Studying spin system dynamics concerns different rapidly growing fields of technology such as developing new types of information transfer systems [1], quantum computing [2, 3], new approaches for magnetic recording and reading [4]. The most common way to excite spin oscillations is by using the inverse Faraday effect (IFE). It is based on a Raman-like coherent optical scattering process and does not require absorption of light. This gives us two main advantages of this effect: it is instantaneous and non-thermal [5]. IFE results in magnetization induced by high-power laser radiation according to the following formula: Min=χ/16π [E×E*], (1) where χ is magneto-optical susceptibility, E is the electric field of the incident light, and E* is its complex conjugate. The cross product in formula (1) is zero for linearly polarized incident light and is maximum for circularly polarized light. The excitation of high order spin waves requires the nonuniform distribution of the electromagnetic field in the medium. It is commonly achieved by using the nanostructured materials in which the resonant phenomena can occur breaking the uniformity of the field. For example, in work [6] the all-dielectric 1D grating was used to generate spin waves due to the excitation of propagating waveguide modes. Another way to excite spin waves is the utilization of anisotropic materials in which the polarization conversion of the incident light occurs. Such a transformation leads to the spatial dependency of magnetization induced via IFE. This nonuniformity of the magnetic torque allows one to excite the spin waves of a high order. Let us consider the case of biaxial crystals the influence on the incident light polarization of which is described by the permittivity tensor εij. The diagonal components of this tensor are assumed not to be equal ε11≠ε22≠ε33 and connected with cartesian coordinates x, y, and z respectively. Let the light fall under the normal incidence to the plane of the material and propagate along the z-axis. Placing the material under study in an external magnetic field along the z-axis leads to the appearance of additional off-diagonal components which are ε12=-i×g and ε21=i×g. Polarization of the light propagating in such a medium transforms due to the anisotropy and Faraday effect. This process is described theoretically in [7]. To be more specific, consider the YFeO3 crystal with an orthorhombic cell. Its crystallographic axes a, b, and c are oriented along x, y, and z axes respectively. The main refractive indices of such material are n1=2.365, n2=2.4, n3=2.337 at the wavelength of 633 nm (ε'' is assumed to be zero). The transformation of the incident light with circular polarization when it passes through anisotropic medium results in oscillations of the magnetization induced via IFE (blue line on Fig. 1). It worth noting that oscillations of magnetization occur for linearly polarized light. The maximum value of cross-product in formula (1) can be achieved for the polarization of incident light at an angle of 45° to the a crystal axis (green line on Fig. 1). In this case, the material behaves as a quarter-wave plate fully transforming the initial linear polarization to circular. One can observe the oscillations even for light polarized linearly along the crystal axis but their maximum value is two times smaller compared to the previous scenarios (Fig. 2). In this situation, the polarization transformation due to birefringence must disappear but the Faraday effect slightly rotates the polarization off the axis allowing the anisotropy to take its place. The oscillations of IFE due to the birefringent properties of the material under study have been theoretically demonstrated. Such a behavior of the induced magnetization is important for generating spin waves of a high order allowing one to avoid additional nanostructuring of the material. This work was supported by the Ministry of Science and Higher Education of the Russian Federation (mega-grant no. 075-15-2019-1934).

**References:**

[1] S. Neusser and D. Grundler, Advanced Materials, Vol. 21 p. 2927 (2009) [2] K. Ganzhorn, S. Klingler, T. Wimmer, et al, Applied Physics Letters, Vol. 109, p. 022405 (2016) [3] D. Lachance-Quirion, Y. Tabuchi, A. Gloppe, et al, Applied Physics Express, Vol. 12, p. 070101 (2019) [4] D.O. Ignatyeva, C.S. Davies, D.A. Sylgachev, et al, Nature Communications, Vol. 10, p. 1 (2019) [5] A.V. Kimel, A. Kirilyuk, P.A. Usachev, et al, Nature, Vol. 435, p. 655 (2005) [6] A.I. Chernov, M.A. Kozhaev, D.O. Ignatyeva, et al, Nano Letters, Vol. 20, p. 5259 (2020) [7] A.K. Zvezdin, V.A. Kotov, Modern magnetooptics and magnetooptical materials, CRC Press (1997)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9fd7730e609d00e4f4b1fe8becda2c13.jpg)
Fig. 1. Cross product of electric field and its complex conjugate depending on the propagation length for circularly (blue line) and linearly polarized at an angle of 45° to the crystal axis (green line) incident light.

