006
[16]
Takei S, Tserkovnyak Y. Superfluid spin transport through easy-plane ferromagnetic insulators. Phys Rev Lett, 2014, 112, 227201 doi: 10.1103/PhysRevLett.112.227201
[17]
Kim S K, Chung S B. Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition. SciPost Phys, 2021, 10, 068
[18]
Lu X, Fei R, Zhu L, et al. Meron-like topological spin defects in monolayer CrCl3. Nat Commun, 2020, 11, 4724 doi: 10.1038/s41467-020-18573-8
[19]
Augustin M, Jenkins S, Evans R F L, et al. Properties and dynamics of meron topological spin textures in the two-dimensional magnet CrCl3. Nat Commun, 2021, 12, 185 doi: 10.1038/s41467-020-20497-2
Fig. 1.  (Color online) (a–c) Schematic diagrams of different mechanisms of ferroelectric phase transition without applied external magnetic field in (a) Heisenberg model, (b) 2D-XY model, and (c) 2D-Ising model. (d) Theoretical comparison of M–T curves around TC under different mechanisms indicated by corresponding critical exponent β.

Fig. 2.  (Color online) Lattice structure of the CrCl3 monolayer in (a) side view and (b) top view. The sublattice constructed by Cr atoms can be clearly seen.

[1]
Hohenberg P C. Existence of long-range order in one and two dimensions. Phys Rev, 1967, 158, 383 doi: 10.1103/PhysRev.158.383
[2]
Mermin N D, Wagner H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys Rev Lett, 1966, 17, 1133 doi: 10.1103/PhysRevLett.17.1133
[3]
Berezinskiǐ V. Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. Quantum systems. Sov Phys JETP, 1972, 34, 610
[4]
Kosterlitz J M, Thouless D J. Ordering, metastability and phase transitions in two-dimensional systems. J Phys C, 1973, 6, 1181 doi: 10.1088/0022-3719/6/7/010
[5]
Kosterlitz J M. The critical properties of the two-dimensional xy model. J Phys C, 1974, 7, 1046 doi: 10.1088/0022-3719/7/6/005
[6]
Chaikin P M, Lubensky T C. Principles of condensed matter physics. Cambridge, UK: Cambridge University Press, 2020
[7]
Pires T, Sergio A. Theoretical tools for spin models in magnetic systems. IOP ebooks. Bristol, UK: IOP Publishing, 2021
[8]
Bedoya-Pinto A, Ji J R, Pandeya A K, et al. Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer. Science, 2021, 374, 616 doi: 10.1126/science.abd5146
[9]
Huang B, Clark G, Navarro-Moratalla E, et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature, 2017, 546, 270 doi: 10.1038/nature22391
[10]
Ghazaryan D, Greenaway M T, Wang Z, et al. Magnon-assisted tunneling in van der Waals heterostructures based on CrBr3. Nat Electron, 2018, 1, 344 doi: 10.1038/s41928-018-0087-z
[11]
Gong C, Li L, Li Z L, et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature, 2017, 546, 265 doi: 10.1038/nature22060
[12]
Deng Y J, Yu Y J, Song Y C, et al. Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3GeTe2. Nature, 2018, 563, 94 doi: 10.1038/s41586-018-0626-9
[13]
Bonilla M, Kolekar S, Ma Y J, et al. Strong room-temperature ferromagnetism in VSe2 monolayers on van der Waals substrates. Nat Nanotechnol, 2018, 13, 289 doi: 10.1038/s41565-018-0063-9
[14]
Webster L, Yan J A. Strain-tunable magnetic anisotropy in monolayer CrCl3, CrBr3, and CrI3. Phys Rev B, 2018, 98, 144411 doi: 10.1103/PhysRevB.98.144411
[15]
St?hr J, Siegman H C. Magnetism: From fundamentals to nanoscale dynamics. Berlin, Germany: Springer, 2006
[16]
Takei S, Tserkovnyak Y. Superfluid spin transport through easy-plane ferromagnetic insulators. Phys Rev Lett, 2014, 112, 227201 doi: 10.1103/PhysRevLett.112.227201
[17]
Kim S K, Chung S B. Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition. SciPost Phys, 2021, 10, 068
[18]
Lu X, Fei R, Zhu L, et al. Meron-like topological spin defects in monolayer CrCl3. Nat Commun, 2020, 11, 4724 doi: 10.1038/s41467-020-18573-8
[19]
Augustin M, Jenkins S, Evans R F L, et al. Properties and dynamics of meron topological spin textures in the two-dimensional magnet CrCl3. Nat Commun, 2021, 12, 185 doi: 10.1038/s41467-020-20497-2

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    Received: 16 December 2021 Revised: Online: Accepted Manuscript: 17 November 2021Published: 03 December 2021

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      Jiesu Wang. Berezinskii-Kosterlitz-Thouless phase transition in a 2D-XY ferromagnetic monolayer[J]. Journal of Semiconductors, 2021, 42(12): 120401. doi: 10.1088/1674-4926/42/12/120401 ****J S Wang, Berezinskii-Kosterlitz-Thouless phase transition in a 2D-XY ferromagnetic monolayer[J]. J. Semicond., 2021, 42(12): 120401. doi: 10.1088/1674-4926/42/12/120401.
      Citation:
      Jiesu Wang. Berezinskii-Kosterlitz-Thouless phase transition in a 2D-XY ferromagnetic monolayer[J]. Journal of Semiconductors, 2021, 42(12): 120401. doi: 10.1088/1674-4926/42/12/120401 ****
      J S Wang, Berezinskii-Kosterlitz-Thouless phase transition in a 2D-XY ferromagnetic monolayer[J]. J. Semicond., 2021, 42(12): 120401. doi: 10.1088/1674-4926/42/12/120401.

      Berezinskii-Kosterlitz-Thouless phase transition in a 2D-XY ferromagnetic monolayer

      DOI: 10.1088/1674-4926/42/12/120401

      • Beijing Academy of Quantum Information Sciences, Beijing 100193, China

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      • Jiesu Wang：earned her bachelor’s degree from Minzu University of China in 2013, and her PhD from Institute of Physics, Chinese Academy of Sciences (IOP, CAS) in 2018. Subsequently, Wang worked as a postdoc. in Prof. Kuijuan Jin’s group in IOP, CAS. Since June 2020, Wang has started as an Assistant Research Scientist in Beijing Academy of Quantum Information Sciences
      • Corresponding author: wangjs@baqis.ac.cn
      • Received Date: 2021-12-16
      • Published Date: 2021-12-10

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