- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review A

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Transverse spin angular momentum of a space-time surface plasmon polariton wave packet

Naoki Ichiji1,2, Daigo Oue3,4,5, Murat Yessenov6, Kenneth L. Schepler6, Ayman F. Abouraddy6, and Atsushi Kubo7,*

  • 1Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8571, Japan
  • 2Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-Ku, Tokyo 153-8505, Japan
  • 3Instituto de Telecomunicações, Instituto Superior Técnico, University of Lisbon, 1049-001 Lisbon, Portugal
  • 4Department of Physics, Kyoto University, Kyoto 606-8502, Japan
  • 5The Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom
  • 6CREOL, The College of Optics & Photonics, University of Central Florida, Orlando, Florida 32816, USA
  • 7Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8571, Japan

  • *kubo.atsushi.ka@u.tsukuba.ac.jp
PDF

Phys. Rev. A 107, 063517 – Published 28 June, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.063517

Abstract

In addition to longitudinal spin angular momentum (SAM) along the axis of propagation of light, spatially structured electromagnetic fields such as evanescent waves and focused beams have recently been found to possess transverse SAM in the direction perpendicular to the axis of propagation. In particular, the SAM of surface plasmon polaritons (SPPs) with spatial structure has been extensively studied in the last decade after it became clear that evanescent fields with spatially structured energy flow generate three-dimensional spin texture. Here we present numerical calculations of the space-time surface plasmon polariton (ST-SPP) wave packet, a plasmonic bullet that propagates at an arbitrary group velocity while maintaining its spatial distribution. ST-SPP wave packets with complex spatial structure and energy flow density distribution determined by the group velocity are found to propagate with accompanying three-dimensional spin texture and finite topological charge density. Furthermore, the spatial distribution of the spin texture and topological charge density determined by the spatial structure of the SPP is controllable, and the deformation associated with propagation is negligible. ST-SPP wave packets, which can stably transport customizable three-dimensional spin textures and topological charge densities, can be excellent subjects of observation in studies of spin photonics and optical topological materials.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (119)