![](https://assets.underline.io/uploads/markdown_image/1/image/a63c9245721032602764f78c072ba99b.jpg)
Fig. 2. Cross product of electric field and its complex conjugate depending on the propagation length for incident light polarized along the a crystal axis.

 Oscillating Behavior of Inverse Faraday Effect in YFeO3

Up-to-date technologies require modern information devices to process large amounts of data at high rates. Methods of the ultrafast magnetism are very promising in this respect since they allow controlling the magnetization of a magnetic material by the femtosecond laser pulses at a picosecond time scales. Ferrimagnetic alloy of gadolinium-iron-cobalt (GdFeCo) is one of the most promising materials for further development of the information storage devices, since it allows to perform a single-shot all-optical magnetization switching during a few picoseconds in the area of pulse action on the GdFeCo film. A mechanism of all-optical switching originates from the ultrafast spin dynamics of the exchange-coupled Gd and FeCo sublattices which are thrown out of balance due to the light-induced thermal heating of the spin sublattices. If the delivered energy exceeds the threshold, the magnetizations of the two sublattices are reversed at the picosecond timescales due to the difference of the relaxation times for these sublattices. Thus, ultrafast all-optical magnetization switching depends on the amount of energy delivered by the optical pulse and is characterized by a threshold femtosecond pulse intensity required for the magnetization switching. Nowadays many efforts are put to study how to control the process of all-optical switching via tailoring the properties of the femtosecond pulse and via the additional patterning of the magnetic structure. In this work we propose a design of photonic nanostructure where the parameters of the dielectric layers determine the spatial light distribution and the resonances of the absorption in the GdFeCo layers. We propose to use the magnetophotonic crystal (MPC) structures, that were shown to perform tunable localization of light at the resonant frequencies enabling the enhancement of the optomagnetic interaction in a magnetic material. The proposed magnetophotonic crystal with thin smooth or patterned layers of GdFeCo ferrimagnetic alloy provides the local magnetization control and targeted remagnetization of the single layers of the multilayer structure. By the frequency tuning of the input femtosecond laser pulses one can select the magnetic layer of GdFeCo in which the energy of the laser pulse is mostly concentrated and exceeds the magnetization reversal threshold, while in others it is 1.5-2 times lower. In other words, the proposed MPC allows to ‘turn on’ one certain magnetic layer of the structure and leave all other layers ‘turned off’. As GdFeCo material is perspective for data storage applications allowing a significant increase of the writing speed, the proposed structure can be implemented for the purposes of the record density increase in such a device. Usually, the magnetic bit cells are arranged in the plane of a single magnetic layer. Using the proposed MPC, bit cells can be arranged in several magnetic layers separated by the submicron dielectric spacers and addressed individually. This configuration is quite simple for fabrication and doesn’t require a precise positioning of the laser pulse. Besides that, another configuration of the chirped MPC structure with the patterned GdFeCo layers is addressed. For the higher density of the information recording the magnetic layer can be nanostructured to separate bit cells in the lateral direction. The patterning of the magnetic layer can be implemented along both axes in the plane of the structure layers. In our work we limited ourselves by one-dimensional patterning for the sake of the modelling simplicity. It should be stressed that the patterned chirped MPC allows combining two approaches instantaneously, the bit cells arranged in plane and the bit cells arranged in different layers. It opens up the ample opportunities for the significant increase of the information recording density. We also provide the method of an all-optical single-wavelength information reading in this multilayered structure. Thus, the designed MPC with GdFeCo layers could serve as a basis of 3D information storage devices. To sum up, a design of the MPC structure providing a selective magnetization switching in the different magnetic layers at different frequencies is proposed. The MPC contains the thin layers of GdFeCo as magnetic counterparts. By illuminating the MPC by femtosecond laser pulses at the certain frequencies we create the conditions for the highest concentration of the electromagnetic field in the necessary layer of the structure while in the other GdFeCo layers the intensity is at least 1.5 times smaller. Thus, one can achieve selective all-optical magnetization reversal in a single layer of the multilayered stack determined by the laser frequency without any impact on the other layers. The magnetic layers of the MPC are separated from each other by the non-magnetic layers, and can be patterned, so, they can serve as the unit cells for information storage. We also provide a mechanism of single-wavelength reading of the information stored in such a multilayered stack. The approach was demonstrated for the 4 layers of SiO2, TiO2 and GdFeCo for the sake of simplicity, however it could be extended to the larger number of layers by the proper design of the chirped photonic crystal. The work was supported by Russian Science Foundation, grant No. 19-72-10139.

