Nanoscale magnetophotonics

During the past two decades, our ability to control materials at the nanoscale allowed a more attentive study of nanoscale light–matter interactions, leading to the advent of nanophotonics and nano-optics. One particularly efficient way of confining light into subwavelength volumes is by using the collective electromagnetic-induced electronic excitations known as plasmons. Unlike conventional optics, plasmonics enables unrivaled concentration and enhancement of electromagnetic radiation well beyond the diffraction limit of light.^1–4 Besides its fundamental scientific importance, manipulation of light at the nanoscale is of great interest due to its potential exploitation toward real-life applications such as energy harvesting and photovoltaics, wave-guiding and lasing, optoelectronics, biochemistry, and medicine.

To achieve new functionalities, the combination of plasmonics with other material properties has become increasingly appealing. In particular, magnetoplasmonics and magnetophotonics are emerging areas that aim at combining magnetism, plasmonics, and photonics^5–11 to find new ways of controlling the properties of plasmons using magnetic fields or vice versa, to control magnetic properties with light. Nanoscale magnetophotonics entails the fundamental studies of photon–electronic spin interactions in nanostructured materials;¹² the enhancement of magneto-optical (MO) activity in materials,^13–15 including dielectrics,¹⁶ 2D materials,¹⁷ nanoparticle-decorated graphene,¹⁸ and graphene-based metasurfaces and their topological transformations;¹⁹ the active control of plasmons with weak magnetic fields;²⁰ topological photonics and gyromagnetic photonic crystals;²¹ magnetoplasmonics-based bio- and chemical sensing;²² and magnetophotonic and magnetoplasmonic crystals (MPCs) as modulators of light transmission, reflection, and polarization.^23–25 

Since the early 1970s, investigation of the interaction between magnetism and plasmons has been a topic of high interest. In 1972, Chiu and Quinn showed that an external static magnetic field could control the properties of surface plasmon polaritons (SPPs) such as their propagation or localization²⁶ [Fig. 1(a)]. The exponential growth of fabrication techniques in semiconductor technology during the last two decades boosted engineering of photonic bandgap materials and plasmonic systems operating at optical frequencies. MO properties of photonic crystals and their potential use in integrated optics were thoroughly investigated in 2005 by Belotelov and Zvezdin.²⁷ Shortly after, extraordinary transmission and plasmon-enhanced giant Faraday and Kerr effects were demonstrated in noble metal–dielectric plasmonic systems made of Au films with either a subwavelength hole²⁸ or a slit^29,30 array on top of a magnetic Bi:YIG layer. In parallel, the theoretical study by Yu et al. predicted that a waveguide formed at the interface between a photonic crystal and a metal under a static magnetic field possesses unique dispersion relations resulting in modes propagating in only one allowed direction.³¹ In 2007, González-Díaz et al. demonstrated that the coupling of an external magnetic field to the surface propagating plasmon wave vector can be greatly enhanced in noble metal/ferromagnetic/noble metal trilayers, which allows magnetic control of surface plasmon analogously to semiconductors.³² At the end of the 1990s, Martín-Becerra et al. showed that magnetic modulation of SPP wave vectors could be significantly improved by depositing a dielectric overlayer in such geometries³³ and, later on, that both the real and imaginary parts of SPP wave vectors are affected by the magnetic field in noble/ferromagnetic/noble metal films resulting in spectrally dependent modulations.³⁴ Unfortunately, for noble metal-based plasmonic structures, the magnetic field required to achieve proper control of surface plasmon properties is too high for application purposes. With nanoengineering of complex systems combining ferromagnetic materials and noble metals, which exhibit simultaneously magnetic and plasmonic properties, it became possible to control the plasmon wave vector with a weak (100 mT regime) external magnetic field,^35,36 generate ultrashort SPP pulses,³⁷ and produce SPP-induced magnetization in nickel with an effective magnetic field of 100 Oe by a femtosecond laser pulse.³⁸ Hybrid magnetoplasmonic systems combining noble metal and iron garnets that are typically highly transparent compared to ferromagnetic metals provide magnetic modulation of light transmittance. Enhanced MO effects and strong magnetic modulation of light intensity were found in metallic nanostructures integrated with an iron garnet film.^39–43 Furthermore, plasmon mediated MO transparency was observed in magnetophotonic crystals formed by gold grating stacked on top of bismuth-substituted rare-earth iron garnets deposited on top of gadolinium gallium garnets.²⁵ In similar architectures, a shift of plasmon polariton resonance was manipulated by femtosecond laser pulses.⁴⁴ Finally, in systems that combine plasmonic crystals and magnetic semiconductors, the MO effects could be dramatically enhanced in both transmission and reflection.⁴⁵ 

In parallel to the studies on propagating plasmons, the current rapid advances in nanofabrication enable the broadening of our understanding of optics at the nanoscale with nanostructures also supporting localized surface plasmon resonances (LSPRs) [Fig. 1(b)]. Also here, hybrid structures were proposed to combine the all-in-one advantages of noble metals and magnetic materials.^46,47 Also, pure ferromagnetic nanostructures were demonstrated to support LSPRs⁴⁸ and SPPs^49,50 and at the same time exhibit sizeable magnetic effects under low magnetic fields, leading to a large tunability of the MO response.⁵¹ The strong coupling between SPP and the MO activity leading to a significant enhancement and tunability of the Kerr effect as a result of lattice design was also observed in pure ferromagnetic (Fe, Co, Ni) 2D hexagonal lattices.^52–54 

MO effects can be classified into (i) the Faraday effect giving rise to rotation and ellipticity of an incoming linearly polarized light transmitted through a magnetized medium and (ii) the MO Kerr effect (MOKE) that induces similar effects but in a reflection configuration (see Ref. 55 for a theoretical description of MO effects). Different configurations of the MOKE can be defined depending on the relative orientation between the magnetization vector M, the plane of incidence of the incoming light, and the reflective surface [Fig. 1(c)]. In the longitudinal MOKE (L-MOKE) configuration, M lies both in the plane of the sample and in the plane of incidence of the incoming light [Fig. 1(c)]. In the polar MOKE (P-MOKE) geometry, M is oriented perpendicularly to the reflective surface and parallel to the plane of light incidence [Fig. 1(c)]. Finally, in the transverse MOKE (T-MOKE) configuration, M is lying on the sample surface and oriented perpendicularly to the plane of incidence of the incoming light [Fig. 1(c)].

This Perspective covers a plethora of intriguing effects and phenomena associated with light–matter interactions in nanoscale geometries in the presence of a magnetic field. Section I contains a brief introduction to the field of magnetophotonics and highlights important discoveries in geometries supporting propagating and localized plasmons. For smooth navigation through this Perspective, the reader can always refer to the classification of the MOKE configuration that is given in Fig. 1(c). Section II of this Perspective mainly covers MO effects in magnetoplasmonic and magnetophotonic nanostructures in different configurations. We start with Sec. II A that presents the overview of fundamental works that theoretically explored the origin of MO by analytical models and explained the role of spin–orbit (SO) coupling in the MO activity in nanostructures supporting localized plasmons. We then proceed to Sec. II B where we explain the origin and the resonant enhancement of MO effects in MPCs and derive the dispersion relations. In Sec. II B, we discuss the fundamental limitations and the main strategies used to maximize the MO enhancement in magnetoplasmonic nanostructures and MPCs. In Sec II C, we discuss transversely magnetized MPCs and plasmonic nonreciprocity, specifically focusing on the variety of materials and geometries that provide strong light modulation by the transversely applied magnetic field. Section II D delves into MO effects in longitudinal magnetization and introduces the longitudinal magnetophotonic intensity effect (LMPIE). Finally, we devote Sec. II E to MO effects in dot and antidot periodic arrays and consider special light illumination conditions associated with Wood’s anomalies and second harmonic generation (SHG). In Sec III, we give an overview of applications of nanoscale magnetoplasmonics and magnetophotonics in biological and chemical sensing and light’s polarization and phase control. Section IV is entirely focused on nonlinear-optical processes attainable in the vicinity of SP resonances in the presence of magnetic fields. We continue with Sec. V that introduces the emerging field of magnetically induced spin polarization in semiconductors. Section VI of this Perspective is devoted to ultrafast magnetism and fundamental understanding of the relationship of spin orbital momentum and orbital angular momentum of light and nanoscale magnetism giving a special attention to the inverse Faraday effect (IFE) and helicity-dependent all-optical magnetization switching. We conclude by giving our outlook on the field and by summarizing the recent advances that pave the way to practical magnetophotonic devices.