  1. J. H. Poynting, The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light, Proc. R. Soc. London A 82, 560 (1909).
  2. R. A. Beth, Direct detection of the angular momentum of light, Phys. Rev. 48, 471 (1935).
  3. R. A. Beth, Mechanical detection and measurement of the angular momentum of light, Phys. Rev. 50, 115 (1936).
  4. T. Sugiura, S. Kawata, and S. Minami, Optical rotation of small particles by a circularly-polarized laser beam in an optical microscope, J. Spectrosc. Soc. Jpn. 39, 342 (1990).
  5. E. Higurashi, H. Ukita, H. Tanaka, and O. Ohguchi, Optically induced rotation of anisotropic micro-objects fabricated by surface micromachining, Appl. Phys. Lett. 64, 2209 (1994).
  6. E. Higurashi, O. Ohguchi, T. Tamamura, H. Ukita, and R. Sawada, Optically induced rotation of dissymmetrically shaped fluorinated polyimide micro-objects in optical traps, J. Appl. Phys. 82, 2773 (1997).
  7. M. Friese, T. Nieminen, N. Heckenberg, and H. Rubinsztein-Dunlop, Optical alignment and spinning of laser-trapped microscopic particles, Nature (London) 394, 348 (1998).
  8. J. Ahn, Z. Xu, J. Bang, Y.-H. Deng, T. M. Hoang, Q. Han, R.-M. Ma, and T. Li, Optically Levitated Nanodumbbell Torsion Balance and GHz Nanomechanical Rotor, Phys. Rev. Lett. 121, 033603 (2018).
  9. F. Monteiro, S. Ghosh, E. C. van Assendelft, and D. C. Moore, Optical rotation of levitated spheres in high vacuum, Phys. Rev. A 97, 051802(R) (2018).
  10. R. Reimann, M. Doderer, E. Hebestreit, R. Diehl, M. Frimmer, D. Windey, F. Tebbenjohanns, and L. Novotny, GHz Rotation of an Optically Trapped Nanoparticle in Vacuum, Phys. Rev. Lett. 121, 033602 (2018).
  11. Y. Jin, J. Yan, S. J. Rahman, J. Li, X. Yu, and J. Zhang, 6 GHz hyperfast rotation of an optically levitated nanoparticle in vacuum, Photon. Res. 9, 1344 (2021).
  12. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Transverse Angular Momentum and Geometric Spin Hall Effect of Light, Phys. Rev. Lett. 103, 100401 (2009).
  13. A. Aiello, C. Marquardt, and G. Leuchs, Transverse angular momentum of photons, Phys. Rev. A 81, 053838 (2010).
  14. K. Y. Bliokh and F. Nori, Transverse and longitudinal angular momenta of light, Phys. Rep. 592, 1 (2015).
  15. A. Y. Bekshaev, Oblique section of a paraxial light beam: Criteria for azimuthal energy flow and orbital angular momentum, J. Opt. A: Pure Appl. Opt. 11, 094003 (2009).
  16. M. Antognozzi, C. Bermingham, R. Harniman, S. Simpson, J. Senior, R. Hayward, H. Hoerber, M. Dennis, A. Bekshaev, K. Bliokh et al., Direct measurements of the extraordinary optical momentum and transverse spin-dependent force using a nano-cantilever, Nat. Phys. 12, 731 (2016).
  17. A. Canaguier-Durand and C. Genet, Plasmonic lateral forces on chiral spheres, J. Opt. 18, 015007 (2016).
  18. A. Canaguier-Durand and C. Genet, Transverse spinning of a sphere in a plasmonic field, Phys. Rev. A 89, 033841 (2014).
  19. C. Junge, D. O'Shea, J. Volz, and A. Rauschenbeutel, Strong Coupling between Single Atoms and Nontransversal Photons, Phys. Rev. Lett. 110, 213604 (2013).
  20. A. Aiello, P. Banzer, M. Neugebaueru, and G. Leuchs, From transverse angular momentum to photonic wheels, Nat. Photon. 9, 789 (2015).
  21. X. Zhang, B. Shen, Z. Zhu, G. Rui, J. He, Y. Cui, and B. Gu, Understanding of transverse spin angular momentum in tightly focused linearly polarized vortex beams, Opt. Express 30, 5121 (2022).
  22. D. R. Abujetas and J. A. Sanchez-Gil, Spin angular momentum of guided light induced by transverse confinement and intrinsic helicity, ACS Photon. 7, 534 (2020).
  23. A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, Transverse Spin and Momentum in Two-Wave Interference, Phys. Rev. X 5, 011039 (2015).
