## Introduction

Over the course of more than half a century, local magnetic fields delivered by recording heads in hard-disk drives have successfully driven writing speeds towards gigahertz frequencies and storage densities beyond 1 Tb/in2. However, this progress is now becoming restricted by the onset of the superparamagnetic limit1, and so new approaches that facilitate faster and denser magnetic recording technologies are now being sought2. The process of single-shot all-optical switching3, whereby magnetization can be switched deterministically using just an ultrashort optical pulse of arbitrary polarization, fundamentally promises near-terahertz writing speeds4,5 in ferrimagnetic alloys of gadolinium-iron-cobalt (GdFeCo). In essence, all-optical switching within GdFeCo originates from the ultrafast magnetization dynamics6,7 of the exchange-coupled Gd and FeCo sublattices, triggered by an ultrafast transfer of thermal energy from the light to the spin bath. This process strongly depends on the amount of energy delivered by the optical pulse8. If the incident fluence is below the minimum threshold required for all-optical switching, only ultrafast demagnetization9 with subsequent recovery of the net magnetization is achieved. On the other hand, if too much energy is supplied by the pulse, a random distribution of switched and unswitched magnetic domains are formed in the irradiated region.

A variety of effects can mediate the transfer of energy between the incident optical pulse and the illuminated material. The material property of magnetic circular dichroism or the optical property of interference, for example, can tune the efficiency of energy transfer. These effects and properties can be respectively employed to achieve helicity-dependent all-optical switching8 or to reduce the incident optical fluence needed for all-optical switching by two-thirds10. While optical pulses trigger thermally-driven magnetization dynamics in metallic GdFeCo systems8, it is also possible to non-thermally generate effective magnetic fields using circularly-11 or linearly-polarized12,13,14 femtosecond pulses in alternative materials. In addition, upon illuminating a dielectric/metallic interface with p-polarized light, a surface plasmon polariton (SPP) can be excited15. The optical field enhancement associated with SPPs could offer a pathway towards an even smaller energy cost of all-optically writing a bit13,14,16. At the same time, by confining the optical field using a plasmonic antenna, the optically-addressed region of magnetization has been successfully downscaled to length scales on the order of 50 nm17.

Supplementary to reducing the in-plane size of the optically-addressed region of magnetization, an intriguing possibility for achieving higher storage densities lies in extending magnetic platters in to the third dimension. Recently, substantial research has been directed towards all-optically reversing magnetization in multi-layered heterostructures, motivated by the prospect of stacking multiple magnetic layers on the same platter18,19 or constructing optically-addressable magnetic tunnel junctions20. Using magnetic bilayers, one can already achieve ultrafast single-shot switching of Co/Pt (via exchange-coupling with a Gd21 or GdFeCo22 layer), and realize a form of multi-level magnetic recording based on the generation of spin-polarized currents23. If one, however, considers a simple bilayer of GdFeCo optically-addressed at normal incidence, the directionality of the optical wave vector suggests—at first glance—that the first layer addressed will always and inescapably undergo switching. Until now, no method has been demonstrated that allows for switching in the second layer, without affecting the first.

In this article, we unveil a method of deterministic layer-resolved all-optical switching in a multi-layered heterostructure of GdFeCo, exploiting the properties of SPPs. Using calculations, we design the thermal distributions generated by s- and p-polarized light across the depth of a heterostructure. Upon exposing the bilayer to an s-polarized ultrashort optical pulse, no SPP is generated, and so the energy is concentrated at the first incident layer penetrating only the skin depth. On the contrary, using a p-polarized ultrashort optical pulse, we generate an SPP that concentrates energy in the second layer (the GdFeCo/air interface) rather than the first GdFeCo/glass interface. We experimentally verify this scenario, and moreover exploit the different concentrations of energy in order to all-optically switch the magnetization of targeted nanolayers of GdFeCo independently from each other, using p- and s-polarized ultrashort optical pulses. We therefore demonstrate an approach of polarization-dependent multi-level magnetic recording, whereby each magnetic layer can be independently addressed at will, thus enabling the storage density of optically-addressed magnetic media to be doubled.