Magnetoplasmonic nanostructures and nanostructured magnetophotonic crystals support surface plasmon resonances (localized and/or propagating). Therefore, they exhibit strongly enhanced MO activity at low magnetic fields. Regarding the systems supporting LSPRs, Sepúlveda et al. first explained intuitively this phenomenon in 2010.¹³ They showed that in pure gold nanodisks, the large MO response comes from an increase of the magnetic Lorentz force induced by the large collective movement of the conduction electrons when a LSPR is excited in the presence of a static magnetic field [see Figs. 2(a) and 2(b)].

Few years later, Maccaferri et al.⁵⁶ provided a semi-classical explanation by exploring the influence of the phase of localized plasmon resonances on the MO activity in nickel nanodisks. They demonstrated that these systems can be described as two orthogonal damped oscillators coupled by the SO interaction, proving that only the SO-induced transverse plasmon plays an active role on the MO properties by controlling the relative amplitude and phase lag between the two oscillators [Fig. 2(c)]. Furthermore, a full analytical theoretical description for typical sample geometries was introduced recently by Floess et al.,⁵⁷ who developed a Lorentz nonreciprocal coupled oscillator model [Fig. 2(d)] yielding analytical expressions for the resonantly enhanced MO response. All these models can be transferred to other complex and hybrid nano-optical systems and can significantly facilitate device design. However, the magnetic field-induced modulation of light polarization achieved in magnetophotonic crystals so far is only in the order of a fraction of degree, which is insufficient for any practical purposes. When using conventional ferromagnets, the main obstacles are the exiguity of MO activity arising from the SO coupling and the rather inefficient excitation and/or propagation of plasmon modes, due to their high dissipative losses. One of the key challenges is indeed to increase the strength of SO coupling without increasing the plasmon damping. The main strategies currently pursued with conventional ferromagnetic materials, namely, without increasing the intrinsic SO coupling, are (i) periodic arrangements of magnetoplasmonic nanoantennas;^58,59 (ii) 3D ferromagnets⁶⁰ and composite ferromagnetic/noble metal⁶¹ and ferromagnetic/dielectric/noble metal nanostructures,⁶² and (iii) heterogeneous units comprising multiple nanoantennas placed in proximity to enable their near-field interaction.^63–67 Initial investigations have shown that the enhancement of polarization rotation by one order of magnitude can indeed be achieved following these strategies. Finally, it is worth noticing that exploiting high-index all-dielectric nanostructures, one can reduce high losses that are inherent in magnetic materials.¹⁶ The use of these materials can lead to peculiar novel phenomena where magnetic dipoles are responsible for the MO activity, thus opening interesting perspectives in the engineering of novel nanoscale MO effects.

Periodically nanostructured metal–dielectric systems allow excitation of propagating plasmonic modes by incident light. On the other hand, their periodicity is of the order of wavelength of SPPs propagating at the metal–dielectric interface, and at some frequency range, constructive interference takes place and bandgaps appear. Therefore, such type of structures can be referred to the plasmonic crystals in analogy to photonic crystals. If some magnetic substances are involved, then such a periodic structure is called a magnetoplasmonic crystal (MPC).

There are several designs of MPCs including one-dimensional (1D) [Figs. 3(a) and 3(b)] and two-dimensional (2D) [Figs. 3(c)–3(f)] crystals.

Generally, excitation of plasmonic resonance provides enhancement of MO effects. A noble metal plasmonic crystal without any magnetic media can be also made an MPC if a high external magnetic field is applied. If the magnetic field is in-plane and transverse with respect to SPP propagation, then it provides some enhancement of the T-MOKE.⁶⁸ In this case, the MO properties are due to the Lorentz force acting on free electrons in a magnetic field. A resonant increase of the T-MOKE was reported for one-dimensional Co, Fe, and Ni gratings.^69,70 Pronounced resonance of the T-MOKE in a sample of 1D trilayer SiO₂/Fe/Ag MPC fabricated on a commercial blue-ray disc also allowed us to consider a refractive index sensor on its basis⁷¹ [Fig. 3(a)]. Though the propagation length of SPPs in ferromagnetic metals is rather small and does not exceed several micrometers, it still counts several periods of the structure and the periodicity plays an important role in the SPPs excitation and their interplay with MO effects. A several times increase of the T-MOKE at the plasmonic resonances of the grating with respect to the smooth ferromagnets was reported. The concepts of hybrid MPC based on noble metal/ferromagnetic metal multilayers as well as nanocorrugated 2D films were also comprehensively studied in Refs. 72–76 [Figs. 3(b) and 3(c)] and in Refs. 77 and 78 [Figs. 3(d) and 3(f)], respectively. Since the overall optical losses for such systems are lower than for pure ferromagnetic metals, the effect of resonant increase of the T-MOKE due to propagating SPPs in these structures is more pronounced. It also allows us to consider these structures as highly sensitive plasmonic biosensors.^71,79 The concept of MPC works not only with transverse magnetization. Recently, Maccaferri et al. investigated longitudinally magnetized MPCs and observed an increase of the L-MOKE at the SPP resonances⁴⁹ [Fig. 3(e)].

The MPC structures can also be referred to as magnetophotonic metasurfaces, though the term of metasurface is more general and also includes all-dielectric and semiconductor materials consisting of substrates covered with cylinders and spheres sustaining Mie resonances.^80,81 An example of magnetoplasmonic metasurface is represented by two-dimensional arrays of Si nanodisks covered by a thin Ni film.⁸² Optical resonances in such samples lead to enhanced MO response like Faraday rotation of 0.8 °, which is reasonably large taking in mind that the magnetic part is only 5 nm thick.

The main disadvantage of most of the aforementioned approaches is that the optical losses associated with the presence of a ferromagnetic metal are still relatively high. This fact limits exploiting fully the potential gain of the combined concepts of nanostructuring and plasmonics in magneto-optics. If the ferromagnetic metals were avoided as in cases of pure semiconductors or noble metal systems, huge external magnetic fields exceeding several Tesla would be necessary to make the T-MOKE at least comparable with the effect in ferromagnets. That is why it seems that the plasmonic crystals containing low-loss ferromagnetic dielectrics and noble metals can provide even better results.^9,14,83 The most pronounced enhancement of the MO effects takes place for high-quality resonances that are achieved if the ferromagnetic metal is substituted by a low absorptive noble one and the dielectric layer is magnetized. Probably, the best candidates for magnetic dielectric are bismuth rare-earth iron garnet films of the composition Bi_xR_3 − xFe₅O₁₂, where R is a rare-earth element.⁸⁴ Therefore, we will consider main properties of MPCs taking this type of structures as examples and study their properties in detail.

Let us consider an MPC consisting of a smooth magnetic dielectric on a substrate and a noble metal film periodically perforated with subwavelength array(s) of slits and holes. In such a structure, SPPs can propagate along the upper interface, the air/metal interface, or the bottom interface between the metal and magnetic dielectric. Though the metal film is not continuous, the SPP can still propagate along the structure if the air gap size is notably smaller than the SPP wavelength and air takes a relatively small part of the MPC crystal lattice. During SPP propagation, some part of its energy continuously leaks in the far-field due to SPP scattering on the metal grating. This mechanism also contributes to the SPP energy decrease in MPCs together with conventional energy dissipation in lossy metal and dielectric layers.

Strictly speaking, the absolute value of the wavevector $β$ of the grating SPP in Eq. (1) deviates from the one for the smooth metal–dielectric interface determined by $k 0 ε 1 ε 2 ε 1 + ε 2$⁠, where $ε 1$ and $ε 2$ are dielectric permittivities for the metal and dielectric, respectively. In the case of a metal grating with narrow slits/holes on a smooth dielectric, this deviation is usually rather small and formulas for smooth interfaces are well applicable. However, the periodicity of the slits/holes does not allow describing SPP dispersion fully by the effective medium approach. This becomes mostly pronounced at $k=u(π/d)$ with an integer u, where the dispersion curve splits into two branches: low and high frequency, and a bandgap appears. This phenomenon is a general feature of any periodic structure with a period comparable with the wavelength of the wave propagating through it. Such periodic structures dealing with photons are called photonic crystals. That is why periodic metal–dielectric structures considered here can be referred to as plasmonic crystals. Plasmonic crystals allow tailoring dispersion of SPP in a desired way and concentration of electromagnetic energy in a small volume near the metal/dielectric interface. The latter was shown recently to have a great potential for ultrafast nanophotonics since it allows switching permittivity of gold by a short laser pulse at a time scale of several hundreds of femtoseconds.⁴⁴ 

It should be noted that most of the results on magnetoplasmonics-assisted light control were obtained at the visible and near-IR spectral range. However, modern telecommunication technologies rely on 1.55 μm light. At this wavelength, plasmonic properties of noble metals still remain relevant while one should be careful about the choice of a magnetic dielectric. In particular, bismuth-substituted rare-earth iron garnets have rather low MO activity at 1.55 μm. In this case, the use of cerium substituted iron garnets seems to be more preferable.⁸⁵ 

Excitation of the SPP influences optical transmission and reflection spectra of the MPC providing an asymmetric shape (the so-called Fano-shaped resonances). The magnetization-induced changes in SPP dispersion shift the Fano resonances and the MO intensity shift appears.