  24. K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, Extraordinary momentum and spin in evanescent waves, Nat. Commun. 5, 3300 (2014).
  25. Oleh Y. Yermakov, Anton I. Ovcharenko, Andrey A. Bogdanov, I. V. Iorsh, K. Y. Bliokh, and Y. S. Kivshar, Spin control of light with hyperbolic metasurfaces, Phys. Rev. B 94, 075446 (2016).
  26. K. Y. Bliokh, H. Punzmann, H. Xia, F. Nori, and M. Shats, Field theory spin and momentum in water waves, Sci. Adv. 8, eabm1295 (2022).
  27. K. Y. Bliokh and F. Nori, Transverse spin of a surface polariton, Phys. Rev. A 85, 061801(R) (2012).
  28. K.-Y. Kim, I.-M. Lee, J. Kim, J. Jung, and B. Lee, Time reversal and the spin angular momentum of transverse-electric and transverse-magnetic surface modes, Phys. Rev. A 86, 063805 (2012).
  29. K.-Y. Kim and A. X. Wang, Spin angular momentum of surface modes from the perspective of optical power flow, Opt. Lett. 40, 2929 (2015).
  30. K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, Optical Momentum, Spin, and Angular Momentum in Dispersive Media, Phys. Rev. Lett. 119, 073901 (2017).
  31. Y. Dai, M. Dabrowski, V. A. Apkarian, and H. Petek, Ultrafast microscopy of spin-momentum-locked surface plasmon polaritons, ACS Nano 12, 6588 (2018).
  32. K. Y. Bliokh, D. Smirnova, and F. Nori, Quantum spin Hall effect of light, Science 348, 1448 (2015).
  33. T. V. Mechelen and Z. Jacob, Universal spin-momentum locking of evanescent waves, Optica 3, 118 (2016).
  34. D. O'Connor, P. Ginzburg, F. J. Rodriguez-Fortuno, G. A. Wurtz, and A. V. Zayats, Spin-orbit coupling in surface plasmon scattering by nanostructures, Nat. Commun. 5, 5327 (2014).
  35. F. J. Rodriguez-Fortuno, G. Marino, P. Ginzburg, D. O'Connor, A. Martinez, G. A. Wurtz, and A. V. Zayats, Near-field interference for the unidirectional excitation of electromagnetic guided modes, Science 340, 328 (2013).
  36. Y. Dai and H. Petek, Plasmonic spin-Hall effect in surface plasmon polariton focusing, ACS Photon. 6, 2005 (2019).
  37. P. Shi, L. Du, and X. Yuan, Spin photonics: From transverse spin to photonic skyrmions, Nanophotonics 10, 3927 (2021).
  38. F. Cardano and L. Marrucci, Spin-orbit photonics, Nat. Photon. 9, 776 (2015).
  39. L. Du, A. Yang, A. V. Zayats, and X. Yuan, Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum, Nat. Phys. 15, 650 (2019).
  40. Y. Dai, Z. Zhou, A. Ghosh, R. S. K. Mong, A. Kubo, C.-B. Huang, and H. Petek, Plasmonic topological quasiparticle on the nanometre and femtosecond scales, Nature (London) 588, 616 (2020).
  41. X. Lei, A. Yang, P. Shi, Z. Xie, L. Du, A. V. Zayats, and X. Yuan, Photonic Spin Lattices: Symmetry Constraints for Skyrmion and Meron Topologies, Phys. Rev. Lett. 127, 237403 (2021).
  42. Q. Zhang, Z. Xie, L. Du, P. Shi, and X. Yuan, Bloch-type photonic skyrmions in optical chiral multilayers, Phys. Rev. Res. 3, 023109 (2021).
  43. A. Ghosh, S. Yang, Y. Dai, Z. Zhou, T. Wang, C.-B. Huang, and H. Petek, A topological lattice of plasmonic merons, Appl. Phys. Rev. 8, 041413 (2021).
  44. Y. Dai, Z. Zhou, A. Ghosh, K. Kapoor, M. Dabrowski, A. Kubo, C.-B. Huang, and H. Petek, Ultrafast microscopy of a twisted plasmonic spin skyrmion, Appl. Phys. Rev. 9, 011420 (2022).
  45. P. Shi, L. Du, M. Li, and X. Yuan, Symmetry-protected photonic chiral spin textures by spin-orbit coupling, Laser Photon. Rev. 15, 2000554 (2021).
  46. P. Shi, L. Du, C. Li, A. V. Zayats, and X. Yuan, Transverse spin dynamics in structured electromagnetic guided waves, Proc. Natl. Acad. Sci. USA 118, e2018816118 (2021).
  47. C. Taneja, D. Paul, and G. V. P. Kumar, Experimental observation of transverse spin of plasmon polaritons in a single crystalline silver nanowire, Appl. Phys. Lett. 119, 161108 (2021).
  48. Y. Dai, A. Ghosh, S. Yang, Z. Zhou, C.-b. Huang, and H. Petek, Poincare engineering of surface plasmon polaritons, Nat. Rev. Phys. 4, 562 (2022).
