Polar magneto-optical Kerr rotation (MOKR) is defined as the rotation of the polarization plane of a reflective beam with respective to that of a linearly polarized incident beam, when it impinges on samples under an external magnetic field placed perpendicular to the surface of the sample and parallel to the plane of incidence [1]. As one of two parameters of the magneto-optical Kerr effect (MOKE), MOKR occurs in a different reflective plane with Kerr ellipticity in the polar MOKE configuration; thus, the polar MOKE magnetization geometry possess higher sensitivity than transverse and longitudinal magnetization geometries [1,2], which can be used in high-performance biosensors and transducers devices. For this, elaborate efforts have been made to explore Kerr rotation spectra with a narrow bandwidth and high intensity.

By using optical nanostructures including ferromagnetic materials, researchers have made intensive efforts to pursue Kerr rotation spectra with a high intensity and narrow bandwidth. Magnetoplasmons as an universal phenomenon in these nanostructures, combining magnetization and plasmonic properties [3], possess all the properties of surface plasmons such as the trapping of light in subwavelength-scale volumes, interact with other optical modes, and arbitrarily channel an electromagnetic filed [4, 5]. Moreover, it can also be controlled by an external magnetic field [6]. These multi-freedom controllable properties of magnetoplasmons would yield diverse and novel polar MOKR information and high-performance magneto-optical materials can be acquired. The Au-Co_xFe_3−xO₄ core shell embedded in porous alumina membranes demonstrated an s-shaped Kerr rotation signal near Au plasma resonances [7]. The polar MOKR was enhanced by magnetoplasmons in Co/Au multilayer hole arrays made by nanosphere lithography [8]. Belotelov theoretically studied the modulated Kerr rotation in a metal-dielectric system, in which an Au film with subwavelength holes covered a YIG film, high-intensity and resonant Kerr rotation was obtained owing to the extraordinary optical transmission (EOT) phenomenon [9]. In nanostructured ferromagnetic systems, polar MOKR was modulated by both the intensity [10] and the phase [11] of the introduced magnetoplasmons.

Magnetoplasmons have played key roles in the intensity enhancement and resonant frequency of polar MOKR, but they have resulted in a large loss of metals and a strong broadening of polar MOKR spectra. A well-established method for overcoming the disadvantages of magnetoplasmons is coupling with other optical modes [12], such as waveguide modes, Fabry– Pérot modes, and Wood–Rayleigh anomalies (WRA). WRA originate from the diffraction order in plasmonic gratings [13, 14], and abrupt changes occur at the Rayleigh cut-off wavelength in reflection spectra. The abrupt changes due to WRA can highlight the performance of other optical modes through interaction between them. Improved extraordinary optical transimission was achieved through Fabry–Pérot resonance coupling with WRA [15]. The disadvantage of bandwidth broadening due to localized surface plasmons could be overcome with coupling to WRA and extremely narrow plasmon resonances achieved [16]. Studies on the coupling between WRA and magnetoplasmons are scarce [17]. However, regular periodic structures employed in nanostructured magneto-optical material would facilitate WRAs [18, 19]. In a deliberately designed system with magnetoplasmons, WRA resonance, and the interaction between them, high-performance polar MOKR can be achieved.

The self-assembly of 2D nanospheres is a cost-efficient, easily scalable, and variable nanofabrication technique. Combined with glancing-angle film deposition, diverse subwavelength shapes were formed at both the bottom and top of nanospheres, and different optical modes could be manipulated [20, 21]. Furthermore, highly hexaganol arrayed monolayers of uniform sphere combined with metallic film would beneficial for WRA occurring. Inspired by these ideas, in this paper, by using 2D monolayer PSS self-assembly on a glass (substrate)/Cr/Ag/Fe film, with the aid of angle-depended Ag film sputtering, different forms of surface plasmons could be manipulated. Both the polar MOKR and reflection properties could be elucidated by optical modes and their interaction occurred. And, narrow and high-intensity Kerr rotation peaks were assigned to the coupling of WRA and magnetoplasmons.