Due to the T-MOKE, light intensity can be controlled by a magnetic field without any polarizers or other additional optical elements. T-MOKE is mostly determined by the interface between nonmagnetic and magnetic media and, therefore, is highly sensitive to the magnetization near the sample surface and can sustain decent values even for ultra-thin films. Moreover, its inverse counterpart is of primary importance in ultrafast magnetic phenomena.³⁶ 

The T-MOKE for a bare iron garnet film is very small (δ ∼ 10⁻⁵), while for an MPC, it reaches 1.5 × 10⁻² as was demonstrated in Ref. 14 [Figs. 4(a) and 4(c)]. Optimization of the MPC structure along with excitation of the hybrid modes—waveguide plasmon polaritons—provided further increase of the T-MOKE up to 15%⁴⁴ [Fig. 4(d)].

A next step forward in this direction was made by Chekhov et al.,⁸³ where an additional layer of bismuth iron garnet was deposited on top of the gold grating [Fig. 4(e)]. In contrast to the traditional Au/garnet MPCs, spectra of the T-MOKE measured in transmission demonstrate rather specific features: a high-quality resonance for the long-range SPP and a broad 60 nm wide resonance for the short-range SPP [Fig. 4(f)].

A sophisticated multilayer structure consisting of an MPC, with a rare-earth iron garnet microresonator layer and a plasmonic grating deposited on top of it, was fabricated and studied in order to combine the functionalities of photonic and plasmonic crystals (Fig. 5).⁴¹ The plasmonic pattern also allows excitation of hybrid plasmonic waveguide modes localized in dielectric Bragg mirrors of the MPC or waveguide modes inside the microresonator layer. These modes give rise to additional resonances in the optical spectra of the structure and to the enhancement of the T-MOKE.

T-MOKE in MPCs was shown as an efficient tool for the MO investigation of ultra-thin magnetic films, which allows us to access their magnetization state and MO properties.⁸⁹ For magnetic films thicker than 40 nm, the T-MOKE marginally depends on the film thickness. A further decrease in the film thickness diminishes the T-MOKE since for such thicknesses the SPP field partially penetrates inside the non-magnetic substrate. Nevertheless, the T-MOKE remains measurable even for a few-nm-thick films.

Recently, magnetoplasmonic quasicrystals have been introduced and demonstrated to provide a unique MO response⁹⁰ [Figs. 5(c) and 5(d)]. The quasicrystal consists of a magnetic dielectric film covered by a thin gold layer perforated by slits, forming a Fibonacci-like binary sequence. The T-MOKE acquires controllable multiple plasmon-related resonances, resulting in a MO response over a wide frequency range. A multiband T-MOKE might be valuable for numerous nanophotonic applications, including optical sensing, control of light, all-optical control of magnetization, etc.

The T-MOKE configuration is of particular interest since it also provides new ways of routing the directivity of light emission by using an external magnetic field. The routing of emission for excitons in a diluted-magnetic-semiconductor quantum well was demonstrated in hybrid plasmonic semiconductor structures.⁹¹ In that case, a CdMnTe quantum well sandwiched between a CdMgTe buffer and spacer layers was covered with 1D gold grating to allow SPP excitation, which led to enhanced light emission directionality of up to 60%.

As we have discussed so far, the implementation of nanostructured hybrid materials provides a remarkable increase of the T-MOKE. Interestingly, plasmonic structures can give origin to novel MO phenomena as well.^25,40 In particular, the plasmonic crystal consisting of a 1D gold grating on top of a magnetic waveguide layer allows observing the MO intensity effect in longitudinal configuration, where a magnetic field is applied in the plane of the magnetic film and perpendicular to the slits in the gold grating [Fig. 6]. Longitudinal magnetization of the structure modifies the field distribution of the optical modes and thus changes the mode excitation conditions. In the optical far-field, this manifests in the alteration of the optical transmittance or reflectance when the structure is magnetized. Thus, this effect is described similarly to the T-MOKE by relative change of the transmittance or reflectance, but this time one should compare demagnetized (T₀) and longitudinally magnetized (T_M) states: δ = (T₀ − T_M)/T₀. Such MO response represents a novel class of effects related to the magnetic field-induced modification of the Bloch modes of the periodic hybrid structure. Therefore, we define it as the longitudinal magnetophotonic intensity effect (LMPIE).

From the Maxwell’s equations with the appropriate boundary conditions, the two principal modes of the magnetic layer—transverse magnetic (TM) and transverse electric (TE) modes—acquire in the longitudinal magnetic field additional field components, which are linear in gyration g, and thus turn into quasi-TM and quasi-TE modes, respectively^25,92 [Fig. 6]. Thus, the coupling between the TE and TM field components emerges in the magnetized layer. This leads to the origin of the LMPIE.

Experimental demonstration of the LMPIE was performed for an MPC based again on a bismuth iron garnet film.²⁵ A prominent feature of this sample is that it was designed such that the dispersion curves of the principal TM and TE modes correspond to the second diffraction order intersection at the Γ point (κ = 0) of the Brillouin zone. As a consequence, both modes can be excited by normally incident light at the same frequency. The LMPIE was observed in transmission. No intensity modulation occurs for the bare magnetic film [Fig. 6(e), green curve]. The longitudinally applied magnetic field resonantly increases transmittance by 24% at λ = 840 nm, where both modes are excited [Figs. 6(e) and 6(f)]. There are also resonances at about 825 nm and 801 nm, corresponding to excitation of the TE modes only, though their values are several times smaller. The measured magnetophotonic intensity effect with 24% modulation can be considered giant since it is a second-order effect in gyration (as it is an even function of the magnetic field). The modulation level can be increased even further by using materials with higher MO response, thus enabling the use of the LMPIE in modern telecommunication devices. Furthermore, the effect of mode switching is of great interest in the framework of active plasmonics and metamaterials.^92,93 Recently, the LMPIE in an MPC was used for magnetometry.⁹⁴ The experimental study revealed that such an approach allows us to reach the nT sensitivity level, which was limited by the noise of the laser. Moreover, the sensitivity can be improved up to fT/Hz^1/2 and micrometer spatial resolution can be reached.

Metallic gratinglike structures can provide the basis for the excitation of both SPPs and surface lattice resonances (SLRs).^95–98 By employing modern nanolithography techniques, 2D grating geometries can be designed at will, thus facilitating further tunability in the launching and control of the momentum of such plasmon modes.

To illustrate the use of this geometric construction and its utility in designing an MPC, we refer to the well-studied case of hexagonal antidot arrays,^50,52–54 schematically shown in Fig. 7(a). Different cases of illumination geometry are illustrated in Figs. 7(d)–7(g). In adopting this approach, we utilize the transformation into reciprocal space to examine the wave vector relationships for the light, propagating plasmon modes and reciprocal lattice vectors [Figs. 7(b) and 7(c)]. This representation can yield direct insights into the possible momentum amplitudes and directions with respect to the reciprocal lattice that can enable SPP modes. It is also possible to examine the conditions for excitation of collinear or non-collinear plasmon modes with respect to $k / / →$ or the reciprocal lattice vectors, as well as the direction of propagation (back or forward). SPPs in magnetoplasmonic hexagonal antidot structures of Ni were recently imaged using photo-emission electron microscopy.⁵⁰ The photo-emitted electron density can be correlated to the local electric field strength, which is modified by the presence of SPPs. This local field intensification leads to an increase of the pure MO contribution in terms of Fresnel reflection coefficients, such as $r sp$⁠, which are proportional to the electric field inside the MO layer and result in enhanced Kerr rotation.⁵⁰ 

In contrast, a periodic arrangement of metallic particles can also result in sharp resonances, which are referred to as SLRs in the literature.^{58,59,97,100–102} This phenomenon arises from the diffracted light propagating in the plane of the sample, strongly coupling to localized plasmon resonances of individual particles, collectively resulting in a dramatic narrowing of the plasmon resonances. Whenever such a condition is met by tuning the angle of incidence and wavelength of the light, abrupt changes in reflectivity are observed, which are commonly referred to as Wood’s anomalies.¹⁰³ If the metallic particle array is composed of ferromagnetic materials, Wood’s anomalies are accompanied by an enhancement of the MOKE, in a similar fashion to the case of SPPs,^58,59 as shown in Fig. 8.