  49. A. Ghosh, S. Yang, Y. Dai, and H. Petek, The spin texture topology of polygonal plasmon fields, ACS Photon. 10, 13 (2023).
  50. Y. Shen, E. C. Martinez, and C. Rosales-Guzman, Generation of optical skyrmions with tunable topological textures, ACS Photon. 9, 296 (2022).
  51. Y. Shen, Topological bimeronic beams, Opt. Lett. 46, 3737 (2021).
  52. Z.-L. Deng, T. Shi, A. Krasnok, X. Li, and A. Alu, Observation of localized magnetic plasmon skyrmions, Nat. Commun. 13, 8 (2022).
  53. L. Xiong, Y. Li, D. Halbertal, M. Sammon, Z. Sun, S. Liu, J. H. Edgar, T. Low, M. M. Fogler, C. R. Dean, A. J. Millis, and D. N. Basov, Polaritonic vortices with a half-integer charge, Nano Lett. 21, 9256 (2021).
  54. S. Tsesses, E. Ostrovsky, K. Cohen, B. Gjonaj, N. H. Lindner, and G. Bartal, Optical skyrmion lattice in evanescent electromagnetic fields, Science 361, 993 (2018).
  55. T. J. Davis, D. Janoschka, P. Dreher, B. Frank, F.-J. M. zu Heringdorf, and H. Giessen, Ultrafast vector imaging of plasmonic skyrmion dynamics with deep subwavelength resolution, Science 368, eaba6415 (2020).
  56. N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotechnol. 8, 899 (2013).
  57. W. Jiang, P. Upadhyaya, W. Zhang, G. Yu, M. B. Jungfleisch, F. Y. Fradin, J. E. Pearson, Y. Tserkovnyak, K. L. Wang, O. Heinonen, S. G. E. te Velthuis, and A. Hoffmann, Blowing magnetic skyrmion bubbles, Science 349, 283 (2015).
  58. S. Woo, K. Litzius, B. Krueger, M.-Y. Im, L. Caretta, K. Richter, M. Mann, A. Krone, R. M. Reeve, M. Weigand, P. Agrawal, I. Lemesh, M.-A. Mawass, P. Fischer, M. Klaeui, and G. R. S. D. Beach, Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets, Nat. Mater. 15, 501 (2016).
  59. W. Jiang, G. Chen, K. Liu, J. Zang, S. G. E. te Velthuis, and A. Hoffmann, Skyrmions in magnetic multilayers, Phys. Rep. 704, 1 (2017).
  60. S. L. Zhang, W. W. Wang, D. M. Burn, H. Peng, H. Berger, A. Bauer, C. Pfleiderer, G. van der Laan, and T. Hesjedal, Manipulation of skyrmion motion by magnetic field gradients, Nat. Commun. 9, 2115 (2018).
  61. C. Bai, J. Chen, Y. Zhang, D. Zhang, and Q. Zhan, Dynamic tailoring of an optical skyrmion lattice in surface plasmon polaritons, Opt. Express 28, 10320 (2020).
  62. M. Lin, W. Zhang, C. Liu, L. Du, and X. Yuan, Photonic spin skyrmion with dynamic position control, ACS Photon. 8, 2567 (2021).
  63. N. Ichiji, Y. Otake, and A. Kubo, Femtosecond imaging of spatial deformation of surface plasmon polariton wave packet during resonant interaction with nanocavity, Nanophotonics 11, 1321 (2022).
  64. Y. Wang, C. Ming, Y. Zhang, J. Xu, F. Feng, L. Li, and X. Yuan, Spatiotemporal manipulation on focusing and propagation of surface plasmon polariton pulses, Opt. Express 28, 33516 (2020).
  65. A. Karalis and J. D. Joannopoulos, Plasmonic Metasurface “Bullets” and other “Moving Objects”: Spatiotemporal Dispersion Cancellation for Linear Passive Subwavelength Slow Light, Phys. Rev. Lett. 123, 067403 (2019).
  66. K. L. Schepler, M. Yessenov, Y. Zhiyenbayev, and A. F. Abouraddy, Space-time surface plasmon polaritons: A new propagation-invariant surface wave packet, ACS Photon. 7, 2966 (2020).
  67. H. E. Kondakci and A. F. Abouraddy, Diffraction-free space-time beams, Nat. Photon. 11, 733 (2017).
  68. B. Bhaduri, M. Yessenov, and A. F. Abouraddy, Meters-long propagation of diffraction-free space-time light sheets, Opt. Express 26, 20111 (2018).
  69. M. Yessenov, L. A. Hall, K. L. Schepler, and A. F. Abouraddy, Space-time wave packets, Adv. Opt. Photon. 14, 455 (2022).
  70. N. Ichiji, H. Kikuchi, M. Yessenov, K. L. Schepler, A. F. Abouraddy, and A. Kubo, Observation of ultrabroadband striped space-time surface plasmon polaritons, ACS Photon. 10, 374 (2023).