## Results

### Surface plasmon-polaritons in a multi-layered GdFeCo heterostructure

Although the imaginary part of the dielectric permittivity of GdFeCo at the wavelength of 800 nm is large, the real part of the permittivity is negative and so the ferromagnetic metal can support the excitation of an SPP (εGdFeCo = −5.91 + 19.17i)24. At a semi-infinite air/GdFeCo interface, the transverse propagation length15 and penetration depth inside the GdFeCo film15 of an SPP is 2.6 μm and 17 nm respectively. To facilitate the excitation of an SPP, we have fabricated and studied the magnetic multi-layered heterostructure prism/glass/Si3N4(5)/Gd26.0Fe64.8Co9.2(10)/Si3N4(80)/Gd27.0Fe63.9Co9.1(10)/Si3N4(10) (Fig. 1a), where the number in parentheses indicates the layer thickness in nanometres. The ferrimagnetic GdFeCo layers were deliberately designed to have different concentrations of gadolinium, and will be discussed in detail later on. The glass substrate is coupled directly to a 60° SiO2 prism, allowing for an SPP to be optically excited via the Kretschmann scheme15 at the bottom GdFeCo/air interface. The thin (10 nm- and 5 nm-thick) Si3N4 layers merely protect the GdFeCo from oxidation, and have negligible impact on the electromagnetic field distribution. On the other hand, the 80 nm-thick Si3N4 layer blocks the exchange interaction and diminishes the magneto-dipole interaction between the GdFeCo layers, ensuring their magnetization states are effectively decoupled. The 80 nm-thick Si3N4 layer also plays an integral role in allowing an incident p- and s-polarized pulses at the wavelength of 800 nm to deliver drastically different electromagnetic field distributions across the two GdFeCo layers (in general, this difference could be observed for Si3N4 layers with thickness up to 120 nm).

In order to demonstrate this effect, we model the optical absorption inside each GdFeCo layer by

$$A = {\int} {\delta A\left( z \right)\mathrm{d}z} = \frac{{k_0}}{{n_{{\mathrm{pr}}}\cos \left( \theta \right)}}{\int} {\left| {e\left( z \right)} \right|^2{\mathrm{Im}} \left( {\varepsilon _{{\mathrm{GdFeCo}}}} \right)\mathrm{d}z} ,$$
(1)

where npr is the refractive index of the coupling prism, k0 is the optical wavenumber in vacuum, θ is the angle of incidence, δA(z) is the partial absorption, and e(z) is the normalized electric field (see “Methods”). Figure 1b, c show the calculated distribution of |e(z)|2 and δA(z) across the depth of the studied heterostructure for p- and s-polarized light at the wavelength of 800 nm incident on the top Gd26(FeCo)74 layer at an angle of 59°. The p-polarized light excites an SPP that is localized at the bottom Gd27(FeCo)73 layer (i.e. the GdFeCo/air interface), predominantly pumping the energy of the laser pulse into this layer. The calculations (Fig. 1e) show a strong dependence of |e|2 at the bottom interface of the Gd27(FeCo)73 layer on the angle of incidence, with a maximum at 56°. We note that this is a characteristic feature associated with the Kretschmann geometry25, and does not correspond to the maximum of the absorption in this layer. If the incident light is instead s-polarized, no SPP is excited, and therefore the light energy is partly reflected or partly dissipated in the top Gd26(FeCo)74 layer.

To tune the efficiency of SPP excitation15, one can tune the material refractive index, the photon energy or the angle of incidence of light. We therefore numerically consider the former parameters to be fixed (mimicking experimental conditions), and calculate the angular dependence of the maximum absorbed energy in the top Gd26(FeCo)74 and bottom Gd27(FeCo)73 layers for incident p- and s-polarized light. Presented in Fig. 1d are the corresponding results, revealing that the SPP resonance is rather wide. Nevertheless, the graphs clearly show that if the angle of incidence is above 50°, the absorption of p-polarized light in the bottom Gd27(FeCo)73 layer is greater than in the top Gd26(FeCo)74 layer. This represents the necessary condition for layer-selective magnetic recording and the region that satisfies this condition is shaded green in Fig. 1d. As a result of this absorption difference, one may tune the pulse fluence such that the energy dissipated in the two magnetic layers is below or above the threshold required for the switching8. Hence layer selective switching with subwavelength resolution can be achieved. To verify this predicted angular dependence of absorption, we measured and calculated the angle-resolved reflectivity of p- and s-polarized light (Fig. 1e). Excellent qualitative and rather good quantitative agreement between the computationally predicted and experimentally observed angle dependencies evidences the high quality of the fabricated multi-layers and inspires our experimental search for layer selective all-optical magnetic recording in the heterostructures.