An interesting situation arises when the grating period Λ is such that $λ/4< Λ<λ/2$ (or $2 k 0<G<4 k 0$⁠), where in the non-linear-optical regime the sample can be treated as a grating structure, while in the linear regime, the sample behaves as a metasurface.^102,104,105 This situation is graphically depicted in Fig. 9, for the case of a sample composed of Ni nanodimers, having different periodicities along the x- and y-directions, defining grating- and metasurfacelike behavior in the nonlinear and linear response, respectively. The second harmonic generation exhibits a grating behavior, with associated Wood’s anomalies. A decrease in specularly reflected intensity of an order of magnitude larger than the linear effect (in the grating regime) is observed, accompanied by a sizeable magnetic contrast.¹⁰² 

A remarkable property of nanostructured metal systems is their ability to concentrate the optical energy on a nanoscale volume. Plasmons (propagating and localized) are strongly confined at the interface between two media with permittivities of opposite sign, such as the interface between a dielectric and a metal. When the incident radiation couples to such plasmon modes, clear signatures, viz., plasmon resonances, in the optical response of the system are observed. The operating principle of plasmon-based sensors is based on the registration of the spectral and angular positions of these resonances, which depend strongly on the optical properties of the surrounding medium, such as, for instance, its refractive index [Fig. 10]. This is why plasmonic nanostructures are often used as transducers for single molecular recognition and for gas sensing applications.^106–108 Due to their sharp LSPRs or SPPs resonances, noble metals are the preferred materials to build such sensors, although recently it has been proved quite widely that a remarkable exception is the application of magnetoplasmonic structures in label-free molecular detection, bio-chemo-sensing, and determination of nanoscale distances. In these cases, despite the insignificant MO activity and large absorption losses, MPCs and nanoantennas were found to enable a radically improved sensitivity, clearly outperforming conventional plasmon-based sensors and rulers. In MO-active systems, the excitation of the plasmonic modes also affects their MO response. Furthermore, the enhancement of the sensor sensitivity (which is the derivative of the acquired measurement with respect to the analyzed refractive index change) and the resolution limit, as well as reliability and reproducibility, remain essential. A way to improve the sensitivity of nanostructures can be represented by the use of magnetoplasmonic nanostructures instead of the classical noble metal-based nanosensors. In this case, rather than measuring the usual transmission or reflection signals, tracking of the MO response can lead to a real sensitivity advantage when compared to absorbance-based measurements. As such, magnetoplasmonic nanostructures could form the basis of highly sensitive label-free biosensors. In 2006, Sepulveda et al.¹⁰⁹ showed an increase in the limit of detection by a factor of 3 in changes of the refractive index and in the adsorption of biomolecules compared with regular plasmon sensors. Years later, Regatos et al. presented an improvement of the previous approach, demonstrating a twofold increase in the MO-based sensors’ detection limit with respect to the intensity-interrogated SPP-based biosensors operating with refractive index changes.¹¹⁰ In 2013, Martín-Becerra et al. showed that the modulation of the SPP wavevector induced by an external applied magnetic field represents a new parameter with a higher sensitivity to the refractive index than the SPP wavevector, so monitoring it can lead to sensors with improved properties.¹¹¹ In 2014, Manera et al. demonstrated that magnetoplasmonic sensors can be used for investigating biomolecular interactions in the liquid phase with higher sensing performance in terms of sensitivity and lower limit of detection with respect to traditional SPR sensors.¹¹² 

Rella and Manera used hybrid Au/Co/Au magnetoplasmonic nanoparticles as novel transducer probes to achieve enhanced sensitivity in SPP-based chemosensors¹¹³ [Fig. 10(b)]. Similar systems supporting SPPs and MO functionalities with improved sensitivities were then proposed by other groups.^114–116 More recently, Ignatyeva et al. presented a novel concept of magnetoplasmonic sensor with ultranarrow resonances and high sensitivity, with a quality factor exceeding 1000¹¹⁷ [Fig. 10(d)]. In another work, they showed that high-quality factor surface modes in photonic crystal/iron garnet film heterostructures can also be used for sensor applications.¹¹⁸ In 2016, Caballero et al. proposed Au–Co–Au films perforated with a periodic array of subwavelength holes as transducers in MO-SPP sensors, introducing a detection scheme showing figures of merit that are two orders of magnitude larger than those of any other type of plasmonic sensor⁷⁹ [Fig. 10(c)]. A similar structure has been later proposed also by Diaz-Valencia et al.¹¹⁹ 

All the previously mentioned systems were based on the excitation of propagating plasmons. Until 2011, nobody thought of using magnetoplasmonic systems supporting LSPRs as sensors, when Bonanni et al. showed that nickel nanoantennas can be used as highly sensitive detectors of refractive index changes.⁵¹ In 2012, Zhang and Wang proposed magnetoplasmonic FePt–Au nanorods as a novel type of nano-bioprobe that allow simultaneous magnetic manipulation and optical imaging for single molecule measurements, drug delivery, and in vitro and in vivo diagnostics and therapy.¹²⁰ Later, Pineider et al. used gold nanoparticles dispersed in liquid solvents for refractometric sensing by magnetic circular dichroism (MCD) measurements.¹²¹ Similarly, Manera et al. showed recently that monitoring the MO response of gold nanoantennas measured in the Kretschmann configuration has the practical advantage to pursuit a better signal-to-noise ratio, an essential requirement for high resolution sensing signals.¹²² In 2015, Maccaferri et al. brought up a novel application for magnetoplasmonic antennas made of pure nickel, suggesting to monitor the polarization ellipticity variation of the transmitted and reflected light, showing a raw surface sensitivity (that is, without applying fitting procedures) corresponding to a mass of less than 1 ag per nanoantenna of polyamide-based molecules, which are representative for a large variety of polymers, peptides, and proteins¹²³ [Fig. 10(a)]. A similar approach has been also used recently by Tang et al. to increase the performances of refractive index sensors by magnetoplasmons in nanogratings,¹²⁴ and also by other groups implementing the method of tracking the ellipticity (and rotation) of the transmitted or reflected light using chiroptical nanostructures¹²⁵ and pure plasmonic nanoantennas.¹²⁶ In 2015, Zubritskaya et al. demonstrated that nickel dimers are able to report nanoscale distances while optimizing their own spatial orientation with about two orders of magnitude higher precision than current state-of-the-art plasmon rulers.⁶⁶ In 2016, Herreño-Fierro et al. showed that ellipsometric phase-based transducers can be used for bio-chemical sensing purposes.¹²⁷ In 2018, Pourjamal et al. showed that hybrid Ni/SiO₂/Au dimer arrays display improved sensing performances if compared to random distributions of pure Ni nanodisks and/or their random counterpart.¹²⁸ Finally, it is worth mentioning that, depending on the specific application, it could be more appropriate to exploit systems supporting either SPPs or LSPRs. Specific binding events can be detected using either SPPs¹¹³ and LSPRs,¹²⁶ but LSPRs or localized modes in general have been proved to be superior in molecular sensing of single molecules.¹²⁹ 

The investigation of the phenomena arising from the mutual interplay of magnetism and light–matter interactions in spatially confined geometries is decisive for data communication, photonic integrated circuits, sensing, all-optical magnetic data storage, and light detection and ranging. Light polarization rotators and nonreciprocal optical isolators are essential building blocks in these technologies. These macroscopic passive devices are commonly based on the MO Faraday and Kerr effects. Magnetoplasmonic nanoantennas and MPCs enable the magnetic control of the non-reciprocal light propagation and thus offer a promising route to bring these devices to the nanoscale, featuring dynamic tunability of light’s polarization and phase. Because noble metals provide outstanding light localization and focusing, combining them with ferromagnets became a wise strategy in design of active magnetoplasmonic devices operating with SPP.^{25,28–30,32–42,44} A similar approach was later utilized with nanostructures supporting localized plasmons. Magnetic field-dependent modulation of the polarization of reflected/transmitted light (magneto-optic Kerr/Faraday effects), owing to the intertwined plasmonic and MO properties, has been reported in Au/Co/Au multilayered^46,130 nanoantennas. It was long believed that ferromagnetic nanostructures alone cannot support localized plasmons due to high damping. The discovery of plasmons and their near-field mapping in nickel⁴⁸ opened up a promising route of magnetoplasmonic devices for light polarization control, now also in transmission due to their transparent nature. In 2011, Bonanni et al. discovered strong magneto-plasmon localization and plasmon-induced enhancement and tunability of MO activity in pure Ni nanoantennas⁵¹ [Fig. 11(a)]. Similar effects were also demonstrated along the years in nano-perforated/corrugated ferromagnetic films.^{49,50,52–54} In 2013, Maccaferri et al. developed an analytical model that highlighted the role of SO coupling on MO response.⁵⁶ In 2014, this work was followed by the derivation of MO design rules for engineering of nanoantennas with tailored MO response in all Kerr effect configurations (longitudinal, polar, and transverse) by Lodewijks et al.⁶⁰ Giant enhancement of MO effects was also observed in hybrid ferromagnetic/noble metal films (MPCs) by Chin et al. [Fig. 11(c)],²³ Caballero et al.,⁷⁹ and Kalish et al.,⁹² graphene/noble metal nanowires,¹³¹ and in a ferromagnetic metal/dielectric nanoparticle system where non-metallic high-refractive index semiconductor (“all-dielectric”) nanoantennas support optical Mie resonances.¹³² Theoretical systems of pure all-dielectric and ferromagnetic nanoantennas with strongly enhanced MO has been proposed.¹³³ Furthermore, another intriguing and interesting advance in the field is also represented by the manipulation of structured light, namely, light carrying orbital and/or spin angular momentum (SAM) information.^134–136 In these works, either the spin or the orbital angular momenta were shown to be actively tuned by applying an external magnetic field. In particular, an interesting direction might be the merging of the strong chiral response and the angular momentum selectivity reported in Ref. 135 with the strong magnetic field modulation (beyond 100%) reported in Ref. 136 where, on the contrary, the overall chiral response was very weak due to the 2D geometry of the system. Along this direction, it is worth mentioning that a detailed analysis that might help us to reach this goal was reported by Feng et al.,¹³⁷ where they analyzed the contributions from optical chirality, optical anisotropy, and magnetic modulation of circular dichroism (CD) to the global optical response in Au/Co split-ring geometries. In this particular case, they showed a system that has a strong chiral response with a MO-mediated magnetic modulation of CD of about 25% [Fig. 11(d)].