  71. N. Ichiji, M. Yessenov, K. L. Schepler, A. F. Abouraddy, and A. Kubo, Exciting space-time surface plasmon polaritons by irradiating a nanoslit structure, arXiv:2212.05450.
  72. N. Lassaline, R. Brechbuhler, S. J. W. Vonk, K. Ridderbeek, M. Spieser, S. Bisig, B. Le Feber, F. T. Rabouw, and D. J. Norris, Optical fourier surfaces, Nature (London) 582, 506 (2020).
  73. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, Optical properties of metallic films for vertical-cavity optoelectronic devices, Appl. Opt. 37, 5271 (1998).
  74. A. Kubo, N. Pontius, and H. Petek, Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface, Nano Lett. 7, 470 (2007).
  75. L. Zhang, A. Kubo, L. Wang, H. Petek, and T. Seideman, Imaging of surface plasmon polariton fields excited at a nanometer-scale slit, Phys. Rev. B 84, 245442 (2011).
  76. J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, Cosine-Gauss Plasmon Beam: A Localized Long-Range Nondiffracting Surface Wave, Phys. Rev. Lett. 109, 093904 (2012).
  77. H. E. Kondakci and A. F. Abouraddy, Optical space-time wave packets of arbitrary group velocity in free space, Nat. Commun. 10, 929 (2019).
  78. M. Yessenov and A. F. Abouraddy, Accelerating and Decelerating Space-Time Optical Wave Packets in Free Space, Phys. Rev. Lett. 125, 233901 (2020).
  79. L. A. Hall, M. Yessenov, and A. F. Abouraddy, Arbitrarily accelerating space-time wave packets, Opt. Lett. 47, 694 (2022).
  80. M. Yessenov, L. A. Hall, and A. F. Abouraddy, Engineering the optical vacuum: Arbitrary magnitude, sign, and order of dispersion in free space using space-time wave packets, ACS Photon. 8, 2274 (2021).
  81. L. A. Hall and A. F. Abouraddy, Free-space group-velocity dispersion induced in space-time wave packets by v-shaped spectra, Phys. Rev. A 104, 013505 (2021).
  82. H. He, C. Guo, and M. Xiao, Nondispersive space-time wave packets propagating in dispersive media, Laser Photon. Rev. 16, 2100634 (2022).
  83. P. Saari and K. Reivelt, Evidence of X-Shaped Propagation-Invariant Localized Light Waves, Phys. Rev. Lett. 79, 4135 (1997).
  84. J. N. Brittingham, Focus waves modes in homogeneous Maxwell's equations: Transverse electric mode, J. Appl. Phys. 54, 1179 (1983).
  85. A. Sezginer, A general formulation of focus wave modes, J. Appl. Phys. 57, 678 (1985).
  86. J. Durnin, J. J. Miceli, and J. H. Eberly, Diffraction-Free Beams, Phys. Rev. Lett. 58, 1499 (1987).
  87. F. Gori, G. Guattari, and C. Padovani, Bessel-Gauss beams, Opt. Commun. 64, 491 (1987).
  88. M. Yessenov, B. Bhaduri, L. Mach, D. Mardani, H. E. Kondakci, M. A. Alonso, G. A. Atia, and A. F. Abouraddy, What is the maximum differential group delay achievable by a space-time wave packet in free space? Opt. Express 27, 12443 (2019).
  89. A. Y. Bekshaev and M. Soskin, Transverse energy flows in vectorial fields of paraxial beams with singularities, Opt. Commun. 271, 332 (2007).
  90. M. V. Berry, Optical currents, J. Opt. A 11, 094001 (2009).
  91. A. Bekshaev, K. Y. Bliokh, and M. Soskin, Internal flows and energy circulation in light beams, J. Opt. 13, 053001 (2011).
  92. A. Y. Bekshaev, Subwavelength particles in an inhomogeneous light field: Optical forces associated with the spin and orbital energy flows, J. Opt. 15, 044004 (2013).
  93. T. Fösel, V. Peano, and F. Marquardt, L lines, C points and Chern numbers: Understanding band structure topology using polarization fields, New J. Phys. 19, 115013 (2017).
  94. M. Dennis, Polarization singularities in paraxial vector fields: Morphology and statistics, Opt. Commun. 213, 201 (2002).
  95. M. Neugebauer, T. Bauer, A. Aiello, and P. Banzer, Measuring the Transverse Spin Density of Light, Phys. Rev. Lett. 114, 063901 (2015).
  96. J. Deschamps, M. Fitaire, and M. Lagoutte, Inverse Faraday Effect in a Plasma, Phys. Rev. Lett. 25, 1330 (1970).