### Resolving the magnetization of different layers

In order to distinguish the four different states of the magnetizations of the two Gdx(FeCo)100−x layers with the help of a conventional magneto-optical microscope, the magnetic layers were deliberately designed to have slightly different concentrations of gadolinium, with x = 26 (x = 27) in the top (bottom) layer. This resulted in a significant difference in the magnetization compensation temperatures TM (TM ≈ 210 K and TM ≈ 315 K for Gd26(FeCo)74 and Gd27(FeCo)73 respectively)26,27. Consequently, the magnetizations28 as well as the coercive fields and the magneto-optical Faraday rotation of the layers at room temperature were also different. Both magnetic layers exhibit deterministic all-optical switching, with nearly the same optical fluence29. Since the values of TM lie on either side of room temperature, the net magnetization of the Gd26(FeCo)74 and Gd27(FeCo)73 layers is antiparallel and parallel respectively to the magnetization of the constituent Gd sublattice. The difference in coercive fields makes it possible to obtain four stable hysteretic states. After applying and removing an out-of-plane spatially-uniform magnetic field HB, the four magnetic states of the heterostructure can be realized with mutually parallel (↑↑ and ↓↓) or antiparallel (↑↓ and ↓↑) alignment of the magnetizations in the layers28,30. In the notation adopted here, the first and second arrow denotes the polarity of magnetization of gadolinium in the top and bottom layer of GdFeCo respectively.

To evaluate whether deterministic layer-resolved all-optical switching can be achieved, we employ static imaging of the heterostructure using the polar magneto-optical Kerr effect. Subsequent to all tests of all-optical switching, we recorded magneto-optical images of the multi-layered system as a function of HB. In Fig. 2b are shown raw images recorded for different values of HB. The different magneto-optical signals from the two layers allow us to directly distinguish the magnetic state of each layer, via the different contrast levels (which is mainly proportional to the out-of-plane component of magnetization Mz of iron31. Moreover, by averaging all pixel intensities within the magneto-optical images, we are able to generate a characteristic hysteresis loop, as presented in Fig. 2a. This represents a superposition of the hysteresis loops belonging to both layers27,30. We use this loop to conclusively discern the four different magnetic states that can be achieved in our binary heterostructure.

### Layer-selective magnetization reversal

To test the scenario of plasmon-enabled deterministic all-optical switching, we focused a 100 fs-long optical pulse, of central wavelength 800 nm, through the coupling prism at an angle of incidence of 59° onto the surface of the top Gd26(FeCo)74 layer (see Methods and Supplementary Note 1 for details). It follows from Fig. 1b that absorption of the p-polarized pulse at 59° in the bottom layer is about 2.5 times larger than in the top layer. At the same time, for these conditions the absorption of the s-polarized pulse in the top layer is about 2.2 times larger than in the bottom layer. Therefore, at this angle of incidence one should expect the layer-selective switching. The diameter of the focused spot was characterized32 to be 37 µm. The magnetization of gadolinium within the heterostructure was initially set to the configuration ↓↑ (Fig. 2), and the linear polarization of the optical pulse was rotated to achieve p- or s-polarization. After exposing the sample to optical pulses, magneto-optical images were recorded and identified with one of the four states (↑↑, ↓↓, ↑↓ or ↓↑) using the values of the magneto-optical contrast in different parts of the hysteresis loop.

Exactly as predicted, we observed layer-selective single-shot switching of magnetization, with the choice of addressed layer dictated by the polarization of the optical pulse. Figure 3a shows a background-corrected magneto-optical image taken after the multi-layered heterostructure was exposed to a single p-polarized (left) and s-polarized (right) optical pulse, of fluence 10 mJ/cm2 (electric field |E|720 MV/m). There is a clear difference in contrast between the two irradiated regions, indicating different magnetic states have been obtained. To irrefutably identify which layer(s) have undergone switching, we present also a cross-section taken from the magneto-optical image. By comparing this cross-section to those recorded in the presence of varying HB (Fig. 2), we conclusively demonstrate that the magnetization in the bottom Gd27(FeCo)73 and top Gd26(FeCo)74 layer has been independently toggled by the p-polarized and s-polarized optical pulse respectively. This layer-resolved magnetization reversal effect was observed for all four different starting magnetic states (see Supplementary Note 3), and the deterministic switching of magnetization in different layers could be achieved by delivering several optical pulses (see Supplementary Note 4). Finally, upon removing the coupling prism, we were unable to achieve layer-resolved all-optical switching, verifying further the critical role the SPP plays in this mechanism.