Two series of glass/Cr/Ag/Fe/PSS/Ag samples were fabricated using angle-dependent Ag film sputtering onto glass/Cr/Ag/Fe/PSS templates. The fabrication details of the templates were reported in ref [22]. Firstly, a Cr(20 nm)/Ag(200 nm)/Fe(10 nm) film was deposited on glass by three-source dc magnetron sputtering from Cr, Ag, and Fe targets in turn, where Cr (20 nm) was deposited as a buffer before Ag to strengthen the adhesion of Ag. Then, 2D arrays of PSSs with different diameters were aligned on Fe films through self-assembly. The schematic plot in Fig. 1 depicts the placement of templates during the deposition of the uppermost-layer Ag film (a) parallel to the sample stage θ = 0° or (d) with a glancing angle θ = 30° relative to the sample stage. The depositions were performed thrice by rotating the sample stage at angle intervals of 60°, and an Ag film of thickness 35 nm was deposited each time. In the experiment, PSSs with diameter d = 280, 300, and 414 nm were used. The morphologies of samples with d = 300 nm were characterized using a commercial atomic force microscopy (AFM) instrument (Slover P47, NT-MDT). Fig. 1 (b) and (e) show top-view AFM images of samples deposited at θ = 0° and θ = 30°, respectively. Clearly, the Ag film deposited at θ = 0°(b) demonstrated a circular shape on top of PSS arrays, whereas that deposited at θ = 30°(e) seemed like trianglar patches on top of PSS arrays. After all measurements (both polar MOKR and reflectivity measurements), PSSs were washed off by immersing the two series of samples with d = 300 nm in chlorobenzene to study the shape of Ag patches at the bottom of PSS arrays. Scanning electron microscopy (SEM) images of samples with d = 300 nm without PSS deposited at θ = 0°(c) and θ = 30°(f) were acquired. The triangle and circle nanostructures at the bottom of PSS could be deduced as in Fig. 1(c) and (f), respectively. This result is in good agreement with ref [20].

 

Fig. 1 Schematic of Ag films deposited onto glass/Cr/Ag/Fe/PSS templates placed at θ = 0° (a) or θ = 30° (d) relative to the sample stage. Top-view AFM images of samples (b,e) and SEM images (c,f) of Ag structures deposited at θ = 0° and θ = 30°.

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The spectra of polar MOKR θ_k and optical reflectance R were measured at room temperature by using a home-made Kerr spectrometer from 300 nm to 800 nm and by using a reflectometer from 200 nm to 1200 nm, respectively [22]. The θ_k measurements were carried out at an incident angle of 5° under an external magnetic field of 1.0 T. In the reflectivity measurements, the data were normalized with respect to the reflectivity of Al films. The reflection spectra and electromagnetic (EM)-field distribution simulation were performed using commercial software FDTD solution based on finite difference time domain (FDTD) method with mesh of 0.1 nm. The data of Ag and Fe came from measured data using ellipsometry.

The measured spectra of polar MOKR θ_k are displayed in Fig. 2 for the samples with θ = 0° (a–c) and θ = 30° (d–f). The diameters of PSSs were d = 280 (a, d), 300 (b, e), and 414 (c, f) nm. For clarity, the MOKR peaks are marked in Fig. 2. Evidently, the polar MOKR spectra of these two series demonstrated different behaviors. For samples deposited at θ = 0°, prominent but broad 1^st peaks were revealed at λ = 600 (a), 640 (b), and 755 (c) nm in Fig. 2. The 2^nd peaks located at λ = 358 (a), 380 (b), and 438 (c) nm were shallow and hardly discernible. However, for the samples deposited at θ = 30°, in addition to the 1^st broad peaks located at λ = 625 (d), 654 (e), 785 (f) nm, pronounced and narrow 2^nd peaks were observed at λ = 367 (d), 389 (e), and 460 (f) nm, respectively.

 

Fig. 2 θ_k spectra as functions of the wavelength of samples with deposition angle θ = 0° (a–c) and θ = 30°(d–f). The PSS diameter d = 280 (a, d), 300 (b, e), and 414 (c, f) nm.

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This tremendous discrepancy was not found in the reflection spectra (measured without external magnetic field) of the two series of samples in Fig. 3, where both the measured (black squares) and calculated (red triangles) reflection spectra of the two series of samples were layered out. The agreement between the measured and calculated reflection spectra in Fig. 3 consolidated our material research base and method reliability. The reflection spectra of samples with Ag deposited at θ = 0° (a–c) and θ = 30°(d–f) showed the same behavior, and no significant discrepancy was observed in the reflection spectra of these two series of samples as in MOKR spectra, except that the 2^nd dips in Fig. 3 (d–f) were slightly deeper and narrower than those in Fig. 3 (a–b). Evidently, the reflection dips in Fig. 3 corresponded to MOKR peaks in Fig. 2 well. For samples deposited at θ = 0°, broad 1^st dips were presented at λ = 596 (a), 622 (b), and 756 (c) nm, and the 2^nd narrow ones located at λ = 361 (a), 381 (b), and 448 (c) nm. For the samples deposited at θ = 30°, broad 1^st dips were near λ = 630 (d), 669 (e), 796 (f) nm, and the narrow 2^nd ones were observed at λ = 368 (d), 397 (e), and 466 (f) nm, respectively.