  97. Z. M. Sheng and J. Meyer-ter-Vehn, Inverse Faraday effect and propagation of circularly polarized intense laser beams in plasmas, Phys. Rev. E 54, 1833 (1996).
  98. R. Hertel, Theory of the inverse Faraday effect in metals, J. Magn. Magn. Mater. 303, L1 (2006).
  99. H.-L. Zhang, Y.-Z. Wang, and X.-J. Chen, A simple explanation for the inverse Faraday effect in metals, J. Magn. Magn. Mater. 321, L73 (2009).
  100. D. Oue and M. Matsuo, Electron spin transport driven by surface plasmon polaritons, Phys. Rev. B 101, 161404(R) (2020).
  101. T. J. Wijaya, D. Oue, M. Matsuo, Y. Ito, K. Elphick, H. Uchida, M. Inoue, and A. Hirohata, Spin current generation by a surface plasmon polariton, arXiv:2004.12348.
  102. A. Bekshaev, Spin-accumulation and spin-transport effects induced by surface plasmon-polariton waves, J. Opt. Soc. Am. B 39, 3187 (2022).
  103. D. Oue and M. Matsuo, Effects of surface plasmons on spin currents in a thin film system, New J. Phys. 22, 033040 (2020).
  104. D. Oue and M. Matsuo, Optically induced electron spin currents in the Kretschmann configuration, Phys. Rev. B 102, 125431 (2020).
  105. M. S. Ukhtary, Y. Tian, and R. Saito, Spin current generation by edge plasmons in graphene ribbons, Phys. Rev. B 103, 245428 (2021).
  106. Y. Tian, M. S. Ukhtary, and R. Saito, Switching performance of optically generated spin current at the graphene edge, Phys. Rev. B 106, 045420 (2022).
  107. B. Göbel, I. Mertig, and O. A. Tretiakov, Beyond skyrmions: Review and perspectives of alternative magnetic quasiparticles, Phys. Rep. 895, 1 (2021).
  108. S.-H. Yang, R. Naaman, Y. Paltiel, and S. S. P. Parkin, Chiral spintronics, Nat. Rev. Phys. 3, 328 (2021).
  109. K. Hamamoto, M. Ezawa, and N. Nagaosa, Purely electrical detection of a skyrmion in constricted geometry, Appl. Phys. Lett. 108, 112401 (2016).
  110. D. Maccariello, W. Legrand, N. Reyren, K. Garcia, K. Bouzehouane, S. Collin, V. Cros, and A. Fert, Electrical detection of single magnetic skyrmions in metallic multilayers at room temperature, Nat. Nanotechnol. 13, 233 (2018).
  111. T. Schulz, R. Ritz, A. Bauer, M. Halder, M. Wagner, C. Franz, C. Pfleiderer, K. Everschor, M. Garst, and A. Rosch, Emergent electrodynamics of skyrmions in a chiral magnet, Nat. Phys. 8, 301 (2012).
  112. P. Bruno, V. K. Dugaev, and M. Taillefumier, Topological Hall Effect and Berry Phase in Magnetic Nanostructures, Phys. Rev. Lett. 93, 096806 (2004).
  113. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. Böni, Topological Hall Effect in the A Phase of MnSi, Phys. Rev. Lett. 102, 186602 (2009).
  114. M. Lee, W. Kang, Y. Onose, Y. Tokura, and N. P. Ong, Unusual Hall Effect Anomaly in MnSi Under Pressure, Phys. Rev. Lett. 102, 186601 (2009).
  115. Y. Jiang, H. Y. Yuan, Z.-X. Li, Z. Wang, H. W. Zhang, Y. Cao, and P. Yan, Twisted Magnon as a Magnetic Tweezer, Phys. Rev. Lett. 124, 217204 (2020).
  116. A. Karnieli, S. Tsesses, G. Bartal, and A. Arie, Emulating spin transport with nonlinear optics, from high-order skyrmions to the topological Hall effect, Nat. Commun. 12, 1092 (2021).
  117. A. Nisbet, Hertzian electromagnetic potentials and associated gauge transformations, Proc. R. Soc. London A 231, 250 (1955).
  118. S. Hacyan, R. Jáuregui, F. Soto, and C. Villarreal, Spectrum of electromagnetic fluctuations in the Casimir effect, J. Phys. A: Math. Gen. 23, 2401 (1990).
  119. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1999).

Outline

Information

Phys. Rev. A 107, 063517– Published 28 June, 2023
  • Received 15 February 2023
  • Revised 10 June 2023
  • Accepted 13 June 2023
Article part of CHORUS
Crossmark - Check for updates button

©2023 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation