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Optical spin–orbit coupling in the presence of magnetization: photonic skyrmion interaction with magnetic domains

Lei, Xinrui, Du, Luping, Yuan, Xiaocong, Zayats, Anatoly V.·2021·Nanophotonics
DOI 10.1515/nanoph-2021-0201
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Abstract

Polarization and related spin properties are important characteristics of electromagnetic waves and their manipulation is crucial in almost all photonic applications. Magnetic materials are often used for controlling light polarization through the magneto‐optical Kerr or Faraday effects. Recently, complex topological structures of the optical spin have been demonstrated in the evanescent light field, which in the presence of the spin–orbit coupling may form photonic skyrmions. Here, we investigate the optical spin–orbit coupling in the presence of magnetization and the interaction between photonic skyrmions and magnetic domains. We demonstrate that the magnetization is responsible for the modulation of the optical spin distribution, resulting in twisted Neel‐type skyrmions. This effect can be used for the visualization of magnetic domain structure with both in plane and polar orientation of magnetization, and in turn for creation of complex optical spin distributions using magnetization patterns. The demonstrated interplay between photonic skyrmions and magneto‐optical effects may also provide novel opportunities for investigation and manipulation of magnetic skyrmions using optical spin–orbit coupling.

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Figures

Figure 1 (A) Geometry of surface wave propagation in a multilayer consisting of both magnetic and nonmagnetic layers. Red and green arrows represent the magnetization orientation corresponding to longitudinal and polar magnetization, respectively. (B,C) Simulated in-plane electric fields of the surface wave propagating in x direction at an interface of air and magnetized semi-in fi nite medium (Co): (B) Ex and (C) Ey fi eld components for different magnetization orientations. The difference between the Ex fi elds in the case of polar and longitudinal magnetizations is negligible. The permittivity ε 2 andthegyration vector g of Co are taken from the experimental data as ε 2= -12.5 + 18.46 i [43] and g = 0.59 -0.48 i [44].
Figure 1 (A) Geometry of surface wave propagation in a multilayer consisting of both magnetic and nonmagnetic layers. Red and green arrows represent the magnetization orientation corresponding to longitudinal and polar magnetization, respectively. (B,C) Simulated in-plane electric fields of the surface wave propagating in x direction at an interface of air and magnetized semi-in fi nite medium (Co): (B) Ex and (C) Ey fi eld components for different magnetization orientations. The difference between the Ex fi elds in the case of polar and longitudinal magnetizations is negligible. The permittivity ε 2 andthegyration vector g of Co are taken from the experimental data as ε 2= -12.5 + 18.46 i [43] and g = 0.59 -0.48 i [44].CC-BY · From the PDF
Figure 2 (A, B) Electric field profile of (A) TM polarized evanescent vortex induced by an electric Hertz vector potential and (B) TE polarized evanescent vortex induced by a magnetic Hertz vector potential, both with topological charge l = 1 in the absence of magnetization. (C) Distribution of the photonic spin orientation formed by the evanescent vortex beam with topological charge l =1. The opaque arrows indicate the direction of the unit spin vector in (A), while the semitransparent arrows represent the modulated spin vectors in the presence of the polar MO effect. (D) The same as (C) for a topological charge l = -1. (E, F) Top view of the spin vectors in the presence of MO effect in (C) and (D), respectively. The in plane wavevector ( kr ) of the evanescent vortex for the simulations is set to 1.012 k , where k is the wavevector in the medium, and η is set to 0.3 + 0.03 i . In (A) and (B), x and y axis scales are normalized to the in-plane wavelength of the guided mode k r .
Figure 2 (A, B) Electric field profile of (A) TM polarized evanescent vortex induced by an electric Hertz vector potential and (B) TE polarized evanescent vortex induced by a magnetic Hertz vector potential, both with topological charge l = 1 in the absence of magnetization. (C) Distribution of the photonic spin orientation formed by the evanescent vortex beam with topological charge l =1. The opaque arrows indicate the direction of the unit spin vector in (A), while the semitransparent arrows represent the modulated spin vectors in the presence of the polar MO effect. (D) The same as (C) for a topological charge l = -1. (E, F) Top view of the spin vectors in the presence of MO effect in (C) and (D), respectively. The in plane wavevector ( kr ) of the evanescent vortex for the simulations is set to 1.012 k , where k is the wavevector in the medium, and η is set to 0.3 + 0.03 i . In (A) and (B), x and y axis scales are normalized to the in-plane wavelength of the guided mode k r .CC-BY · From the PDF
