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Yuan S, Chen Z, Prokhorenko S, Nahas Y, Bellaiche L, Liu C, Xu B, Chen L, Das S, Martin LW. Hexagonal Close-Packed Polar-Skyrmion Lattice in Ultrathin Ferroelectric PbTiO_{3} Films. PHYSICAL REVIEW LETTERS 2023; 130:226801. [PMID: 37327425 DOI: 10.1103/physrevlett.130.226801] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2022] [Revised: 02/24/2023] [Accepted: 05/05/2023] [Indexed: 06/18/2023]
Abstract
Polar skyrmions are topologically stable, swirling polarization textures with particlelike characteristics, which hold promise for next-generation, nanoscale logic and memory. However, the understanding of how to create ordered polar skyrmion lattice structures and how such structures respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO_{3} films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel's law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics.
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Affiliation(s)
- Shuai Yuan
- School of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen 518055, China and Flexible Printed Electronics Technology Center, Harbin Institute of Technology, Shenzhen 518055, China
| | - Zuhuang Chen
- School of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen 518055, China and Flexible Printed Electronics Technology Center, Harbin Institute of Technology, Shenzhen 518055, China
| | - Sergei Prokhorenko
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Yousra Nahas
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Laurent Bellaiche
- Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, Arkansas 72701, USA
| | - Chenhan Liu
- Micro- and Nano-scale Thermal Measurement and Thermal Management Laboratory, School of Energy and Mechanical Engineering, Nanjing Normal University, Nanjing, 210046, People's Republic of China
| | - Bin Xu
- Institute of Theoretical and Applied Physics and School of Physical Science and Technology, Soochow University, Suzhou, Jiangsu 215006, China
| | - Lang Chen
- Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Sujit Das
- Materials Research Centre, Indian Institute of Science, Bangalore, 560012, India
| | - Lane W Martin
- Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA and Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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Eskildsen MR, Dewhurst CD, Hoogenboom BW, Petrovic C, Canfield PC. Hexagonal and square flux line lattices in CeCoIn5. PHYSICAL REVIEW LETTERS 2003; 90:187001. [PMID: 12786036 DOI: 10.1103/physrevlett.90.187001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2002] [Indexed: 05/24/2023]
Abstract
Using small-angle neutron scattering, we have imaged the magnetic flux line lattice (FLL) in the d-wave heavy-fermion superconductor CeCoIn5. At low fields we find a hexagonal FLL. Around 0.6 T this undergoes what is most likely a first-order transition to square symmetry, with the nearest neighbors oriented along the gap node directions. This orientation of the square FLL is consistent with theoretical predictions based on the d-wave order parameter symmetry.
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Safar H, Gammel PL, Huse DA, Alers GB, Bishop DJ, Lee WC, Giapintzakis J, Ginsberg DM. Vortex dynamics below the flux-lattice melting transition in YBa2Cu3O7- delta. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:6211-6214. [PMID: 9981846 DOI: 10.1103/physrevb.52.6211] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Keimer B, Shih WY, Aksay IA, Lynn JW, Erwin RW. Keimer et al. reply. PHYSICAL REVIEW LETTERS 1995; 75:1423. [PMID: 10060292 DOI: 10.1103/physrevlett.75.1423] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Yaron U, Gammel PL, Huse DA, Kleiman RN, Oglesby CS, Bucher E, Batlogg B, Bishop DJ, Mortensen K, Clausen KN. Structural evidence for a two-step process in the depinning of the superconducting flux-line lattice. Nature 1995. [DOI: 10.1038/376753a0] [Citation(s) in RCA: 163] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Keimer B, Shih WY, Erwin RW, Lynn JW, Dogan F, Aksay IA. Vortex lattice symmetry and electronic structure in YBa2Cu 3O7. PHYSICAL REVIEW LETTERS 1994; 73:3459-3462. [PMID: 10057386 DOI: 10.1103/physrevlett.73.3459] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Hess HF, Murray CA, Waszczak JV. Flux lattice and vortex structure in 2H-NbSe2 in inclined fields. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:16528-16540. [PMID: 9976040 DOI: 10.1103/physrevb.50.16528] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Yaron U, Gammel PL, Huse DA, Kleiman RN, Oglesby CS, Bucher E, Batlogg B, Bishop DJ, Mortensen K, Clausen K, Bolle CA. Neutron diffraction studies of flowing and pinned magnetic flux lattices in 2H-NbSe2. PHYSICAL REVIEW LETTERS 1994; 73:2748-2751. [PMID: 10057182 DOI: 10.1103/physrevlett.73.2748] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Barford W, Harrison M. Abrikosov flux lattice in planar crystals of YBa2Cu3O7- delta. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:13748-13755. [PMID: 9975575 DOI: 10.1103/physrevb.50.13748] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Lynn JW, Rosov N, Grigereit TE, Zhang H, Clinton TW. Vortex dynamics and melting in niobium. PHYSICAL REVIEW LETTERS 1994; 72:3413-3416. [PMID: 10056192 DOI: 10.1103/physrevlett.72.3413] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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