The ability to externally control optical states could be a key feature in nanophotonic applications such as nanoscale local polarization detection, chirality recognition, and polarization spectroscopy, as well as magnetic field sensing⁹⁴ or tunable near-field emission of a desired optical state.¹³⁸ MO properties of CoPt nanostructures with antiparallel magnetic alignment combined with noble metal (Au and Ag) fine grains were recently investigated by Yamane et al.¹³⁹ revealing the enhancement of MO effects via LSPRs in the grains. Previously, the same group achieved an impressive rotation of 20° in the visible spectral region by using the CoPt/ZnO/Ag multilayered structure that works like a MO Fabry–Pérot cavity.¹⁴⁰ Almpanis et al. also predicted similar impressive values of the polarization rotation in the near-IR region in a magnetic garnet film sandwiched between two metallic layers, patterned with periodically spaced parallel grooves on their outer sides.¹⁴¹ An intriguing case of magnetic field-assisted dynamic alignment resulting in enhancement/cancelation of plasmon optical response rather than polarization was demonstrated utilizing multisegmented Au/Ni/Au nanorods.²⁴ The recent comparison study on hybrid magnetoplasmonic gold–magnetite nanoparticles with core–shell, dumbbell-like, and cross-linked geometries suggests the improvement of tunability, light scattering enhancement, and local field enhancement at the interface between magnetic and plasmonic constituents.¹⁴² 

It is worth mentioning that a magnetic manipulation of propagating plasmons in MPCs made of magnetic garnets²⁷ can also lead to strongly enhanced MO activity, which gives rise to exotic optical properties such as MO transparency¹⁴³ and extraordinary transmission in sub-wavelength nanohole arrays.¹⁴⁴ In similar garnet materials, Subkhangulov et al. suggested recently a novel concept for ultrafast MO polarization modulation using terbium gallium garnet (Tb₃Ga₅O₁₂), where MO modulation with frequencies up to 1.1 THz is continuously tunable by means of an external magnetic field.¹⁴⁵ Finally, in 2016, Firby et al. proposed a magnetoplasmonic Faraday rotator by incorporating Bi:YIG into a hybrid ridge–plasmonic waveguide structure, which seems to overcome the phase-matching limitations between photonic TE and plasmonic TM modes, thus inducing a 99.4% polarization conversion within a length of 830 μm.¹⁴⁶ Similarly, in 2017, Floess et al. realized a hybrid magnetoplasmonic thin film structure that in transmission geometry displays a giant Faraday rotation of over 14° for a thickness of less than 200 nm and a magnetic field of 5 T at T = 20 K¹⁴⁷ [Fig. 11(b)].

The SPPs and the waveguide modes of smooth semiconductors in the presence of an external magnetic field were considered in Refs. 148 and 149. In these works, Kushwaha and Halevi have undertaken a theoretical study of magnetoplasma waves in a thin, semiconducting film, and they showed that the magnetic field does not introduce any linear magnetization terms in the modes dispersion, but it induces transverse electromagnetic field components and the appearance of modes with a negative group velocity, which are a magnetoplasma generalization of the Fuchs–Kliewer modes.

The polarization rotation MO effects were studied in different types of smooth multilayered metal/dielectric structures with either metallic or dielectric magnetized components.^{147,150–153,176} Probably, one of the first experimental demonstration of the influence of the plasmonic modes on the Faraday effect was published in Ref. 154. Without making reference to surface plasma waves, Judy¹⁵⁴ reported an optically enhanced Kerr rotation in thin iron films, magnetized in the longitudinal orientation, near what has become identified as the plasmon angle.

In some papers,^152,153 plasmon-induced P- or L-MOKE enhancement was claimed, but it was usually accompanied by decrease in the intensity of the signal. The SPP-assisted pronounced increase of the Faraday effect was reported in the Bi-substituted iron garnet film covered with thin corrugated silver and gold layers.¹⁵¹ It was assumed that the main contribution in the enhancement of the Faraday effect in such systems is made by the polarization rotation of the SPPs excited on the metal/dielectric interface.

Faraday and Kerr effects in periodic metal–dielectric structures were also considered recently.^{70,72,74,144,155–158} In particular, Diwekar et al.¹⁵⁵ experimentally investigated the Kerr effect upon reflection of visible light from a perforated cobalt film magnetized perpendicular to the surface. It was revealed that, in the vicinity of the region of anomalous transmission of light, the Kerr effect is reduced by one order of magnitude. There are a number of works dealing with the metal–dielectric structures characterized by a considerable enhancement of the Faraday effect.^156–158 In those works, a magnetic medium was placed either inside holes in the metal¹⁵⁶ or the metal itself was ferromagnetic.^157,158

The plasmonic crystals of perforated gold on top of the smooth thick ferromagnetic layer were also investigated by measuring the cross-polarized transmission and polar Kerr rotation as a function of the external magnetic field.¹⁴⁴ Although the effects of plasmons on these processes were observed, the enhancement of the MO effects via SPPs was not clearly demonstrated.

Though most of the periodic structures were fabricated by means of electron beam lithography and subsequent etching, some other fabrication approaches were also used. Sapozhnikov et al. fabricated a 2D MPC by sputtering Co or Ni on top of a PMMA colloidal crystal. It was found that there are some resonance peculiarities in the Kerr rotation spectra. They were attributed to the SPPs and to the resonances related to the multiple interference reflections between the colloidal crystal substrate and the nanostructured film.⁷⁷ It was found that there are some resonance peculiarities in the Kerr rotation spectra. They were attributed to the SPP resonances and to the resonances related to the multiple reflections from the interference between reflections from the colloidal crystal substrate and from the nanostructured film. Torrado et al. also used the self-assembling method. They prepared a plasmonic crystal from a polymeric monolayers replicated on nickel. The SPP-assisted increase of the polar and transverse Kerr effects due to the excitation of Ni SPPs modes is reported. However, the effect of disorder was shown to decrease the amount of that enhancement. One more magnetoplasmonic periodic structure was fabricated by depositing Co/Pt multilayers on arrays of polystyrene spheres.¹⁵⁹ 

It should be noted that the increase of the Faraday and Kerr rotation was reported recently for pure dielectric systems at wavelengths of waveguide mode resonances^160,161 and in plasmonic structures containing graphene in the THz frequency range.¹⁶² 

In what follows, we focus on the Faraday effect in MPC based on iron garnet films. At non-resonant frequencies, the Faraday rotation is close to that of a single magnetic film and is defined by the film’s thickness. At the eigenmode’s excitation wavelength, resonant features of the MO response are expected. The eigenmodes that are essential for MO behavior are the SPP at the metal/dielectric interface and the waveguide modes of the dielectric layer.