As discussed earlier, the all-optical switching of magnetization in a single layer can only be achieved if the density of the absorbed optical fluence w exceeds a minimum threshold value wthreshold, which is almost identical22 in both layers. Therefore, for a certain incident optical fluence F, the density of the absorbed fluence wj = AjF in layer j depends only on the angle of incidence and polarization (which enter the absorption term, Aj). If one increases the optical fluence, it is conceivable that one could achieve all-optical switching in both layers, since the fluence threshold in both layers can be simultaneously surpassed (i.e., wtop,bottom > wthreshold). Upon therefore increasing the optical fluence to 12 mJ/cm2 (E790 MV/m), as shown in Fig. 3b, we observe a new feature with different contrast at the centre of the irradiated region. Due to the Gaussian distribution of the optical pulse energy, it is expected that there is a higher thermal load supplied at the centre. Quantitative analysis (bottom panel of Fig. 3b) reveals that, at the centre, both layers have indeed undergone all-optical switching, irrespective of the optical polarization. These observations not only reveal an important prerequisite for layer-resolved all-optical switching in terms of the laser fluence, but also shows that by tuning both the polarization and fluence of the laser pulses, one can realize all four states of the magnetizations of the layers (↑↑, ↓↓, ↑↓ and ↓↑).

The crucial role of the plasmon-polariton in the layer selective magnetic switching is further emphasized by experiments on optical control of the magnetizations in the multi-layer structure performed at different angles of incidence. The model presented in Fig. 1d–e predicts that angles of incidence above 50° will allow a p-polarized optical pulse to switch magnetization in the bottom GdFeCo layer only. We therefore varied the angle of incidence between 34° and 67°, and the switching of the bottom layer was only seen within the range of 53° and 67°. If instead the angle was tuned between 34° and 47°, the top Gd26(FeCo)74 layer always underwent switching, irrespective of the optical polarization. All magneto-optical images underpinning this conclusion are supplied in Supplementary Note 5. The black arrows in Fig. 1d–e indicate the angles at which plasmon-enabled switching was observed, and the grey arrows indicate the opposite, demonstrating excellent agreement of the experimental results with the model. This finding not only proves the important role of the SPP in the demonstrated mechanism, but also uncovers the robustness of the effect, since the reversal is unaffected despite adjusting the angle of incidence by at least 30°.

## Discussion

In conclusion, we have revealed an elegant solution to the problem of layer-selective all-optical magnetic recording in multi-layered heterostructures. Our approach is based on the layer selective deposition of optical energy through the polarization-dependent excitation of a surface plasmon-polariton at a targeted interface of the heterostructure. The numerically-predicted and experimentally-verified fact that the polarization-selective magnetization reversal occurs only in the vicinity of the surface plasmon-polariton’s resonance (and is otherwise absent) clearly and conclusively shows the key role played by the surface plasmon-polaritons in the process of layer-resolved all-optical reversal of magnetization.

While, for the sake of simplicity, we have restricted ourselves to studying a multi-layered heterostructure containing only two magnetic layers, it is straightforward to incorporate more magnetic layers. To suitably address these different layers individually without affecting the others, one needs to adjust not only the polarization-axis of the incident optical pulse but also the wavelength and/or the angle of incidence15. More intrinsically, each GdFeCo layer could be neighboured by different dielectric layers with specifically designed refractive indices. This could assist or obstruct the process of switching within the particular layer for a certain optical pulse. Indeed, since we do not need to tune the energy of the optical pulse to switch either of the two GdFeCo layers studied here, the ultimate recording density is limited not by the number/thickness of magnetic layers but rather by the number of distinct appropriately-tailored energy distributions achievable across the multi-layered stack using different optical parameters. The dielectric prism may also be replaced with an etched or transient33 grating, with the SPP resonance position controlled by the grating periodicity. In this way, a complete multi-level magnetic recording architecture could be developed, with different optical parameters dictating the choice of which magnetic layer is addressed.

## Methods

### Numerical calculations

Partial and full absorption inside the lossy planar structure, in the case of the oblique optical incidence, is calculated using the energy conservation law

$$W = S_z^{{\mathrm{inc}}} \cdot s + S_z^{\mathrm{t}} \cdot s + S_z^{\mathrm{r}} \cdot s,$$
(2)

where Sz is the z-component of the Poynting vector of the incident (inc), transmitted (t) or reflected (r) light, and s is the surface area parallel to the xy-plane. W is the energy absorbed by the volume that, according to the Joule-Lenz law, depends on the conductivity σ via

$$W = \frac{1}{2}{\int} {\sigma \left| E \right|^2} s\mathrm{d}z.$$
(3)

Taking in to account A = 1 – RT, where A, R and T correspond to the absorption, reflection and transmission coefficients respectively, Eq. (2) can be rearranged to obtain

$$\frac{W}{{S_z^{i{\mathrm{nc}}}}} = 1 - R - T,$$
(4)