**References:**

A. Kirilyuk, A.V. Kimel, T. Rasing. Rev. Mod. Phys. Vol. 82, p. 2731 (2010). A.V. Kimel, A. Kirilyuk, P.A. Usachev, et al. Nature Vol. 435, p. 655 (2005). J.Y. Bigot, M. Vomir, E. Beaurepaire. Nature Physics Vol. 5, p. 515 (2009). A.I. Chernov, M.A. Kozhaev, D.O. Ignatyeva, et al. Nano Letters Vol. 20, p. 5259 (2020). U. Atxitia, T.A. Ostler. Appl. Phys. Lett. Vol. 113, p. 062402 2018). M. Inoue, et al. J. Phys. D. Appl. Phys. Vol. 39, p. R151 (2006).

**Images:**

 Chirped Photonic Crystals with GdFeCo for Layer-Selective Magnetization Control

Spin control in magnetic materials is a fundamental basis of the most current energy efficient devices, such as magnetic memory, Boolean and quantum logical elements [1]. In the last few decades, femtosecond laser systems opened up opportunities for ultrafast spin control in various magnetic materials such as ferromagnetic metals, iron garnets, and even antiferromagnetic dielectric oxides [2]. Special attention is paid to nonthermal spin wave control via inverse magnetooptical effects, such as inverse Faraday, inverse transverse magnetooptical Kerr, or inverse Voigt effects. Moreover, recent advances in fabrication techniques provide capabilities for light localization at the nanoscale regions together with optical modes excitation in the nanostructures [3,4]. The aforementioned advances of the nanostructures increase the efficiency of light-matter interaction and bring new horizons to all-optical spin control in magnetic materials. Here we report on spin wave amplitude enhancement in all-dielectric iron garnet nanostructure based on one-dimensional iron garnet grating. The grating consists of solitary strips of 400 nm width on gadolinium gallium garnet substrate placed with subwavelength period (600 nm). The height of the nanostructure was 225 nm. For spin wave launch pump-probe technique is utilized in Voigt configuration [2]. For pumping a circularly polarized pulse of ~200 fs duration at 600 nm and normal incidence was used. Probe pulse of 200 fs duration at 820 nm (transparency region of the structure) was linearly polarized. The probe angle of incidence was ~30 deg. The external magnetic field was equal to 100 mT. The nanostructure support propagation of waveguiding modes that are well defined in transmittance spectra at ~600 nm (Figure 1). The electromagnetic field localization and enhancement inside the nanostrips due to waveguiding mode excitation result in spin wave amplitude enhancement (up to 2 times). Moreover, as can be noted from figure 2 there is a shift in spin wave frequency between pure film and nanostructure. The effect can be associated with the existence of additional boundaries between magnetic strips and external media. This work was financially supported by the Russian Ministry of Education and Science, Megagrant project N 075-15-2019-1934

**References:**

1. A. V. Chumak et. al. Nature Physics, Vol. 11(6), p. 453, (2015) 2. A. Kirilyuk et. al. Reviews of Modern Physics, Vol. 82(3), p. 2731, (2010). 3. A. I. Chernov et. al. Nano Letters, Vol. 20(7), p. 5259, (2020). 4. A. L. Chekhov et. al. Nano letters, Vol. 18(5), p. 2970, (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ff4ec02eadaa48a1da002f1ada82a1fc.jpg)
Figure 1 Transmission of the nanostructure as a function of incident angle and wavelength

![](https://assets.underline.io/uploads/markdown_image/1/image/0f50b3bfdc75944256271a9c07bf3f25.jpg)
Figure 2 Spin wave precession for a pristine garnet film of 225 nm thickness (black) and nanostructure (red)

 Optically induced spin wave excitation in one-dimensional iron-garnet nanostripes