The Faraday rotation can be considered qualitatively as a result of the conversion of the TE–TM field components. Two mechanisms inducing a resonant behavior of the Faraday effect are possible. Let the incident wave be TM-polarized. First, at the frequency ω_TM, where either a TM mode or a SPP can be excited, the TM field is partly converted in a TE mode. But, since the excitation condition for the TE mode is not fulfilled at this frequency, the TE field component is re-emitted contributing to the far-field. Moreover, the enhancement of the Faraday effect is due to the fact that the effective path of either the TM mode or the SPP is larger than in the nonresonant case. Second, at the frequency ω_TE, the electromagnetic field re-emitted by the structure is partially converted in the TE mode. Also, at this frequency, the TE mode has a large effective path that causes the enhancement of the Faraday effect. Thus, the mechanism for the Faraday rotation enhancement depends on the type of the excited eigenmode.

If the magnetic film thickness is comparable to the wavelength of the incoming light, the waveguide modes become essential.³⁰ As shown in Fig. 12(a), the Faraday rotation displays both negative and positive peaks. Furthermore, the positive Faraday rotation peak at λ = 883 nm corresponds to more than fourfold enhancement compared to the signal of a continuous magnetic layer of the same thickness. In addition, the positive Faraday rotation peak coincides with the resonance in transmission, allowing about 40% of the incident energy flux to be transmitted. At the same time, the negative Faraday maximum at λ = 818 nm corresponds to almost negligible transmission. The peaks of the Faraday rotation are also accompanied by abrupt changes in the light’s ellipticity. However, the ellipticity becomes zero at the resonance wavelength and the transmitted light remains linearly polarized, but with substantial rotation of the polarization plane.

The experimental demonstration of the Faraday effect enhancement in MPCs similar to the one considered above was done in Ref. 23 [Fig. 12(b)]. The spectra of the Faraday rotation exhibit resonant features. The spectra of the Faraday rotation exhibit resonant features. The sample with 495 nm lattice period reaches a maximum Faraday rotation of 0.80° at λ = 963 nm, which is 8.9 times larger than the −0.09° Faraday rotation of the bare iron garnet film. As seen from Fig.12(c), the same sample also shows a 36% transmittance at the resonant wavelength.

Strong localization and enhancement of electromagnetic fields represents one of the most prominent features of plasmonics. Obviously, this enhancement can be exploited to boost up the efficiency of a plethora of nonlinear-optical processes, such as, to name a few, Raman scattering or second harmonic generation (SHG), constituting the core of nonlinear plasmonics.¹⁶³ The tunability of magnetoplasmonic resonances with external magnetic fields discussed in the previous sections paves the way to the convenient control of the efficiency of nonlinear-optical effects. There, at the crossroads of non-linear optics, plasmonics, and magneto-optics, emerges the field of nonlinear magnetoplasmonics aiming at understanding the fundamentals of nonlinear magneto-optics when SPPs are excited.

It is possible to point out a few central aspects of nonlinear magnetoplasmonics. First of its interest is the tunability of the nonlinear-optical response, attainable in the vicinity of SPP resonances using magnetic fields. Second, it aims at enhancing (otherwise weak) MO effects by means of SPP-driven light localization at the nanoscale. Notably, in both of these approaches, the magnetic part of the story is provided by an external DC magnetic field which is used to control the magnetization of the plasmonic medium. This should not be confused with the situations where magnetic field of light at optical frequencies is coupled to the plasmon resonance of medium that does not have to be ferromagnetic. Nonlinear-optical effects associated with the excitation of these magnetic dipole-induced resonances in plasmonic nanostructures^164–170 will not be discussed here.

It is thus clear that the role of SPP resonances on the variations of magnetic contrast can be restricted to their modification of either $ξ$ or $Δφ$⁠. Indeed, despite boosting the total SHG output, the prominent SPP-induced enhancement of the local fields alone is unable to change $ρ 2 ω$⁠, as both crystallographic and magnetic SHG contributions are equally enhanced. Reported rather long ago,¹⁷³ the first experimental evidence for this might have resulted in delaying the development of nonlinear magnetoplasmonics.

The plasmon-induced variations of $ξ$ can originate in the anisotropy of the $χ ( 2 )$ tensor. Indeed, the excitation of LSPRs in anisotropic nanostructures results in unequal resonant enhancement of various $χ ( 2 )$ components responsible for the crystallographic and mSHG, respectively. Absent in spherical nanoparticles, this effect has been demonstrated in anisotropic Ni nanopillars.¹⁷⁴ In the chosen combination of polarizations, crystallographic and magnetic SHG contributions are given by $χ z y y ( 2 )$ and $χ x y y ( 2 )$ components, respectively. LSPR modes in these structures facilitate strong enhancement of $E z( 2 ω)$ along the main axis of the pillars, which is equivalent to the resonance in $χ z j k ( 2 )$ (but not in $χ x j k ( 2 )$⁠) components. As such, the effective ratio $ξ$ is modified, giving rise to the LSPR-induced variations of $ρ 2 ω$⁠. Although this particular system allows for a very clear demonstration of the anisotropy mechanism, the mSHG-LSPR effects in more complicated geometries can be understood in a similar way.¹⁷⁵ 

At the same time, the experimentally observed propagating SPP-induced variations of the SHG magnetic contrast have been ascribed to the non-locality of the nonlinear-optical response.^176–180 Yet, a large number of interfaces and respective nonzero components of the $χ ( 2 )$ tensor did not allow for a clear picture of relevant non-linear magnetoplasmonic effects in the studied trilayer films. Shortly after, Kirilyuk et al. demonstrated SPP-induced variations of the SFG magnetic contrast in the near-field spectral region,¹⁸¹ pointing out the high promise of this technique for studying magnetic surface excitations.

Preliminary indications of the resonant variations of $Δφ$ as the origin of the propagating (either on gratings or using prism coupling) SPP-induced mSHG modification were found by Newman et al.^182,183 It took, however, about a decade until this has been clearly verified by direct SHG interferometry^184,185 and complex polarization analysis.^186,187 Interestingly, similar phase behavior has been reported upon excitation of a collective plasmonic mode in an array of nanodisks.¹⁸⁸ Apparently, the SPP-induced variations of $Δφ$ and $ξ$ are not always possible to disentangle, as, for example, both are present in many practical situations. For instance, mSHG yield from an isotropic magnetic interface in P-in, P-out combination of polarizations is governed by crystallographic $χ z z z ( 2 ), χ z x x ( 2 ), χ x z x ( 2 )= χ x x z ( 2 )$ and magneto-induced $χ x z z ( 2 ), χ x x x ( 2 ), χ z z x ( 2 )= χ z x z ( 2 )$ complex tensor components, so that the effective $χ ( 2 , c r )$ and $χ ( 2 , m )$ are given by the interference effects. All of them contribute to the total SHG output, resulting in strong intertwining of the amplitude and phase variations originating in the SPP-induced electric field enhancement. Yet, the sign change of magnetic contrast clearly indicates the importance of the SPP-induced phase shift between the $χ ( 2 )$ components.

Interestingly, the most characteristic feature of nonlinear plasmonics is its sensitivity to the resonances at frequencies different to the fundamental one (2ω for SHG).^189,190 This can be exploited for novel mSHG effects where the SPP at the frequency 2ω results in stronger mSHG contrasts than the fundamental SPP resonance.^191,192 Importantly, the system has to support SPP resonances at both ω and 2ω, which is not the case for purely Au-based structures and typical 1.55 eV photon energy excitation. Large values of $ρ 2 ω$ (up to 33%) can be further optimized by adjusting the thickness of the plasmonic Ag layer¹⁹¹ and the excitation wavelength, thus shifting the SPP resonances at the fundamental and SHG frequencies closer to each other due to the SPP dispersion. The latter opens an interesting perspective on the study of resonances overlapping at multiple frequencies to get stronger magnetic modulation of nonlinear-optical effects.

We emphasize the large magnitude of MO effects in nonlinear optics as compared to their linear counterparts. Indeed, if linear magnetoplasmonics typically deals with 0.5%–1% reflectivity modulation, in SHG, one can quite easily obtain an order of magnitude enhancement. These large effects are not bound to one particular class of objects but are ubiquitous in ferromagnetic metal-based structures, ferromagnetic–noble metal multilayers, and hybrid noble metal–magnetic dielectric systems.¹⁹³ Yet, for sensing and switching applications, not only magnetic modulation but also total efficiency of nonlinear-optical conversion is important. However, the strongest SHG modulation is often observed at the minima of the total SHG yield, originating in the destructive interference of multiple contributions. Designing a novel system with overlapping large nonlinear-optical signals and their strong modulation upon magnetization reversal remains one of the open challenges of nonlinear magnetoplasmonics.