 

Fig. 3 Reflectivity spectra as functions of the wavelength of samples with deposition angle θ = 0° (a–c) and θ = 30°(d–f). The PSS diameter d = 280 (a, d), 300 (b, e) and 414 (c, f) nm.

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By combining the MOKR and reflection spectra in Fig. 2 and Fig. 3, we analyze these novel phenomena based on the theory of diffraction and surface plasmon plaritons (SPPs). When light perpendicularly impinges on the 2D hexagonal PSS arrays covered by Ag film from air, SPPs occur at Ag-PSS and PSS-Fe-Ag hybrid interface [23], the diffraction or SPP resonance order can be calculated by [13,14,24]

To further study the physical mechanism of the MOKR peaks in Fig. 2, the simulated EM-field distribution in the xz-plane (denoted in Fig. 1) of the 1^st and the 2^nd reflection dips (corresponding to the 1^st and the 2^nd KR peaks) of samples with top layer Ag deposited at θ = 0°(a–c) and θ = 30°(d–f) is presented in Fig. 4 and Fig. 5, respectively.

 

Fig. 4 Field-amplitude distribution in the xz-plane of the 1^st reflection dips for samples deposited at θ = 0°(a–c) and θ = 30°(d–f). The location of EM-field is near λ = 596 (a), 622 (b), 756 (c), 630 (d), 669 (e) and 796 (f) nm.

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Fig. 5 Field-amplitude distribution in the xz-plane of the 2^nd reflection dips for samples deposited at θ = 0°(a–c) and θ = 30°(d–f), the location of EM-field is near λ = 361 (a), 381 (b), 448 (c), 368 (d), 397 (e), and 466 (f) nm.

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The location of EM-field of the 1^st dips in Fig. 3 is shown in Fig. 4 for samples with top layer Ag deposited at θ = 0°(a–c) and θ = 30°(d–f), respectively, which exhibit similar behavior. The EM-field of the 1^st reflection dips samples with d= 280 and 300 nm in Fig. 4(a, d) and (b, e) were strongly distributed in the upper part of the interior of the nanospheres and weakly distributed in free space. However, the EM-field distribution for samples with d = 414 nm in Fig. 4 (c, f) was mainly localized in the upper spaces between nanospheres. But they all demonstrated diffraction pattern in free space, and we could ascribe the 1^st MOKR peaks in Fig. 2(a–c) and (d–f) to the coupling between F-P resonance and Bragg plasmons at the upper capped Ag-PSS interface.

The EM-field distribution of the 2^nd reflection dips is illustrated in Fig. 5 for samples with top layer Ag deposited at θ = 0°(a–c) and at θ = 30°(d–f), respectively. The white dashed line shows the Ag-PSS and PSS-Fe interfaces. Obviously, distinct differences were revealed in the EM-field distribution of the 2^nd reflection dips between the two series samples. The EM-field of the 2^nd dips of samples deposited at θ = 0°(a–c) were located at the PSS-Ag interface and the bottom of the inside of nanospheres. Whereas the EM-field of the 2^nd dips of samples deposited at θ = 30°(d–f) were strongly localized in the complicated Ag-PSS and PSS-Fe interfaces, in addition to the bottom of the inside of nanospheres. Such localized magnetoplasmons coupled with WRA would enhance the interaction of the EM-field with ferromagnetic materials and lead to intensive and narrow polar MOKR, as could be seen in Fig. 2 (d–f). In contrast, for the EM-field located at the bottom of the inside of nanospheres and PSS-Ag interface, only weak polar MOKR peaks were observed in Fig. 2 (a–c). This distinct difference was not found in reflection spectra, because the localized EM-field in both PSS-Ag and PSS-Fe interface would all lead to similar reflection results without external magnetic field, as indicated by the 2^nd dips in reflection spectra in Fig. 3 (a–c) and (d–f).

In conclusion, by using a nanosphere template and glancing-angle film deposition, we presented a facile method to investigate the impact of coupling between different optical modes on polar MOKR. Intensive and narrow polar MOKR spectra were demonstrated for samples with the deposition angle θ = 30°. Through a numerical analysis and simulation of EM-field distribution, the polar MOKRs of glass/Cr/Ag/Fe/PSS/Ag systems were assigned to modulation by the coupling between WRA, F-P and different surface plasmons. The coupling between WRA and magnetoplasmons on the PSS-Fe interfaces led to intensive and narrow polar MOKR peaks. The study of narrow and high-intensity polar MOKR spectra might pave the way to the discovery of new physics and design of high-performance MO devices.