Faraday effect was a first demonstration of magnet influence on the light. Since then many generations of scientists tried to strengthen it. A decade ago, a breakthrough based on plasmonics was proposed for a significant enhancement of the magneto-optical interaction. However, all metals, even noble ones, introduce rather notable absorption which worsen quality factor of the optical resonances and constrains their role in the magneto-optical enhancement. Here we demonstrate that low lossy all-dielectric magnetic structures are more advantageous in this respect. We propose a specially designed all-dielectric magnetic meta-surface allowing a novel mechanism of the magneto-optical intensity effect [1]. It consists of a 2D array of iron-garnet nanopillars on an ultrathin iron-garnet slab. The nanostructure exhibits high transparency and superior quality-factor resonances followed by multifold increase of the magnetooptical intensity modulation. Unlike the magneto-optical intensity effects in smooth films and plasmonic gratings the photonic crystal metasurface provides the magnetically induced modulation of light intensity not only in a single light polarization, e.g. p-polarization, but also in the orthogonal one (s-polarization). It is due the wide variety of the excited mode types in the all-dielectric nanostructure. It is very promising for sensing, magnetometry and light modulation applications. This work was financially supported by the Russian Ministry of Education and Science, Megagrant project N 075-15-2019-1934.

**References:**

[1] D.O. Ignatyeva et al., Nature Communications 11, 5487 (2020).

**Images:**

 All-dielectric magnetophotonics INVITED

Among a variety of magneto-optical effects we focus on the inverse Faraday effect (IFE) that plays a crusial role for optical magnetic switching. The IFE is the emergence of magnetization in a transparent medium illuminated by a circularly polarized high-frequency electromagnetic wave [1]. It provides a new way for efficient control of magnetization at GHz and THz rates. Quantitatively the IFE magnetic field is determined by the distribution of the electric field inside the magnetic layer [2]: HIFE∼[E×E*]. Recently it has been demonstrated that optical confinement of light in the magnetophotonic crystals (MPC) or in magnetophotonic microcavity leads to the significant increase of the IFE [2-4]. It happens due to the photonic crystal (PC) defect mode existing in such magnetophotonic crystals or microcavities. These states are spectrally located inside the band gaps and reveal themselves as a sharp peaks in transmittance spectra of a nanostructure. These defect modes also provide strong localization of light inside the magnetic layer that leads to the significant enhancement of the IFE. In this work we propose the novel design of the MPC nanostructures with gradual variation of the magnetic layer thickness. So, the spectral position of the defect mode of the MPC nanostructure depends on the spatial position of input light spot on the sample surface. Therefore, the resonant enhancement of the IFE associated with the peak in transmittance band gap also changes with the input light spot position. Besides that, the design of the MPC nanostructure with perforated magnetic layer provide a spatially localized emergence of the IFE in the spots of several microns that seems very promising for practical applications. The principle scheme of the PC nanostructure with smooth magnetic layer consist of the magnetic layer sandwiched between two non-magnetic Bragg mirrors (Fig. 1). Iron-garnet films doped with bismuth (or BIG films) provide a large Faraday effect and have a relatively low optical absorption in the long-wavelengths visible spectral range [2]. Illuminating this nanostructure by the circularly polarized light at the normal incidence one can observe a defect mode, when the resonance peak appears in the bandgap of the transmittance spectrum. The spectral position and amplitude of this peak depend on the thickness of the magnetic layer h. The spectral position of the defect mode changes from 0.6 μm for 120nm-thick magnetic layer to 0.675 μm for 180nm-thick one. So, the gradual tuning of the resonance spectral position can be realized in sample with the gradient change of the BIG layer thickness. The IFE is determined by the electromagnetic field intensity localized in magnetic layer. In Fig. 2 the spectral dependence of the total energy in the BIG layer normalized by the layer thickness is presented for several values of h. Therefore, the magnitude of the inverse Faraday effect can also be detuned by moving the input beam along the gradient direction of the sample. Besides the smooth gradient magnetic layer, the PC nanostructure with the magnetic layer with etched discs is proposed. In the BIG magnetic layer with the constant thickness the discs with diameter of dozen microns are etched. The etching depth is different for various discs. As a result, the thickness of the magnetic layer is smaller in the area of these discs. Therefore, the enhanced IFE occurs at the different frequencies for each disc. This approach allows us to achieve spatial localization of the IFE limited just by the disc diameter. To sum up, we propose two designs of the MPC nanostructures with gradient of the magnetic layer thickness for tunable inverse Faraday effect. The spectral position and amplitude of the transmittance peak and resonant IFE depend on the thickness of the magnetic layer. The first design of the MPC nanostructure has smooth magnetic layer with thickness gradient that allows to tune the spectral position of peak in transmittance spectra and the IFE gradually. The second design has perforated magnetic layer and provide spatially localized emergence of the IFE in the spots of several microns. The sample fabrication and the experimental verification of the reported results is expected. This study was supported by Russian Science Foundation (project No. 19-72-10139).