Combining Eqs. (2) and (3) yields

$$A = \frac{1}{2}\frac{{{\int} {\sigma \left| E \right|^2} s\mathrm{d}z}}{{S_z^{{\mathrm{inc}}}}}.$$
(5)

Using the identities $$\sigma = \frac{{\omega {\mathrm{Im}} \left[ \varepsilon \right]}}{{4\pi }}$$ and $$S_z^{{\mathrm{inc}}} = \frac{{cn_{{\mathrm{prism}}}}}{{8\pi }}\left| {E_{{\mathrm{inc}}}} \right|^2\cos \theta$$, where ω and c are the frequency and speed of light, and ε is the permittivity, one obtains Eq. 1, i.e., $$A = {\int} {\delta A\left( z \right)\mathrm{d}z} = \frac{{k_0}}{{n_{{\mathrm{prism}}}\cos \left( \theta \right)}}{\int} {\left| {e\left( z \right)} \right|^2{\mathrm{Im}} \left( \varepsilon \right)\mathrm{d}z}$$. Here, e(z) is the electric field normalized to the value of the electric field for the incident light, i.e., e(z) = E(z)/|Einc|, and the magnitude of the electric field is given by $$\left| {E_{{\mathrm{inc}}}} \right| = \sqrt {2I/c\varepsilon _0n_{{\mathrm{prism}}}}$$.

### Sample fabrication

For the experimental study, we prepared multi-layered heterostructure deposited by magnetron sputtering on an atomically flat glass substrate. The ferrimagnetic GdFeCo nanolayers were fabricated by co-sputtering of Gd, Fe, and Co elements with the direct current (DC) magnetron sputtering method. As an advantage of amorphous alloy systems, we can tune concentration of alloy continuously by controlling the relative deposition rates and can precisely design the coercive field at room temperature as shown in Fig. 2. The thin Si3N4 layers were fabricated by reactive radio frequency (RF) magnetron sputtering of Si with nitrogen gas. Calibration of deposition rate and optical characterization were performed by spectroscopic ellipsometry. Thin film with high refractive index (~2.00 at wavelength of 800 nm) was obtained on the optimal deposition conditions.

### Experimental setup for measuring the reflectance angular spectra

The reflectance angular spectra at the pump wavelength was measured using a rotating motorized platform STANDA 8MR174-11. Incident light was generated by a single-mode diode laser THORLABS L785P090, with a spectral line width of about 0.1 nm. The temperature of the laser case was stabilized with an accuracy of 0.02 °C. A parallel light beam was formed using an aspheric lens with a focal length of 6 mm. Then the light passed through a film polarizer, an optical chopper modulating light at a frequency of about 500 Hz, and a diaphragm. The intensity of the reflected light was measured using a THORLABS FDS1010 silicon photodiode connected to a low-noise transimpedance amplifier. The signal from the amplifier was digitized by a National Instruments USB-6351 data acquisition board.

### Experimental setup for achieving and detecting polarization-dependent toggle-switching

To achieve polarization-dependent all-optical switching of magnetization, we used an amplified Ti:Sapphire laser system to generate 100 fs optical pulses, with a central wavelength of 800 nm and a Gaussian spatial distribution. The optical pulses either had a repetition rate of 1 kHz (used when aligning or measuring the power) or were triggered in single-shot mode (when achieving all-optical switching). A polarizer and half-wave plate were used to rotate the polarization-axis of the linearly polarized pulse, and the pulse was then routed towards the coupling prism, and focussed using a lens of focal length 25 cm. The angle of incidence (relative to the coupling prism) was measured by taking and analysing a photograph of two diaphragms centred on the laser beam.

Detection of the magnetic state of the multi-layered heterostructure was achieved using a magneto-optical microscope. A Euromex 100 W halogen LE.5210 lamp supplied illumination, which was linearly polarized by a polarizing sheet and then directed through an objective lens (Mitsutoyo, G Plan APO × 20, NA = 0.28). Upon reflection, the polarization-axis of the illuminating light was rotated due to the polar magneto-optical Kerr effect. The reflected beam was then spatially separated using a non-polarizing beam splitter, and passed through a Glan-Taylor polarizer (the latter was almost crossed with the former polarizing film). Finally, a spatially-resolved image (with an amplitude proportional to the out-of-plane component of magnetization) was recorded using a CCD (QImaging, Retiga R3) coupled to a variable magnifier. All images were recorded with an exposure time of 250 ms. A short-pass filter, with a cut-off wavelength of 750 nm, was used to prevent the 800 nm optical pulse from polluting the CCD. An electromagnetic pole was positioned directly behind the coupling prism in order to supply an out-of-plane magnetic field (maximum attainable strength ± 320 Oe).