A recent and intriguing development in the field of combining plasmons and magnetism is the extension of the activities toward material systems, incorporating semiconductors. It has been long suggested¹⁹⁴ that future electronic technologies will be relying not only on the control of the charge of the electrons but also on their spin degree of freedom. Already in the 1990s, various routes were explored to induce magnetic order or spin polarization in semiconductors, utilizing light.^195–197 In these first studies, no particular weight was placed on the effect plasmon resonances might have on the interaction of light with magnetism in semiconductors, as the majority of investigated systems were thin films.^195,195 Indications of interesting physical effects being present in semiconducting particle systems, emerged in works by Gupta et al.¹⁹⁷ and by Beaulac et al.¹⁹⁸ In the latter, the photomagnetic effects in the form of photoexcited exchange fields leading to strong Zeeman splittings in the band structure were reported to persist up to room temperature.

Existing approaches for achieving spin polarization in semiconductors have mostly focused on researching dilute magnetic semiconductors or magnetic oxides.^199,200 The approach involving light to achieve spin polarization or spontaneous magnetization in semiconductors could potentially add an extra route, adding tunability into the scheme, via the control of size and shape of semiconductor nanoparticles. As an example, ZnO nanocrystals have been shown to exhibit plasmon resonances in the near-infrared region, supported by the observation of a strong magnetic circular dichroism (MCD) signal, which is temperature independent and linearly dependent on the applied magnetic field.²⁰¹ More specifically, the temperature independent MCD was attributed to a Pauli-like paramagnetic behavior of the nanocrystals, more common for alkali or noble metals. Recently, non-resonant coupling between cyclotron magnetoplasmonic modes and excitonic states was reported, leading to spin polarization and Zeeman splitting of the excitonic states under externally applied magnetic fields²⁰² [Fig. 13]. Surprisingly, also for this case the effects persist up to room temperature. Beyond the generation of spin polarized carrier populations in semiconducting materials, recent works have also been reporting on schemes for optical detection of spin currents in hybrid devices. These so far have been based on molecular semiconductors, such as fullerenes.²⁰³ 

These recent developments open up the way for a fresh look on the plasmon–exciton and plasmon–spin interaction in semiconductors. Combined, they offer the possibility for optical → spin and spin → optical conversion, necessary for a complete framework for an emerging new technology. Expanding this approach also to metal/oxide systems, where plasmon resonances have also been shown to generate and transfer spin currents,^204,205 opens up a completely new landscape. Surely, magnetophotonics and magnetoplasmonics will play a crucial role in upcoming developments, concerning material and device designs, holding promises for applicability in information processing and technology.²⁰⁶ 

The ability to manipulate optical pulses on timescales well into the femtosecond regime has opened the door for attempts to control magnetism in an unprecedented, ultrafast way. In 1996, Beaurepaire et al.²⁰⁷ made a seminal discovery when they observed that a short laser pulse (60 fs, $λ=620 nm$⁠) could demagnetize a thin Ni film by 50% on a sub-picosecond timescale. This timescale was much shorter than what was expected from the spin–lattice relaxation at that time. The discovery of the ultrafast quenching of the magnetic order initiated much research and eventually led to the birth of a new scientific branch, ultrafast magnetism, poised on the intersection of magnetism and photonics. The microscopic mechanism of the ultrafast suppression of the spin magnetization gave rise to much debate and controversy in the scientific community (see Refs. 208 and 209 for reviews). Obviously, a detailed microscopic understanding of how spin angular momentum can be controlled ultrafast can have far reaching consequences for the future development of ultrafast spintronics, i.e., spintronic devices that can operate at THz frequencies or faster.

While the initial discovery of Beaurepaire et al.²⁰⁷ demonstrated the ultrafast decay of spin moment, a second discovery, made by Stanciu et al.²¹⁰ showed that optical laser pulses could be used to deterministically reverse the spin moment. Investigating a particular ferri-magnetic alloy, Gd₂₂Fe_74.6Co_3.4, they found that the magnetization direction of magnetic domains could be reverted just by applying continuous radiation or by short laser pulses. This discovery could have important technological implications, since, for example, switching the spin magnetization by an ultrashort pulse could lead to much faster writing of magnetic bits in magnetic recording media. The origin of the all-optical switching (AOS) was initially thought to be linked to the helicity of the laser pulse, i.e., the injected photonic spin moment, but subsequent investigations showed that solely fast laser heating was sufficient to trigger the magnetization reversal.²¹¹ The origin of the helicity-independent switching in GdFeCo alloys was then analyzed to be related to the presence of a magnetization compensation point (antiparallel and nearly compensating moments on Fe, Co, and Gd) and the quite different spin-dynamic timescales of the laser excited 3d spin moments on Fe, Co, and the rather slow dynamics of the localized 4f moment on Gd.^212,211,213 Investigating other ferromagnetic compounds and multilayer systems, Mangin et al.^214,215 showed that helicity-dependent all-optical switching (HD-AOS) was achievable for a broad range of ferromagnetic materials, even for the hard-magnetic recording material FePt that does not exhibit any compensation point. This discovery prompted that there must exist suitable, but as yet poorly known, ways to employ the photon spin angular momentum (SAM) to act on the material’s spin moment to trigger spin reversal of the latter.

Irrespective of what the deeper origin of the photon–spin interaction is, the spatial resolution of the area where the magnetization could be switched was limited by the light focal spot to domain sizes mostly larger than 10 × 10 μm². It was consequently realized that, to reach ultrafast light-magnetism operations at the nanoscale, a further aspect needed to come in. Plasmonics offers precisely the ability to concentrate and enhance electromagnetic radiation much below the diffraction limit, which is essential for opto-magnetic applications in spintronics, where a major goal is deterministic control of nanometer-sized magnetic bits. While plasmonics and magnetoplasmonics (see Ref. 5) have already developed over a longer period, the combination of plasmonics with opto-magnetism represents a new challenge. Circular magnetoplasmonic modes resulting in the shift of the plasmon resonance frequency in Au nanoparticles were investigated by Pineider et al. suggesting a new detection scheme for label-free refractometric sensing.¹²¹ Thermal effects associated with LSPR in nanoparticles such as hot-electron generation and its dynamics were studied by Saavedra et al.²²¹ A first attempt to utilize plasmonics to achieve all-optical spin switching on the nanometer scale was made in 2015 by Liu et al.²²² who deposited 200 nm Au nano-antennas on a ferri-magnetic TbFeCo film. In this way, they could use high local heating and concentrate on the area that exhibits spin switching to about 50 nm diameter. However, it was observed that some areas switched and others did not. This could be related to a composition inhomogeneity of the TbFeCo film on a sub-100 nm scale. Earlier investigations of AOS in GdFeCo films showed that the switching depends sensitively on the Gd/Fe concentration ratio.²²³ An x-ray diffraction study by Graves et al.²²⁴ on GdFeCo showed that a composition inhomogeneity could lead to local variations in the switching behavior. A different investigation was made by Kataja et al.,²²⁵ who could observe both plasmon-induced demagnetization magnetic switching in a Ni nanoparticle array, excited by a femtosecond laser pulse, which they explained by the plasmonic local heating of the nanoparticles above the Curie temperature. A next step in this direction could be the fabrication of GdFeCo nanoparticle arrays.

To explain the IFE in bulk materials, several models have been proposed recently. The deeper understanding of the origin of the IFE and how it can be utilized is still the subject of ongoing investigations. Hertel developed a plasma model, in which the constant κ in Eq. (11) is proportional to $ω p 2/ ω 3$⁠, where $ω p$ is the plasma frequency and ω is the frequency of the incident radiation.²²⁶ Nadarajah and Sheldon used this model to estimate the magnetic moment that could be induced in a Au nanoparticle.²²⁷ Popova et al.²²⁸ employed a four-level hydrogen model with impulsive Raman scattering to show that such a process could lead to a net induced magnetization. Using relativistic electrodynamics, Mondal et al. showed that there exists an electromagnetic wave–electron spin interaction that provides a linear coupling of the photon SAM to the electron spin, which then acts as an optomagnetic field that generates the induced magnetization.²²⁹ A different approach was developed by Battiato et al.²¹⁸ and Berritta et al.,²¹⁹ who used a second-order density matrix perturbation theory to derive quantum theory expression for the IFE constant κ in which the optical absorption is taken into account and that is moreover suitable for ab initio calculations. Such calculations are important as they can quantify the size of the opto-magnetic interaction. Carrying out ab initio calculations for bulk Au, Berritta et al.²¹⁹ computed that a moment of 7.5 × 10⁻³ μ_B per Au atom could be induced by pumping with continuous circular electromagnetic radiation with a 10 GW/cm² intensity and 800 nm wavelength. Detailed measurements of the light-induced magnetization in Au, however, do not yet exist. In an early pioneering investigation, Zheludev et al.²³⁰ could measure an induced MO polarization rotation of ∼7 × 10⁻⁴° in an Au film upon pumping with a laser intensity of 1 GW/cm² and 1260 nm wavelength, a value that is within an order of magnitude consistent with the ab initio calculated induced moment.