**References:**

A. Kirilyuk, A.V. Kimel, and T. Raising, Rev. Mod. Phys. Vol. 82, pp. 2731 (2010). M.A. Kozhaev, A.I. Chernov et al., Sci. Rep. Vol. 8, p. 11435 (2018). T. Goto, A.V. Baryshev, M. Inoue et al., Phys. Rev. B, Vol. 79, p. 125103 (2009). M. Inoue, et al., J. Phys. D. Appl. Phys. Vol. 39, p. R151 (2006).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/3d88bf2c81e92be02ad6b0e66654c6dd.jpg)
Fig. 1. The principle scheme of the photonic crystal nanostructure with smooth magnetic layer (the gradient of the magnetic layer thickness isn’t shown).

![](https://assets.underline.io/uploads/markdown_image/1/image/3327d1b959c15f1285f79297fab57267.jpg)
Fig. 2. Spectra of the total energy localized in the magnetic layer of the MPC for various values of h.

 Photonic Crystal Nanostructures with the Magnetic Layer of Gradient Thickness for Optical Magnetic Switching

In recent years, various methods have been reported to boost the magneto-optical (MO) response. Several works have reported the enhancements of the MO response relying on the plasmonic effects attributed to the strongly confined electromagnetic field in the structures1-3. However, the nonnegligible disadvantage of this approach is the optical losses due to the high absorption coefficient of the metal materials1. Therefore, combining the all-dielectric metasurfaces which have high-refractive-index and low intrinsic loss with planar photonic structures offers an alternative route to these problems4,5 .But most of the observations so far are focused on enhancement of existing magneto-optical effects in planar MO thin films. A high index contrast, all dielectric magneto-optical metasurface featuring strong Mie resonance modes have not been fabricated. Here, we report observation of circular displacement current induced novel magneto-optical effects in a high index contrast Si/Ce:YIG/YIG/SiO2 all dielectric metasurface. We observe giant transverse magneto-optical Kerr effect (TMOKE) up to 7 % under s-polarized incidence, which is non-existent in planar magneto-optical thin films. This phenomenon is essentially originated from the unique circular displacement current when exciting the magnetic resonance modes, which changes the incident electric field direction locally. These results indicate promising potential of controlling light propagation by utilizing the complex Mie resonance modes in magneto-optical all dielectric metasurfaces. Our work may inspire the development of novel magneto-nanophotonic devices such as vectoral magnetic field sensing, free space non-reciprocal photonic devices and magneto-optical imaging.

![](https://assets.underline.io/uploads/markdown_image/1/image/d3d7bd3c840418fd37285dae4d310845.jpg)

Figure 1. (a) Schematic diagram of the metasurface. (b) Scanning electron microscope image of a fabricated device.

![](https://assets.underline.io/uploads/markdown_image/1/image/22950e3df3d860eae0c79b53767f7e8a.jpg)

Figure 2. (a) Schematic diagram of s-polarized TMOKE characterization set-up. (b)Measured s-polarized TMOKE and reflection spectra of the metasurface compared with bare Ce:YIG/YIG thin films. (c) Measured TMOKE hysteresis for the metasurface and the bare MO films at 1230 nm wavelength. (d) Simulated reflection spectra and TMOKE responses of the metasurface for s-polarized light.

Circular Displacement Current induced Novel Magneto-Optical Effects in All-dielectric Metasurfaces

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Oscillating Behavior of Inverse Faraday Effect in YFeO3

Chirped Photonic Crystals with GdFeCo for Layer-Selective Magnetization Control

Optically induced spin wave excitation in one-dimensional iron-garnet nanostripes

All-dielectric magnetophotonics INVITED

Photonic Crystal Nanostructures with the Magnetic Layer of Gradient Thickness for Optical Magnetic Switching

Circular Displacement Current induced Novel Magneto-Optical Effects in All-dielectric Metasurfaces

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