Figure 3 (A) Schematic diagram for the generation of a photonic skyrmion in a ferromagnetic material on the example of the SPP excited on a surface of a thin (50 nm) Co fi lm by a tightly focused ( NA =1.49) radially polarized beam. Incident angles below 40 ° are blocked to stabilize the generation of photonic skyrmions. The permittivity and the gyration vector constant of cobalt at wavelength of 633 nm are the same as in a Figure 1. (B,C) Spin states of (B) positive and (C) negative skyrmions generated with l = ± 1 RP beam, respectively, with the Co magnetization in a positive z direction. (D) Spatial distribution of Δ γ s for the skyrmions in (B) and (C). Corresponding theoretical distributions of Δ γ s obtained from Equation (9) is depicted in the bottom left inset. (E) The same as (D) for the magnetization oriented in negative z direction. (F,G) Spatial distributions of Δ γ s for the magnetic structure consisting of two domains with opposite magnetization orientation: the domain wall is at (F) x =0and(G) x = -1 μ m. (H, I) Cross-sections marked in (F, G) with a green dashed line. Inset in (H) is a zoomed view of the spin structure of the area indicated with light green box in (H).
Figure 3 (A) Schematic diagram for the generation of a photonic skyrmion in a ferromagnetic material on the example of the SPP excited on a surface of a thin (50 nm) Co fi lm by a tightly focused ( NA =1.49) radially polarized beam. Incident angles below 40 ° are blocked to stabilize the generation of photonic skyrmions. The permittivity and the gyration vector constant of cobalt at wavelength of 633 nm are the same as in a Figure 1. (B,C) Spin states of (B) positive and (C) negative skyrmions generated with l = ± 1 RP beam, respectively, with the Co magnetization in a positive z direction. (D) Spatial distribution of Δ γ s for the skyrmions in (B) and (C). Corresponding theoretical distributions of Δ γ s obtained from Equation (9) is depicted in the bottom left inset. (E) The same as (D) for the magnetization oriented in negative z direction. (F,G) Spatial distributions of Δ γ s for the magnetic structure consisting of two domains with opposite magnetization orientation: the domain wall is at (F) x =0and(G) x = -1 μ m. (H, I) Cross-sections marked in (F, G) with a green dashed line. Inset in (H) is a zoomed view of the spin structure of the area indicated with light green box in (H).CC-BY · From the PDF
Figure 4 (A -C) Simulated distributions of Δ γ s for different magnetization orientations in the plane of the fi lm ( xy plane): (A) φ 0 =0,(B) φ 0 = π /4, (C) φ 0 = π /2. (D -I) The same as (A -C) for the domain structure with the domain wall located at (D) x =0,(E -F) y =0,(G) x = -1 μ m,(H,I) y = -1 μ m. The magnetic domain can be visualized by the features of Δ γ s distributions, while the magnetization orientation can be unveiled from the ' central zero line ' , which is normal to the magnetization direction. Inserts show the magnetization orientation in the domains. The illumination con fi guration is the same as in Figure 3(A).
Figure 4 (A -C) Simulated distributions of Δ γ s for different magnetization orientations in the plane of the fi lm ( xy plane): (A) φ 0 =0,(B) φ 0 = π /4, (C) φ 0 = π /2. (D -I) The same as (A -C) for the domain structure with the domain wall located at (D) x =0,(E -F) y =0,(G) x = -1 μ m,(H,I) y = -1 μ m. The magnetic domain can be visualized by the features of Δ γ s distributions, while the magnetization orientation can be unveiled from the ' central zero line ' , which is normal to the magnetization direction. Inserts show the magnetization orientation in the domains. The illumination con fi guration is the same as in Figure 3(A).CC-BY · From the PDF
Figure 5 Simulated spatial distributions of Δ γ s for the domain structures with two orthogonal domain walls located at x = 0 and y = 0: (A) Polar magnetization and (B) in-plane magnetization. Inserts show the magnetization orientation in the domains. The illumination con fi guration is the same as in Figure 3(A).
Figure 5 Simulated spatial distributions of Δ γ s for the domain structures with two orthogonal domain walls located at x = 0 and y = 0: (A) Polar magnetization and (B) in-plane magnetization. Inserts show the magnetization orientation in the domains. The illumination con fi guration is the same as in Figure 3(A).CC-BY · From the PDF

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Metadata

Authors
Lei, X., Du, L., Yuan, X., & Zayats, A. V.
Venue
Nanophotonics
Publisher
Wiley
Published
2021-08-24
Volume
10
Issue
14
Pages
3667-3675
ISSN
2192-8614
DOI
10.1515/nanoph-2021-0201
Cited by
69
References
4
Language
en
Licence
Funders
  • Natural Science Foundation of Guangdong Province (2016A030312010)
  • National Natural Science Foundation of China (61427819, 61622504, 61705135, 61935013, 62075139, U1701661)
  • Shenzhen Peacock Plan (KQTD2015071016560101, KQTD20170330110444030)

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