The use of plasmonics for the design of strongly enhanced magnetophotonic interactions can now be perceived to be possible in distinct ways. First, plasmonic nanostructures can be tailor-made to concentrate on the electromagnetic near field at nano-sized spots, where the enhanced intensity $|E | 2$ can generate a substantial local magnetization $M i n d$ via the IFE. It is clear that not only an enhanced intensity is needed but also the local field must be circularly polarized too. This implies that a special design of the nanostructures is needed (see, e.g., Refs. 231 and 232) to ensure that a high magnetic induction pulse is generated. Such modeling can be carried out with Maxwell solvers such as COMSOL or Lumerical. Tsiatmas et al.²³¹ predicted in this way that Ni–Au nanorings excited with a fluence of ∼0.1 J/cm² at plasmon resonance could sustain thermoelectric currents that cause a magnetic induction pulse of ∼0.2 T. A different route has been followed by Hurst et al.,²³³ who used a quantum hydrodynamic model to study the magnetic moment induced by circularly polarized radiation in individual Au nanoparticles [Fig. 14(a)]. Circularly polarized radiation can excite electric dipolelike LSPRs in two orthonormal directions on the nanoparticle with a phase difference between them. An orbital magnetization density, $m(t)∝r(t)× d r ( t ) d t$⁠, appears in the nanoparticle as a result of the free electron motion, leading to a non-vanishing electron current density J on the surface of the nanoparticle, see Fig. 14(b). Consequently, the free electron cloud will rotate around the nanoparticle. The magnetic induction B due to the circulating current, computed with the Biot–Savart law in the center of the nanoparticle and shown in Fig. 14(c), is predicted to reach 0.3 T for laser intensities of 10³ GW/cm². The magnetic moment M induced by this plasmonic IFE can reach ∼0.6 μ_B per Au atom, depending on the size of the nanoparticle and laser intensity, see Fig. 14(d). Even though the assumed laser intensities are very high, the induced moments and generated magnetic fields predicted for the plasmonic IFE²³³ of nanoparticles are notably much larger than those computed ab initio for the IFE in bulk materials.²¹⁹ This strongly increased magnetic moment of the Au nanoparticle nicely illustrates the huge impact that plasmonics could potentially have in the area of opto-magnetism. Specifically, the collective motion of the free electron cloud in the surface plasmon resonance can lead to a much larger total induced magnetization than the excited motions of individual bound electrons.

All of the above considerations were built upon exploiting the spin angular momentum functionality of the electromagnetic field. A number of years ago, it was realized that an optical beam can also carry a well-defined optical angular momentum (OAM).^234–237 For years, the OAM has been considered an exotic, yet benign, feature, but more recently its potential usefulness is becoming realized.^238,239 Beams with high OAM values can nowadays be made in the lab (see, e.g., Refs. 240–242). Combining OAM with plasmonics, it has been demonstrated that subfemtosecond dynamics of OAM can be realized in nanoplasmonic vortices.²³⁹ Hence, plasmonic vortices carrying OAM can be confined to deep subwavelength spatial dimension and could offer an excellent time resolution.

The OAM can, therefore, be expected to soon enter the developing area of magnetophotonics, where the OAM could offer a new functionality to control the nanoscale magnetism.¹³⁵ There are, however, many open questions that will have to be solved before this ultimately can be achieved. On short length scales comparable to the wavelength of light, the spin angular momentum (SAM) and OAM of a light beam become strongly coupled,²⁴³ and it will be difficult to separate their respective contributions. Also, although there is an emerging understanding of the IFE coupling of the SAM of a beam to the electron spin, a similar understanding of the interaction of OAM with spin or orbital magnetism has still to be established. Recently, a first observation of interaction of magnetism and an OAM vortex beam in the THz regime was reported.²⁴⁴ It can already be perceived that taking both spin and orbital degrees of freedom of photonic beams into account will become paramount for the future development of magnetophotonics.

Research on linear and non-linear magnetoplasmonic nanoantennas and nanoscale magnetophotonics has up to now clearly demonstrated the feasibility of active magnetic manipulation of light at the nanoscale. An impact of such active control on applications has been so far hindered by the weak coupling between magnetism and electromagnetic radiation and the high dissipative losses in the used materials. Several strategies, the most promising of which are summarized in this Perspective, have been identified to overcome these limitations. Thereby, this rapidly developing field holds great promise to provide a smart toolbox for actively tunable optical materials and devices in a variety of future disruptive technologies, such as flat nanophotonics, ultrasensitive detection, all-optical and quantum information technologies, and spintronics. Nanoscale magnetophotonics could play a prominent role in the design of next-generation technology for computer memory, as the hard disk drive industry is facing a major challenge in continuing to provide increased areal density, driven by the ever-increasing data storage requirements. The heat-assisted magnetic recording approach provides a combination of high coercive field magnetic materials with local heating by a plasmon nanoantenna.^245,246 This approach currently allows up to record-breaking 1 Tb in.² storage densities. Another practical application of nanoscale magnetophotonics is the use of nanoparticles in medicine, diagnostic techniques, and drug delivery due to their potential for direct magnetic manipulation.^120,247 In this regard, solutions of chemically synthetized magnetoplasmonic nanoparticles²⁴⁸ are fundamental, also in view of potential applications that go beyond nanomedicine, such as the manipulation of the thermal properties of such nanoparticles and/or their environment.²⁴⁹ Magnetoplasmonic Au–Fe alloy nanoparticles were proved to provide high sensitivity and high resolution in magnetic resonance imaging (MRI), x-ray tomography (CT), and surface enhanced Raman scattering (SERS).²⁵⁰ It has been recently demonstrated that magnetochromic hydrogels can be synthetized and used as magnetic field-modulated color displays.²⁵¹ Eventually, multiband MO response would represent another advance in the field.⁹⁰ Furthermore, magnetoplasmonic effects can be used for metrology and, recently, many works pointing in this direction have appeared.^89,252,253 We also foresee that the control of the many degrees of freedom of light (specifically, the optical orbital angular momentum) is within reach with nanoscale magnetophotonics.

The combination of nanophotonics, magnetoplasmonics, and spintronics opens new horizons for practical implementation of magnetic field controllable nanoscale devices for ultrafast information processing and storage. Newly emerged designs and concepts may help to overcome some of the limitations including plasmon dissipation losses, low efficiency of plasmon excitation in magnetic materials, and high magnetic fields required for sufficient modulation. A recent demonstration of tunable multimode lasing modes with magnetoplasmonic nanoparticles in combination with organic gain material paves the way for loss-compensated magnetoplasmonic devices.²⁵⁴ Ultrafast optical excitation also provides means for more efficient excitation of plasmons via the sub-picosecond thermal diffusion of hot electrons due to the formation of nanometer-sized hotspots.²⁵⁵ Ultrafast control of optical response with spintronics and optical generation of spin waves are very recent advances in the field of nanoscale magnetophotonics as well. Optical excitation of spin waves^256,257 and optical control of magnetization dynamics^258,259 in GdFeCo and TbFeCo films and magnetic dielectrics by circularly polarized femtosecond laser pulses open the route for spin wave based devices. Spintronic platforms typically operating with very weak magnetic fields may become the next candidates for high-speed photonic devices in mid- and far-IR regions via the change in resistivity due to the giant magnetoresistance.²⁶⁰ Local manipulation of the magnetic moments at the submicrometer scale in MO nanodevices with an electrically driven domain wall was recently experimentally implemented.²⁶¹ Overall, creating practical magnetophotonic devices will require all-optical and plasmon-assisted control of the magnetic spin and magnetic control of light–matter interactions with low magnetic fields on the nanoscale.

N.M. acknowledges financial support from the Luxembourg National Research Fund (FNR CORE Grant No. 13624497 ‘ULTRON’) and from the FEDER program (grant n. 2017-03-022-19 Lux-Ultra-Fast). I.Z. acknowledges the financial support from the Knut and Alice Wallenberg Foundation for the postdoctoral grant. I.Z. and A.D. acknowledge the Swedish Foundation for Strategic Research (SSF) Future Research Leader Grant. I.Z., I.-A.C., V.K., P.M.O., and A.D. acknowledge the Knut and Alice Wallenberg Foundation for the project “Harnessing light and spins through plasmons at the nanoscale” (No. 2015.0060). This work was furthermore supported by the European Union’s Horizon2020 Research and Innovation program, Grant Agreement No. 737709 (FEMTOTERABYTE). I.R. and P.M.O. acknowledge financial support through the CRC/TRR (No. 227). V.B. acknowledges the financial support from the Russian Science Foundation (Grant No. 17-72-20260). We thank Michele Dipalo for the help with Fig. 1 and Jerome Hurst for the help with Fig. 14.